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Uncertainty about welfare effects of consumption fluctuations
European Economic Review 59 (2013) 35–62
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Uncertainty about welfare effects of consumption fluctuations Romain Houssa a,b,c,n a
University of Namur, Centre of Research in the Economics of Development (CRED), Center for Research in Finance and Management (CeReFiM), Rempart de la Vierge 8, B-5000 Namur, Belgium b University of Leuven, Center for Economic Studies (CES), Naamsestraat 69, B-3000 Leuven, Belgium c CESifo, Poschingerstr. 5, 81679 Munich, Germany
a r t i c l e i n f o
abstract
Article history: Received 25 January 2011 Accepted 14 December 2012 Available online 31 December 2012
This paper proposes Bayesian estimates for welfare effects of consumption fluctuations and growth. Annual data from 82 developed and developing countries indicate a large degree of uncertainty as regards point estimates. Moreover, the comparison between the welfare gain from consumption stabilization and the welfare gain from growth yields inconclusive results for many developed and developing countries. These findings suggest the need for caution in drawing policy conclusions from point estimates. & 2012 Elsevier B.V. All rights reserved.
JEL classification: E63 O50 H50 C11 Keywords: Business cycles Growth Welfare Bayesian inference
1. Introduction Lucas (1987) measures the welfare cost of consumption fluctuations as the percentage increase in consumption, across all dates and states, required to leave a representative agent indifferent between consumption fluctuations and a smooth consumption path. According to this definition, he obtains an estimate of 0.042% of consumption in the USA.1 Lucas then estimates the welfare loss of a 1% reduction in the growth rate at 20% of consumption. These results lead Lucas to conclude that further stabilization would yield little welfare gain in the USA and that growth should be the priority of macroeconomic policies. A large body of research has challenged Lucas’ estimations by altering his modeling framework. First, whereas Lucas employs a model based on a trend-stationary consumption process and a CRRA utility function, Obstfeld (1994) and Dolmas (1998) adopt a martingale consumption process and recursive preferences of Epstein and Zin (1989). The predictions of their model indicate higher welfare costs of fluctuations ranging from 0.1% to 4.3%. Second, another line of research relaxes Lucas’ assumptions on homogenous agents and perfect capital markets. For instance, Imrohoruglu (1989) considers a general equilibrium model with idiosyncratic shocks and liquidity constraints and finds the welfare cost of
n
Tel.: þ32 81 724 947; fax: þ32 81 724 840. E-mail address: [email protected] 1 This result is obtained with a coefficient of relative risk aversion equal to 5. For risk aversion levels of 10 and 20, Lucas estimates the welfare cost of fluctuations at 0.084% and 1.7%, respectively. 0014-2921/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.euroecorev.2012.12.006
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R. Houssa / European Economic Review 59 (2013) 35–62
fluctuations in the range of 0.3–1.5%. Atkeson and Phelan (1994) extend Imrohoruglu (1989) to the endogenous labor supply and asset pricing. Their results indicate little welfare gain from stabilization as does Lucas (1987). In a related study, Krusell and Smith (1999) propose a model with a variety of heterogeneity including employment status, wealth and preferences. They find that poor unemployed individuals who face liquidity constraints and rich individuals would benefit from stabilization while the middle-income class would lose. As a result, the welfare gain from eliminating fluctuations is negligible for the aggregate economy. However, Krebs (2007) observes that unemployed workers face persistent income loss even after they are re-employed. Given that such risks are not insured in asset markets the author claims that unemployment risks would cause a larger welfare cost compared to previous studies. To come to this conclusion Krebs (2007) introduces long-term earning losses of job displacement into a general equilibrium model. Depending on parameter values he finds estimates of the welfare cost of business cycles in the range of 0.2–9.0%. Third, Tallarini (2000) addresses the problem in a real business cycle (RBC) model with Epstein–Zin type preferences, which are calibrated to be consistent with observed asset prices in the USA. He finds much larger welfare cost of fluctuations as of 44%. Otrok (2001) also considers an RBC model. However, he finds little welfare gain from stabilization with non-separable preferences, the parameter values of which are chosen to match observed fluctuations in the USA. The fourth strand of the literature is based on endogenous growth models. For instance, Barlevy (2004) proposes a framework with diminishing returns on investment. As a result, stabilization generates higher growth through the reallocation of investment from periods of high investment to periods of low investment. In turn, he finds the welfare cost of fluctuations to be substantially higher than in the original Lucas exercise. However, Francois and Lloyd-Ellis (2006) challenge this finding in a model where fluctuations and growth are endogenously determined. Moreover, their model generates a positive relationship between fluctuations and growth as in Blackburn (1999). In this set-up, stabilization induces welfare costs. For a detailed survey of the literature, see Barlevy (2005), Imrohoroglu (2008) and Lucas (2003). This brief review shows that different modeling assumptions yield different estimated values for the welfare cost of fluctuations. In this paper, I take a different approach to examining the welfare effects of consumption fluctuations and growth. Instead of proposing another model economy, I investigate the impact of parameter uncertainty on welfare effects.2 For this purpose, I use the model economy proposed in Dolmas (1998) and Obstfeld (1994) and assess parameter uncertainty with Bayesian inference. In particular, the sample from the posterior distribution of welfare effects is obtained by repeatedly drawing parameters of a consumption process from their posterior distribution. Moreover, I estimate the posterior distribution for the difference between the welfare cost of consumption fluctuations and the welfare effects of growth. Subsequently, a 90% credible interval is constructed to gauge the uncertainty on estimates of welfare effects.3 This metric also allows to examine whether the welfare gain from consumption stabilization and the welfare gain from growth are significantly different from one another. Lucas (1987) and subsequent studies have relied on point estimates for such welfare comparison, thereby neglecting the uncertainty surrounding their estimates. However, by ignoring uncertainty, one cannot make statements about how likely these estimates are from their population values. As a result, policy conclusions drawn from point estimates should be taken with caution. My second contribution to the discussion relates to a large number of countries included in the empirical analysis. In particular, I examine data on 82 developed and developing countries while earlier studies mostly focus on the USA. The few existing cross-country studies include Pallage and Robe (2003) who compare point estimates for welfare effects across a group of African countries and the USA. Giannone and Reichlin (2005) compare consumption responses to technology shocks between the Euro area and the USA and interpret the results in terms of the welfare cost of fluctuations. Finally, Van Wincoop (1994) examines the welfare gain from international risk sharing in the USA, Japan and EuropeanOECD countries. Consumption data have three main characteristics: the trend growth, the size of fluctuations, and the degree of persistence of these fluctuations. Given the differences in these three parameters and their uncertainty, how large are welfare effects of consumption fluctuations and growth in developing countries compared to those in developed countries? Are these welfare effects similar across countries in each group? For instance, are welfare effects of consumption fluctuations different between the USA and the European industrialized countries? Analysis of data from a large number of developing and developed countries enables these general questions to be addressed. Moreover, developing countries represent a natural framework for the Lucas-type welfare comparison. In particular, these countries display strong volatility in consumption such that successful stabilization policies should substantially improve the welfare of their residents. However, there has been an increasing emphasis on growth in these countries. For instance, The World Bank (2004) argues that Africa needs to achieve a 7% long-term growth rate in order to meet the target for poverty reduction of the Millennium Development Goals. To what extent then should developing countries focus on stabilization or on growth4 or on both policies?
2
Eichenbaum (1991) made a similar point on the uncertainty in parameter estimates of real business cycle models. The credible interval has a different interpretation than the confidence interval notion used in frequentist statistics. For instance, a 90% credible interval (or region) gives the interval of minimum length that contains the true value of a parameter with probability 90%. 4 Blackburn (1999) provides a theoretical support for the trade-off between stabilization and growth. Using an endogenous growth model, he shows that monetary stabilization policies lead to a lower long-term growth. This result is based on a positive link between growth and volatility found in Blackburn (1999). However, the relationship between growth and volatility hinges on the mechanism that generates technological progress. When it is generated by the creative destructive mechanism, the link between growth and volatility is positive (see, for example, Aghion and Saint-Paul, 1998a, 3
R. Houssa / European Economic Review 59 (2013) 35–62
37
Table 1 Posterior quantiles of welfare effects in developed countries. Countries
l (%)
Australia Austria Belgium Canada Denmark Finland France Greece Iceland Ireland Israel Italy Japan Korea New Zealand Norway Portugal Spain Sweden UK USA
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.89 2.10 2.79 1.63 2.05 3.54 1.90 5.63 12.87 4.31 4.07 3.25 8.54 5.55 2.86 2.00 9.90 4.54 2.52 2.01 1.16
1.24 4.74 8.68 2.83 2.92 5.12 4.09 14.20 23.17 8.57 6.29 8.11 23.49 8.13 5.01 2.92 19.72 10.27 4.93 3.72 2.07
1.81 20.12 47.72 6.33 4.46 7.87 17.34 55.55 54.46 25.40 11.42 44.01 78.95 12.67 12.25 4.42 52.74 36.27 14.59 10.18 5.33
18.59 17.26 17.80 18.21 19.50 17.23 17.54 16.10 17.02 16.72 17.05 17.20 16.67 13.75 20.19 17.63 16.07 16.87 19.30 17.66 17.45
19.45 18.83 20.40 19.77 20.94 18.86 19.27 18.85 20.14 18.86 18.32 19.62 20.96 15.28 22.09 18.89 19.37 19.59 21.47 19.12 18.61
20.42 22.84 31.57 21.54 22.63 20.88 23.38 26.53 26.20 23.16 20.11 29.74 32.57 17.33 24.85 20.41 25.94 26.77 25.17 21.34 20.14
19.10 16.59 16.72 18.57 19.51 15.59 17.38 12.14 5.92 14.34 14.22 15.50 9.72 9.53 19.42 17.40 8.10 14.27 19.17 17.23 17.80
18.20 14.14 11.84 16.87 17.98 13.68 15.12 4.58 2.76 10.27 12.06 11.42 2.72 7.12 17.00 15.98 0.23 9.37 16.40 15.35 16.49
17.23 1.66 18.37 13.39 16.30 11.09 4.39 31.19 30.65 4.99 7.42 15.73 46.76 3.36 10.76 14.39 29.08 10.65 8.23 9.66 13.39
The results show wide credible intervals for the welfare cost of consumption fluctuations in developed and developing countries, which indicate large uncertainty as regards point estimates. Moreover, credible intervals for the difference between the welfare gain from consumption stabilization and the welfare gain from growth include zero for many developed and developing countries. These findings are robust as regards sub-samples analysis and on different assumptions about the risk aversion parameter and the intertemporal elasticity of substitution. This paper is further organized as follows: Section 2 presents the theoretical framework; Section 3 gives empirical results; Section 4 provides the sensitivity and sub-period analysis; and the last section concludes.
2. Theoretical framework 2.1. Model economy The model is taken from Dolmas (1998) and Obstfeld (1994). The ingredients are the recursive preferences of Epstein and Zin (1989) and a stationary autoregressive process for consumption growth.
2.1.1. Consumption Denote real per capita consumption by C t ,t ¼ 0, . . . ,T, and assume that the growth rate g t ¼ C t =C t1 1 follows an ARð‘Þ stationary process g t ¼ f0 þ
‘ X
fi g ti þ et ,
ð1Þ
i¼1
where f0 is the constant term, the fi , i ¼ 1, . . . ,‘, are AR coefficients, and et is the error term, which is assumed to be i:i:d: normally distributed as et Nð0, s2 Þ. From Eq. (1) the long-term growth rate of consumption is defined as the P unconditional mean of g t : g ¼ Eg t ¼ f0 =ð1 ‘i ¼ 1 fi Þ. Using the approximation lnð1 þ g t Þ Cg t , Eq. (1) is equivalent to assuming that ln C t follows an I(1) process with serially correlated increments.5 This implies that innovations in growth have permanent effects on consumption. (footnote continued) 1998b; Caballero and Hammour, 1994). However, if the mechanism generating technological progress is learning by doing, the relationship between growth and volatility is found to be negative (see, for example, Martin and Rogers, 1997; Ramey and Ramey, 1991). 5 Merton (1971) shows that consumption follows a random walk process in an intertemporal optimization framework. Empirical studies also support the random walk hypothesis (see, for example, Nelson and Plosser, 1982; Cooley and Ogaki, 1996; Ogaki, 1992).
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R. Houssa / European Economic Review 59 (2013) 35–62
2.1.2. Preferences With persistent shocks, Obstfeld (1994) argues that the risk aversion parameter and the intertemporal elasticity of substitution (IES) play specific roles in the welfare effects of consumption fluctuations and growth. For instance, to the Table 2 Posterior quantiles of welfare effects in developing countries. Countries
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican, Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Hong Kong Honduras India Indonesia Iran Jamaica Jordan Kenya Luxembourg Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Netherlands Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Switzerland Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
15.86 16.24 8.75 8.20 6.42 8.53 31.78 24.67 30.09 5.67 14.57 5.17 49.89 8.58 20.85 5.20 5.64 12.72 20.47 51.38 52.89 25.59 5.06 7.44 9.29 5.56 3.66 8.39 29.91 18.64 47.10 19.08 1.50 8.51 7.74 11.91 15.17 28.89 6.18 10.02 3.05 3.09 47.23 6.88 12.59 8.66 17.92 2.36 44.38 3.68 8.87 8.07 1.80 49.30 6.21 5.91 25.45 16.85 23.70 47.86 64.43
25.17 25.72 13.29 12.32 11.57 12.64 53.50 50.33 51.07 10.76 22.52 12.41 78.46 16.37 33.18 10.23 8.31 27.55 34.92 78.85 80.23 42.36 13.44 10.91 18.69 8.05 5.26 15.88 49.83 36.44 77.75 32.58 2.12 12.72 11.90 22.61 24.63 47.55 10.87 17.74 4.53 6.01 75.45 10.10 20.01 12.77 28.90 4.15 70.74 7.38 13.29 11.96 4.17 76.55 11.90 11.02 41.54 31.53 48.05 75.82 87.93
43.95 46.03 21.93 20.36 30.17 20.94 89.10 92.10 87.03 28.99 38.33 52.82 97.69 46.00 62.36 33.01 12.88 75.23 69.64 97.80 97.76 78.06 64.51 17.43 52.10 12.37 8.04 43.04 87.11 84.53 97.70 66.05 3.14 20.67 20.99 60.04 47.43 85.40 28.35 42.52 7.42 15.94 97.55 15.88 35.57 20.38 51.77 9.37 96.09 23.26 21.69 19.29 15.54 97.74 35.46 33.49 77.44 76.46 90.58 97.50 98.90
21.00 19.69 20.11 20.59 22.13 16.46 23.26 21.48 17.70 13.43 20.03 20.03 23.09 19.00 16.79 19.41 17.35 19.67 20.07 18.82 22.40 24.43 21.71 21.61 13.86 20.94 18.19 14.80 20.31 21.73 23.32 24.71 17.19 27.91 18.94 15.84 20.63 16.11 18.66 18.94 20.70 17.64 25.66 17.50 18.01 18.30 19.12 19.30 21.89 19.44 23.31 16.22 19.74 18.24 22.51 15.15 18.17 20.84 20.80 25.74 19.98
26.01 24.20 23.44 24.02 25.00 18.86 31.49 28.06 23.36 15.34 24.39 23.35 31.14 22.76 20.67 22.36 19.36 25.10 25.13 24.47 29.55 32.53 25.78 24.72 16.44 23.52 19.92 17.30 26.60 28.26 31.45 30.94 18.22 33.03 21.56 19.13 24.80 20.94 21.63 22.01 22.48 19.63 33.02 19.81 21.00 21.12 23.71 20.87 29.49 21.96 27.44 18.60 21.89 23.40 25.58 17.36 23.30 25.40 27.67 34.67 25.59
33.88 31.99 28.09 28.88 30.87 22.32 44.19 39.04 31.93 18.96 31.68 32.32 40.56 29.87 28.38 28.68 22.09 36.57 34.30 31.84 37.94 46.67 39.52 29.20 22.00 26.93 22.13 22.51 36.64 41.53 42.70 42.71 19.39 41.08 25.48 25.82 32.08 28.96 26.78 28.07 24.79 22.99 42.52 22.98 25.90 25.24 31.91 22.89 39.41 26.87 33.42 21.75 26.29 29.62 31.90 21.60 32.31 34.04 39.65 46.82 32.32
8.22 6.48 14.24 15.64 18.28 9.90 5.15 0.10 10.44 8.92 8.52 16.89 23.55 13.48 2.20 17.03 13.77 10.35 2.19 30.39 27.55 2.89 19.35 17.45 5.86 18.49 16.74 8.01 7.25 6.77 19.53 9.55 17.24 25.70 13.54 5.81 7.87 11.07 15.19 10.76 19.90 16.65 18.63 12.87 7.28 12.19 3.47 18.83 18.96 18.22 18.49 10.20 20.20 28.96 19.03 10.94 5.32 6.72 0.55 17.99 41.29
0.87 1.58 10.29 11.51 13.50 6.16 21.68 22.13 27.63 4.68 1.74 10.97 46.24 6.32 12.52 11.82 11.04 2.21 9.73 53.61 49.82 9.92 12.03 13.83 2.28 15.41 14.63 1.42 22.83 8.41 44.87 1.32 16.08 20.22 9.74 3.53 0.32 26.38 10.53 4.12 18.00 13.68 41.76 9.75 0.96 8.37 5.12 16.71 40.40 14.53 14.11 6.54 17.62 52.32 13.50 6.28 18.24 6.40 20.01 39.57 61.25
12.97 15.97 3.76 5.88 1.13 0.01 48.91 58.26 57.65 11.13 9.53 21.54 63.76 18.60 36.00 6.55 7.09 41.89 37.60 70.96 66.33 34.32 26.71 8.91 32.46 11.60 12.17 21.87 52.84 46.19 65.79 27.49 14.78 14.34 2.06 35.30 17.49 57.67 3.20 15.97 15.14 4.49 61.50 5.08 11.91 2.52 22.78 11.91 62.62 1.62 8.15 0.90 8.24 72.28 5.11 12.25 47.56 44.02 55.08 59.78 72.77
R. Houssa / European Economic Review 59 (2013) 35–62
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Table 3 Summary results. Developed
Developing
Growth
Stabilization
Australia Austria Canada Denmark Finland France Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Inconclusive
Growth
Stabilization
Inconclusive
Belgium Greece Hong Kong Iceland Ireland Italy Japan Portugal Spain
Benin Burkina Faso Egypt Guinea Honduras India Madagascar Malawi Nepal Pakistan Paraguay Philippines Senegal South Africa Sri Lanka
Burundi Chile Congo Dominican,Rep. Gabon Gambia Iran Jamaica Jordan Mauritius Nigeria Rwanda Syria Trinidad & Tobago Zambia Zimbabwe
Argentina Brazil Barbados Bolivia Cameroon China Colombia Costa Rica Cote d’Ivoire Ecuador El Salvador Ethiopia Ghana Guatemala Indonesia Kenya Malaysia Mali Mexico Morocco Panama Peru Tanzania Thailand Uruguay Venezuela
Table 4 Median posterior welfare effects in France.
l (%)
g ¼ 1:5 g¼2 g ¼ 2:5 g¼5
z (%)
y ¼ 1:5
y¼2
y ¼ 2:5
y¼5
y ¼ 1:5
y¼2
y ¼ 2:5
y¼5
0.73 1.20 1.68 4.09
0.59 0.96 1.34 3.26
0.50 0.81 1.11 2.69
0.31 0.46 0.60 1.36
18.78 18.85 18.92 19.27
14.57 14.63 14.72 15.13
11.87 11.93 12.02 12.41
6.04 6.09 6.14 6.40
extent that a risk averse agent prefers a smooth consumption path, an increase in the risk averse parameter will imply a larger welfare cost of fluctuations. In addition, given that current shocks persist over all future periods, the total welfare cost of fluctuations is a discounted sum of static welfare costs. Obstfeld (1994) shows that the discount rate of static welfare costs increases with IES.6 As such, a higher IES would imply a larger total welfare cost of fluctuations for reasons that are not related to the risk aversion parameter. The standard CRRA utility function cannot account for such a specific role because it assumes that IES is the inverse of the risk aversion parameter, so a recursive utility formulation is more appropriate for welfare analysis in the presence of persistent shocks. Assume the representative agent has the recursive preferences of Epstein and Zin (1989), 1g
y U t ¼ ðC 1 þ b½Et ðU t þ 1 Þð1yÞ=ð1gÞ Þ1=ð1yÞ , t
ð2Þ
which is increasing, concave, and homogenous of degree one in C t ; where b, 0 o b o1, is a constant discount factor; g, 0 o ga1, is the coefficient of relative risk aversion, and 1=y, 0 o ya1, is IES for deterministic consumption paths.7
6 This result holds provided that the mean adjusted growth rate is positive. When the mean adjusted growth is negative the opposite relationship is true (see Obstfeld, 1994). In any case when shocks are persistent, IES affects welfare effects of consumption fluctuations and growth for reasons that are not related to the risk aversion parameter. P j 1g 7 Note that (2) reduces to the CRRA utility function if g ¼ y : U t ¼ E 1 j ¼ 0 b ð1=ð1gÞÞC t þ j .
40
R. Houssa / European Economic Review 59 (2013) 35–62
Fig. 1. The role of persistence, volatility and growth on welfare effects. Notes: Figures obtained with an AR(2) process and g ¼ 2 : 5; y ¼ 5. The top panel assumes f1 ¼ 0:20 and the value of f2 is allowed to vary between 0.1 and 0.25. Moreover, g ¼ 1:6%.
2.2. Welfare effects Let l lðf, s2 ,gÞ and z zðf, s2 ,gÞ denote the welfare effects of consumption fluctuations and growth, respectively, where f ¼ ðf0 f1 . . . f‘ Þ0 . As in Lucas (1987), l represents the percentage increase in consumption, across all dates and states, required to leave the representative agent indifferent between consumption instability and a perfectly smooth consumption path. Alternatively, l can be interpreted as the willingness to pay in order to eliminate all volatility in consumption or as representing the welfare gain that would be obtained if consumption were completely stabilized. In the same way, z measures the additional consumption, across all dates and states, that the representative agent would obtain if the trend growth g increases by 1%.8 The calculation of l and z follows from the value function iteration method employed in Dolmas (1998).9 Rewrite (2) as vðct Þ ¼ ð1 þ b½Eðct þ 1 vðct þ 1 Þ9c t Þ1g ð1yÞ=ð1gÞ Þ1=ð1yÞ ,
ð3Þ
where ct ¼ C t =C t1 ; c t ¼ ðct , . . . ,ct‘ þ 1 Þ; vðct Þ is a normalized value function defined as C t vðct Þ ¼ VðC t ,ct Þ, with VðC t ,ct Þ U t . The stochastic consumption process in Eq. (1) is approximated by a finite state Markov chain process with the methodology proposed by Tauchen (1986). As such, the normalized value functions can be expressed in terms of discrete values of consumption growth fc 1 ,c 2 , . . . ,c n g across n states. Subsequently, the discrete normalized value functions are solved iteratively10 until successive values differ by no more than 108 . After solving for the normalized value functions, the welfare cost of consumption fluctuation gives11
l¼
vdet 1, vsto
ð4Þ
8 This benchmark of 1% long-term growth is used to make the results comparable with the literature (see, for example, Dolmas, 1998; Lucas, 1987; Obstfeld, 1994; Pallage and Robe, 2003). 9 However, Dolmas (1998) assumes an AR(1) consumption process. Moreover, when the autoregressive coefficients fi are restricted to zero Obstfeld (1994) derives close form solutions for l and z. 10 Under Blackwell’ (1965) conditions, it can be shown that the value function iteration method yields a unique solution (see for instance Stokey et al., 1989; Sargent and Ljungqvist, 2000). 11 This expression is obtained under the assumption of homogeneity of the utility function.
R. Houssa / European Economic Review 59 (2013) 35–62
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Table 5 Summary results with higher risk aversion. Developed
Developing
Growth
Stabilization
Inconclusive
Growth
Stabilization
Inconclusive
Australia Canada Denmark Finland Norway USA Luxembourg
Iceland Portugal Hong Kong
Austria Belgium France Greece Ireland Israel Italy Japan Korea New Zealand Spain Sweden UK Netherlands Switzerland
India Nepal
Argentina Barbados Burundi Cameroon Chile Cote d’Ivoire Congo Dominican, Rep. El Salvador Ethiopia Gabon Gambia Ghana Indonesia Iran Jamaica Jordan Kenya Mali Mauritius Nigeria Panama Peru Rwanda Syria Trinidad Venezuela Zambia Zimbabwe
Benin Burkina Faso Bolivia Brazil China Colombia Costa Rica Ecuador Egypt Guatemala Guinea Honduras Madagascar Malawi Mexico Morocco Pakistan Paraguay South Africa Senegal Sri Lanka Tanzania Thailand Uruguay
Table 6 Summary results with higher IES. Developed Growth Australia Canada Denmark Finland France Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Developing Stabilization
Inconclusive
Growth
Stabilization
Inconclusive
Austria Belgium Greece Hong Kong Iceland Ireland Italy Japan Portugal Spain
Benin Burkina Faso Egypt Guinea Honduras India Madagascar Malawi Nepal Pakistan Paraguay Philippines Senegal South Africa Sri Lanka
Burundi Cameroon Chile Congo Dominican, Rep. Gabon Gambia Iran Jordan Mauritius Nigeria Rwanda Syria Trinidad & Tobago Zambia Zimbabwe
Argentina Barbados Bolivia Brazil China Cote d’Ivoire Colombia Costa Rica Ecuador El Salvador Ethiopia Ghana Guatemala Indonesia Jamaica Kenya Malaysia Mali Mexico Morocco Panama Peru Tanzania Thailand Uruguay Venezuela
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R. Houssa / European Economic Review 59 (2013) 35–62
7 Developed Developing
6 5 4 3 2 1 0 1970
1975
1980
1985
1990
1995
2000
Fig. 2. Rolling standard deviation of consumption growth. Notes: The value for 1970 is the standard deviation of per capita growth rates for the period 1961–1970. The value for 1971 refers to 1962–1971, etc.
Table 7 Summary results: 1960–1985. Developed
Developing
Growth
Stabilization
Inconclusive
Growth
Stabilization
Inconclusive
Australia Korea New Zealand Switzerland UK
Austria Canada Finland Hong Kong Norway Portugal
Belgium Denmark France Greece Iceland Ireland Israel Italy Japan Luxembourg Netherlands Spain Sweden USA
Nepal
Brazil Cameroon Chile Cote d’Ivoire Dominican. Rep., Egypt El Salvador Gabon India Indonesia Jordan Kenya Malaysia Mauritius Morocco Nigeria Pakistan Paraguay Peru Sri Lanka Syria Thailand Trinidad & Tobago Venezuela Zimbabwe
Argentina Barbados Benin Burkina Faso Bolivia Burundi China Colombia Congo Costa Rica Ecuador Ethiopia Gambia Ghana Guatemala Guinea Honduras Iran Jamaica Madagascar Malawi Mali Mexico Panama Philippines Rwanda South Africa Senegal Tanzania Uruguay Zambia
where vdet ¼ ½1=ð1bÞð1 þgÞ1y 1=ð1yÞ is the normalized value function for deterministic consumption paths obtained by plugging the deterministic consumption growth g in Eq. (3), and vsto is the corresponding value function for the stochastic consumption process. In particular, vsto is estimated as the weighted average of the normalized value functions across the n states where the weights are the invariant probabilities pj ,j ¼ 1, . . . ,n. Formally, vsto ¼
n X j¼1
pj vðc j Þ:
ð5Þ
R. Houssa / European Economic Review 59 (2013) 35–62
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Table 8 Summary results: 1986–2003. Developed
Developing
Growth
Stabilization
Austria Belgium Canada Finland France Iceland Israel Italy Luxembourg Norway Switzerland USA
Inconclusive
Growth
Stabilization
Inconclusive
Australia Denmark Greece Hong Kong Ireland Japan Korea Netherlands New Zealand Portugal Spain Sweden UK
Benin Bolivia Brazil Chile Ecuador Egypt Guatemala Honduras India Mauritius Pakistan Philippines Senegal Sri Lanka
Ethiopia Gambia Jordan Mali Nigeria Peru Rwanda Syria Trinidad & Tobago Zambia Zimbabwe
Argentina Barbados Burkina Faso Burundi Cameroon China Cote d’Ivoire Colombia Congo Costa Rica Dominican, Rep. El Salvador Gabon Ghana Guinea Indonesia Iran Jamaica Kenya Madagascar Malawi Malaysia Mexico Morocco Nepal Panama Paraguay South Africa Tanzania Thailand Uruguay Venezuela
The welfare gain from growth is obtained in an analogous way12: Pn
pgi vðc jg Þ 1, j j ¼ 1 pj vðc Þ
z ¼ Pjn¼ 1
ð6Þ
where pgj , j ¼ 1, . . . ,n, is the invariant probability associated with the value function vðc jg Þ for state j (when the mean growth rate is increased by 1%). There are two issues related to the finite state Markov chain approximation: the lag length in the AR process and the number of discrete states. With respect to the lag length, a preliminary analysis of the data indicates that the fourth AR coefficient is not statistically different from zero at the 10% significance level for any country. Therefore, I start by estimating an AR(3) process. If the third AR coefficient is not significant at 10% for a country the corresponding lag regressor is removed and the model is re-estimated. This procedure continues until an AR coefficient is significant at 10%. If no AR coefficient is significantly different from zero, I simply regress the growth rate on the constant term. In the case where the lag length is greater than one, the AR process is rewritten as a VAR(1) model, which is also approximated by a finite state Markov chain process.13 See Tauchen (1986) for technical details. For the selection of the number of states, I follow the procedure used by Otrok et al. (2002). In particular, the number of discrete states is chosen such that the first four moments and the six auto-correlations of the Markov process match the ones of the continuous AR process. In general, I find a good approximation when the number of discrete states is set to n ¼19 for the AR(1) process and to n ¼ 5‘ for the VAR(1) process.14 P P 12 An alternative way of estimating welfare effects is: l ¼ ni¼ 1 pi lðc i Þ and z ¼ ni¼ 1 pgi zðc ig Þ where lðc i Þ ¼ vdet =lðc i Þ1 and zðc ig Þ ¼ vðc ig Þ=vðc i Þ1. I thank a referee for drawing my attention to this point. However, the qualitative results of the paper remain the same across the two methods. 13 Otrok et al. (2002) use a similar approach. Chris Otrok also generously posts the approximation codes of the VAR(1) process on his web page http://web.missouri.edu/ otrokc. 14 Note that the number of total possible states for the VAR(1) process has a general formula n ¼ n‘1 where n1 is the number of grid points for each of the ‘ variables. For instance, ‘ ¼ 2 in the case of an AR(2) process. Therefore, for each discrete value of variable 1, variable 2 can take any of the n1 grid points.
44
R. Houssa / European Economic Review 59 (2013) 35–62
Table 9 Summary results, PWT6.1. Developed Growth
Developing Stabilization
Australia Austria Canada Denmark Finland France Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Inconclusive
Growth
Stabilization
Inconclusive
Belgium Greece Hong Kong Iceland Ireland Italy Japan Portugal Spain
Benin Burkina Faso Brazil Egypt Guinea Honduras India Madagascar Malawi Nepal Pakistan Paraguay Philippines South Africa Senegal Sri Lanka
Burundi Cameroon Chile Congo Dominican, Rep. Gabon Gambia Iran Jordan Mauritius Nigeria Rwanda Syria Trinidad Zambia Zimbabwe
Argentina Barbados Bolivia China Cote d’Ivoire Colombia Costa Rica Ecuador El Salvador Ethiopia Ghana Guatemala Indonesia Jamaica Kenya Malaysia Mali Mexico Morocco Panama Peru Tanzania Thailand Uruguay Venezuela
Table 10 Summary results, PWT6.3. Developed Growth Australia Austria Canada Denmark Finland France Ireland Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Developing Stabilization
Inconclusive
Growth
Stabilization
Inconclusive
Belgium Greece Hong Kong Iceland Italy Japan Portugal Spain
Bolivia Ecuador Egypt Guinea Honduras India Nepal Pakistan Paraguay Philippine Senegal
Burkina Faso Burundi Chile Congo Dominican, Rep. Gabon Gambia Jordan Malawi Mauritius Nigeria Rwanda Syria Trinidad Venezuela Zambia Zimbabwe
Argentina Barbados Benin Brazil Cameroon China Cote d’Ivoire Colombia Costa Rica El Salvador Ethiopia Ghana Guatemala Indonesia Iran Jamaica Kenya Madagascar Malaysia Mali Mexico Morocco Panama Peru South Africa Sri Lanka Tanzania Thailand Uruguay
R. Houssa / European Economic Review 59 (2013) 35–62
45
2.3. Posterior distributions of welfare effects This section discusses the proposed Bayesian inference on l and z. For this purpose, it is assumed that only uncertainty related to the estimation of f and s2 matter for inference on l and z. Moreover, l and z are complicated functions of f and Table 11 Summary results with the unit root test. Developed
Developing
Growth
Stabilization
Australia Austria Canada Denmark Finland France Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Inconclusive
Growth
Stabilization
Inconclusive
Belgium Greece Hong Kong Iceland Ireland Italy Japan Portugal Spain
Benin Burkina Faso Costa Rica Egypt Guinea Honduras India Madagascar Malawi Nepal Pakistan Paraguay Philippine South Africa Senegal Sri Lanka
Burundi Cameroon Chile Congo Dominican, Rep. Gabon Gambia Iran Jordan Mauritius Nigeria Peru Rwanda Syria Trinidad Venezuela Zambia Zimbabwe
Argentina Barbados Bolivia Brazil China Cote d’Ivoire Colombia Ecuador El Salvador Ethiopia Ghana Guatemala Indonesia Jamaica Kenya Malaysia Mali Mexico Morocco Panama Tanzania Thailand Uruguay
Table A1 OLS estimates of the AR process in developed countries. Countries Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
f0
f1
f2
f3
0.11(0.16)
0:29nn ð0:16Þ 0:06ð0:16Þ
nnn
0:02 ð0:00Þ 0:02nnn ð0:01Þ 0.01 (0.01) 0:02nnn ð0:00Þ 0:02nnn ð0:00Þ 0:03nnn ð0:01Þ 0:01nnn ð0:00Þ 0:02nnn ð0:01Þ 0:03nnn ð0:01Þ 0:03nnn ð0:01Þ 0:02nnn ð0:01Þ 0:05nnn ð0:01Þ 0:01n ð0:01Þ 0:01n ð0:01Þ 0:05nnn ð0:01Þ 0:03nnn ð0:00Þ 0:01nnn ð0:00Þ 0:01nnn ð0:00Þ 0:03nnn ð0:00Þ 0:02nnn ð0:01Þ 0:01nnn ð0:00Þ 0:01nnn ð0:00Þ 0:00nnn ð0:00Þ 0:02nnn ð0:00Þ 0:02nnn ð0:00Þ
0:33nn ð0:15Þ 0:25n ð0:14Þ
0:60nnn ð0:13Þ 0.22(0.15) 0:34nn ð0:15Þ 0:27n ð0:15Þ 0:29nn ð0:15Þ 0:42nnn ð0:14Þ 0:07ð0:14Þ 0:43nnn ð0:15Þ 0:45nn ð0:15Þ
0:33nnn ð0:15Þ
0:47nnn ð0:14Þ 0:12ð0:17Þ nn
0:31 ð0:15Þ
0:42nnn ð0:14Þ 0:37nn ð0:16Þ 0:30n ð0:16Þ 0:27n ð0:15Þ 0:64nnn ð0:11Þ 0:44nnn ð0:14Þ 0:63nnn ð0:12Þ 0:55nnn ð0:16Þ 0:31nn ð0:15Þ
0:43nnn ð0:15Þ
0:28n ð0:15Þ
0:31nn ð0:15Þ
LAR
g (%)
s (%)
0:00 0:60 0:85 0:25 0:00 0:00 0:60 0:69 0:34 0:54 0:42 0:68 0:78 0:83 0:00 0:00 0:42 0:54 0:00 0:27 0:64 0:44 0:63 0:53 0:31
2.12 2.72 2.13 2.09 1.60 2.67 2.42 3.19 4.98 3.29 2.87 2.96 2.46 3.18 5.07 2.79 2.34 1.31 2.51 3.29 2.69 1.52 1.32 2.51 2.60
1.60 1.90 1.52 1.88 2.38 3.30 1.38 2.73 4.83 5.75 2.72 4.04 1.73 2.12 4.65 2.17 2.21 2.39 2.48 4.87 1.91 1.84 1.18 1.80 1.56
Notes: Standard errors in parentheses. LAR is the modulus of the largest root of the characteristic polynomial. nSignificant at 10%; nnn Significant at 1%.
nn
Significant at 5%;
46
R. Houssa / European Economic Review 59 (2013) 35–62
s2 such that the functional form of their posterior distributions cannot be directly obtained. To overcome this difficulty, a Markov Chain Monte Carlo (MCMC) method is used to simulate the posterior distributions of l and z. At each step k, ðkÞ ðkÞ k ¼ 1, . . . ,K, of the chain, f and s2 are drawn from their posterior distributions, the functional forms of which are
Table A2 OLS estimates of the AR process in developing countries. Countries Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad & Tobago Uruguay Venezuela Zambia Zimbabwe
f0
f1
f2
f3
nnn
0:01 ð0:01Þ 0:01n ð0:01Þ 0:01n ð0:01Þ 0:01n ð0:01Þ 0:01ð0:01Þ 0:03nnn ð0:01Þ 0:00ð0:01Þ 0:01ð0:01Þ 0:03nnn ð0:01Þ 0:04nnn ð0:01Þ 0:01n ð0:01Þ 0:01ð0:01Þ 0:00ð0:02Þ 0:01ð0:01Þ 0:03nnn ð0:01Þ 0:01nnn ð0:00Þ 0:03nnn ð0:01Þ 0:01ð0:01Þ 0:02ð0:01Þ 0:02ð0:02Þ 0:00ð0:02Þ 0:00ð0:01Þ 0:00ð0:00Þ 0:01ð0:01Þ 0:01nn ð0:01Þ 0:02nnn ð0:01Þ 0:03nnn ð0:01Þ 0:02ð0:01Þ 0:00ð0:01Þ 0:00ð0:01Þ 0:00ð0:01Þ 0:01ð0:01Þ 0:02ð0:01Þ 0:03ð0:01Þ 0:02ð0:01Þ 0:04ð0:01Þ 0:01ð0:01Þ 0:02ð0:01Þ 0:01ð0:01Þ 0:00ð0:02Þ 0:02ð0:01Þ 0:03nnn ð0:01Þ 0:02nnn ð0:01Þ 0:02nn ð0:01Þ 0:02nnn ð0:00Þ 0:01ð0:01Þ 0:01nn ð0:00Þ 0:00ð0:01Þ 0:03nnn ð0:01Þ 0:04nnn ð0:02Þ 0:00ð0:01Þ nnn
0:03 ð0:01Þ 0:02ð0:01Þ 0:01ð0:01Þ 0:01ð0:01Þ 0:01ð0:01Þ 0:01ð0:02Þ
0.22(0.14)
0.14(0.13)
0.04(0.15)
0:37nnn ð0:15Þ
0:41ð0:13Þ
0:31nn ð0:15Þ 0:01ð0:14Þ
0:45nnn ð0:14Þ
0:30nn
ð0:14Þ
0:39nnn
ð0:14Þ
0:56nnn 0:28n
ð0:13Þ ð0:15Þ
0:94nnn ð0:15Þ
0:55nnn ð0:20Þ
0:24
ð0:15Þ
0:32 0:18ð0:16Þ 0:24ð0:15Þ
ð0:15Þ 0:28ð0:15Þ
0:26 0:24 0:37
ð0:15Þ ð0:15Þ ð0:15Þ
0:25 0:28ð0:14Þ 0:37ð0:15Þ 0:04ð0:15Þ
ð0:15Þ 0:23ð0:11Þ
0:36nn ð0:15Þ
0:45ð0:15Þ
0:36ð0:15Þ
0:40nnn ð0:15Þ
0:00ð0:16Þ
0:44nnn
ð0:14Þ
0:35nn 0:18ð0:16Þ
0:23n ð0:14Þ
0:32nn ð0:13Þ
0:06ð0:17Þ
0:41nnn ð0:17Þ
0:32nn ð0:14Þ
ð0:15Þ
nn
0:33 ð0:15Þ 0:23n ð0:15Þ 0:38nn ð0:15Þ
Notes: Standard errors in parentheses. LAR is the modulus of the largest root of the characteristic polynomial. n Significant at 10%.
nnn
LAR
g (%)
s (%)
0:00 0:00 0:00 0:00 0:75 0:00 0:00 0:63 0:00 0:31 0:00 0:68 0:00 0:30 0:00 0:39 0:00 0:56 0:28 0:00 0:00 0:00 0:81 0:00 0:00 0:00 0:24 0:00 0:32 0:62 0:24 0:00 0:26 0:24 0:37 0:00 0:25 0:64 0:37 0:67 0:00 0:36 0:00 0:00 0:74 0:00 0:44 0:00 0:00 0:35 0:73 0:33 0:00 0:77 0:38 0:00 0:00
0.84 1.43 1.17 0.95 0.58 3.09 0.27 0.89 2.87 5.23 1.23 1.44 0.21 1.60 3.22 1.47 2.57 1.38 1.46 2.25 0.43 0.23 0.53 0.63 0.91 2.15 4.21 1.57 0.65 0.17 0.25 1.24 1.81 3.56 1.23 3.79 1.76 2.33 1.08 0.23 2.45 2.45 2.02 1.74 1.67 0.82 1.46 0.06 3.20 3.00 0.38 3.89 2.49 1.30 0.96 0.66 0.69
6.10 6.39 4.73 4.50 3.53 5.16 8.00 5.63 9.07 3.96 5.94 2.52 1.05 3.91 7.86 2.83 4.13 3.41 8.36 11.56 1.63 6.99 1.28 4.18 3.69 3.25 4.82 8.37 5.24 7.54 7.14 3.89 5.34 5.44 7.31 9.29 3.53 5.00 3.35 1.26 4.48 7.18 4.87 6.83 2.10 9.64 2.24 4.34 5.06 13.76 3.29 3.66 8.24 5.96 5.76 9.25 12.69
Significant at 1%;
nn
Significant at 5%;
R. Houssa / European Economic Review 59 (2013) 35–62 ðkÞ
47
ðkÞ
explicitly known. Subsequently, l and z are calculated with the methodology explained in Section 2.2. This procedure is repeated until convergence. Given Eq. (1) the likelihood function, conditional on the data ¼ fx; ðg 0 , . . . ,g ‘1 Þg, is 1 ð7Þ Lðf, s2 9dataÞ ¼ ð2ps2 ÞðT‘ þ 1Þ=2 exp 2 ðxX fÞ0 ðxX fÞ , 2s where ðg 0 , . . . ,g ‘1 Þ are treated as fixed initial conditions, x ¼ ðg ‘ , . . . ,g T Þ0 , e ¼ ðe‘ , . . . , eT Þ0 , f ¼ ðf0 f1 . . . f‘ Þ0 and X is a ðT‘ þ 1Þ ð‘ þ1Þ matrix of ones and lagged observations on x. Eq. (7) implies that conditional on s2 , f has a normal distribution. In the same way, conditional on f, s2 has an inverted Gamma distribution. Assuming natural conjugate priors for f9s2 and s2 9f, n d ð8Þ f9s2 Nðf , S0 ÞIsðfÞ and s2 9f IG 0 , 0 2 2 yields the following conditional posterior distributions:
f9s2 , data Nðf~ , S1 ÞIsðfÞ ,
ð9Þ
Table B1 Posterior quantiles of welfare effects in developed countries. Countries
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
1.77 4.27 2.79 3.34 4.14 7.30 3.92 12.48 20.65 24.74 9.48 7.19 3.25 18.08 11.68 2.95 6.54 5.49 4.11 21.63 9.95 5.32 3.96 4.00 2.38
2.48 10.43 8.68 6.02 6.02 10.53 9.12 30.77 40.70 47.53 19.34 11.17 8.11 46.11 17.35 4.33 13.80 10.16 5.87 43.44 22.02 11.07 8.92 7.62 4.50
3.62 42.95 47.72 14.40 9.11 16.91 36.55 81.30 85.08 88.56 58.92 20.82 44.01 90.87 28.74 6.51 45.86 28.29 8.79 86.50 66.86 38.37 36.18 24.07 12.05
18.72 17.87 17.80 18.69 19.77 17.66 18.03 17.34 15.20 18.61 17.72 17.49 17.20 18.26 14.44 17.46 18.49 20.92 17.98 17.70 17.75 19.99 20.54 18.12 17.80
19.59 19.56 20.40 20.20 21.30 19.48 19.92 20.78 18.39 22.49 20.20 18.87 19.62 23.24 16.10 18.50 20.70 22.82 19.24 21.66 20.99 22.27 22.63 19.60 18.90
20.59 25.29 31.57 22.40 23.04 21.73 25.21 28.56 24.57 28.49 26.38 20.99 29.74 31.39 18.61 19.78 25.99 26.27 20.82 28.47 29.38 28.19 28.54 22.70 20.81
18.14 14.38 16.72 16.78 17.27 11.88 15.21 5.83 4.37 4.99 9.52 11.23 15.50 1.00 3.75 15.62 13.30 16.90 15.24 2.74 8.95 16.11 17.93 15.27 16.50
17.10 9.18 11.84 14.06 15.25 8.86 10.71 9.93 22.42 24.97 0.86 7.70 11.42 22.70 1.28 14.19 7.00 12.52 13.37 21.82 0.93 11.14 13.64 11.83 14.36
15.83 18.73 18.37 6.71 12.49 3.64 11.92 54.07 61.98 61.51 33.84 0.43 15.73 61.86 10.88 12.05 19.39 2.68 10.71 59.52 39.69 11.30 8.68 2.14 7.79
Table B2 Posterior quantiles of welfare effects in developing countries. Countries
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
35.73 37.04 19.17 17.54 6.42 18.39 61.82 44.42 60.40 12.04 32.27
59.00 60.49 29.77 27.42 11.57 28.48 87.00 76.18 85.11 24.14 52.68
91.85 92.54 53.27 48.92 30.17 49.42 98.67 97.64 98.79 66.64 88.23
23.60 22.24 21.62 22.20 22.13 17.66 25.11 24.32 19.52 14.29 22.33
29.77 27.88 25.56 26.16 25.00 20.62 31.38 30.02 24.08 16.65 27.94
38.48 35.77 31.83 32.47 30.87 25.33 38.42 37.42 29.01 21.86 36.16
9.72 12.37 4.37 6.61 18.28 0.72 33.89 17.07 39.33 3.00 7.68
28.94 32.26 4.16 1.27 13.50 7.93 54.70 45.49 60.76 7.67 24.82
56.90 58.97 22.96 17.87 1.13 24.99 67.15 65.22 73.61 45.53 53.48
48
R. Houssa / European Economic Review 59 (2013) 35–62
Table B3 Posterior quantiles of welfare effects in developing countries. Countries
Colombia Congo Cost Rica Dominican, Rep. Ecuador Egypt EL Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad & Tobago Uruguay Venezuela Zambia Zimbabwe
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
11.02 75.90 18.50 46.91 11.20 11.76 27.08 41.64 74.94 78.65 53.85 5.06 15.64 11.65 7.53 18.41 60.00 36.87 1.96 38.32 18.61 14.72 26.29 28.87 58.99 12.59 19.83 5.44 68.98 14.41 24.72 18.24 41.84 2.365 72.64 7.99 19.20 17.40 71.21 6.21 12.52 54.60 16.85 45.53 75.80 64.43
26.92 93.42 37.51 73.46 23.05 17.82 56.19 67.39 94.09 91.86 79.51 13.44 24.04 17.39 10.98 36.94 85.67 67.37 82.46 63.66 28.65 24.06 49.99 49.68 84.40 25.14 37.74 8.20 90.10 22.12 40.60 28.01 66.37 4.154 91.85 16.43 29.24 26.29 91.82 11.90 25.07 81.04 31.53 76.00 92.92 87.93
76.00 99.36 84.61 97.28 69.38 28.86 93.25 95.43 99.18 99.59 97.78 64.51 41.84 28.32 17.25 79.77 98.52 96.55 99.10 93.67 49.68 47.63 90.45 86.34 98.63 64.84 80.54 14.06 99.23 36.53 75.68 47.60 94.99 9.371 99.31 50.73 50.12 44.83 99.34 35.46 69.32 98.07 76.46 97.57 99.09 98.90
21.28 22.69 20.81 18.98 20.62 18.15 21.91 22.79 17.98 21.52 27.22 21.71 22.75 21.86 18.72 16.16 22.10 24.25 0.13 27.45 29.80 19.92 17.58 22.65 18.21 19.98 20.30 21.25 27.02 18.50 19.48 19.53 22.03 19.302 22.52 20.36 25.32 17.39 19.23 22.51 16.15 20.70 20.84 23.49 25.92 19.98
25.11 27.48 25.36 23.63 24.08 20.51 28.03 28.05 22.21 25.28 34.40 25.78 26.69 24.80 20.68 19.34 27.44 30.71 28.15 34.57 35.83 23.03 21.58 27.62 22.13 23.46 24.30 22.99 32.08 21.25 23.12 22.94 27.35 20.866 27.10 23.14 29.96 20.09 22.80 25.58 18.82 25.28 25.40 29.35 30.69 25.59
34.10 33.43 33.43 29.16 31.86 23.74 36.09 35.25 25.00 30.57 43.18 39.52 32.56 29.13 23.16 25.19 33.61 39.09 36.31 44.27 45.03 28.51 27.91 35.45 26.55 30.35 31.62 25.54 37.99 25.33 29.51 28.10 34.77 22.887 32.58 29.74 37.56 24.29 26.93 31.90 24.61 30.95 34.04 37.35 38.03 32.32
11.85 49.72 4.28 26.27 11.37 7.82 2.47 16.43 53.45 53.97 23.39 19.35 9.60 12.37 12.73 1.16 35.64 10.41 1.82 8.22 15.43 6.89 7.25 4.38 38.77 9.16 1.63 17.44 39.06 5.69 3.52 2.89 18.04 18.834 47.20 14.12 8.96 1.30 50.04 19.03 4.74 32.08 6.72 18.88 45.22 41.29
1.91 65.54 12.12 49.52 0.72 2.80 28.54 39.33 71.09 67.03 44.10 12.03 2.47 7.40 9.64 17.22 57.36 35.74 52.44 28.81 7.00 1.10 28.17 21.72 61.84 1.67 13.45 14.79 57.14 0.77 17.62 4.98 38.53 16.705 63.64 6.61 0.66 6.30 68.56 13.50 6.32 55.33 6.40 45.52 60.96 61.25
43.27 72.91 52.77 70.89 37.59 6.30 60.78 63.91 77.20 73.91 61.35 26.71 11.47 1.10 4.49 55.39 70.34 62.03 69.02 54.68 8.15 21.24 64.21 53.70 75.38 36.17 49.90 9.63 67.57 12.95 46.70 20.84 63.37 11.907 72.56 20.89 15.02 22.15 76.54 5.11 45.83 70.81 44.02 65.76 68.99 72.77
s2 9f, data IG
n1 d1 2
,
2
,
ð10Þ
~ ¼ ðf þ s2 X 0 XÞ1 ðS1 f þ s2 X 0 cÞ, S ¼ ðS1 þ s2 X 0 XÞ, n ¼ n þðT‘ þ 1Þ, and d ¼ d þ ðxX fÞ0 ðxX fÞ, with the where f 1 1 0 1 0 0 0 following diffuse prior parametrization: S0 ¼ 4000I‘ ; f ¼ ð0 0, . . . ,0Þ0 and n0 ¼ d0 ¼ 0. IsðfÞ is an indicator function that puts a zero prior mass on the region of the parameter space where draws on ðf, s2 Þ are not stationary.15 Moreover, draws that generate negative values or values that lie outside the unit circle for l, and z are discarded. These restrictions derive from l and z being able to be interpreted as shares of consumption that the agent is willing to pay for in order to eliminate fluctuations and to reduce growth, respectively. Given the dependence between the posterior distributions of f9s2 and s2 9f, a Gibbs sampling method, which also belongs to the class of MCMC methods, is used. More formally, the algorithm used to estimate the conditional posterior ð0Þ distributions of f, s2 , l, and z can be summarized as follows. After choosing a starting value f , the MCMC method
15
Stationarity requires that the roots of the characteristic equation ð1f1 zf2 z2 f‘ z‘ ¼ 0Þ lie outside the unit circle.
R. Houssa / European Economic Review 59 (2013) 35–62
49
Table C1 Posterior quantiles of welfare effects in developed countries. Countries
l (%)
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
1.29 3.42 4.38 2.35 2.73 5.64 3.04 10.25 22.40 21.26 7.17 6.75 5.44 15.80 13.12 2.43 4.65 3.49 3.09 17.62 7.56 3.24 2.34 2.97 1.85
1.79 7.68 13.95 4.12 3.85 8.09 6.50 24.62 42.30 36.20 14.18 10.34 13.34 41.05 18.97 3.40 9.00 6.14 4.41 33.42 16.77 6.39 5.29 5.57 3.31
2.61 31.81 63.22 9.25 5.82 12.25 25.68 75.05 85.91 73.21 39.97 18.94 55.64 89.71 28.62 5.18 25.86 14.81 6.54 73.30 54.59 18.50 20.63 15.17 8.30
31.13 29.40 23.11 30.29 29.55 30.98 29.04 27.78 31.01 28.30 29.43 31.65 24.94 23.27 35.17 32.19 29.32 28.37 31.25 28.17 27.14 28.11 27.51 30.69 31.47
32.07 32.82 30.98 31.79 30.80 32.93 32.32 33.05 37.10 32.02 32.90 33.54 31.94 30.72 39.17 33.51 32.00 29.92 32.76 32.71 32.11 30.34 29.98 32.50 33.04
33.03 34.89 34.00 33.58 32.17 35.01 34.47 37.13 43.69 35.85 35.96 35.48 34.95 35.79 43.82 34.97 34.45 31.46 34.34 37.53 35.63 32.32 31.84 34.24 34.57
31.31 30.14 28.20 29.97 28.51 27.88 30.17 24.16 17.22 11.60 26.78 27.31 28.11 17.89 27.12 31.76 28.07 26.87 30.29 16.48 25.93 27.67 28.35 30.00 31.80
30.27 25.04 16.99 27.68 26.94 24.84 25.89 8.43 4.63 3.72 18.72 23.18 18.67 9.68 20.21 30.08 22.85 23.77 28.34 0.42 15.43 23.94 24.61 27.00 29.72
29.03 1.53 40.00 22.28 24.55 20.33 3.76 45.86 49.81 41.97 8.89 14.32 31.30 63.55 9.91 27.87 5.64 14.94 25.77 41.97 25.85 10.94 8.16 16.72 24.01
Table C2 Posterior quantiles of welfare effects in developing countries.
l (%)
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
18.50 20.51 11.05 9.67 7.00 14.67 33.22 28.70 48.27 14.35 17.88
27.08 31.09 15.59 14.10 12.18 21.25 48.81 55.83 71.83 26.31 26.46
42.16 47.77 24.13 21.27 29.23 33.14 77.96 93.18 95.71 65.53 39.87
25.60 26.13 27.05 26.78 26.23 30.02 23.27 23.27 25.70 33.42 26.13
28.05 28.99 29.19 28.83 28.30 33.07 26.13 26.89 29.75 39.02 28.81
31.15 32.34 31.72 31.23 29.99 36.64 29.78 30.64 34.86 45.08 31.99
10.23 8.87 18.91 19.66 21.72 19.15 6.35 0.90 17.68 26.91 11.29
1.09 2.06 13.51 14.87 16.11 12.02 22.67 29.00 41.73 12.92 2.45
14.59 18.97 4.68 6.89 1.53 0.06 51.42 67.38 65.77 28.14 11.42
ðkÞ
ðkÞ
ðkÞ
ðkÞ
generates a sequence of draws ff , s2 , l , z g, k ¼ 1, . . . ,K, in the following steps: ðkÞ
ðk1Þ
is drawn from (10); 1. s2 9f ðk1Þ ðkÞ 2. f 9s2 is drawn from (9); ðkÞ ðkÞ ðkÞ ðkÞ 3. l and z are calculated with the methodology explained in Section 2.2. Moreover, l z is calculated at each iteration; 4. Repeat steps 1–3 K times. The results reported in the paper are based on 2000 draws plus a burn-in phase of 200 replications (i.e. K ¼2200). I check convergence of the chain in two ways. First, I experimented with different numbers of draws ranging from 1000 to 2000 and the results remained qualitatively unchanged. Second, the Geweke (1991) test indicates that convergence cannot be rejected.16 16 The Geweke (1991) convergence test amounts to splitting the 2000 draws on each parameter into three consecutive equally sized sub-samples. Under the null hypothesis of convergence, the moments of the draws in the first and third sub-samples are equal. For the test, I concentrate on the first and second moments.
50
R. Houssa / European Economic Review 59 (2013) 35–62
Table C3 Posterior quantiles of welfare effects in developing countries.
l (%)
Colombia Congo Cost Rica Dominican, Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad & Tobago Uruguay Venezuela Zambia Zimbabwe
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
6.56 54.06 11.19 36.28 6.59 8.77 15.84 26.25 69.37 59.48 23.66 5.74 8.22 6.52 5.33 17.44 38.31 20.47 48.95 17.69 6.54 10.61 21.65 18.56 54.67 8.35 14.27 3.66 46.53 10.43 19.16 12.30 25.25 3.07 49.70 4.86 8.62 14.21 71.38 6.54 11.79 38.62 20.05 28.01 43.63 74.32
15.40 76.83 21.02 54.45 13.16 12.78 32.34 41.59 89.64 82.57 34.69 16.26 11.88 9.30 7.61 32.32 57.79 37.51 78.30 27.76 9.51 15.67 40.15 28.28 76.85 14.66 24.19 5.37 71.70 15.10 29.18 17.49 37.25 5.43 73.59 9.50 12.39 20.36 90.16 12.42 21.39 59.18 36.46 52.37 65.15 91.97
58.48 97.07 54.73 84.82 38.80 19.28 76.13 75.64 99.23 98.43 54.07 63.76 17.97 14.08 11.38 73.31 87.48 79.85 98.17 51.88 14.32 26.69 79.96 48.17 97.21 34.82 52.09 8.73 96.31 22.70 49.12 26.76 59.01 12.55 96.16 28.69 18.87 31.54 99.15 34.01 53.80 88.08 75.40 91.81 93.14 99.38
25.11 22.06 26.56 27.40 26.85 30.05 24.36 25.48 23.26 21.90 23.55 21.61 26.53 27.29 29.86 30.37 24.68 23.49 21.21 23.91 24.11 28.18 28.42 26.10 26.99 27.61 27.08 28.31 22.65 29.45 28.26 28.32 26.22 29.42 22.93 27.52 25.49 30.27 24.99 25.89 30.91 26.03 25.68 23.18 21.63 21.04
29.08 25.07 29.66 31.55 29.82 32.40 28.34 28.66 26.88 24.98 26.01 27.71 28.38 29.02 31.69 35.37 28.01 27.05 24.31 26.30 25.52 30.46 33.06 28.69 31.59 30.35 30.25 29.62 25.24 31.93 31.13 30.89 29.39 30.80 26.08 30.06 27.17 33.36 28.70 28.02 35.11 29.75 28.46 27.02 24.39 24.17
31.74 28.89 32.97 36.62 32.35 34.93 32.23 32.10 31.25 29.02 28.74 30.12 30.39 30.85 33.70 40.69 32.20 30.45 27.72 28.70 27.03 32.93 38.13 31.44 37.39 33.24 33.18 30.97 28.06 34.61 34.30 33.89 33.36 32.33 30.12 32.22 29.03 37.08 32.97 29.75 39.57 34.73 31.37 31.30 27.85 27.79
23.55 28.38 19.15 3.99 23.88 24.15 13.37 3.37 41.90 33.97 2.55 23.08 20.44 23.01 27.03 19.12 10.04 7.46 24.06 9.09 19.37 20.42 12.46 10.61 22.34 22.66 16.93 26.34 20.44 22.11 12.65 19.14 4.58 28.02 22.98 25.97 18.91 19.86 41.82 21.85 24.54 8.59 8.88 0.48 18.89 49.86
13.87 51.62 8.71 22.55 16.85 19.74 3.63 12.85 62.31 57.52 8.61 11.82 16.50 19.80 24.08 3.09 29.76 10.51 53.73 1.40 15.98 14.71 6.76 0.52 44.83 15.84 6.04 24.21 46.40 16.84 1.83 13.38 7.62 25.37 47.40 20.51 14.86 12.99 61.27 15.69 13.69 29.16 7.81 25.04 40.54 67.63
33.66 71.99 25.28 53.58 9.86 12.79 49.73 47.15 73.17 73.54 28.11 40.97 10.31 14.75 19.86 39.46 59.74 53.65 74.54 26.31 10.83 3.48 48.88 19.58 66.13 4.54 23.43 20.50 71.51 9.08 18.21 3.69 29.50 17.97 70.05 0.48 7.94 1.55 71.06 6.98 20.24 58.38 48.71 65.98 69.05 76.17
3. Empirical analysis 3.1. Data I use annual data on real private consumption per capita from 1960 to 2003. The data are expressed in constant dollars (international prices, base year 2000). They are taken from the Penn World Table, version 6.2 (Heston et al., 2006). I restrict the analysis to a balanced data set on countries with at least grade C data quality.17 This leads to a sample of 82 countries, 25 developed and 57 developing countries.18 Tables A1 and A2 in Appendix A report OLS estimation results for the AR consumption process. The data indicate that developing countries display larger shocks (large s2 Þ to consumption than do developed countries. This result is consistent with findings in the literature (see, for example, Agenor et al., 2000; Mendoza, 1995). However, the results in Tables A1 and
17
Heston et al. (2006) provide information on the quality of the data of each country ranging from A to D with grade A representing the best quality. The classification between developed and developing countries is obtained from the World Developing Indicators (2010), where developed countries are defined as high income countries. 18
R. Houssa / European Economic Review 59 (2013) 35–62
51
A2 show a higher persistence of shocks in developed countries. Moreover, these results are in line with the findings of Giannone and Reichlin (2005) that consumption responses to technology shocks are more persistent in the Euro area than in the USA. In this paper, the persistence of shocks is measured by the largest root of the characteristic polynomial of the AR process (see Stock, 1991). Everything else being equal, a higher persistence of shocks will imply a larger welfare cost of consumption fluctuations. The reason is that the more persistent the shocks are, the more long-lasting their effects and the more welfare loss they will generate. As a result, it is interesting to see how the combination of the size and persistence of shocks affect the comparison of welfare effects across countries. 3.2. Main results The entire empirical analysis assumes b ¼ 0:96, which is the value often used in the literature for annual data. For the risk aversion parameter ðgÞ and IES ð1=yÞ, the results presented in this section are based on g ¼ 5:0 and y ¼ 1:5, which are also the values commonly used in empirical macroeconomics. However, there is debate about the value of g in the finance literature. Section 4 presents the results for higher values of g and IES. Tables 1 and 2 present the median together with the 5th and 95th quantiles of the posterior distributions of l, z and lz. Table D1 Posterior quantiles of welfare effects in developed countries. Countries
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.76 1.13 3.20 1.75 2.09 2.91 1.99 4.94 4.43 9.92 3.72 4.34 1.80 5.11 2.79 3.61 6.73 2.98 2.10 20.38 5.51 2.84 1.67 1.24 2.64
1.51 1.78 9.79 2.79 5.62 4.77 7.58 14.03 7.19 19.67 7.24 9.71 5.83 14.88 5.32 8.62 15.53 5.78 3.34 42.36 12.95 6.32 3.94 2.33 5.78
5.07 3.11 54.48 4.89 37.49 8.39 39.63 66.82 13.48 63.38 26.03 31.41 49.77 64.78 13.22 35.47 55.55 17.15 5.78 87.48 52.92 25.62 21.74 8.11 22.34
18.21 15.77 15.70 17.88 18.36 15.69 17.26 14.41 11.67 14.90 17.94 17.21 15.47 13.83 13.05 16.84 16.98 20.54 16.50 15.07 17.44 19.21 18.74 18.39 16.85
19.41 16.91 18.94 19.59 21.49 17.51 20.61 17.54 13.22 18.01 20.10 18.98 17.68 17.01 14.71 18.91 19.71 23.10 18.07 21.14 22.68 21.28 20.68 19.80 18.53
21.15 18.18 31.95 21.74 26.99 19.97 38.00 26.89 15.43 24.72 24.94 22.42 33.12 26.38 17.15 23.86 25.97 27.11 20.08 33.15 36.37 26.04 25.39 21.88 21.57
19.07 2.81 15.09 1.32 19.31 2.20 17.26 11.41 5.09 6.94 16.74 13.74 15.37 10.44 11.69 14.68 12.05 20.40 1.98 3.73 15.50 18.20 19.17 19.09 15.79
17.83 3.50 8.72 2.16 15.60 3.35 12.90 3.51 6.76 1.75 12.44 9.61 12.13 2.19 9.78 10.07 4.01 17.17 2.94 22.05 10.09 14.81 16.60 17.44 12.70
14.72 4.23 23.44 3.01 12.91 4.48 6.74 41.91 8.41 38.92 2.83 9.56 22.77 39.08 1.22 12.97 30.65 7.85 3.85 61.22 25.81 1.41 1.83 12.47 1.48
Table D2 Posterior quantiles of welfare effects in developing countries.
l (%)
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
8.65 14.76 9.81 7.25 11.24 7.41 10.36 12.43 44.75 8.91 9.42
16.89 25.42 16.78 12.15 26.94 12.41 18.95 21.46 75.54 25.64 15.77
50.34 56.62 34.11 24.21 72.31 24.22 47.32 44.54 97.36 81.31 32.22
20.60 19.33 18.32 20.70 22.27 13.70 19.85 17.51 17.63 14.13 16.85
24.67 25.15 22.64 25.05 27.31 16.30 23.43 22.11 24.75 18.49 20.69
32.32 36.55 30.41 32.29 38.01 20.29 30.06 30.54 34.93 27.85 27.67
15.34 0.93 0.19 0.93 13.51 2.73 12.15 0.07 0.47 7.50 0.48
7.68 1.15 1.62 0.58 0.41 4.65 4.41 2.07 3.17 7.00 2.39
18.85 3.29 3.49 2.11 43.65 6.57 19.18 4.13 6.73 55.06 4.36
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R. Houssa / European Economic Review 59 (2013) 35–62
The results indicate large uncertainty on estimates of the welfare cost of consumption fluctuations. For example, looking at the USA results, the 90% credible interval for l is [1.16;5.33]% of consumption. Using identical preference parameter values, Pallage and Robe (2003) find a 2.11% point estimate for l. However, the credible interval for l suggests considerable uncertainty around this value. In international dollar terms—taking the USA average annual real per capita consumption to be $15 790.30 for 1960–2003—these estimates correspond to a welfare cost of about [183;843] per person and per year in 1960–2003. Thus, while the literature shows conflicting point estimates for l across different models, estimates obtained from a particular model display considerable uncertainty. As such, one should account for this uncertainty when comparing z with l. Results for other countries show even greater uncertainty. For instance, the credible intervals for l in France and Morocco are, respectively [1.90;16.77] and [10.02;42.52]% of consumption. Given this large uncertainty, one should be very careful in interpreting the point estimates reported in earlier studies. Note, however, that estimates of z display relatively less uncertainty. In order to compare estimates of l and z between developed and developing countries, I calculate the unweighted average of posterior quantiles in each group. This yields the following 90% credible intervals for l in developed and developing countries, respectively [4.0;24.95] and [17.73;51.26]%. The corresponding figures for z are [17.42;23.98] and [19.85;31.14]. These estimates imply that, while the welfare costs of consumption fluctuations are on average two to four
Table D3 Posterior quantiles of welfare effects in developing countries.
l (%)
Colombia Congo, Rep. Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad & Tobago Uruguay Venezuela Zambia Zimbabwe
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
3.36 19.32 23.72 9.83 8.52 6.73 29.12 4.29 40.55 48.04 26.50 7.92 8.08 7.60 5.15 6.57 34.47 14.93 51.85 37.32 16.20 12.25 5.64 15.81 42.27 9.33 20.43 3.23 39.22 6.93 6.25 5.70 35.70 4.12 28.15 6.36 8.66 11.22 61.92 8.71 1.85 24.89 10.22 35.43 34.02 45.43
9.14 40.80 49.38 23.57 21.89 11.12 60.59 6.86 67.39 77.42 52.30 29.08 20.49 12.73 8.33 10.97 62.23 26.22 81.49 65.65 36.50 23.23 9.20 29.20 71.88 21.79 42.82 5.78 69.81 11.64 12.72 9.57 66.92 8.61 52.58 17.14 14.51 19.54 87.07 23.41 2.92 57.07 19.92 68.07 61.79 75.92
52.59 87.48 92.23 64.84 73.29 20.59 95.03 12.52 94.96 97.62 94.80 84.16 74.42 24.27 15.28 21.01 94.64 56.35 98.11 95.82 82.87 61.97 16.79 66.69 96.91 65.81 87.43 14.99 96.63 22.54 43.26 17.86 95.86 39.43 90.43 65.24 28.90 38.74 98.92 79.14 5.10 92.59 65.52 96.59 95.04 98.03
18.07 17.21 20.27 16.45 17.45 15.82 20.93 20.60 17.80 22.37 30.93 21.64 26.88 19.45 18.74 14.00 18.52 21.68 19.94 28.06 28.72 19.23 15.15 21.19 16.14 18.13 18.00 22.75 24.17 15.59 17.31 15.86 18.33 18.51 19.60 19.63 23.22 16.63 15.25 22.86 15.76 16.05 22.92 18.14 21.04 18.92
20.90 22.59 26.75 19.74 21.07 18.67 28.21 23.72 22.86 31.45 41.09 29.59 35.00 23.56 22.08 16.48 26.28 28.39 26.36 37.46 36.72 22.86 17.55 28.17 22.04 21.70 22.97 25.08 34.12 18.59 19.70 18.41 24.57 21.44 27.94 23.30 29.11 20.39 18.78 30.21 17.27 22.85 26.54 23.66 30.28 26.22
31.36 32.44 36.86 26.29 29.37 23.30 38.43 28.12 30.71 44.08 64.81 50.63 56.69 30.57 26.77 20.21 37.61 41.99 34.20 50.20 52.62 30.39 21.16 42.63 30.67 29.80 31.95 28.40 47.46 23.04 24.75 22.41 32.65 27.60 41.44 34.21 39.16 27.67 22.79 47.10 19.13 32.89 37.65 31.31 44.26 36.40
16.77 1.10 0.17 8.15 10.74 1.40 4.70 0.32 20.09 1.12 11.94 19.14 25.27 0.51 0.08 2.64 0.26 1.66 27.33 4.44 17.68 8.80 2.04 1.70 1.49 11.07 0.44 22.13 8.86 1.51 12.47 1.57 14.33 17.63 0.91 15.21 1.91 0.60 44.58 19.36 2.44 5.21 16.47 14.89 1.26 0.18
11.75 17.88 22.12 3.48 0.33 3.13 31.30 0.76 44.98 1.05 6.39 0.08 14.45 1.10 1.43 4.41 2.15 0.24 53.85 27.44 0.66 0.28 3.61 0.40 4.36 0.01 19.37 19.08 34.78 3.18 7.22 3.13 42.04 12.40 1.31 6.35 0.40 2.68 67.87 6.99 3.35 32.47 7.13 44.31 0.92 2.61
23.10 57.59 59.71 39.97 45.80 4.81 62.22 1.93 69.42 3.90 43.03 43.02 23.41 2.65 2.83 6.25 5.19 2.19 70.88 54.73 37.94 32.49 5.18 2.53 7.79 37.75 57.32 11.47 59.97 4.95 18.85 4.69 67.67 15.56 4.09 32.97 1.22 4.67 79.75 35.39 4.31 64.23 29.68 69.90 3.85 5.89
R. Houssa / European Economic Review 59 (2013) 35–62
53
Table E1 Posterior quantiles of welfare effects in developed countries.
l (%)
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
8.24 0.63 0.53 0.70 1.30 3.01 0.80 4.40 6.16 1.94 1.66 1.05 1.23 2.21 6.42 2.50 3.09 2.46 1.21 1.73 1.48 5.60 0.40 1.84 1.11
17.87 1.07 1.33 1.17 4.06 5.44 2.43 9.32 11.19 4.71 5.00 2.67 3.86 9.08 14.56 5.47 10.26 7.53 2.06 5.50 4.73 15.92 1.24 5.16 3.08
56.62 2.06 18.36 2.21 24.84 11.27 13.16 31.93 25.32 24.45 36.16 10.36 20.11 57.46 52.25 21.72 61.31 48.45 4.14 29.44 36.09 66.37 12.08 33.80 22.39
15.33 18.79 19.21 19.23 18.96 18.07 19.50 20.46 15.78 19.69 14.50 16.69 18.82 19.23 13.38 17.42 19.15 17.66 18.41 16.84 17.15 20.12 21.14 16.67 18.03
18.80 20.12 20.62 20.64 22.38 20.89 21.12 23.77 19.23 23.18 16.50 18.32 20.80 23.63 15.86 19.27 22.46 21.15 20.22 19.27 19.07 24.47 23.02 19.05 19.70
26.50 21.60 25.84 22.38 27.32 25.21 26.34 30.09 25.35 28.35 24.93 21.43 29.53 42.13 19.97 23.19 33.38 28.78 22.46 26.01 25.06 36.10 27.44 26.44 24.36
9:33 20:39 20:81 20:95 21:78 18:74 20:91 19:21 12:87 21:92 14:66 17:63 20:00 20:50 8:64 16:70 18:11 18:85 20:00 17:06 18:11 17:73 23:44 17:18 18:71
0:97 19:03 19:07 19:46 18:41 15:46 18:31 14:14 8:03 18:32 11:37 15:55 17:30 14:32 1:10 13:65 11:97 13:29 18:08 13:53 14:48 8:43 21:65 13:65 16:49
32:83 17:45 9:52 17:80 0:63 10:49 12:24 4:02 3:37 1:51 14:52 7:58 5:20 18:90 34:08 0:03 29:42 22:22 15:75 7:34 16:52 32:96 13:31 7:78 0:41
Table E2 Posterior quantiles of welfare effects in developing countries.
l (%)
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
10.65 14.57 4.89 7.36 0.60 4.66 8.98 13.24 2.55 5.96 17.12
23.95 28.21 8.79 13.48 1.78 8.21 22.98 25.25 4.44 12.42 34.07
69.24 68.55 18.36 31.85 26.06 17.32 78.99 58.45 8.83 39.48 77.64
25.27 17.10 20.39 18.15 20.66 19.68 17.90 23.76 13.59 18.45 21.87
33.24 23.07 24.60 22.81 22.46 23.79 24.36 33.12 15.40 22.10 31.43
51.59 35.95 31.92 31.43 27.90 30.25 36.88 51.20 17.84 28.81 52.97
22:56 6:39 20:88 15:28 22:59 20:06 13:99 19:36 13:12 15:58 11:80
8:94 5:11 15:73 9:32 20:55 15:27 1:49 7:66 10:88 9:62 2:08
24:59 35:52 8:35 4:58 5:88 8:20 46:06 14:17 7:04 12:12 31:51
times larger in developing countries than in developed countries the welfare effects of growth are only marginally larger in the former than in the latter. Comparing the results among developing countries reveals that Sub-Saharan Africa and oil producing countries of the Middle East would gain most from further consumption stabilization, followed by South and Latin American countries and Asian countries. The difference in the magnitude of the welfare cost of fluctuations is mainly due to the size of the shocks. In line with this explanation, oil-producing countries (such as Nigeria, Congo, Gabon, Jordan, Iran, Syria, and Cameroon) and countries that experienced wars and political crises (e.g. Burundi, Rwanda, Zimbabwe) are the ones that would benefit the most from consumption stabilization. Across developed countries, the following countries would also gain relatively more from consumption stabilization: Hong Kong, Iceland, Ireland, Italy, Japan, Greece, Portugal, and Spain. Compared to other developed countries these countries are characterized by larger consumption fluctuations and highly persistent shocks. Developed countries such as Australia, Luxembourg, and the USA would gain relatively less from further consumption stabilization. Let us now compare the welfare gain from consumption stabilization with the welfare gain from long-term growth as in Lucas’ original exercise.19 The last three columns of Tables 1 and 2 report posterior quantiles on lz. Table 3 summarizes 19 Note that this comparison does not take into account the cost of implementing policies. Moreover, it might not be feasible to remove all fluctuations in consumption or to achieve an increase in long-term growth by 1% in a country.
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R. Houssa / European Economic Review 59 (2013) 35–62
results in these three last columns by classifying countries into three categories: (i) growth when the 90 credible interval for lz has negative bounds; (ii) stabilization when it has positive bounds; and (iii) inconclusive when it includes zero. Two main findings can be derived from Table 3. First, the welfare comparison is inconclusive in 34 developed and developing countries, amounting to 42% of the sample size. This is very high. Moreover, the rate of inconclusiveness is somehow higher in developing countries (44%) than in developed countries (36%). Second, when the welfare comparison yields conclusive results, all the developed countries would gain more from growth than from stabilization. In the case of developing countries, one half of the countries would benefit from growth and the other half from stabilization. These findings suggest the need for caution in interpreting point estimates reported in the literature, especially as regards developing countries.
4. Sensitivity and sub-period analysis This section presents sensitivity analysis with respect to the risk aversion parameter ðgÞ and IES ð1=yÞ. Moreover, a subperiod analysis is provided in order to account for a possible parameter instability of the AR process. Before presenting the
Table E3 Posterior quantiles of welfare effects in developing countries.
l (%)
Colombia Congo Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
7.47 3.29 5.09 12.19 3.86 2.38 7.97 42.59 14.34 33.50 4.76 0.27 8.47 1.32 0.87 5.45 12.93 7.36 44.82 25.86 13.44 12.87 12.41 28.11 3.07 10.60 5.58 1.89 39.48 4.16 11.28 9.72 39.67 0.18 40.98 4.94 7.03 2.58 50.50 3.99 6.21 19.08 20.25 19.49 41.62 55.27
17.43 7.53 13.09 33.71 7.95 4.05 23.13 74.94 36.43 64.45 12.65 0.90 20.46 2.27 1.48 9.66 25.32 13.67 74.64 55.26 28.84 27.96 23.54 55.07 5.41 24.97 10.48 4.85 71.03 7.35 26.47 17.78 73.19 0.42 71.98 13.83 12.74 4.54 80.32 9.40 11.42 49.56 46.13 45.32 72.87 84.06
61.95 36.59 56.32 90.95 24.88 8.41 78.11 97.59 84.52 95.19 63.77 9.07 67.54 4.41 2.87 19.65 62.45 30.72 96.99 92.96 77.82 77.44 55.29 93.04 11.01 73.49 28.54 29.65 96.94 15.30 81.37 44.80 97.51 1.60 96.63 62.01 29.21 8.80 98.01 42.63 25.02 94.62 90.87 90.27 97.51 98.78
16.58 18.32 18.38 16.52 23.03 17.85 17.80 14.78 22.42 16.12 19.22 20.60 15.39 21.41 16.26 14.24 17.44 17.96 27.14 23.12 27.08 17.98 14.71 16.59 13.39 18.97 20.68 18.07 18.93 18.61 15.82 20.44 22.99 19.71 17.56 17.99 20.44 14.51 21.34 18.47 13.82 12.16 17.22 27.85 22.40 15.15
20.61 21.43 21.77 22.84 26.47 20.41 22.39 21.40 31.92 23.12 23.14 22.11 19.09 23.68 17.53 16.98 23.51 22.95 38.11 31.52 34.73 22.58 19.26 23.70 15.19 23.93 23.52 20.34 26.79 22.10 20.46 26.52 32.80 20.35 25.83 21.79 25.75 16.45 29.39 22.07 16.61 20.08 24.55 37.64 34.24 21.28
29.62 27.92 30.08 38.52 32.49 23.94 32.78 30.93 44.67 33.76 31.09 25.06 27.33 26.58 19.07 21.44 35.90 31.83 54.14 45.10 51.08 31.51 28.68 35.82 18.04 34.06 28.53 26.17 37.70 27.58 27.60 39.51 46.98 20.96 38.81 30.04 35.72 19.12 39.55 30.09 21.70 32.52 37.10 56.80 52.99 29.99
12.01 18.08 15.88 8.19 22.90 18.90 12.67 25.13 15.12 14.50 16.97 22.60 9.29 23.89 17.37 11.27 8.84 15.14 9.40 1.47 19.70 7.36 5.09 8.67 12.32 11.60 17.65 18.59 16.44 18.73 8.30 16.58 9.96 20.35 18.88 16.31 19.38 14.32 23.27 18.07 10.12 1.61 0.78 14.29 11.55 35.71
3.15 13.70 8.60 12.05 18.30 16.27 0.46 52.88 5.16 40.01 10.22 21.23 1.47 21.37 16.01 7.28 1.58 8.97 34.88 22.22 6.02 5.17 4.20 30.71 9.72 0.81 12.74 15.30 43.20 14.60 5.29 8.47 38.62 19.84 44.97 7.88 13.07 11.92 49.67 12.52 5.22 29.16 23.27 6.17 36.49 61.29
36.38 9.94 28.70 56.16 4.05 12.40 48.36 74.21 42.64 67.84 33.30 15.71 41.35 18.68 14.37 0.84 29.55 3.84 59.00 55.69 33.98 48.09 29.68 62.94 4.93 42.62 1.75 4.70 67.51 8.14 49.70 8.84 63.11 18.86 67.39 36.84 1.28 8.14 68.81 15.01 5.74 70.43 60.32 44.08 60.69 77.18
R. Houssa / European Economic Review 59 (2013) 35–62
55
Table F1 Posterior quantiles of welfare effects in developed countries, PWT6.1.
l
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.87 2.10 2.72 1.60 2.09 3.53 1.93 5.63 9.81 12.87 4.24 4.07 3.29 8.46 5.59 1.50 3.08 2.81 2.04 10.26 4.47 2.47 1.82 2.01 1.15
1.23 4.74 8.12 2.80 2.95 5.08 4.20 14.18 19.12 23.17 8.70 6.29 8.50 23.00 8.18 2.13 6.05 4.89 2.88 19.96 9.65 5.01 4.20 3.76 2.07
1.82 19.88 43.18 6.29 4.39 7.71 15.85 54.03 55.60 54.57 27.04 11.53 39.16 73.91 12.59 3.16 19.11 12.28 4.25 56.49 34.99 16.04 18.72 10.13 5.31
18.61 17.26 17.80 18.32 19.48 17.22 17.54 16.10 13.87 17.03 16.76 17.04 17.16 16.66 13.73 17.14 17.67 20.36 17.59 16.02 16.85 19.24 19.76 17.71 17.50
19.48 18.83 20.36 19.75 20.91 18.83 19.34 18.85 16.53 20.15 18.87 18.33 19.66 20.87 15.25 18.23 19.75 22.06 18.84 19.36 19.41 21.40 21.95 19.13 18.57
20.47 22.78 30.74 21.55 22.59 20.86 23.09 26.24 22.47 26.19 23.54 20.11 27.75 32.09 17.21 19.40 23.39 24.71 20.34 26.56 26.02 25.38 26.54 21.33 20.08
19.17 16.59 16.78 18.57 19.46 15.51 17.42 12.15 5.59 5.94 14.21 14.21 15.39 9.87 9.61 17.21 16.71 19.41 17.30 7.99 14.08 19.05 20.22 17.24 17.74
18.23 14.14 12.11 16.92 17.95 13.70 15.05 4.60 2.61 2.87 10.18 12.06 11.36 2.37 7.10 16.08 13.60 17.08 15.97 0.91 9.73 16.26 17.58 15.33 16.49
17.27 2.17 14.71 13.43 16.21 11.23 6.04 29.42 33.87 30.82 5.04 7.41 10.71 42.93 3.29 14.80 1.65 10.85 14.37 32.61 11.61 6.97 6.66 9.63 13.44
results I first examine how g, y and the parameters of the AR process affect l and z. Table 4 displays medians of the posterior distribution of l and z in France for various combinations of g and y in the set {1.5,2.0,2.5,5.0}. For a given value of y, l increases with the coefficient of relative risk aversion, g. This relationship reflects the preference for a smooth consumption path for risk-averse consumers. As a result, the more risk averse a person is, the more welfare compensation he would require in order to eliminate fluctuations in consumption. Alternatively, with g held constant, l decreases with y. This result captures the positive impact of IES (i.e. 1=yÞ on the welfare cost of consumption fluctuations in the presence of persistent shocks. In particular, when shocks are persistent, the discount factor of static welfare costs of consumption fluctuations over time increases with IES.20 In order to have a better understanding of the impacts of the parameters of the AR process ðs2 , fi ,gÞ on l and z, I consider artificial countries, each characterized by different parametrization of an AR(2) consumption process. Fig. 1, which reports the implied values of l and z, shows that the welfare cost of fluctuations increases with both the size and the persistence of shocks. The larger the shocks, the more consumers find them costly and the more they will be willing to pay in order to have a smooth consumption path. In addition, the more persistent the shocks the more long lasting will be their effects and the more welfare loss they will generate. By contrast, the welfare loss of fluctuations is high for low values of the long-term growth rate. This result suggests that volatility hits poor consumers harder than the rich. In particular, volatility has a very large welfare detrimental effect on consumers that are close to subsistence.
4.1. Higher risk aversion level and IES There is dispute about the empirical values of g and y.21 Due to this debate this section analyzes the impact of doubling the risk aversion ðgÞ and IES ð1=yÞ. In particular, I re-estimate welfare effects under the following two preferences parametrizations: (i) g ¼ 10 and y ¼ 1:5; and (ii) g ¼ 5 and y ¼ 0:75. Tables 5 and 6 report summary results analogous to Table 3. See Appendices B and C for the detailed results. 20 This result holds provided that the mean adjusted growth rate (i.e. g 12 gs2 Þ is positive. When the mean adjusted growth is negative the opposite relationship is true (see Obstfeld, 1994). 21 For instance, Ogaki et al. (1996) find estimated values for y ranging from 2.26 to 2.96 for low-income countries; from 1.32 to 2.51 for lowermiddle-income countries; from 1.26 to 2.38 for upper middle income countries; and from 1.21 to 2.29 for high income countries. Hall (1988) argues that ‘‘the elasticity is unlikely to be much above 0.1, and may well be zero’’ in the USA. Campbell and Mankiw (1989) estimate a value of about 3 for the UK. For the risk aversion parameter, Mehra and Prescott (1985) and Kandel and Stambaugh (1991) argue that values as high as 30 cannot be ruled out. One problem with these estimates is that they are based on the CRRA utility function in which the risk aversion is the inverse of IES.
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R. Houssa / European Economic Review 59 (2013) 35–62
Doubling the risk aversion level leads to a marginal increase of inconclusive cases (39 versus 34 countries). However, the new inconclusive cases primarily concern developed countries (15 versus 9). Doubling the risk aversion level also has other effects. For instance, Iceland, Portugal and Hong Kong shift from inconclusive to stabilization. In the same way, Egypt moves from growth to inconclusive. These re-classifications that occur following increase in risk aversion constitute another aspect of uncertainty of the results. By contrast, doubling IES does not change the classification of developed countries. The results for developing countries also do not change except for two cases: Brazil moves from growth to inconclusive, and Cameroon switches from inconclusive to stabilization. Table F2 Posterior quantiles of welfare effects in developing countries, PWT6.1.
l
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippine Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
16.15 16.40 9.06 8.45 6.34 8.56 31.79 24.65 30.11 5.70 14.59 5.17 49.33 8.87 20.40 5.26 5.69 12.51 20.87 52.54 53.99 25.19 4.95 7.48 5.53 3.65 8.47 29.34 17.42 47.18 19.48 8.59 7.61 11.86 15.36 28.49 6.09 10.14 3.05 47.79 6.75 12.53 8.51 18.67 2.32 42.75 3.61 8.90 8.17 48.89 6.17 5.92 25.87 16.14 23.18 48.08 64.40
25.27 25.54 13.30 12.53 11.38 12.76 52.89 50.12 49.58 10.80 22.60 12.35 76.74 16.34 33.54 10.26 8.29 27.24 35.63 79.44 80.41 41.88 13.95 10.88 8.11 5.26 16.02 49.29 35.52 77.51 32.72 12.64 11.71 22.47 24.52 47.28 11.55 17.79 4.52 75.55 10.07 19.59 12.69 28.79 4.16 70.98 7.56 13.47 11.99 76.11 11.74 10.92 41.70 31.56 47.73 76.39 87.93
43.68 45.59 21.48 19.95 29.96 20.35 89.92 91.19 85.96 32.26 38.90 51.89 97.75 45.20 58.62 32.83 12.83 74.91 71.05 97.71 98.35 77.74 61.51 17.27 12.47 7.99 42.64 88.09 80.76 97.46 64.83 20.72 20.86 58.45 46.59 83.54 29.95 42.06 7.21 96.67 15.86 35.89 20.63 51.48 9.54 96.74 25.78 21.21 19.12 97.25 35.90 31.67 74.84 75.69 90.24 97.42 98.79
21.38 19.68 20.22 20.74 22.10 16.36 23.24 21.48 17.49 13.51 20.19 20.01 22.90 18.92 16.64 19.21 17.34 19.53 20.18 18.84 22.53 24.38 21.63 21.48 20.86 18.20 14.78 20.23 21.50 23.41 24.87 27.82 18.91 15.90 20.55 16.19 18.89 18.93 20.78 25.55 17.54 17.97 18.36 19.22 19.43 21.88 19.37 23.45 16.20 18.13 22.49 15.12 18.22 20.85 20.58 25.84 19.83
25.92 24.30 23.47 24.10 24.99 18.87 31.00 28.04 22.99 15.36 24.47 23.33 30.62 22.91 20.85 22.28 19.40 24.81 25.40 24.44 29.45 32.31 25.73 24.74 23.44 19.92 17.36 26.53 27.90 31.48 31.23 32.99 21.55 19.08 24.58 20.97 21.70 22.00 22.48 33.00 19.76 20.96 21.09 23.89 20.91 29.45 22.03 27.46 18.56 23.46 25.68 17.28 23.35 25.38 27.57 35.02 25.75
34.22 32.52 28.37 28.88 30.66 22.24 43.76 39.19 31.66 19.25 31.50 32.15 39.96 29.82 27.98 28.17 22.27 35.92 34.49 31.94 38.33 46.23 38.63 29.31 27.03 22.06 22.29 37.66 39.62 42.76 43.12 40.44 25.50 25.40 31.37 28.76 26.94 28.04 24.66 42.05 23.15 25.54 25.24 31.74 22.89 39.81 27.00 33.80 21.77 29.48 32.39 21.29 32.03 33.72 39.60 46.75 32.26
8.29 6.16 14.29 15.42 18.08 9.90 5.31 0.03 10.88 9.04 8.59 16.90 23.14 13.22 1.88 16.64 13.72 10.42 1.83 31.62 28.77 3.01 19.32 17.45 18.30 16.65 7.84 6.59 7.61 19.53 9.17 25.39 13.57 5.75 7.77 10.65 15.17 10.67 19.87 18.63 12.94 7.33 12.27 3.13 18.82 18.28 18.31 18.61 10.14 28.61 19.02 10.95 5.55 6.57 1.11 18.52 41.12
0.93 1.21 10.06 11.51 13.56 6.06 21.83 21.93 26.82 4.49 1.82 11.01 45.26 6.40 12.67 11.82 11.14 2.74 10.29 54.07 49.61 9.68 11.50 13.78 15.29 14.68 1.25 22.94 7.75 44.71 1.37 20.11 9.83 3.37 0.17 26.07 10.35 4.06 17.96 41.68 9.74 1.30 8.33 4.90 16.67 40.63 14.35 14.17 6.49 51.96 13.89 6.21 18.44 6.39 19.66 39.56 61.17
13.00 16.16 3.85 5.89 1.79 0.29 49.50 57.84 56.33 13.75 9.66 20.23 63.77 18.48 33.24 6.54 7.44 41.56 38.62 71.20 66.28 35.50 24.63 8.47 11.57 12.05 20.41 52.90 44.89 65.35 25.88 13.99 2.43 34.96 17.58 56.22 4.63 14.94 15.40 61.07 5.01 12.35 2.43 22.57 11.89 62.89 0.59 7.90 0.67 71.14 5.93 11.61 45.00 43.38 56.14 59.20 72.67
R. Houssa / European Economic Review 59 (2013) 35–62
57
Table F3 Posterior quantiles of welfare effects in developed countries, PWT6.3.
l
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.82 2.05 2.55 1.72 2.46 3.27 1.88 4.87 7.36 11.79 3.44 3.85 3.68 8.75 5.36 1.48 3.24 3.06 1.87 8.70 4.03 2.28 1.47 1.79 1.18
1.13 4.40 7.07 3.02 3.47 4.63 3.99 11.63 13.30 20.69 6.66 5.76 8.88 22.97 7.80 2.05 6.21 5.38 2.65 16.14 8.47 4.42 3.24 3.27 2.05
1.63 16.48 33.89 6.90 5.15 6.91 14.64 43.25 34.10 49.03 17.46 10.02 42.10 71.07 11.73 2.98 18.71 13.20 3.86 41.96 29.59 12.61 13.14 7.99 4.98
18.53 17.47 17.86 18.01 18.68 16.98 17.71 15.96 13.50 16.84 16.70 17.42 17.70 17.17 14.01 17.51 17.78 19.85 17.43 16.22 16.48 19.01 19.74 17.82 17.64
19.31 18.96 20.06 19.44 20.12 18.38 19.41 18.24 15.55 19.49 18.46 18.62 20.24 21.12 15.54 18.50 19.83 21.57 18.52 19.00 18.71 20.93 21.51 19.07 18.74
20.19 22.28 27.57 21.17 21.86 20.12 22.93 24.19 19.47 24.86 21.75 20.18 29.65 31.91 17.38 19.63 23.34 24.15 19.75 24.80 23.91 23.90 24.90 20.73 20.09
19.00 16.82 16.94 18.06 18.15 15.47 17.56 12.58 7.51 6.56 14.80 14.82 15.61 9.96 9.94 17.49 16.66 18.56 17.09 9.54 14.01 18.82 20.30 17.48 17.88
18.18 14.57 12.94 16.34 16.65 13.77 15.33 6.59 2.28 1.08 11.80 12.87 11.25 1.64 7.70 16.44 13.53 16.21 15.86 2.81 10.21 16.39 18.17 15.74 16.63
17.31 4.20 8.13 12.59 14.79 11.58 7.43 20.43 15.67 24.43 2.61 9.07 13.05 40.99 4.25 15.24 2.27 9.34 14.42 18.74 6.68 9.21 10.23 11.63 13.91
4.2. Sub-period analysis This section repeats the welfare comparison analysis on two different sub-periods. The motivation for the sub-period analysis is to account for structural breaks in the data. For instance, the literature identifies a decline of fluctuations in many countries from the mid-1980s. This phenomenon is referred to as the great moderation. Fig. 2, which plots the crosscountry unweighted average values of 10-year rolling estimates of the standard deviation of real consumption per capita growth, illustrates this. However, the data show that consumption volatility is still much higher in developing countries compared to their developed counterparts. In order to investigate the impact of the great moderation on the welfare comparison the following two sub-periods are considered: 1960–1985 and 1986–2003.22 For each of the sub-periods, I again carry out the lag-selection exercise and estimate the posterior distribution of l and z assuming g ¼ 5 and y ¼ 1:5. Tables 7 and 8 report summary results analogous to Table 3. See Appendices D and E for the detailed results. The results suggest that the time period under study plays an important role. Taking Belgium as an example, the credible interval for lz includes zero in the first sub-period while it has negative bounds in the second sub-period. This result could be explained by the fact that Belgium faced relatively smaller shocks in the second sub-period. In addition, the persistence of shocks has decreased in the second sub-period for Belgium. As a result, the welfare cost of fluctuations decreased in relative terms across the two periods. Overall, the welfare comparison differs across the two sub-periods. Moreover, the sub-sample analysis shows more inconclusive cases, especially for developing countries. These findings indicate larger uncertainty on earlier estimates obtained with small sample period data.
4.3. Other sensitivity analysis23 Finally, this section performs two other sensitivity analysis. First, given the recent inconsistency reported by Johnson et al. (2009) on GDP data across different versions of PWT I re-estimate welfare effects using data from two other versions of the database: PWT6.1 (1960–2003) and PWT6.3 (1960–2007). Tables 9 and 10 display summary results. Tables F1–F4 in Appendix F presents the median together with the 5th and 95th quantiles of the posterior distributions of l, z and lz, based on g ¼ 5:0 and y ¼ 1:5. In general, the qualitative results are comparable across different versions of PWT. However, there are differences in terms of macroeconomic priorities. From PWT6.2 to PWT6.1 there are only three moves: Brazil moves from inconclusive to growth; Cameroon moves from inconclusive to stabilization, and Jamaica from stabilization to 22 23
The break year of 1985 is also considered in other cross-country studies (see, for example, Kose et al., 2005). I thank the referees for drawing my attention to the points discussed in this section.
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R. Houssa / European Economic Review 59 (2013) 35–62
Table F4 Posterior quantiles of welfare effects in developing countries, PWT6.3. The numbers reported for Gabon, Nigeria and Zambia mean that welfare values explode. Countries
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippine Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
l
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
20.70 17.46 11.33 31.24 5.87 9.54 28.81 19.73 25.01 6.60 17.91 5.13 41.00 8.29 19.48 4.23 6.78 13.19 20.66 0.00 49.09 23.31 6.43 6.46 5.37 3.36 8.04 15.45 13.16 52.15 14.81 21.13 27.77 11.24 17.00 33.81 5.79 8.18 2.79 0.00 7.28 11.46 9.48 16.05 2.51 28.98 5.12 6.88 12.05 44.47 10.14 5.44 41.28 16.75 33.00 0.00 67.70
33.07 27.20 17.03 52.72 10.14 14.01 47.57 38.81 40.78 12.36 27.69 12.32 67.29 15.07 30.45 7.71 9.65 28.11 34.99 0.00 76.64 37.40 17.96 9.23 7.76 4.77 15.13 23.69 24.00 79.99 23.64 33.03 46.97 21.34 27.93 55.22 10.82 13.44 4.04 0.00 10.44 17.41 13.53 24.58 4.38 46.36 11.44 10.28 18.09 70.89 15.97 10.35 67.00 30.93 62.49 0.00 88.95
59.16 48.24 27.98 89.29 24.95 22.58 83.50 83.52 73.88 35.30 47.97 47.37 95.68 40.73 54.40 21.26 14.93 75.98 68.08 0.00 97.79 68.11 65.11 14.59 11.95 7.00 38.40 39.02 58.08 97.87 46.93 60.31 87.54 53.86 54.89 89.01 27.43 28.97 6.33 0.00 16.49 30.36 21.22 42.16 9.83 85.56 41.26 16.07 29.53 96.30 31.48 27.93 94.70 71.93 94.63 0.00 99.08
19.02 18.28 19.47 21.50 22.08 17.09 24.21 21.90 17.29 13.12 20.83 19.12 21.08 18.82 16.08 18.39 16.67 19.27 21.14 0.00 20.03 23.75 19.98 21.72 20.31 18.10 14.82 16.38 21.33 21.66 23.11 25.31 19.00 15.43 21.09 16.68 18.38 19.87 21.04 0.00 17.30 17.57 19.09 18.51 19.08 23.82 18.75 24.44 17.57 17.89 20.48 15.31 16.81 19.86 18.12 0.00 19.41
23.89 22.29 22.97 28.89 24.66 19.69 32.02 27.63 21.94 14.95 25.65 22.10 28.43 22.36 19.69 20.75 18.64 24.35 26.38 0.00 25.56 30.63 24.05 24.56 22.63 19.65 17.24 19.74 26.13 28.09 27.76 32.24 24.51 18.30 25.83 21.79 20.94 22.57 22.56 0.00 19.60 20.25 22.07 22.43 20.65 31.38 21.86 27.96 20.61 22.93 22.87 17.35 22.17 24.18 23.79 0.00 24.63
32.01 29.10 27.96 39.87 29.67 23.30 45.82 37.72 29.93 18.72 34.15 29.70 37.79 28.27 26.01 24.63 21.32 34.92 35.61 0.00 33.27 43.84 34.49 28.48 25.79 21.62 21.76 24.69 34.96 36.27 36.10 44.85 33.01 24.22 33.56 28.68 25.62 27.82 24.44 0.00 22.81 24.05 26.28 29.00 22.62 44.58 28.56 33.04 25.19 29.07 26.67 20.95 28.66 32.09 32.73 0.00 30.52
0.70 3.25 10.68 7.18 18.69 9.57 1.31 4.87 5.94 7.68 5.83 15.99 17.73 13.35 1.80 16.47 11.82 9.38 3.06 45.00 27.01 4.26 15.79 18.58 17.56 16.63 8.14 2.85 11.04 26.41 11.41 8.36 6.62 5.58 6.88 15.55 14.66 13.71 20.21 45.00 12.12 7.91 12.16 4.67 18.43 1.13 16.04 21.69 7.69 24.96 12.18 11.50 22.89 5.44 12.02 45.00 45.28
9.18 5.00 6.03 23.71 14.44 5.59 15.26 11.08 18.64 2.57 2.03 9.75 38.77 7.12 10.74 12.87 8.86 4.15 8.86 0.00 50.33 6.69 5.86 15.27 14.85 14.87 2.00 3.77 2.22 50.90 4.22 0.81 22.36 3.03 2.38 33.49 10.21 9.07 18.55 0.00 9.02 2.84 8.40 2.15 16.28 14.91 10.16 17.71 2.62 47.28 6.86 6.94 44.50 6.78 37.92 0.00 63.94
29.02 20.50 2.37 51.73 2.44 0.76 41.56 49.59 44.76 17.69 16.16 20.09 60.94 14.13 30.39 1.53 4.58 42.59 35.40 70.00 69.00 28.36 32.38 11.09 11.26 12.68 17.62 16.08 25.11 68.49 13.59 18.97 56.19 33.52 24.53 62.36 3.57 2.98 16.33 70.00 4.23 8.26 2.57 15.23 11.22 43.87 15.30 13.19 6.42 69.98 6.14 8.38 68.60 42.03 66.74 70.00 74.32
inconclusive. From PWT6.2 to PWT6.3 there are more movements24: for instance, Bolivia, Ecuador and Ireland move from the group of inconclusive to the one of growth; Benin, Madagascar, South Africa and Sri Lanka from growth to inconclusive; Burkina Faso and Malawi from growth to stabilization; Iran and Jamaica move from stabilization to inconclusive; and Venezuela from inconclusive to the one of stabilization. 24
This result could be related in part to new shocks that occurred in 2004–2007.
R. Houssa / European Economic Review 59 (2013) 35–62
59
Table G1 Posterior quantiles of welfare effects in developed countries.
l
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.86 2.14 2.96 1.63 2.05 3.53 1.88 6.01 9.26 12.93 4.31 4.19 3.53 8.86 5.48 1.50 3.09 2.86 2.02 10.13 4.54 2.52 1.83 2.01 1.16
1.23 4.63 8.59 2.83 2.91 5.05 4.15 14.04 18.51 22.85 8.57 6.32 8.43 25.15 8.05 2.11 6.01 5.01 2.90 19.43 10.27 4.93 4.06 3.72 2.07
1.83 20.42 44.13 6.33 4.39 7.67 15.75 54.01 54.05 55.62 25.40 10.97 35.57 78.23 12.63 3.15 15.94 12.25 4.32 53.78 36.27 14.59 16.17 10.18 5.33
18.43 16.84 17.37 18.21 18.20 16.51 16.88 15.61 13.52 16.29 16.72 16.63 16.54 15.94 13.66 16.84 17.64 20.19 17.33 15.61 16.87 19.30 18.81 17.66 17.45
19.28 18.33 19.99 19.77 19.73 18.12 18.50 18.05 15.94 19.10 18.86 17.90 18.92 20.09 15.08 17.87 19.63 22.09 18.53 18.58 19.59 21.47 20.73 19.12 18.61
20.22 22.15 29.98 21.54 21.41 20.01 21.71 24.61 21.39 24.74 23.16 19.46 26.29 30.56 17.06 19.01 22.99 24.85 19.92 25.16 26.77 25.17 24.57 21.34 20.14
18.93 15.94 16.07 18.57 18.38 14.95 16.53 11.15 5.33 4.98 14.34 13.77 14.50 8.50 9.35 16.82 16.65 19.42 16.90 7.23 14.27 19.17 18.98 17.23 17.80
18.04 13.59 11.14 16.87 16.79 13.04 14.27 3.94 2.67 3.80 10.27 11.50 10.39 4.84 7.01 15.74 13.68 17.00 15.63 0.92 9.37 16.40 16.55 15.35 16.49
17.05 0.94 14.80 13.39 14.96 10.49 4.47 28.99 32.61 32.16 4.99 7.32 9.49 48.90 3.09 14.45 4.49 10.76 14.03 29.97 10.65 8.23 6.55 9.66 13.39
Second, I investigate the role of unit root on estimates of welfare effects. For this purpose follow a two-step approach suggested by a referee. First, I perform the Bayesian unit root test of Phillips and Ploberger (1994) using the package developed by Ouliaris and Phillips (1994). The posterior odds in favor of a unit root (PICU25) suggests that unit root cannot be rejected in 38 cases. Moreover, trend stationary with serial correlation in consumption was only present in three cases. Second, I subsequently estimate welfare effects taking into account the outcome of the first step.26 Tables G1 and G2 in Appendix G present the median together with the 5th and 95th quantiles of the posterior distributions of l, z and lz, based on PWT6.2 and using g ¼ 5:0 and y ¼ 1:5. The summary results displayed in Table 11 show qualitatively similar results in terms of macroeconomic priorities as compared to the ones reported in Table 3. Moreover, only thee movements can be observed: Costa Rica, Peru and Venezuela.
5. Conclusion This paper has proposed a framework for inference on welfare effects of consumption fluctuations and growth. The literature has thus far produced only point estimates. Moreover, the empirical analysis here examines data from 82 developed and developing countries while most existing studies focus on the USA. In addition, the data cover a relatively long time period (1960–2003), and it is shown how the results evolve across sub-periods. The results show large credible intervals on the welfare cost of consumption fluctuations, which suggest great uncertainty as regards previously reported point estimates. Thus, while the literature shows conflicting point estimates of welfare effects across different models, this paper finds that estimates obtained from a particular model economy can display considerable uncertainty. As such, one should account for this uncertainty in the comparison between the welfare gain from consumption stabilization and the welfare gain from growth. Credible intervals for the difference between the welfare gain from consumption stabilization and the welfare gain from growth include zero in many developed and developing countries. Sub-period and sensitivity analysis support these results. These findings suggest the need for caution in drawing strong policy conclusions from point estimates. The framework proposed in this paper can be extended to account for uncertainty about the risk aversion parameter and IES implied by data on consumption. 25
The unit root specification is preferred if PICU 4 1. P In the case of stationary process the ARð‘Þ consumption growth process in Eq. (1) is modified as g t ¼ f0 þ ‘i ¼ 1 fi g ti þ et , where g t ¼ C t =g1 C t1 1, and g1 is derived from the following AR(1) model lnðC t Þ ¼ g0 þ g1 lnðC t1 Þ þ xt at each draw of the MCMC. The normalized value function analogous to the 1g ð1yÞ=ð1gÞ y b½Eðc one in Eq. (6) is vðct Þ ¼ ð1 þ g1 Þ. t þ 1 vðct þ 1 Þ9c t Þ 1 26
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R. Houssa / European Economic Review 59 (2013) 35–62
Table G2 Posterior quantiles of welfare effects in developing countries.
l
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippine Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
15.86 16.24 8.75 8.20 6.42 8.48 31.78 24.67 30.09 5.92 14.57 5.26 50.10 7.38 20.85 5.26 5.65 12.92 20.47 52.05 52.89 25.59 5.11 7.44 5.56 3.67 8.60 29.91 18.17 50.67 19.15 8.51 7.74 12.11 14.93 28.89 6.18 10.35 3.05 47.91 6.85 12.41 8.66 18.51 2.36 44.38 3.68 8.87 8.08 48.69 6.21 5.91 25.45 16.85 23.57 47.86 66.19
25.17 25.72 13.29 12.32 11.57 12.43 53.50 50.33 51.07 10.71 22.52 12.10 78.19 10.85 33.18 10.30 8.30 28.18 34.92 79.53 80.23 42.36 13.97 10.91 8.05 5.25 16.02 49.83 36.81 80.01 32.53 12.72 11.90 22.40 24.27 47.55 11.15 17.80 4.53 74.97 9.94 19.88 12.77 28.50 4.15 70.74 7.38 13.29 11.85 76.32 11.90 11.02 41.54 31.53 47.60 75.82 88.13
43.95 46.03 21.93 20.36 30.17 20.30 89.10 92.10 87.03 28.02 38.33 50.28 97.65 17.38 62.36 31.22 12.82 75.73 69.64 98.12 97.76 78.06 58.14 17.43 12.37 7.85 44.08 87.11 82.88 98.10 64.45 20.67 20.99 57.31 44.25 85.40 28.35 42.42 7.42 96.14 15.82 34.72 20.38 51.98 9.37 96.09 23.26 21.69 18.42 96.54 35.46 33.49 77.44 76.46 89.12 97.50 98.91
21.00 19.69 20.11 20.59 22.13 15.35 23.26 21.48 17.70 13.49 20.03 18.94 20.74 18.70 16.79 18.29 16.80 18.09 20.07 13.12 22.40 24.43 19.98 21.61 20.94 17.96 14.74 20.31 18.70 20.75 15.83 27.91 18.94 15.71 19.01 16.11 17.71 16.51 20.70 13.33 16.95 16.30 18.30 15.48 19.30 21.89 19.44 23.31 16.10 15.55 22.51 15.15 18.17 20.84 19.75 25.74 11.34
26.01 24.20 23.44 24.02 25.00 17.67 31.49 28.06 23.36 15.25 24.39 21.88 28.17 21.62 20.67 21.18 18.79 23.19 25.13 18.16 29.55 32.53 23.89 24.72 23.52 19.71 17.10 26.60 24.71 28.07 22.99 33.03 21.56 18.78 23.15 20.94 20.54 19.16 22.48 20.46 19.19 19.37 21.12 19.59 20.87 29.49 21.96 27.44 18.40 20.47 25.58 17.36 23.30 25.40 26.20 34.67 17.48
33.88 31.99 28.09 28.88 30.87 20.74 44.19 39.04 31.93 18.63 31.68 30.77 37.47 25.67 28.38 26.62 21.35 33.14 34.30 24.32 37.94 46.67 35.42 29.20 26.93 21.79 22.05 36.64 35.58 37.79 33.28 41.08 25.48 25.34 29.10 28.96 25.35 24.67 24.79 29.56 22.24 23.94 25.24 26.03 22.89 39.41 26.87 33.42 21.52 26.42 31.90 21.60 32.31 34.04 37.15 46.82 24.72
8.22 6.48 14.24 15.64 18.28 8.87 5.15 0.10 10.44 8.99 8.52 15.56 25.93 14.42 2.20 15.54 13.12 8.24 2.19 36.66 27.55 2.89 17.30 17.45 18.49 16.43 7.57 7.25 4.06 24.30 2.94 25.70 13.54 5.45 6.96 11.07 14.06 7.86 19.90 28.97 12.26 6.08 12.19 0.17 18.83 18.96 18.22 18.49 9.93 31.17 19.03 10.94 5.32 6.72 1.14 17.99 49.94
0.87 1.58 10.29 11.51 13.50 5.13 21.68 22.13 27.63 4.49 1.74 9.73 49.34 10.75 12.52 10.73 10.52 4.92 9.73 60.88 49.82 9.92 9.53 13.83 15.41 14.42 1.13 22.83 11.43 50.85 9.69 20.22 9.74 3.53 1.19 26.38 9.27 1.61 18.00 53.98 9.17 0.62 8.37 8.95 16.71 40.40 14.53 14.11 6.50 55.33 13.50 6.28 18.24 6.40 20.72 39.57 69.86
12.97 15.97 3.76 5.88 1.13 1.04 48.91 58.26 57.65 10.04 9.53 21.07 67.13 5.52 36.00 6.31 6.45 45.24 37.60 78.32 66.33 34.32 24.96 8.91 11.60 11.96 23.89 52.84 51.58 69.13 37.50 14.34 2.06 33.40 18.45 57.67 4.78 19.00 15.14 74.52 4.38 13.04 2.52 27.75 11.91 62.62 1.62 8.15 0.82 74.25 5.11 12.25 47.56 44.02 56.98 59.78 82.58
Acknowledgments I am grateful to the editor and the referees for their their constructive comments and suggestions. I thank Luc Bauwens, Ales Bulir, Raouf Boucekkine, Geert Dahene, Paul De Grauwe, Hans Dewachter, Lennart Erickson, Andrew Feltenstein, Ayhan Kose, David Liedo, Chris Marsh, Chris Otrok, Michel Robe, Marijke Verpoorten, and Remco Zwinkels for valuable comments and suggestions. In addition, I thank participants at the 2007 Meeting of the EEA in Budapest, the May 2006
R. Houssa / European Economic Review 59 (2013) 35–62
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Spring Meeting of Young Economists in Seville, the February 2005 Doctoral Workshop in UCL, and seminar participants at IMF, at the Nijmegen University, and at CES for useful comments. The usual disclaimer applies. Appendix A. OLS estimation of the AR process OLS estimates of the AR process in developed and developing countries are given in Tables A1 and A2. Appendix B. Higher risk aversion level Posterior quantiles of welfare effects in developed and developing countries are given in Tables B1–B3. Appendix C. Higher intertemporal elasticity of substitution Posterior quantiles of welfare effects in developed and developing countries are given in Tables C1–C3. Appendix D. First sub-period: 1960–1985 Posterior quantiles of welfare effects in developed and developing countries are given in Tables D1–D3. Appendix E. Second sub-period: 1986–2003 Posterior quantiles of welfare effects in developed and developing countries are given in Tables E1–E3. Appendix F. Welfare effects with PWT6.1 and PWT6.3 Posterior quantiles of welfare effects in developed and developing countries, PWT6.1 and PWT6.3 are given in Tables F1–F4. Appendix G. The role of unit root Posterior quantiles of welfare effects in developed and developing countries are given in Tables G1 and G2. References Agenor, P.-R., McDermott, J., Prasad, E., 2000. Macroeconomic fluctuations in developing countries: some stylized facts. World Bank Economic Review 14 (2), 251–285. Aghion, P., Saint-Paul, G., 1998a. Virtues of bad times interaction between productivity growth and economic fluctuations. Macroeconomic Dynamics 2 (3), 322–344. Aghion, P., Saint-Paul, G., 1998b. Uncovering some causal relationships between productivity growth and the structure of economic fluctuations a tentative survey. LABOUR 12 (3), 279–303. Atkeson, A., Phelan, P., 1994. Reconsidering the costs of business cycles with incomplete markets. NBER Working Papers 4719, National Bureau of Economic Research. Barlevy, G., 2004. The cost of business cycles under endogenous growth. American Economic Review 94 (September (4)), 964–990. Barlevy, G., 2005. The cost of business cycles and the benefits of stabilization. Economic Perspectives 29 (1), 32–49. Blackburn, K., 1999. Can stabilization policy reduce long-run growth? Economic Journal 109 (452), 67–77. Blackwell, D., 1965. Discounted dynamic programming. The Annals of Mathematical Statistics 36 (1), 226–235. Caballero, R., Hammour, M., 1994. The cleansing effect of recessions. American Economic Review 84 (5), 1350–1368. Campbell, J.Y., Mankiw, N.G., 1989. Consumption, income and interest rates: reinterpreting the time series evidence. In: NBER Macroeconomics Annual 1989, vol. 4. NBER Chapters. National Bureau of Economic Research, pp. 185–246. Cooley, T.F., Ogaki, M., 1996. A time series analysis of real wages, consumption, and asset returns. Journal of Applied Econometrics 11 (2), 119–134. Dolmas, J., 1998. Risk preferences and the welfare cost of business cycles. Review of Economic Dynamics 1 (2), 646–676. Eichenbaum, M., 1991. Real business-cycle theory: wisdom or whimsy? Journal of Economic Dynamics and Control 15 (October (4)), 607–626. Epstein, L.G., Zin, S.E., 1989. Substitution, risk aversion and the temporal behavior of consumption and asset returns: a theoretical framework. Econometrica 57 (4), 937–969. Francois, P., Lloyd-Ellis, H., 2006. Growth, cycles and welfare: a schumpeterian perspective. Working Papers 1090, Queen’s University, Department of Economics, September. Geweke, J., 1991. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Staff Report 148, Federal Reserve Bank of Minneapolis. Giannone, D., Reichlin, L., 2005. Euro area business cycle: stylized facts and measurement issues. In: Reichlin, L. (Ed.), Euro Area and US Recessions, 1970–2003, C.E.P.R, London, pp. 83–93. Hall, R.E., 1988. Intertemporal substitution in consumption. Journal of Political Economy 96 (2), 339–357. Heston, A.R., Summers, R., Aten, B., 2006. Penn world table version 6.2. Technical Report, Center for International Comparisons at the University of Pennsylvania (CICUP). Imrohoroglu, A., 2008. Welfare costs of business cycles. In: Durlauf, S.N., Blume, L.E. (Eds.), The New Palgrave Dictionary of Economics, Palgrave Macmillan, Basingstoke. Imrohoruglu, A., 1989. Cost of business cycles with indivisibilities and liquidity constraints. Journal of Political Economy 97 (December (6)), 1364–1383. Johnson, S., Larson, W., Papageorgiou, C., Subramanian, A., 2009. Is newer better? Penn world table revisions and their impact on growth estimates. Working Papers 191, Center for Global Development, November.
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Kandel, S., Stambaugh, R.F., 1991. Asset returns and intertemporal preferences. Journal of Monetary Economics 27 (1), 39–71. Kose, M.A., Prasad, E.S., Terrones, M.E., 2005. Growth and volatility in an era of globalization. IMF Staff Papers 52 (SI), 31–63. Krebs, T., 2007. Job displacement risk and the cost of business cycles. American Economic Review 97 (June (3)), 664–686. Krusell, P., Smith, A.A.J., 1999. On the welfare effects of eliminating business cycles. Review of Economic Dynamics 2 (1), 245–272. Lucas, R.E.J., 1987. Models of Business Cycles. Yrjo Jahnsson Lectures. Basil Blackwell, New York. Lucas, R.E.J., 2003. Macroeconomic priorities. The American Economic Review 93 (2), 1–14. Martin, P., Rogers, C.A., 1997. Stabilization policy, learning-by-doing, and economic growth. Oxford Economic Papers 49 (2), 152–166. Mehra, R., Prescott, E.C., 1985. The equity premium: a puzzle. Journal of Monetary Economics 15 (2), 145–161. Mendoza, E.G., 1995. The terms of trade, the real exchange rate, and economic fluctuations. International Economic Review 36 (1), 101–137. Merton, R.C., 1971. Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3 (4), 373–413. Nelson, C.R., Plosser, C.I., 1982. Trends and random walks in macroeconomic time series: some evidence and implications. Journal of Monetary Economics 10 (2), 139–162. Obstfeld, M., 1994. Evaluating risky consumption paths: the role of intertemporal substitutability. European Economic Review 37 (5), 1471–1486. Ogaki, M., 1992. Engel’s law and cointegration. Journal of Political Economy 100 (5), 1027–1046. Ogaki, M., Reinhart, C., Ostry, J., 1996. Saving behavior in low- and middle-income developing countries: a comparison. IMF Staff Papers 43 (1), 38–71. Otrok, C., 2001. On measuring the welfare cost of business cycles. Journal of Monetary Economics 47 (1), 61–92. Otrok, C., Ravikumar, B., Whiteman, C.H., 2002. Evaluating asset-pricing models using the Hansen–Jagannathan bound: a Monte Carlo investigation. Journal of Applied Econometrics 17 (2), 149–174. Ouliaris, S., Phillips, P.C.B., 1994. COINT 2.0: GAUSS Procedures for Cointegrated Regressions. Predicta Software Inc., CT. Pallage, S., Robe, M.A., 2003. On the welfare cost of economic fluctuations in developing countries. International Economic Review 44 (2), 677–698. Phillips, P.C., Ploberger, W., 1994. Posterior odds testing for a unit root with data-based model selection. Econometric Theory 10 (August (3–4)), 774–808. Ramey, G., Ramey, V.A., 1991. Technology commitment and the cost of economic fluctuations. NBER Working Papers 3755, National Bureau of Economic Research. Sargent, T., Ljungqvist, L., 2000. Recursive Macroeconomic Theory, second ed. MIT Press. Stock, J.H., 1991. Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series. Journal of Monetary Economics 28 (3), 435–459. Stokey, N.L., Lucas, R.E.J., Prescott, E.C., 1989. Recursive Methods in Economic Dynamics. Harvard University Press. Tallarini, J.D., 2000. Risk-sensitive real business cycles. Journal of Monetary Economics 45 (3), 507–532. Tauchen, G., 1986. Finite state Markov-chain approximations to univariate and vector autoregressions. Economics Letters 20 (2), 177–181. The World Bank, 2004. Strategic Framework for Assistance to Africa: IDA and the Emerging Partnership Model. Africa Region, Washington, DC. Van Wincoop, E., 1994. Welfare gains from international risk sharing. Journal of Monetary Economics 34 (2), 175–200.
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Uncertainty about welfare effects of consumption fluctuations Romain Houssa a,b,c,n a
University of Namur, Centre of Research in the Economics of Development (CRED), Center for Research in Finance and Management (CeReFiM), Rempart de la Vierge 8, B-5000 Namur, Belgium b University of Leuven, Center for Economic Studies (CES), Naamsestraat 69, B-3000 Leuven, Belgium c CESifo, Poschingerstr. 5, 81679 Munich, Germany
a r t i c l e i n f o
abstract
Article history: Received 25 January 2011 Accepted 14 December 2012 Available online 31 December 2012
This paper proposes Bayesian estimates for welfare effects of consumption fluctuations and growth. Annual data from 82 developed and developing countries indicate a large degree of uncertainty as regards point estimates. Moreover, the comparison between the welfare gain from consumption stabilization and the welfare gain from growth yields inconclusive results for many developed and developing countries. These findings suggest the need for caution in drawing policy conclusions from point estimates. & 2012 Elsevier B.V. All rights reserved.
JEL classification: E63 O50 H50 C11 Keywords: Business cycles Growth Welfare Bayesian inference
1. Introduction Lucas (1987) measures the welfare cost of consumption fluctuations as the percentage increase in consumption, across all dates and states, required to leave a representative agent indifferent between consumption fluctuations and a smooth consumption path. According to this definition, he obtains an estimate of 0.042% of consumption in the USA.1 Lucas then estimates the welfare loss of a 1% reduction in the growth rate at 20% of consumption. These results lead Lucas to conclude that further stabilization would yield little welfare gain in the USA and that growth should be the priority of macroeconomic policies. A large body of research has challenged Lucas’ estimations by altering his modeling framework. First, whereas Lucas employs a model based on a trend-stationary consumption process and a CRRA utility function, Obstfeld (1994) and Dolmas (1998) adopt a martingale consumption process and recursive preferences of Epstein and Zin (1989). The predictions of their model indicate higher welfare costs of fluctuations ranging from 0.1% to 4.3%. Second, another line of research relaxes Lucas’ assumptions on homogenous agents and perfect capital markets. For instance, Imrohoruglu (1989) considers a general equilibrium model with idiosyncratic shocks and liquidity constraints and finds the welfare cost of
n
Tel.: þ32 81 724 947; fax: þ32 81 724 840. E-mail address: [email protected] 1 This result is obtained with a coefficient of relative risk aversion equal to 5. For risk aversion levels of 10 and 20, Lucas estimates the welfare cost of fluctuations at 0.084% and 1.7%, respectively. 0014-2921/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.euroecorev.2012.12.006
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fluctuations in the range of 0.3–1.5%. Atkeson and Phelan (1994) extend Imrohoruglu (1989) to the endogenous labor supply and asset pricing. Their results indicate little welfare gain from stabilization as does Lucas (1987). In a related study, Krusell and Smith (1999) propose a model with a variety of heterogeneity including employment status, wealth and preferences. They find that poor unemployed individuals who face liquidity constraints and rich individuals would benefit from stabilization while the middle-income class would lose. As a result, the welfare gain from eliminating fluctuations is negligible for the aggregate economy. However, Krebs (2007) observes that unemployed workers face persistent income loss even after they are re-employed. Given that such risks are not insured in asset markets the author claims that unemployment risks would cause a larger welfare cost compared to previous studies. To come to this conclusion Krebs (2007) introduces long-term earning losses of job displacement into a general equilibrium model. Depending on parameter values he finds estimates of the welfare cost of business cycles in the range of 0.2–9.0%. Third, Tallarini (2000) addresses the problem in a real business cycle (RBC) model with Epstein–Zin type preferences, which are calibrated to be consistent with observed asset prices in the USA. He finds much larger welfare cost of fluctuations as of 44%. Otrok (2001) also considers an RBC model. However, he finds little welfare gain from stabilization with non-separable preferences, the parameter values of which are chosen to match observed fluctuations in the USA. The fourth strand of the literature is based on endogenous growth models. For instance, Barlevy (2004) proposes a framework with diminishing returns on investment. As a result, stabilization generates higher growth through the reallocation of investment from periods of high investment to periods of low investment. In turn, he finds the welfare cost of fluctuations to be substantially higher than in the original Lucas exercise. However, Francois and Lloyd-Ellis (2006) challenge this finding in a model where fluctuations and growth are endogenously determined. Moreover, their model generates a positive relationship between fluctuations and growth as in Blackburn (1999). In this set-up, stabilization induces welfare costs. For a detailed survey of the literature, see Barlevy (2005), Imrohoroglu (2008) and Lucas (2003). This brief review shows that different modeling assumptions yield different estimated values for the welfare cost of fluctuations. In this paper, I take a different approach to examining the welfare effects of consumption fluctuations and growth. Instead of proposing another model economy, I investigate the impact of parameter uncertainty on welfare effects.2 For this purpose, I use the model economy proposed in Dolmas (1998) and Obstfeld (1994) and assess parameter uncertainty with Bayesian inference. In particular, the sample from the posterior distribution of welfare effects is obtained by repeatedly drawing parameters of a consumption process from their posterior distribution. Moreover, I estimate the posterior distribution for the difference between the welfare cost of consumption fluctuations and the welfare effects of growth. Subsequently, a 90% credible interval is constructed to gauge the uncertainty on estimates of welfare effects.3 This metric also allows to examine whether the welfare gain from consumption stabilization and the welfare gain from growth are significantly different from one another. Lucas (1987) and subsequent studies have relied on point estimates for such welfare comparison, thereby neglecting the uncertainty surrounding their estimates. However, by ignoring uncertainty, one cannot make statements about how likely these estimates are from their population values. As a result, policy conclusions drawn from point estimates should be taken with caution. My second contribution to the discussion relates to a large number of countries included in the empirical analysis. In particular, I examine data on 82 developed and developing countries while earlier studies mostly focus on the USA. The few existing cross-country studies include Pallage and Robe (2003) who compare point estimates for welfare effects across a group of African countries and the USA. Giannone and Reichlin (2005) compare consumption responses to technology shocks between the Euro area and the USA and interpret the results in terms of the welfare cost of fluctuations. Finally, Van Wincoop (1994) examines the welfare gain from international risk sharing in the USA, Japan and EuropeanOECD countries. Consumption data have three main characteristics: the trend growth, the size of fluctuations, and the degree of persistence of these fluctuations. Given the differences in these three parameters and their uncertainty, how large are welfare effects of consumption fluctuations and growth in developing countries compared to those in developed countries? Are these welfare effects similar across countries in each group? For instance, are welfare effects of consumption fluctuations different between the USA and the European industrialized countries? Analysis of data from a large number of developing and developed countries enables these general questions to be addressed. Moreover, developing countries represent a natural framework for the Lucas-type welfare comparison. In particular, these countries display strong volatility in consumption such that successful stabilization policies should substantially improve the welfare of their residents. However, there has been an increasing emphasis on growth in these countries. For instance, The World Bank (2004) argues that Africa needs to achieve a 7% long-term growth rate in order to meet the target for poverty reduction of the Millennium Development Goals. To what extent then should developing countries focus on stabilization or on growth4 or on both policies?
2
Eichenbaum (1991) made a similar point on the uncertainty in parameter estimates of real business cycle models. The credible interval has a different interpretation than the confidence interval notion used in frequentist statistics. For instance, a 90% credible interval (or region) gives the interval of minimum length that contains the true value of a parameter with probability 90%. 4 Blackburn (1999) provides a theoretical support for the trade-off between stabilization and growth. Using an endogenous growth model, he shows that monetary stabilization policies lead to a lower long-term growth. This result is based on a positive link between growth and volatility found in Blackburn (1999). However, the relationship between growth and volatility hinges on the mechanism that generates technological progress. When it is generated by the creative destructive mechanism, the link between growth and volatility is positive (see, for example, Aghion and Saint-Paul, 1998a, 3
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Table 1 Posterior quantiles of welfare effects in developed countries. Countries
l (%)
Australia Austria Belgium Canada Denmark Finland France Greece Iceland Ireland Israel Italy Japan Korea New Zealand Norway Portugal Spain Sweden UK USA
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.89 2.10 2.79 1.63 2.05 3.54 1.90 5.63 12.87 4.31 4.07 3.25 8.54 5.55 2.86 2.00 9.90 4.54 2.52 2.01 1.16
1.24 4.74 8.68 2.83 2.92 5.12 4.09 14.20 23.17 8.57 6.29 8.11 23.49 8.13 5.01 2.92 19.72 10.27 4.93 3.72 2.07
1.81 20.12 47.72 6.33 4.46 7.87 17.34 55.55 54.46 25.40 11.42 44.01 78.95 12.67 12.25 4.42 52.74 36.27 14.59 10.18 5.33
18.59 17.26 17.80 18.21 19.50 17.23 17.54 16.10 17.02 16.72 17.05 17.20 16.67 13.75 20.19 17.63 16.07 16.87 19.30 17.66 17.45
19.45 18.83 20.40 19.77 20.94 18.86 19.27 18.85 20.14 18.86 18.32 19.62 20.96 15.28 22.09 18.89 19.37 19.59 21.47 19.12 18.61
20.42 22.84 31.57 21.54 22.63 20.88 23.38 26.53 26.20 23.16 20.11 29.74 32.57 17.33 24.85 20.41 25.94 26.77 25.17 21.34 20.14
19.10 16.59 16.72 18.57 19.51 15.59 17.38 12.14 5.92 14.34 14.22 15.50 9.72 9.53 19.42 17.40 8.10 14.27 19.17 17.23 17.80
18.20 14.14 11.84 16.87 17.98 13.68 15.12 4.58 2.76 10.27 12.06 11.42 2.72 7.12 17.00 15.98 0.23 9.37 16.40 15.35 16.49
17.23 1.66 18.37 13.39 16.30 11.09 4.39 31.19 30.65 4.99 7.42 15.73 46.76 3.36 10.76 14.39 29.08 10.65 8.23 9.66 13.39
The results show wide credible intervals for the welfare cost of consumption fluctuations in developed and developing countries, which indicate large uncertainty as regards point estimates. Moreover, credible intervals for the difference between the welfare gain from consumption stabilization and the welfare gain from growth include zero for many developed and developing countries. These findings are robust as regards sub-samples analysis and on different assumptions about the risk aversion parameter and the intertemporal elasticity of substitution. This paper is further organized as follows: Section 2 presents the theoretical framework; Section 3 gives empirical results; Section 4 provides the sensitivity and sub-period analysis; and the last section concludes.
2. Theoretical framework 2.1. Model economy The model is taken from Dolmas (1998) and Obstfeld (1994). The ingredients are the recursive preferences of Epstein and Zin (1989) and a stationary autoregressive process for consumption growth.
2.1.1. Consumption Denote real per capita consumption by C t ,t ¼ 0, . . . ,T, and assume that the growth rate g t ¼ C t =C t1 1 follows an ARð‘Þ stationary process g t ¼ f0 þ
‘ X
fi g ti þ et ,
ð1Þ
i¼1
where f0 is the constant term, the fi , i ¼ 1, . . . ,‘, are AR coefficients, and et is the error term, which is assumed to be i:i:d: normally distributed as et Nð0, s2 Þ. From Eq. (1) the long-term growth rate of consumption is defined as the P unconditional mean of g t : g ¼ Eg t ¼ f0 =ð1 ‘i ¼ 1 fi Þ. Using the approximation lnð1 þ g t Þ Cg t , Eq. (1) is equivalent to assuming that ln C t follows an I(1) process with serially correlated increments.5 This implies that innovations in growth have permanent effects on consumption. (footnote continued) 1998b; Caballero and Hammour, 1994). However, if the mechanism generating technological progress is learning by doing, the relationship between growth and volatility is found to be negative (see, for example, Martin and Rogers, 1997; Ramey and Ramey, 1991). 5 Merton (1971) shows that consumption follows a random walk process in an intertemporal optimization framework. Empirical studies also support the random walk hypothesis (see, for example, Nelson and Plosser, 1982; Cooley and Ogaki, 1996; Ogaki, 1992).
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R. Houssa / European Economic Review 59 (2013) 35–62
2.1.2. Preferences With persistent shocks, Obstfeld (1994) argues that the risk aversion parameter and the intertemporal elasticity of substitution (IES) play specific roles in the welfare effects of consumption fluctuations and growth. For instance, to the Table 2 Posterior quantiles of welfare effects in developing countries. Countries
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican, Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Hong Kong Honduras India Indonesia Iran Jamaica Jordan Kenya Luxembourg Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Netherlands Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Switzerland Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
15.86 16.24 8.75 8.20 6.42 8.53 31.78 24.67 30.09 5.67 14.57 5.17 49.89 8.58 20.85 5.20 5.64 12.72 20.47 51.38 52.89 25.59 5.06 7.44 9.29 5.56 3.66 8.39 29.91 18.64 47.10 19.08 1.50 8.51 7.74 11.91 15.17 28.89 6.18 10.02 3.05 3.09 47.23 6.88 12.59 8.66 17.92 2.36 44.38 3.68 8.87 8.07 1.80 49.30 6.21 5.91 25.45 16.85 23.70 47.86 64.43
25.17 25.72 13.29 12.32 11.57 12.64 53.50 50.33 51.07 10.76 22.52 12.41 78.46 16.37 33.18 10.23 8.31 27.55 34.92 78.85 80.23 42.36 13.44 10.91 18.69 8.05 5.26 15.88 49.83 36.44 77.75 32.58 2.12 12.72 11.90 22.61 24.63 47.55 10.87 17.74 4.53 6.01 75.45 10.10 20.01 12.77 28.90 4.15 70.74 7.38 13.29 11.96 4.17 76.55 11.90 11.02 41.54 31.53 48.05 75.82 87.93
43.95 46.03 21.93 20.36 30.17 20.94 89.10 92.10 87.03 28.99 38.33 52.82 97.69 46.00 62.36 33.01 12.88 75.23 69.64 97.80 97.76 78.06 64.51 17.43 52.10 12.37 8.04 43.04 87.11 84.53 97.70 66.05 3.14 20.67 20.99 60.04 47.43 85.40 28.35 42.52 7.42 15.94 97.55 15.88 35.57 20.38 51.77 9.37 96.09 23.26 21.69 19.29 15.54 97.74 35.46 33.49 77.44 76.46 90.58 97.50 98.90
21.00 19.69 20.11 20.59 22.13 16.46 23.26 21.48 17.70 13.43 20.03 20.03 23.09 19.00 16.79 19.41 17.35 19.67 20.07 18.82 22.40 24.43 21.71 21.61 13.86 20.94 18.19 14.80 20.31 21.73 23.32 24.71 17.19 27.91 18.94 15.84 20.63 16.11 18.66 18.94 20.70 17.64 25.66 17.50 18.01 18.30 19.12 19.30 21.89 19.44 23.31 16.22 19.74 18.24 22.51 15.15 18.17 20.84 20.80 25.74 19.98
26.01 24.20 23.44 24.02 25.00 18.86 31.49 28.06 23.36 15.34 24.39 23.35 31.14 22.76 20.67 22.36 19.36 25.10 25.13 24.47 29.55 32.53 25.78 24.72 16.44 23.52 19.92 17.30 26.60 28.26 31.45 30.94 18.22 33.03 21.56 19.13 24.80 20.94 21.63 22.01 22.48 19.63 33.02 19.81 21.00 21.12 23.71 20.87 29.49 21.96 27.44 18.60 21.89 23.40 25.58 17.36 23.30 25.40 27.67 34.67 25.59
33.88 31.99 28.09 28.88 30.87 22.32 44.19 39.04 31.93 18.96 31.68 32.32 40.56 29.87 28.38 28.68 22.09 36.57 34.30 31.84 37.94 46.67 39.52 29.20 22.00 26.93 22.13 22.51 36.64 41.53 42.70 42.71 19.39 41.08 25.48 25.82 32.08 28.96 26.78 28.07 24.79 22.99 42.52 22.98 25.90 25.24 31.91 22.89 39.41 26.87 33.42 21.75 26.29 29.62 31.90 21.60 32.31 34.04 39.65 46.82 32.32
8.22 6.48 14.24 15.64 18.28 9.90 5.15 0.10 10.44 8.92 8.52 16.89 23.55 13.48 2.20 17.03 13.77 10.35 2.19 30.39 27.55 2.89 19.35 17.45 5.86 18.49 16.74 8.01 7.25 6.77 19.53 9.55 17.24 25.70 13.54 5.81 7.87 11.07 15.19 10.76 19.90 16.65 18.63 12.87 7.28 12.19 3.47 18.83 18.96 18.22 18.49 10.20 20.20 28.96 19.03 10.94 5.32 6.72 0.55 17.99 41.29
0.87 1.58 10.29 11.51 13.50 6.16 21.68 22.13 27.63 4.68 1.74 10.97 46.24 6.32 12.52 11.82 11.04 2.21 9.73 53.61 49.82 9.92 12.03 13.83 2.28 15.41 14.63 1.42 22.83 8.41 44.87 1.32 16.08 20.22 9.74 3.53 0.32 26.38 10.53 4.12 18.00 13.68 41.76 9.75 0.96 8.37 5.12 16.71 40.40 14.53 14.11 6.54 17.62 52.32 13.50 6.28 18.24 6.40 20.01 39.57 61.25
12.97 15.97 3.76 5.88 1.13 0.01 48.91 58.26 57.65 11.13 9.53 21.54 63.76 18.60 36.00 6.55 7.09 41.89 37.60 70.96 66.33 34.32 26.71 8.91 32.46 11.60 12.17 21.87 52.84 46.19 65.79 27.49 14.78 14.34 2.06 35.30 17.49 57.67 3.20 15.97 15.14 4.49 61.50 5.08 11.91 2.52 22.78 11.91 62.62 1.62 8.15 0.90 8.24 72.28 5.11 12.25 47.56 44.02 55.08 59.78 72.77
R. Houssa / European Economic Review 59 (2013) 35–62
39
Table 3 Summary results. Developed
Developing
Growth
Stabilization
Australia Austria Canada Denmark Finland France Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Inconclusive
Growth
Stabilization
Inconclusive
Belgium Greece Hong Kong Iceland Ireland Italy Japan Portugal Spain
Benin Burkina Faso Egypt Guinea Honduras India Madagascar Malawi Nepal Pakistan Paraguay Philippines Senegal South Africa Sri Lanka
Burundi Chile Congo Dominican,Rep. Gabon Gambia Iran Jamaica Jordan Mauritius Nigeria Rwanda Syria Trinidad & Tobago Zambia Zimbabwe
Argentina Brazil Barbados Bolivia Cameroon China Colombia Costa Rica Cote d’Ivoire Ecuador El Salvador Ethiopia Ghana Guatemala Indonesia Kenya Malaysia Mali Mexico Morocco Panama Peru Tanzania Thailand Uruguay Venezuela
Table 4 Median posterior welfare effects in France.
l (%)
g ¼ 1:5 g¼2 g ¼ 2:5 g¼5
z (%)
y ¼ 1:5
y¼2
y ¼ 2:5
y¼5
y ¼ 1:5
y¼2
y ¼ 2:5
y¼5
0.73 1.20 1.68 4.09
0.59 0.96 1.34 3.26
0.50 0.81 1.11 2.69
0.31 0.46 0.60 1.36
18.78 18.85 18.92 19.27
14.57 14.63 14.72 15.13
11.87 11.93 12.02 12.41
6.04 6.09 6.14 6.40
extent that a risk averse agent prefers a smooth consumption path, an increase in the risk averse parameter will imply a larger welfare cost of fluctuations. In addition, given that current shocks persist over all future periods, the total welfare cost of fluctuations is a discounted sum of static welfare costs. Obstfeld (1994) shows that the discount rate of static welfare costs increases with IES.6 As such, a higher IES would imply a larger total welfare cost of fluctuations for reasons that are not related to the risk aversion parameter. The standard CRRA utility function cannot account for such a specific role because it assumes that IES is the inverse of the risk aversion parameter, so a recursive utility formulation is more appropriate for welfare analysis in the presence of persistent shocks. Assume the representative agent has the recursive preferences of Epstein and Zin (1989), 1g
y U t ¼ ðC 1 þ b½Et ðU t þ 1 Þð1yÞ=ð1gÞ Þ1=ð1yÞ , t
ð2Þ
which is increasing, concave, and homogenous of degree one in C t ; where b, 0 o b o1, is a constant discount factor; g, 0 o ga1, is the coefficient of relative risk aversion, and 1=y, 0 o ya1, is IES for deterministic consumption paths.7
6 This result holds provided that the mean adjusted growth rate is positive. When the mean adjusted growth is negative the opposite relationship is true (see Obstfeld, 1994). In any case when shocks are persistent, IES affects welfare effects of consumption fluctuations and growth for reasons that are not related to the risk aversion parameter. P j 1g 7 Note that (2) reduces to the CRRA utility function if g ¼ y : U t ¼ E 1 j ¼ 0 b ð1=ð1gÞÞC t þ j .
40
R. Houssa / European Economic Review 59 (2013) 35–62
Fig. 1. The role of persistence, volatility and growth on welfare effects. Notes: Figures obtained with an AR(2) process and g ¼ 2 : 5; y ¼ 5. The top panel assumes f1 ¼ 0:20 and the value of f2 is allowed to vary between 0.1 and 0.25. Moreover, g ¼ 1:6%.
2.2. Welfare effects Let l lðf, s2 ,gÞ and z zðf, s2 ,gÞ denote the welfare effects of consumption fluctuations and growth, respectively, where f ¼ ðf0 f1 . . . f‘ Þ0 . As in Lucas (1987), l represents the percentage increase in consumption, across all dates and states, required to leave the representative agent indifferent between consumption instability and a perfectly smooth consumption path. Alternatively, l can be interpreted as the willingness to pay in order to eliminate all volatility in consumption or as representing the welfare gain that would be obtained if consumption were completely stabilized. In the same way, z measures the additional consumption, across all dates and states, that the representative agent would obtain if the trend growth g increases by 1%.8 The calculation of l and z follows from the value function iteration method employed in Dolmas (1998).9 Rewrite (2) as vðct Þ ¼ ð1 þ b½Eðct þ 1 vðct þ 1 Þ9c t Þ1g ð1yÞ=ð1gÞ Þ1=ð1yÞ ,
ð3Þ
where ct ¼ C t =C t1 ; c t ¼ ðct , . . . ,ct‘ þ 1 Þ; vðct Þ is a normalized value function defined as C t vðct Þ ¼ VðC t ,ct Þ, with VðC t ,ct Þ U t . The stochastic consumption process in Eq. (1) is approximated by a finite state Markov chain process with the methodology proposed by Tauchen (1986). As such, the normalized value functions can be expressed in terms of discrete values of consumption growth fc 1 ,c 2 , . . . ,c n g across n states. Subsequently, the discrete normalized value functions are solved iteratively10 until successive values differ by no more than 108 . After solving for the normalized value functions, the welfare cost of consumption fluctuation gives11
l¼
vdet 1, vsto
ð4Þ
8 This benchmark of 1% long-term growth is used to make the results comparable with the literature (see, for example, Dolmas, 1998; Lucas, 1987; Obstfeld, 1994; Pallage and Robe, 2003). 9 However, Dolmas (1998) assumes an AR(1) consumption process. Moreover, when the autoregressive coefficients fi are restricted to zero Obstfeld (1994) derives close form solutions for l and z. 10 Under Blackwell’ (1965) conditions, it can be shown that the value function iteration method yields a unique solution (see for instance Stokey et al., 1989; Sargent and Ljungqvist, 2000). 11 This expression is obtained under the assumption of homogeneity of the utility function.
R. Houssa / European Economic Review 59 (2013) 35–62
41
Table 5 Summary results with higher risk aversion. Developed
Developing
Growth
Stabilization
Inconclusive
Growth
Stabilization
Inconclusive
Australia Canada Denmark Finland Norway USA Luxembourg
Iceland Portugal Hong Kong
Austria Belgium France Greece Ireland Israel Italy Japan Korea New Zealand Spain Sweden UK Netherlands Switzerland
India Nepal
Argentina Barbados Burundi Cameroon Chile Cote d’Ivoire Congo Dominican, Rep. El Salvador Ethiopia Gabon Gambia Ghana Indonesia Iran Jamaica Jordan Kenya Mali Mauritius Nigeria Panama Peru Rwanda Syria Trinidad Venezuela Zambia Zimbabwe
Benin Burkina Faso Bolivia Brazil China Colombia Costa Rica Ecuador Egypt Guatemala Guinea Honduras Madagascar Malawi Mexico Morocco Pakistan Paraguay South Africa Senegal Sri Lanka Tanzania Thailand Uruguay
Table 6 Summary results with higher IES. Developed Growth Australia Canada Denmark Finland France Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Developing Stabilization
Inconclusive
Growth
Stabilization
Inconclusive
Austria Belgium Greece Hong Kong Iceland Ireland Italy Japan Portugal Spain
Benin Burkina Faso Egypt Guinea Honduras India Madagascar Malawi Nepal Pakistan Paraguay Philippines Senegal South Africa Sri Lanka
Burundi Cameroon Chile Congo Dominican, Rep. Gabon Gambia Iran Jordan Mauritius Nigeria Rwanda Syria Trinidad & Tobago Zambia Zimbabwe
Argentina Barbados Bolivia Brazil China Cote d’Ivoire Colombia Costa Rica Ecuador El Salvador Ethiopia Ghana Guatemala Indonesia Jamaica Kenya Malaysia Mali Mexico Morocco Panama Peru Tanzania Thailand Uruguay Venezuela
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R. Houssa / European Economic Review 59 (2013) 35–62
7 Developed Developing
6 5 4 3 2 1 0 1970
1975
1980
1985
1990
1995
2000
Fig. 2. Rolling standard deviation of consumption growth. Notes: The value for 1970 is the standard deviation of per capita growth rates for the period 1961–1970. The value for 1971 refers to 1962–1971, etc.
Table 7 Summary results: 1960–1985. Developed
Developing
Growth
Stabilization
Inconclusive
Growth
Stabilization
Inconclusive
Australia Korea New Zealand Switzerland UK
Austria Canada Finland Hong Kong Norway Portugal
Belgium Denmark France Greece Iceland Ireland Israel Italy Japan Luxembourg Netherlands Spain Sweden USA
Nepal
Brazil Cameroon Chile Cote d’Ivoire Dominican. Rep., Egypt El Salvador Gabon India Indonesia Jordan Kenya Malaysia Mauritius Morocco Nigeria Pakistan Paraguay Peru Sri Lanka Syria Thailand Trinidad & Tobago Venezuela Zimbabwe
Argentina Barbados Benin Burkina Faso Bolivia Burundi China Colombia Congo Costa Rica Ecuador Ethiopia Gambia Ghana Guatemala Guinea Honduras Iran Jamaica Madagascar Malawi Mali Mexico Panama Philippines Rwanda South Africa Senegal Tanzania Uruguay Zambia
where vdet ¼ ½1=ð1bÞð1 þgÞ1y 1=ð1yÞ is the normalized value function for deterministic consumption paths obtained by plugging the deterministic consumption growth g in Eq. (3), and vsto is the corresponding value function for the stochastic consumption process. In particular, vsto is estimated as the weighted average of the normalized value functions across the n states where the weights are the invariant probabilities pj ,j ¼ 1, . . . ,n. Formally, vsto ¼
n X j¼1
pj vðc j Þ:
ð5Þ
R. Houssa / European Economic Review 59 (2013) 35–62
43
Table 8 Summary results: 1986–2003. Developed
Developing
Growth
Stabilization
Austria Belgium Canada Finland France Iceland Israel Italy Luxembourg Norway Switzerland USA
Inconclusive
Growth
Stabilization
Inconclusive
Australia Denmark Greece Hong Kong Ireland Japan Korea Netherlands New Zealand Portugal Spain Sweden UK
Benin Bolivia Brazil Chile Ecuador Egypt Guatemala Honduras India Mauritius Pakistan Philippines Senegal Sri Lanka
Ethiopia Gambia Jordan Mali Nigeria Peru Rwanda Syria Trinidad & Tobago Zambia Zimbabwe
Argentina Barbados Burkina Faso Burundi Cameroon China Cote d’Ivoire Colombia Congo Costa Rica Dominican, Rep. El Salvador Gabon Ghana Guinea Indonesia Iran Jamaica Kenya Madagascar Malawi Malaysia Mexico Morocco Nepal Panama Paraguay South Africa Tanzania Thailand Uruguay Venezuela
The welfare gain from growth is obtained in an analogous way12: Pn
pgi vðc jg Þ 1, j j ¼ 1 pj vðc Þ
z ¼ Pjn¼ 1
ð6Þ
where pgj , j ¼ 1, . . . ,n, is the invariant probability associated with the value function vðc jg Þ for state j (when the mean growth rate is increased by 1%). There are two issues related to the finite state Markov chain approximation: the lag length in the AR process and the number of discrete states. With respect to the lag length, a preliminary analysis of the data indicates that the fourth AR coefficient is not statistically different from zero at the 10% significance level for any country. Therefore, I start by estimating an AR(3) process. If the third AR coefficient is not significant at 10% for a country the corresponding lag regressor is removed and the model is re-estimated. This procedure continues until an AR coefficient is significant at 10%. If no AR coefficient is significantly different from zero, I simply regress the growth rate on the constant term. In the case where the lag length is greater than one, the AR process is rewritten as a VAR(1) model, which is also approximated by a finite state Markov chain process.13 See Tauchen (1986) for technical details. For the selection of the number of states, I follow the procedure used by Otrok et al. (2002). In particular, the number of discrete states is chosen such that the first four moments and the six auto-correlations of the Markov process match the ones of the continuous AR process. In general, I find a good approximation when the number of discrete states is set to n ¼19 for the AR(1) process and to n ¼ 5‘ for the VAR(1) process.14 P P 12 An alternative way of estimating welfare effects is: l ¼ ni¼ 1 pi lðc i Þ and z ¼ ni¼ 1 pgi zðc ig Þ where lðc i Þ ¼ vdet =lðc i Þ1 and zðc ig Þ ¼ vðc ig Þ=vðc i Þ1. I thank a referee for drawing my attention to this point. However, the qualitative results of the paper remain the same across the two methods. 13 Otrok et al. (2002) use a similar approach. Chris Otrok also generously posts the approximation codes of the VAR(1) process on his web page http://web.missouri.edu/ otrokc. 14 Note that the number of total possible states for the VAR(1) process has a general formula n ¼ n‘1 where n1 is the number of grid points for each of the ‘ variables. For instance, ‘ ¼ 2 in the case of an AR(2) process. Therefore, for each discrete value of variable 1, variable 2 can take any of the n1 grid points.
44
R. Houssa / European Economic Review 59 (2013) 35–62
Table 9 Summary results, PWT6.1. Developed Growth
Developing Stabilization
Australia Austria Canada Denmark Finland France Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Inconclusive
Growth
Stabilization
Inconclusive
Belgium Greece Hong Kong Iceland Ireland Italy Japan Portugal Spain
Benin Burkina Faso Brazil Egypt Guinea Honduras India Madagascar Malawi Nepal Pakistan Paraguay Philippines South Africa Senegal Sri Lanka
Burundi Cameroon Chile Congo Dominican, Rep. Gabon Gambia Iran Jordan Mauritius Nigeria Rwanda Syria Trinidad Zambia Zimbabwe
Argentina Barbados Bolivia China Cote d’Ivoire Colombia Costa Rica Ecuador El Salvador Ethiopia Ghana Guatemala Indonesia Jamaica Kenya Malaysia Mali Mexico Morocco Panama Peru Tanzania Thailand Uruguay Venezuela
Table 10 Summary results, PWT6.3. Developed Growth Australia Austria Canada Denmark Finland France Ireland Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Developing Stabilization
Inconclusive
Growth
Stabilization
Inconclusive
Belgium Greece Hong Kong Iceland Italy Japan Portugal Spain
Bolivia Ecuador Egypt Guinea Honduras India Nepal Pakistan Paraguay Philippine Senegal
Burkina Faso Burundi Chile Congo Dominican, Rep. Gabon Gambia Jordan Malawi Mauritius Nigeria Rwanda Syria Trinidad Venezuela Zambia Zimbabwe
Argentina Barbados Benin Brazil Cameroon China Cote d’Ivoire Colombia Costa Rica El Salvador Ethiopia Ghana Guatemala Indonesia Iran Jamaica Kenya Madagascar Malaysia Mali Mexico Morocco Panama Peru South Africa Sri Lanka Tanzania Thailand Uruguay
R. Houssa / European Economic Review 59 (2013) 35–62
45
2.3. Posterior distributions of welfare effects This section discusses the proposed Bayesian inference on l and z. For this purpose, it is assumed that only uncertainty related to the estimation of f and s2 matter for inference on l and z. Moreover, l and z are complicated functions of f and Table 11 Summary results with the unit root test. Developed
Developing
Growth
Stabilization
Australia Austria Canada Denmark Finland France Israel Korea Luxembourg Netherlands New Zealand Norway Sweden Switzerland UK USA
Inconclusive
Growth
Stabilization
Inconclusive
Belgium Greece Hong Kong Iceland Ireland Italy Japan Portugal Spain
Benin Burkina Faso Costa Rica Egypt Guinea Honduras India Madagascar Malawi Nepal Pakistan Paraguay Philippine South Africa Senegal Sri Lanka
Burundi Cameroon Chile Congo Dominican, Rep. Gabon Gambia Iran Jordan Mauritius Nigeria Peru Rwanda Syria Trinidad Venezuela Zambia Zimbabwe
Argentina Barbados Bolivia Brazil China Cote d’Ivoire Colombia Ecuador El Salvador Ethiopia Ghana Guatemala Indonesia Jamaica Kenya Malaysia Mali Mexico Morocco Panama Tanzania Thailand Uruguay
Table A1 OLS estimates of the AR process in developed countries. Countries Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
f0
f1
f2
f3
0.11(0.16)
0:29nn ð0:16Þ 0:06ð0:16Þ
nnn
0:02 ð0:00Þ 0:02nnn ð0:01Þ 0.01 (0.01) 0:02nnn ð0:00Þ 0:02nnn ð0:00Þ 0:03nnn ð0:01Þ 0:01nnn ð0:00Þ 0:02nnn ð0:01Þ 0:03nnn ð0:01Þ 0:03nnn ð0:01Þ 0:02nnn ð0:01Þ 0:05nnn ð0:01Þ 0:01n ð0:01Þ 0:01n ð0:01Þ 0:05nnn ð0:01Þ 0:03nnn ð0:00Þ 0:01nnn ð0:00Þ 0:01nnn ð0:00Þ 0:03nnn ð0:00Þ 0:02nnn ð0:01Þ 0:01nnn ð0:00Þ 0:01nnn ð0:00Þ 0:00nnn ð0:00Þ 0:02nnn ð0:00Þ 0:02nnn ð0:00Þ
0:33nn ð0:15Þ 0:25n ð0:14Þ
0:60nnn ð0:13Þ 0.22(0.15) 0:34nn ð0:15Þ 0:27n ð0:15Þ 0:29nn ð0:15Þ 0:42nnn ð0:14Þ 0:07ð0:14Þ 0:43nnn ð0:15Þ 0:45nn ð0:15Þ
0:33nnn ð0:15Þ
0:47nnn ð0:14Þ 0:12ð0:17Þ nn
0:31 ð0:15Þ
0:42nnn ð0:14Þ 0:37nn ð0:16Þ 0:30n ð0:16Þ 0:27n ð0:15Þ 0:64nnn ð0:11Þ 0:44nnn ð0:14Þ 0:63nnn ð0:12Þ 0:55nnn ð0:16Þ 0:31nn ð0:15Þ
0:43nnn ð0:15Þ
0:28n ð0:15Þ
0:31nn ð0:15Þ
LAR
g (%)
s (%)
0:00 0:60 0:85 0:25 0:00 0:00 0:60 0:69 0:34 0:54 0:42 0:68 0:78 0:83 0:00 0:00 0:42 0:54 0:00 0:27 0:64 0:44 0:63 0:53 0:31
2.12 2.72 2.13 2.09 1.60 2.67 2.42 3.19 4.98 3.29 2.87 2.96 2.46 3.18 5.07 2.79 2.34 1.31 2.51 3.29 2.69 1.52 1.32 2.51 2.60
1.60 1.90 1.52 1.88 2.38 3.30 1.38 2.73 4.83 5.75 2.72 4.04 1.73 2.12 4.65 2.17 2.21 2.39 2.48 4.87 1.91 1.84 1.18 1.80 1.56
Notes: Standard errors in parentheses. LAR is the modulus of the largest root of the characteristic polynomial. nSignificant at 10%; nnn Significant at 1%.
nn
Significant at 5%;
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R. Houssa / European Economic Review 59 (2013) 35–62
s2 such that the functional form of their posterior distributions cannot be directly obtained. To overcome this difficulty, a Markov Chain Monte Carlo (MCMC) method is used to simulate the posterior distributions of l and z. At each step k, ðkÞ ðkÞ k ¼ 1, . . . ,K, of the chain, f and s2 are drawn from their posterior distributions, the functional forms of which are
Table A2 OLS estimates of the AR process in developing countries. Countries Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad & Tobago Uruguay Venezuela Zambia Zimbabwe
f0
f1
f2
f3
nnn
0:01 ð0:01Þ 0:01n ð0:01Þ 0:01n ð0:01Þ 0:01n ð0:01Þ 0:01ð0:01Þ 0:03nnn ð0:01Þ 0:00ð0:01Þ 0:01ð0:01Þ 0:03nnn ð0:01Þ 0:04nnn ð0:01Þ 0:01n ð0:01Þ 0:01ð0:01Þ 0:00ð0:02Þ 0:01ð0:01Þ 0:03nnn ð0:01Þ 0:01nnn ð0:00Þ 0:03nnn ð0:01Þ 0:01ð0:01Þ 0:02ð0:01Þ 0:02ð0:02Þ 0:00ð0:02Þ 0:00ð0:01Þ 0:00ð0:00Þ 0:01ð0:01Þ 0:01nn ð0:01Þ 0:02nnn ð0:01Þ 0:03nnn ð0:01Þ 0:02ð0:01Þ 0:00ð0:01Þ 0:00ð0:01Þ 0:00ð0:01Þ 0:01ð0:01Þ 0:02ð0:01Þ 0:03ð0:01Þ 0:02ð0:01Þ 0:04ð0:01Þ 0:01ð0:01Þ 0:02ð0:01Þ 0:01ð0:01Þ 0:00ð0:02Þ 0:02ð0:01Þ 0:03nnn ð0:01Þ 0:02nnn ð0:01Þ 0:02nn ð0:01Þ 0:02nnn ð0:00Þ 0:01ð0:01Þ 0:01nn ð0:00Þ 0:00ð0:01Þ 0:03nnn ð0:01Þ 0:04nnn ð0:02Þ 0:00ð0:01Þ nnn
0:03 ð0:01Þ 0:02ð0:01Þ 0:01ð0:01Þ 0:01ð0:01Þ 0:01ð0:01Þ 0:01ð0:02Þ
0.22(0.14)
0.14(0.13)
0.04(0.15)
0:37nnn ð0:15Þ
0:41ð0:13Þ
0:31nn ð0:15Þ 0:01ð0:14Þ
0:45nnn ð0:14Þ
0:30nn
ð0:14Þ
0:39nnn
ð0:14Þ
0:56nnn 0:28n
ð0:13Þ ð0:15Þ
0:94nnn ð0:15Þ
0:55nnn ð0:20Þ
0:24
ð0:15Þ
0:32 0:18ð0:16Þ 0:24ð0:15Þ
ð0:15Þ 0:28ð0:15Þ
0:26 0:24 0:37
ð0:15Þ ð0:15Þ ð0:15Þ
0:25 0:28ð0:14Þ 0:37ð0:15Þ 0:04ð0:15Þ
ð0:15Þ 0:23ð0:11Þ
0:36nn ð0:15Þ
0:45ð0:15Þ
0:36ð0:15Þ
0:40nnn ð0:15Þ
0:00ð0:16Þ
0:44nnn
ð0:14Þ
0:35nn 0:18ð0:16Þ
0:23n ð0:14Þ
0:32nn ð0:13Þ
0:06ð0:17Þ
0:41nnn ð0:17Þ
0:32nn ð0:14Þ
ð0:15Þ
nn
0:33 ð0:15Þ 0:23n ð0:15Þ 0:38nn ð0:15Þ
Notes: Standard errors in parentheses. LAR is the modulus of the largest root of the characteristic polynomial. n Significant at 10%.
nnn
LAR
g (%)
s (%)
0:00 0:00 0:00 0:00 0:75 0:00 0:00 0:63 0:00 0:31 0:00 0:68 0:00 0:30 0:00 0:39 0:00 0:56 0:28 0:00 0:00 0:00 0:81 0:00 0:00 0:00 0:24 0:00 0:32 0:62 0:24 0:00 0:26 0:24 0:37 0:00 0:25 0:64 0:37 0:67 0:00 0:36 0:00 0:00 0:74 0:00 0:44 0:00 0:00 0:35 0:73 0:33 0:00 0:77 0:38 0:00 0:00
0.84 1.43 1.17 0.95 0.58 3.09 0.27 0.89 2.87 5.23 1.23 1.44 0.21 1.60 3.22 1.47 2.57 1.38 1.46 2.25 0.43 0.23 0.53 0.63 0.91 2.15 4.21 1.57 0.65 0.17 0.25 1.24 1.81 3.56 1.23 3.79 1.76 2.33 1.08 0.23 2.45 2.45 2.02 1.74 1.67 0.82 1.46 0.06 3.20 3.00 0.38 3.89 2.49 1.30 0.96 0.66 0.69
6.10 6.39 4.73 4.50 3.53 5.16 8.00 5.63 9.07 3.96 5.94 2.52 1.05 3.91 7.86 2.83 4.13 3.41 8.36 11.56 1.63 6.99 1.28 4.18 3.69 3.25 4.82 8.37 5.24 7.54 7.14 3.89 5.34 5.44 7.31 9.29 3.53 5.00 3.35 1.26 4.48 7.18 4.87 6.83 2.10 9.64 2.24 4.34 5.06 13.76 3.29 3.66 8.24 5.96 5.76 9.25 12.69
Significant at 1%;
nn
Significant at 5%;
R. Houssa / European Economic Review 59 (2013) 35–62 ðkÞ
47
ðkÞ
explicitly known. Subsequently, l and z are calculated with the methodology explained in Section 2.2. This procedure is repeated until convergence. Given Eq. (1) the likelihood function, conditional on the data ¼ fx; ðg 0 , . . . ,g ‘1 Þg, is 1 ð7Þ Lðf, s2 9dataÞ ¼ ð2ps2 ÞðT‘ þ 1Þ=2 exp 2 ðxX fÞ0 ðxX fÞ , 2s where ðg 0 , . . . ,g ‘1 Þ are treated as fixed initial conditions, x ¼ ðg ‘ , . . . ,g T Þ0 , e ¼ ðe‘ , . . . , eT Þ0 , f ¼ ðf0 f1 . . . f‘ Þ0 and X is a ðT‘ þ 1Þ ð‘ þ1Þ matrix of ones and lagged observations on x. Eq. (7) implies that conditional on s2 , f has a normal distribution. In the same way, conditional on f, s2 has an inverted Gamma distribution. Assuming natural conjugate priors for f9s2 and s2 9f, n d ð8Þ f9s2 Nðf , S0 ÞIsðfÞ and s2 9f IG 0 , 0 2 2 yields the following conditional posterior distributions:
f9s2 , data Nðf~ , S1 ÞIsðfÞ ,
ð9Þ
Table B1 Posterior quantiles of welfare effects in developed countries. Countries
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
1.77 4.27 2.79 3.34 4.14 7.30 3.92 12.48 20.65 24.74 9.48 7.19 3.25 18.08 11.68 2.95 6.54 5.49 4.11 21.63 9.95 5.32 3.96 4.00 2.38
2.48 10.43 8.68 6.02 6.02 10.53 9.12 30.77 40.70 47.53 19.34 11.17 8.11 46.11 17.35 4.33 13.80 10.16 5.87 43.44 22.02 11.07 8.92 7.62 4.50
3.62 42.95 47.72 14.40 9.11 16.91 36.55 81.30 85.08 88.56 58.92 20.82 44.01 90.87 28.74 6.51 45.86 28.29 8.79 86.50 66.86 38.37 36.18 24.07 12.05
18.72 17.87 17.80 18.69 19.77 17.66 18.03 17.34 15.20 18.61 17.72 17.49 17.20 18.26 14.44 17.46 18.49 20.92 17.98 17.70 17.75 19.99 20.54 18.12 17.80
19.59 19.56 20.40 20.20 21.30 19.48 19.92 20.78 18.39 22.49 20.20 18.87 19.62 23.24 16.10 18.50 20.70 22.82 19.24 21.66 20.99 22.27 22.63 19.60 18.90
20.59 25.29 31.57 22.40 23.04 21.73 25.21 28.56 24.57 28.49 26.38 20.99 29.74 31.39 18.61 19.78 25.99 26.27 20.82 28.47 29.38 28.19 28.54 22.70 20.81
18.14 14.38 16.72 16.78 17.27 11.88 15.21 5.83 4.37 4.99 9.52 11.23 15.50 1.00 3.75 15.62 13.30 16.90 15.24 2.74 8.95 16.11 17.93 15.27 16.50
17.10 9.18 11.84 14.06 15.25 8.86 10.71 9.93 22.42 24.97 0.86 7.70 11.42 22.70 1.28 14.19 7.00 12.52 13.37 21.82 0.93 11.14 13.64 11.83 14.36
15.83 18.73 18.37 6.71 12.49 3.64 11.92 54.07 61.98 61.51 33.84 0.43 15.73 61.86 10.88 12.05 19.39 2.68 10.71 59.52 39.69 11.30 8.68 2.14 7.79
Table B2 Posterior quantiles of welfare effects in developing countries. Countries
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
35.73 37.04 19.17 17.54 6.42 18.39 61.82 44.42 60.40 12.04 32.27
59.00 60.49 29.77 27.42 11.57 28.48 87.00 76.18 85.11 24.14 52.68
91.85 92.54 53.27 48.92 30.17 49.42 98.67 97.64 98.79 66.64 88.23
23.60 22.24 21.62 22.20 22.13 17.66 25.11 24.32 19.52 14.29 22.33
29.77 27.88 25.56 26.16 25.00 20.62 31.38 30.02 24.08 16.65 27.94
38.48 35.77 31.83 32.47 30.87 25.33 38.42 37.42 29.01 21.86 36.16
9.72 12.37 4.37 6.61 18.28 0.72 33.89 17.07 39.33 3.00 7.68
28.94 32.26 4.16 1.27 13.50 7.93 54.70 45.49 60.76 7.67 24.82
56.90 58.97 22.96 17.87 1.13 24.99 67.15 65.22 73.61 45.53 53.48
48
R. Houssa / European Economic Review 59 (2013) 35–62
Table B3 Posterior quantiles of welfare effects in developing countries. Countries
Colombia Congo Cost Rica Dominican, Rep. Ecuador Egypt EL Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad & Tobago Uruguay Venezuela Zambia Zimbabwe
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
11.02 75.90 18.50 46.91 11.20 11.76 27.08 41.64 74.94 78.65 53.85 5.06 15.64 11.65 7.53 18.41 60.00 36.87 1.96 38.32 18.61 14.72 26.29 28.87 58.99 12.59 19.83 5.44 68.98 14.41 24.72 18.24 41.84 2.365 72.64 7.99 19.20 17.40 71.21 6.21 12.52 54.60 16.85 45.53 75.80 64.43
26.92 93.42 37.51 73.46 23.05 17.82 56.19 67.39 94.09 91.86 79.51 13.44 24.04 17.39 10.98 36.94 85.67 67.37 82.46 63.66 28.65 24.06 49.99 49.68 84.40 25.14 37.74 8.20 90.10 22.12 40.60 28.01 66.37 4.154 91.85 16.43 29.24 26.29 91.82 11.90 25.07 81.04 31.53 76.00 92.92 87.93
76.00 99.36 84.61 97.28 69.38 28.86 93.25 95.43 99.18 99.59 97.78 64.51 41.84 28.32 17.25 79.77 98.52 96.55 99.10 93.67 49.68 47.63 90.45 86.34 98.63 64.84 80.54 14.06 99.23 36.53 75.68 47.60 94.99 9.371 99.31 50.73 50.12 44.83 99.34 35.46 69.32 98.07 76.46 97.57 99.09 98.90
21.28 22.69 20.81 18.98 20.62 18.15 21.91 22.79 17.98 21.52 27.22 21.71 22.75 21.86 18.72 16.16 22.10 24.25 0.13 27.45 29.80 19.92 17.58 22.65 18.21 19.98 20.30 21.25 27.02 18.50 19.48 19.53 22.03 19.302 22.52 20.36 25.32 17.39 19.23 22.51 16.15 20.70 20.84 23.49 25.92 19.98
25.11 27.48 25.36 23.63 24.08 20.51 28.03 28.05 22.21 25.28 34.40 25.78 26.69 24.80 20.68 19.34 27.44 30.71 28.15 34.57 35.83 23.03 21.58 27.62 22.13 23.46 24.30 22.99 32.08 21.25 23.12 22.94 27.35 20.866 27.10 23.14 29.96 20.09 22.80 25.58 18.82 25.28 25.40 29.35 30.69 25.59
34.10 33.43 33.43 29.16 31.86 23.74 36.09 35.25 25.00 30.57 43.18 39.52 32.56 29.13 23.16 25.19 33.61 39.09 36.31 44.27 45.03 28.51 27.91 35.45 26.55 30.35 31.62 25.54 37.99 25.33 29.51 28.10 34.77 22.887 32.58 29.74 37.56 24.29 26.93 31.90 24.61 30.95 34.04 37.35 38.03 32.32
11.85 49.72 4.28 26.27 11.37 7.82 2.47 16.43 53.45 53.97 23.39 19.35 9.60 12.37 12.73 1.16 35.64 10.41 1.82 8.22 15.43 6.89 7.25 4.38 38.77 9.16 1.63 17.44 39.06 5.69 3.52 2.89 18.04 18.834 47.20 14.12 8.96 1.30 50.04 19.03 4.74 32.08 6.72 18.88 45.22 41.29
1.91 65.54 12.12 49.52 0.72 2.80 28.54 39.33 71.09 67.03 44.10 12.03 2.47 7.40 9.64 17.22 57.36 35.74 52.44 28.81 7.00 1.10 28.17 21.72 61.84 1.67 13.45 14.79 57.14 0.77 17.62 4.98 38.53 16.705 63.64 6.61 0.66 6.30 68.56 13.50 6.32 55.33 6.40 45.52 60.96 61.25
43.27 72.91 52.77 70.89 37.59 6.30 60.78 63.91 77.20 73.91 61.35 26.71 11.47 1.10 4.49 55.39 70.34 62.03 69.02 54.68 8.15 21.24 64.21 53.70 75.38 36.17 49.90 9.63 67.57 12.95 46.70 20.84 63.37 11.907 72.56 20.89 15.02 22.15 76.54 5.11 45.83 70.81 44.02 65.76 68.99 72.77
s2 9f, data IG
n1 d1 2
,
2
,
ð10Þ
~ ¼ ðf þ s2 X 0 XÞ1 ðS1 f þ s2 X 0 cÞ, S ¼ ðS1 þ s2 X 0 XÞ, n ¼ n þðT‘ þ 1Þ, and d ¼ d þ ðxX fÞ0 ðxX fÞ, with the where f 1 1 0 1 0 0 0 following diffuse prior parametrization: S0 ¼ 4000I‘ ; f ¼ ð0 0, . . . ,0Þ0 and n0 ¼ d0 ¼ 0. IsðfÞ is an indicator function that puts a zero prior mass on the region of the parameter space where draws on ðf, s2 Þ are not stationary.15 Moreover, draws that generate negative values or values that lie outside the unit circle for l, and z are discarded. These restrictions derive from l and z being able to be interpreted as shares of consumption that the agent is willing to pay for in order to eliminate fluctuations and to reduce growth, respectively. Given the dependence between the posterior distributions of f9s2 and s2 9f, a Gibbs sampling method, which also belongs to the class of MCMC methods, is used. More formally, the algorithm used to estimate the conditional posterior ð0Þ distributions of f, s2 , l, and z can be summarized as follows. After choosing a starting value f , the MCMC method
15
Stationarity requires that the roots of the characteristic equation ð1f1 zf2 z2 f‘ z‘ ¼ 0Þ lie outside the unit circle.
R. Houssa / European Economic Review 59 (2013) 35–62
49
Table C1 Posterior quantiles of welfare effects in developed countries. Countries
l (%)
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
1.29 3.42 4.38 2.35 2.73 5.64 3.04 10.25 22.40 21.26 7.17 6.75 5.44 15.80 13.12 2.43 4.65 3.49 3.09 17.62 7.56 3.24 2.34 2.97 1.85
1.79 7.68 13.95 4.12 3.85 8.09 6.50 24.62 42.30 36.20 14.18 10.34 13.34 41.05 18.97 3.40 9.00 6.14 4.41 33.42 16.77 6.39 5.29 5.57 3.31
2.61 31.81 63.22 9.25 5.82 12.25 25.68 75.05 85.91 73.21 39.97 18.94 55.64 89.71 28.62 5.18 25.86 14.81 6.54 73.30 54.59 18.50 20.63 15.17 8.30
31.13 29.40 23.11 30.29 29.55 30.98 29.04 27.78 31.01 28.30 29.43 31.65 24.94 23.27 35.17 32.19 29.32 28.37 31.25 28.17 27.14 28.11 27.51 30.69 31.47
32.07 32.82 30.98 31.79 30.80 32.93 32.32 33.05 37.10 32.02 32.90 33.54 31.94 30.72 39.17 33.51 32.00 29.92 32.76 32.71 32.11 30.34 29.98 32.50 33.04
33.03 34.89 34.00 33.58 32.17 35.01 34.47 37.13 43.69 35.85 35.96 35.48 34.95 35.79 43.82 34.97 34.45 31.46 34.34 37.53 35.63 32.32 31.84 34.24 34.57
31.31 30.14 28.20 29.97 28.51 27.88 30.17 24.16 17.22 11.60 26.78 27.31 28.11 17.89 27.12 31.76 28.07 26.87 30.29 16.48 25.93 27.67 28.35 30.00 31.80
30.27 25.04 16.99 27.68 26.94 24.84 25.89 8.43 4.63 3.72 18.72 23.18 18.67 9.68 20.21 30.08 22.85 23.77 28.34 0.42 15.43 23.94 24.61 27.00 29.72
29.03 1.53 40.00 22.28 24.55 20.33 3.76 45.86 49.81 41.97 8.89 14.32 31.30 63.55 9.91 27.87 5.64 14.94 25.77 41.97 25.85 10.94 8.16 16.72 24.01
Table C2 Posterior quantiles of welfare effects in developing countries.
l (%)
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
18.50 20.51 11.05 9.67 7.00 14.67 33.22 28.70 48.27 14.35 17.88
27.08 31.09 15.59 14.10 12.18 21.25 48.81 55.83 71.83 26.31 26.46
42.16 47.77 24.13 21.27 29.23 33.14 77.96 93.18 95.71 65.53 39.87
25.60 26.13 27.05 26.78 26.23 30.02 23.27 23.27 25.70 33.42 26.13
28.05 28.99 29.19 28.83 28.30 33.07 26.13 26.89 29.75 39.02 28.81
31.15 32.34 31.72 31.23 29.99 36.64 29.78 30.64 34.86 45.08 31.99
10.23 8.87 18.91 19.66 21.72 19.15 6.35 0.90 17.68 26.91 11.29
1.09 2.06 13.51 14.87 16.11 12.02 22.67 29.00 41.73 12.92 2.45
14.59 18.97 4.68 6.89 1.53 0.06 51.42 67.38 65.77 28.14 11.42
ðkÞ
ðkÞ
ðkÞ
ðkÞ
generates a sequence of draws ff , s2 , l , z g, k ¼ 1, . . . ,K, in the following steps: ðkÞ
ðk1Þ
is drawn from (10); 1. s2 9f ðk1Þ ðkÞ 2. f 9s2 is drawn from (9); ðkÞ ðkÞ ðkÞ ðkÞ 3. l and z are calculated with the methodology explained in Section 2.2. Moreover, l z is calculated at each iteration; 4. Repeat steps 1–3 K times. The results reported in the paper are based on 2000 draws plus a burn-in phase of 200 replications (i.e. K ¼2200). I check convergence of the chain in two ways. First, I experimented with different numbers of draws ranging from 1000 to 2000 and the results remained qualitatively unchanged. Second, the Geweke (1991) test indicates that convergence cannot be rejected.16 16 The Geweke (1991) convergence test amounts to splitting the 2000 draws on each parameter into three consecutive equally sized sub-samples. Under the null hypothesis of convergence, the moments of the draws in the first and third sub-samples are equal. For the test, I concentrate on the first and second moments.
50
R. Houssa / European Economic Review 59 (2013) 35–62
Table C3 Posterior quantiles of welfare effects in developing countries.
l (%)
Colombia Congo Cost Rica Dominican, Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad & Tobago Uruguay Venezuela Zambia Zimbabwe
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
6.56 54.06 11.19 36.28 6.59 8.77 15.84 26.25 69.37 59.48 23.66 5.74 8.22 6.52 5.33 17.44 38.31 20.47 48.95 17.69 6.54 10.61 21.65 18.56 54.67 8.35 14.27 3.66 46.53 10.43 19.16 12.30 25.25 3.07 49.70 4.86 8.62 14.21 71.38 6.54 11.79 38.62 20.05 28.01 43.63 74.32
15.40 76.83 21.02 54.45 13.16 12.78 32.34 41.59 89.64 82.57 34.69 16.26 11.88 9.30 7.61 32.32 57.79 37.51 78.30 27.76 9.51 15.67 40.15 28.28 76.85 14.66 24.19 5.37 71.70 15.10 29.18 17.49 37.25 5.43 73.59 9.50 12.39 20.36 90.16 12.42 21.39 59.18 36.46 52.37 65.15 91.97
58.48 97.07 54.73 84.82 38.80 19.28 76.13 75.64 99.23 98.43 54.07 63.76 17.97 14.08 11.38 73.31 87.48 79.85 98.17 51.88 14.32 26.69 79.96 48.17 97.21 34.82 52.09 8.73 96.31 22.70 49.12 26.76 59.01 12.55 96.16 28.69 18.87 31.54 99.15 34.01 53.80 88.08 75.40 91.81 93.14 99.38
25.11 22.06 26.56 27.40 26.85 30.05 24.36 25.48 23.26 21.90 23.55 21.61 26.53 27.29 29.86 30.37 24.68 23.49 21.21 23.91 24.11 28.18 28.42 26.10 26.99 27.61 27.08 28.31 22.65 29.45 28.26 28.32 26.22 29.42 22.93 27.52 25.49 30.27 24.99 25.89 30.91 26.03 25.68 23.18 21.63 21.04
29.08 25.07 29.66 31.55 29.82 32.40 28.34 28.66 26.88 24.98 26.01 27.71 28.38 29.02 31.69 35.37 28.01 27.05 24.31 26.30 25.52 30.46 33.06 28.69 31.59 30.35 30.25 29.62 25.24 31.93 31.13 30.89 29.39 30.80 26.08 30.06 27.17 33.36 28.70 28.02 35.11 29.75 28.46 27.02 24.39 24.17
31.74 28.89 32.97 36.62 32.35 34.93 32.23 32.10 31.25 29.02 28.74 30.12 30.39 30.85 33.70 40.69 32.20 30.45 27.72 28.70 27.03 32.93 38.13 31.44 37.39 33.24 33.18 30.97 28.06 34.61 34.30 33.89 33.36 32.33 30.12 32.22 29.03 37.08 32.97 29.75 39.57 34.73 31.37 31.30 27.85 27.79
23.55 28.38 19.15 3.99 23.88 24.15 13.37 3.37 41.90 33.97 2.55 23.08 20.44 23.01 27.03 19.12 10.04 7.46 24.06 9.09 19.37 20.42 12.46 10.61 22.34 22.66 16.93 26.34 20.44 22.11 12.65 19.14 4.58 28.02 22.98 25.97 18.91 19.86 41.82 21.85 24.54 8.59 8.88 0.48 18.89 49.86
13.87 51.62 8.71 22.55 16.85 19.74 3.63 12.85 62.31 57.52 8.61 11.82 16.50 19.80 24.08 3.09 29.76 10.51 53.73 1.40 15.98 14.71 6.76 0.52 44.83 15.84 6.04 24.21 46.40 16.84 1.83 13.38 7.62 25.37 47.40 20.51 14.86 12.99 61.27 15.69 13.69 29.16 7.81 25.04 40.54 67.63
33.66 71.99 25.28 53.58 9.86 12.79 49.73 47.15 73.17 73.54 28.11 40.97 10.31 14.75 19.86 39.46 59.74 53.65 74.54 26.31 10.83 3.48 48.88 19.58 66.13 4.54 23.43 20.50 71.51 9.08 18.21 3.69 29.50 17.97 70.05 0.48 7.94 1.55 71.06 6.98 20.24 58.38 48.71 65.98 69.05 76.17
3. Empirical analysis 3.1. Data I use annual data on real private consumption per capita from 1960 to 2003. The data are expressed in constant dollars (international prices, base year 2000). They are taken from the Penn World Table, version 6.2 (Heston et al., 2006). I restrict the analysis to a balanced data set on countries with at least grade C data quality.17 This leads to a sample of 82 countries, 25 developed and 57 developing countries.18 Tables A1 and A2 in Appendix A report OLS estimation results for the AR consumption process. The data indicate that developing countries display larger shocks (large s2 Þ to consumption than do developed countries. This result is consistent with findings in the literature (see, for example, Agenor et al., 2000; Mendoza, 1995). However, the results in Tables A1 and
17
Heston et al. (2006) provide information on the quality of the data of each country ranging from A to D with grade A representing the best quality. The classification between developed and developing countries is obtained from the World Developing Indicators (2010), where developed countries are defined as high income countries. 18
R. Houssa / European Economic Review 59 (2013) 35–62
51
A2 show a higher persistence of shocks in developed countries. Moreover, these results are in line with the findings of Giannone and Reichlin (2005) that consumption responses to technology shocks are more persistent in the Euro area than in the USA. In this paper, the persistence of shocks is measured by the largest root of the characteristic polynomial of the AR process (see Stock, 1991). Everything else being equal, a higher persistence of shocks will imply a larger welfare cost of consumption fluctuations. The reason is that the more persistent the shocks are, the more long-lasting their effects and the more welfare loss they will generate. As a result, it is interesting to see how the combination of the size and persistence of shocks affect the comparison of welfare effects across countries. 3.2. Main results The entire empirical analysis assumes b ¼ 0:96, which is the value often used in the literature for annual data. For the risk aversion parameter ðgÞ and IES ð1=yÞ, the results presented in this section are based on g ¼ 5:0 and y ¼ 1:5, which are also the values commonly used in empirical macroeconomics. However, there is debate about the value of g in the finance literature. Section 4 presents the results for higher values of g and IES. Tables 1 and 2 present the median together with the 5th and 95th quantiles of the posterior distributions of l, z and lz. Table D1 Posterior quantiles of welfare effects in developed countries. Countries
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
l (%)
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.76 1.13 3.20 1.75 2.09 2.91 1.99 4.94 4.43 9.92 3.72 4.34 1.80 5.11 2.79 3.61 6.73 2.98 2.10 20.38 5.51 2.84 1.67 1.24 2.64
1.51 1.78 9.79 2.79 5.62 4.77 7.58 14.03 7.19 19.67 7.24 9.71 5.83 14.88 5.32 8.62 15.53 5.78 3.34 42.36 12.95 6.32 3.94 2.33 5.78
5.07 3.11 54.48 4.89 37.49 8.39 39.63 66.82 13.48 63.38 26.03 31.41 49.77 64.78 13.22 35.47 55.55 17.15 5.78 87.48 52.92 25.62 21.74 8.11 22.34
18.21 15.77 15.70 17.88 18.36 15.69 17.26 14.41 11.67 14.90 17.94 17.21 15.47 13.83 13.05 16.84 16.98 20.54 16.50 15.07 17.44 19.21 18.74 18.39 16.85
19.41 16.91 18.94 19.59 21.49 17.51 20.61 17.54 13.22 18.01 20.10 18.98 17.68 17.01 14.71 18.91 19.71 23.10 18.07 21.14 22.68 21.28 20.68 19.80 18.53
21.15 18.18 31.95 21.74 26.99 19.97 38.00 26.89 15.43 24.72 24.94 22.42 33.12 26.38 17.15 23.86 25.97 27.11 20.08 33.15 36.37 26.04 25.39 21.88 21.57
19.07 2.81 15.09 1.32 19.31 2.20 17.26 11.41 5.09 6.94 16.74 13.74 15.37 10.44 11.69 14.68 12.05 20.40 1.98 3.73 15.50 18.20 19.17 19.09 15.79
17.83 3.50 8.72 2.16 15.60 3.35 12.90 3.51 6.76 1.75 12.44 9.61 12.13 2.19 9.78 10.07 4.01 17.17 2.94 22.05 10.09 14.81 16.60 17.44 12.70
14.72 4.23 23.44 3.01 12.91 4.48 6.74 41.91 8.41 38.92 2.83 9.56 22.77 39.08 1.22 12.97 30.65 7.85 3.85 61.22 25.81 1.41 1.83 12.47 1.48
Table D2 Posterior quantiles of welfare effects in developing countries.
l (%)
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
8.65 14.76 9.81 7.25 11.24 7.41 10.36 12.43 44.75 8.91 9.42
16.89 25.42 16.78 12.15 26.94 12.41 18.95 21.46 75.54 25.64 15.77
50.34 56.62 34.11 24.21 72.31 24.22 47.32 44.54 97.36 81.31 32.22
20.60 19.33 18.32 20.70 22.27 13.70 19.85 17.51 17.63 14.13 16.85
24.67 25.15 22.64 25.05 27.31 16.30 23.43 22.11 24.75 18.49 20.69
32.32 36.55 30.41 32.29 38.01 20.29 30.06 30.54 34.93 27.85 27.67
15.34 0.93 0.19 0.93 13.51 2.73 12.15 0.07 0.47 7.50 0.48
7.68 1.15 1.62 0.58 0.41 4.65 4.41 2.07 3.17 7.00 2.39
18.85 3.29 3.49 2.11 43.65 6.57 19.18 4.13 6.73 55.06 4.36
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R. Houssa / European Economic Review 59 (2013) 35–62
The results indicate large uncertainty on estimates of the welfare cost of consumption fluctuations. For example, looking at the USA results, the 90% credible interval for l is [1.16;5.33]% of consumption. Using identical preference parameter values, Pallage and Robe (2003) find a 2.11% point estimate for l. However, the credible interval for l suggests considerable uncertainty around this value. In international dollar terms—taking the USA average annual real per capita consumption to be $15 790.30 for 1960–2003—these estimates correspond to a welfare cost of about [183;843] per person and per year in 1960–2003. Thus, while the literature shows conflicting point estimates for l across different models, estimates obtained from a particular model display considerable uncertainty. As such, one should account for this uncertainty when comparing z with l. Results for other countries show even greater uncertainty. For instance, the credible intervals for l in France and Morocco are, respectively [1.90;16.77] and [10.02;42.52]% of consumption. Given this large uncertainty, one should be very careful in interpreting the point estimates reported in earlier studies. Note, however, that estimates of z display relatively less uncertainty. In order to compare estimates of l and z between developed and developing countries, I calculate the unweighted average of posterior quantiles in each group. This yields the following 90% credible intervals for l in developed and developing countries, respectively [4.0;24.95] and [17.73;51.26]%. The corresponding figures for z are [17.42;23.98] and [19.85;31.14]. These estimates imply that, while the welfare costs of consumption fluctuations are on average two to four
Table D3 Posterior quantiles of welfare effects in developing countries.
l (%)
Colombia Congo, Rep. Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad & Tobago Uruguay Venezuela Zambia Zimbabwe
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
3.36 19.32 23.72 9.83 8.52 6.73 29.12 4.29 40.55 48.04 26.50 7.92 8.08 7.60 5.15 6.57 34.47 14.93 51.85 37.32 16.20 12.25 5.64 15.81 42.27 9.33 20.43 3.23 39.22 6.93 6.25 5.70 35.70 4.12 28.15 6.36 8.66 11.22 61.92 8.71 1.85 24.89 10.22 35.43 34.02 45.43
9.14 40.80 49.38 23.57 21.89 11.12 60.59 6.86 67.39 77.42 52.30 29.08 20.49 12.73 8.33 10.97 62.23 26.22 81.49 65.65 36.50 23.23 9.20 29.20 71.88 21.79 42.82 5.78 69.81 11.64 12.72 9.57 66.92 8.61 52.58 17.14 14.51 19.54 87.07 23.41 2.92 57.07 19.92 68.07 61.79 75.92
52.59 87.48 92.23 64.84 73.29 20.59 95.03 12.52 94.96 97.62 94.80 84.16 74.42 24.27 15.28 21.01 94.64 56.35 98.11 95.82 82.87 61.97 16.79 66.69 96.91 65.81 87.43 14.99 96.63 22.54 43.26 17.86 95.86 39.43 90.43 65.24 28.90 38.74 98.92 79.14 5.10 92.59 65.52 96.59 95.04 98.03
18.07 17.21 20.27 16.45 17.45 15.82 20.93 20.60 17.80 22.37 30.93 21.64 26.88 19.45 18.74 14.00 18.52 21.68 19.94 28.06 28.72 19.23 15.15 21.19 16.14 18.13 18.00 22.75 24.17 15.59 17.31 15.86 18.33 18.51 19.60 19.63 23.22 16.63 15.25 22.86 15.76 16.05 22.92 18.14 21.04 18.92
20.90 22.59 26.75 19.74 21.07 18.67 28.21 23.72 22.86 31.45 41.09 29.59 35.00 23.56 22.08 16.48 26.28 28.39 26.36 37.46 36.72 22.86 17.55 28.17 22.04 21.70 22.97 25.08 34.12 18.59 19.70 18.41 24.57 21.44 27.94 23.30 29.11 20.39 18.78 30.21 17.27 22.85 26.54 23.66 30.28 26.22
31.36 32.44 36.86 26.29 29.37 23.30 38.43 28.12 30.71 44.08 64.81 50.63 56.69 30.57 26.77 20.21 37.61 41.99 34.20 50.20 52.62 30.39 21.16 42.63 30.67 29.80 31.95 28.40 47.46 23.04 24.75 22.41 32.65 27.60 41.44 34.21 39.16 27.67 22.79 47.10 19.13 32.89 37.65 31.31 44.26 36.40
16.77 1.10 0.17 8.15 10.74 1.40 4.70 0.32 20.09 1.12 11.94 19.14 25.27 0.51 0.08 2.64 0.26 1.66 27.33 4.44 17.68 8.80 2.04 1.70 1.49 11.07 0.44 22.13 8.86 1.51 12.47 1.57 14.33 17.63 0.91 15.21 1.91 0.60 44.58 19.36 2.44 5.21 16.47 14.89 1.26 0.18
11.75 17.88 22.12 3.48 0.33 3.13 31.30 0.76 44.98 1.05 6.39 0.08 14.45 1.10 1.43 4.41 2.15 0.24 53.85 27.44 0.66 0.28 3.61 0.40 4.36 0.01 19.37 19.08 34.78 3.18 7.22 3.13 42.04 12.40 1.31 6.35 0.40 2.68 67.87 6.99 3.35 32.47 7.13 44.31 0.92 2.61
23.10 57.59 59.71 39.97 45.80 4.81 62.22 1.93 69.42 3.90 43.03 43.02 23.41 2.65 2.83 6.25 5.19 2.19 70.88 54.73 37.94 32.49 5.18 2.53 7.79 37.75 57.32 11.47 59.97 4.95 18.85 4.69 67.67 15.56 4.09 32.97 1.22 4.67 79.75 35.39 4.31 64.23 29.68 69.90 3.85 5.89
R. Houssa / European Economic Review 59 (2013) 35–62
53
Table E1 Posterior quantiles of welfare effects in developed countries.
l (%)
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
8.24 0.63 0.53 0.70 1.30 3.01 0.80 4.40 6.16 1.94 1.66 1.05 1.23 2.21 6.42 2.50 3.09 2.46 1.21 1.73 1.48 5.60 0.40 1.84 1.11
17.87 1.07 1.33 1.17 4.06 5.44 2.43 9.32 11.19 4.71 5.00 2.67 3.86 9.08 14.56 5.47 10.26 7.53 2.06 5.50 4.73 15.92 1.24 5.16 3.08
56.62 2.06 18.36 2.21 24.84 11.27 13.16 31.93 25.32 24.45 36.16 10.36 20.11 57.46 52.25 21.72 61.31 48.45 4.14 29.44 36.09 66.37 12.08 33.80 22.39
15.33 18.79 19.21 19.23 18.96 18.07 19.50 20.46 15.78 19.69 14.50 16.69 18.82 19.23 13.38 17.42 19.15 17.66 18.41 16.84 17.15 20.12 21.14 16.67 18.03
18.80 20.12 20.62 20.64 22.38 20.89 21.12 23.77 19.23 23.18 16.50 18.32 20.80 23.63 15.86 19.27 22.46 21.15 20.22 19.27 19.07 24.47 23.02 19.05 19.70
26.50 21.60 25.84 22.38 27.32 25.21 26.34 30.09 25.35 28.35 24.93 21.43 29.53 42.13 19.97 23.19 33.38 28.78 22.46 26.01 25.06 36.10 27.44 26.44 24.36
9:33 20:39 20:81 20:95 21:78 18:74 20:91 19:21 12:87 21:92 14:66 17:63 20:00 20:50 8:64 16:70 18:11 18:85 20:00 17:06 18:11 17:73 23:44 17:18 18:71
0:97 19:03 19:07 19:46 18:41 15:46 18:31 14:14 8:03 18:32 11:37 15:55 17:30 14:32 1:10 13:65 11:97 13:29 18:08 13:53 14:48 8:43 21:65 13:65 16:49
32:83 17:45 9:52 17:80 0:63 10:49 12:24 4:02 3:37 1:51 14:52 7:58 5:20 18:90 34:08 0:03 29:42 22:22 15:75 7:34 16:52 32:96 13:31 7:78 0:41
Table E2 Posterior quantiles of welfare effects in developing countries.
l (%)
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
10.65 14.57 4.89 7.36 0.60 4.66 8.98 13.24 2.55 5.96 17.12
23.95 28.21 8.79 13.48 1.78 8.21 22.98 25.25 4.44 12.42 34.07
69.24 68.55 18.36 31.85 26.06 17.32 78.99 58.45 8.83 39.48 77.64
25.27 17.10 20.39 18.15 20.66 19.68 17.90 23.76 13.59 18.45 21.87
33.24 23.07 24.60 22.81 22.46 23.79 24.36 33.12 15.40 22.10 31.43
51.59 35.95 31.92 31.43 27.90 30.25 36.88 51.20 17.84 28.81 52.97
22:56 6:39 20:88 15:28 22:59 20:06 13:99 19:36 13:12 15:58 11:80
8:94 5:11 15:73 9:32 20:55 15:27 1:49 7:66 10:88 9:62 2:08
24:59 35:52 8:35 4:58 5:88 8:20 46:06 14:17 7:04 12:12 31:51
times larger in developing countries than in developed countries the welfare effects of growth are only marginally larger in the former than in the latter. Comparing the results among developing countries reveals that Sub-Saharan Africa and oil producing countries of the Middle East would gain most from further consumption stabilization, followed by South and Latin American countries and Asian countries. The difference in the magnitude of the welfare cost of fluctuations is mainly due to the size of the shocks. In line with this explanation, oil-producing countries (such as Nigeria, Congo, Gabon, Jordan, Iran, Syria, and Cameroon) and countries that experienced wars and political crises (e.g. Burundi, Rwanda, Zimbabwe) are the ones that would benefit the most from consumption stabilization. Across developed countries, the following countries would also gain relatively more from consumption stabilization: Hong Kong, Iceland, Ireland, Italy, Japan, Greece, Portugal, and Spain. Compared to other developed countries these countries are characterized by larger consumption fluctuations and highly persistent shocks. Developed countries such as Australia, Luxembourg, and the USA would gain relatively less from further consumption stabilization. Let us now compare the welfare gain from consumption stabilization with the welfare gain from long-term growth as in Lucas’ original exercise.19 The last three columns of Tables 1 and 2 report posterior quantiles on lz. Table 3 summarizes 19 Note that this comparison does not take into account the cost of implementing policies. Moreover, it might not be feasible to remove all fluctuations in consumption or to achieve an increase in long-term growth by 1% in a country.
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R. Houssa / European Economic Review 59 (2013) 35–62
results in these three last columns by classifying countries into three categories: (i) growth when the 90 credible interval for lz has negative bounds; (ii) stabilization when it has positive bounds; and (iii) inconclusive when it includes zero. Two main findings can be derived from Table 3. First, the welfare comparison is inconclusive in 34 developed and developing countries, amounting to 42% of the sample size. This is very high. Moreover, the rate of inconclusiveness is somehow higher in developing countries (44%) than in developed countries (36%). Second, when the welfare comparison yields conclusive results, all the developed countries would gain more from growth than from stabilization. In the case of developing countries, one half of the countries would benefit from growth and the other half from stabilization. These findings suggest the need for caution in interpreting point estimates reported in the literature, especially as regards developing countries.
4. Sensitivity and sub-period analysis This section presents sensitivity analysis with respect to the risk aversion parameter ðgÞ and IES ð1=yÞ. Moreover, a subperiod analysis is provided in order to account for a possible parameter instability of the AR process. Before presenting the
Table E3 Posterior quantiles of welfare effects in developing countries.
l (%)
Colombia Congo Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippines Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
z (%)
l (%) z (%)
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
7.47 3.29 5.09 12.19 3.86 2.38 7.97 42.59 14.34 33.50 4.76 0.27 8.47 1.32 0.87 5.45 12.93 7.36 44.82 25.86 13.44 12.87 12.41 28.11 3.07 10.60 5.58 1.89 39.48 4.16 11.28 9.72 39.67 0.18 40.98 4.94 7.03 2.58 50.50 3.99 6.21 19.08 20.25 19.49 41.62 55.27
17.43 7.53 13.09 33.71 7.95 4.05 23.13 74.94 36.43 64.45 12.65 0.90 20.46 2.27 1.48 9.66 25.32 13.67 74.64 55.26 28.84 27.96 23.54 55.07 5.41 24.97 10.48 4.85 71.03 7.35 26.47 17.78 73.19 0.42 71.98 13.83 12.74 4.54 80.32 9.40 11.42 49.56 46.13 45.32 72.87 84.06
61.95 36.59 56.32 90.95 24.88 8.41 78.11 97.59 84.52 95.19 63.77 9.07 67.54 4.41 2.87 19.65 62.45 30.72 96.99 92.96 77.82 77.44 55.29 93.04 11.01 73.49 28.54 29.65 96.94 15.30 81.37 44.80 97.51 1.60 96.63 62.01 29.21 8.80 98.01 42.63 25.02 94.62 90.87 90.27 97.51 98.78
16.58 18.32 18.38 16.52 23.03 17.85 17.80 14.78 22.42 16.12 19.22 20.60 15.39 21.41 16.26 14.24 17.44 17.96 27.14 23.12 27.08 17.98 14.71 16.59 13.39 18.97 20.68 18.07 18.93 18.61 15.82 20.44 22.99 19.71 17.56 17.99 20.44 14.51 21.34 18.47 13.82 12.16 17.22 27.85 22.40 15.15
20.61 21.43 21.77 22.84 26.47 20.41 22.39 21.40 31.92 23.12 23.14 22.11 19.09 23.68 17.53 16.98 23.51 22.95 38.11 31.52 34.73 22.58 19.26 23.70 15.19 23.93 23.52 20.34 26.79 22.10 20.46 26.52 32.80 20.35 25.83 21.79 25.75 16.45 29.39 22.07 16.61 20.08 24.55 37.64 34.24 21.28
29.62 27.92 30.08 38.52 32.49 23.94 32.78 30.93 44.67 33.76 31.09 25.06 27.33 26.58 19.07 21.44 35.90 31.83 54.14 45.10 51.08 31.51 28.68 35.82 18.04 34.06 28.53 26.17 37.70 27.58 27.60 39.51 46.98 20.96 38.81 30.04 35.72 19.12 39.55 30.09 21.70 32.52 37.10 56.80 52.99 29.99
12.01 18.08 15.88 8.19 22.90 18.90 12.67 25.13 15.12 14.50 16.97 22.60 9.29 23.89 17.37 11.27 8.84 15.14 9.40 1.47 19.70 7.36 5.09 8.67 12.32 11.60 17.65 18.59 16.44 18.73 8.30 16.58 9.96 20.35 18.88 16.31 19.38 14.32 23.27 18.07 10.12 1.61 0.78 14.29 11.55 35.71
3.15 13.70 8.60 12.05 18.30 16.27 0.46 52.88 5.16 40.01 10.22 21.23 1.47 21.37 16.01 7.28 1.58 8.97 34.88 22.22 6.02 5.17 4.20 30.71 9.72 0.81 12.74 15.30 43.20 14.60 5.29 8.47 38.62 19.84 44.97 7.88 13.07 11.92 49.67 12.52 5.22 29.16 23.27 6.17 36.49 61.29
36.38 9.94 28.70 56.16 4.05 12.40 48.36 74.21 42.64 67.84 33.30 15.71 41.35 18.68 14.37 0.84 29.55 3.84 59.00 55.69 33.98 48.09 29.68 62.94 4.93 42.62 1.75 4.70 67.51 8.14 49.70 8.84 63.11 18.86 67.39 36.84 1.28 8.14 68.81 15.01 5.74 70.43 60.32 44.08 60.69 77.18
R. Houssa / European Economic Review 59 (2013) 35–62
55
Table F1 Posterior quantiles of welfare effects in developed countries, PWT6.1.
l
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.87 2.10 2.72 1.60 2.09 3.53 1.93 5.63 9.81 12.87 4.24 4.07 3.29 8.46 5.59 1.50 3.08 2.81 2.04 10.26 4.47 2.47 1.82 2.01 1.15
1.23 4.74 8.12 2.80 2.95 5.08 4.20 14.18 19.12 23.17 8.70 6.29 8.50 23.00 8.18 2.13 6.05 4.89 2.88 19.96 9.65 5.01 4.20 3.76 2.07
1.82 19.88 43.18 6.29 4.39 7.71 15.85 54.03 55.60 54.57 27.04 11.53 39.16 73.91 12.59 3.16 19.11 12.28 4.25 56.49 34.99 16.04 18.72 10.13 5.31
18.61 17.26 17.80 18.32 19.48 17.22 17.54 16.10 13.87 17.03 16.76 17.04 17.16 16.66 13.73 17.14 17.67 20.36 17.59 16.02 16.85 19.24 19.76 17.71 17.50
19.48 18.83 20.36 19.75 20.91 18.83 19.34 18.85 16.53 20.15 18.87 18.33 19.66 20.87 15.25 18.23 19.75 22.06 18.84 19.36 19.41 21.40 21.95 19.13 18.57
20.47 22.78 30.74 21.55 22.59 20.86 23.09 26.24 22.47 26.19 23.54 20.11 27.75 32.09 17.21 19.40 23.39 24.71 20.34 26.56 26.02 25.38 26.54 21.33 20.08
19.17 16.59 16.78 18.57 19.46 15.51 17.42 12.15 5.59 5.94 14.21 14.21 15.39 9.87 9.61 17.21 16.71 19.41 17.30 7.99 14.08 19.05 20.22 17.24 17.74
18.23 14.14 12.11 16.92 17.95 13.70 15.05 4.60 2.61 2.87 10.18 12.06 11.36 2.37 7.10 16.08 13.60 17.08 15.97 0.91 9.73 16.26 17.58 15.33 16.49
17.27 2.17 14.71 13.43 16.21 11.23 6.04 29.42 33.87 30.82 5.04 7.41 10.71 42.93 3.29 14.80 1.65 10.85 14.37 32.61 11.61 6.97 6.66 9.63 13.44
results I first examine how g, y and the parameters of the AR process affect l and z. Table 4 displays medians of the posterior distribution of l and z in France for various combinations of g and y in the set {1.5,2.0,2.5,5.0}. For a given value of y, l increases with the coefficient of relative risk aversion, g. This relationship reflects the preference for a smooth consumption path for risk-averse consumers. As a result, the more risk averse a person is, the more welfare compensation he would require in order to eliminate fluctuations in consumption. Alternatively, with g held constant, l decreases with y. This result captures the positive impact of IES (i.e. 1=yÞ on the welfare cost of consumption fluctuations in the presence of persistent shocks. In particular, when shocks are persistent, the discount factor of static welfare costs of consumption fluctuations over time increases with IES.20 In order to have a better understanding of the impacts of the parameters of the AR process ðs2 , fi ,gÞ on l and z, I consider artificial countries, each characterized by different parametrization of an AR(2) consumption process. Fig. 1, which reports the implied values of l and z, shows that the welfare cost of fluctuations increases with both the size and the persistence of shocks. The larger the shocks, the more consumers find them costly and the more they will be willing to pay in order to have a smooth consumption path. In addition, the more persistent the shocks the more long lasting will be their effects and the more welfare loss they will generate. By contrast, the welfare loss of fluctuations is high for low values of the long-term growth rate. This result suggests that volatility hits poor consumers harder than the rich. In particular, volatility has a very large welfare detrimental effect on consumers that are close to subsistence.
4.1. Higher risk aversion level and IES There is dispute about the empirical values of g and y.21 Due to this debate this section analyzes the impact of doubling the risk aversion ðgÞ and IES ð1=yÞ. In particular, I re-estimate welfare effects under the following two preferences parametrizations: (i) g ¼ 10 and y ¼ 1:5; and (ii) g ¼ 5 and y ¼ 0:75. Tables 5 and 6 report summary results analogous to Table 3. See Appendices B and C for the detailed results. 20 This result holds provided that the mean adjusted growth rate (i.e. g 12 gs2 Þ is positive. When the mean adjusted growth is negative the opposite relationship is true (see Obstfeld, 1994). 21 For instance, Ogaki et al. (1996) find estimated values for y ranging from 2.26 to 2.96 for low-income countries; from 1.32 to 2.51 for lowermiddle-income countries; from 1.26 to 2.38 for upper middle income countries; and from 1.21 to 2.29 for high income countries. Hall (1988) argues that ‘‘the elasticity is unlikely to be much above 0.1, and may well be zero’’ in the USA. Campbell and Mankiw (1989) estimate a value of about 3 for the UK. For the risk aversion parameter, Mehra and Prescott (1985) and Kandel and Stambaugh (1991) argue that values as high as 30 cannot be ruled out. One problem with these estimates is that they are based on the CRRA utility function in which the risk aversion is the inverse of IES.
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R. Houssa / European Economic Review 59 (2013) 35–62
Doubling the risk aversion level leads to a marginal increase of inconclusive cases (39 versus 34 countries). However, the new inconclusive cases primarily concern developed countries (15 versus 9). Doubling the risk aversion level also has other effects. For instance, Iceland, Portugal and Hong Kong shift from inconclusive to stabilization. In the same way, Egypt moves from growth to inconclusive. These re-classifications that occur following increase in risk aversion constitute another aspect of uncertainty of the results. By contrast, doubling IES does not change the classification of developed countries. The results for developing countries also do not change except for two cases: Brazil moves from growth to inconclusive, and Cameroon switches from inconclusive to stabilization. Table F2 Posterior quantiles of welfare effects in developing countries, PWT6.1.
l
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippine Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
16.15 16.40 9.06 8.45 6.34 8.56 31.79 24.65 30.11 5.70 14.59 5.17 49.33 8.87 20.40 5.26 5.69 12.51 20.87 52.54 53.99 25.19 4.95 7.48 5.53 3.65 8.47 29.34 17.42 47.18 19.48 8.59 7.61 11.86 15.36 28.49 6.09 10.14 3.05 47.79 6.75 12.53 8.51 18.67 2.32 42.75 3.61 8.90 8.17 48.89 6.17 5.92 25.87 16.14 23.18 48.08 64.40
25.27 25.54 13.30 12.53 11.38 12.76 52.89 50.12 49.58 10.80 22.60 12.35 76.74 16.34 33.54 10.26 8.29 27.24 35.63 79.44 80.41 41.88 13.95 10.88 8.11 5.26 16.02 49.29 35.52 77.51 32.72 12.64 11.71 22.47 24.52 47.28 11.55 17.79 4.52 75.55 10.07 19.59 12.69 28.79 4.16 70.98 7.56 13.47 11.99 76.11 11.74 10.92 41.70 31.56 47.73 76.39 87.93
43.68 45.59 21.48 19.95 29.96 20.35 89.92 91.19 85.96 32.26 38.90 51.89 97.75 45.20 58.62 32.83 12.83 74.91 71.05 97.71 98.35 77.74 61.51 17.27 12.47 7.99 42.64 88.09 80.76 97.46 64.83 20.72 20.86 58.45 46.59 83.54 29.95 42.06 7.21 96.67 15.86 35.89 20.63 51.48 9.54 96.74 25.78 21.21 19.12 97.25 35.90 31.67 74.84 75.69 90.24 97.42 98.79
21.38 19.68 20.22 20.74 22.10 16.36 23.24 21.48 17.49 13.51 20.19 20.01 22.90 18.92 16.64 19.21 17.34 19.53 20.18 18.84 22.53 24.38 21.63 21.48 20.86 18.20 14.78 20.23 21.50 23.41 24.87 27.82 18.91 15.90 20.55 16.19 18.89 18.93 20.78 25.55 17.54 17.97 18.36 19.22 19.43 21.88 19.37 23.45 16.20 18.13 22.49 15.12 18.22 20.85 20.58 25.84 19.83
25.92 24.30 23.47 24.10 24.99 18.87 31.00 28.04 22.99 15.36 24.47 23.33 30.62 22.91 20.85 22.28 19.40 24.81 25.40 24.44 29.45 32.31 25.73 24.74 23.44 19.92 17.36 26.53 27.90 31.48 31.23 32.99 21.55 19.08 24.58 20.97 21.70 22.00 22.48 33.00 19.76 20.96 21.09 23.89 20.91 29.45 22.03 27.46 18.56 23.46 25.68 17.28 23.35 25.38 27.57 35.02 25.75
34.22 32.52 28.37 28.88 30.66 22.24 43.76 39.19 31.66 19.25 31.50 32.15 39.96 29.82 27.98 28.17 22.27 35.92 34.49 31.94 38.33 46.23 38.63 29.31 27.03 22.06 22.29 37.66 39.62 42.76 43.12 40.44 25.50 25.40 31.37 28.76 26.94 28.04 24.66 42.05 23.15 25.54 25.24 31.74 22.89 39.81 27.00 33.80 21.77 29.48 32.39 21.29 32.03 33.72 39.60 46.75 32.26
8.29 6.16 14.29 15.42 18.08 9.90 5.31 0.03 10.88 9.04 8.59 16.90 23.14 13.22 1.88 16.64 13.72 10.42 1.83 31.62 28.77 3.01 19.32 17.45 18.30 16.65 7.84 6.59 7.61 19.53 9.17 25.39 13.57 5.75 7.77 10.65 15.17 10.67 19.87 18.63 12.94 7.33 12.27 3.13 18.82 18.28 18.31 18.61 10.14 28.61 19.02 10.95 5.55 6.57 1.11 18.52 41.12
0.93 1.21 10.06 11.51 13.56 6.06 21.83 21.93 26.82 4.49 1.82 11.01 45.26 6.40 12.67 11.82 11.14 2.74 10.29 54.07 49.61 9.68 11.50 13.78 15.29 14.68 1.25 22.94 7.75 44.71 1.37 20.11 9.83 3.37 0.17 26.07 10.35 4.06 17.96 41.68 9.74 1.30 8.33 4.90 16.67 40.63 14.35 14.17 6.49 51.96 13.89 6.21 18.44 6.39 19.66 39.56 61.17
13.00 16.16 3.85 5.89 1.79 0.29 49.50 57.84 56.33 13.75 9.66 20.23 63.77 18.48 33.24 6.54 7.44 41.56 38.62 71.20 66.28 35.50 24.63 8.47 11.57 12.05 20.41 52.90 44.89 65.35 25.88 13.99 2.43 34.96 17.58 56.22 4.63 14.94 15.40 61.07 5.01 12.35 2.43 22.57 11.89 62.89 0.59 7.90 0.67 71.14 5.93 11.61 45.00 43.38 56.14 59.20 72.67
R. Houssa / European Economic Review 59 (2013) 35–62
57
Table F3 Posterior quantiles of welfare effects in developed countries, PWT6.3.
l
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.82 2.05 2.55 1.72 2.46 3.27 1.88 4.87 7.36 11.79 3.44 3.85 3.68 8.75 5.36 1.48 3.24 3.06 1.87 8.70 4.03 2.28 1.47 1.79 1.18
1.13 4.40 7.07 3.02 3.47 4.63 3.99 11.63 13.30 20.69 6.66 5.76 8.88 22.97 7.80 2.05 6.21 5.38 2.65 16.14 8.47 4.42 3.24 3.27 2.05
1.63 16.48 33.89 6.90 5.15 6.91 14.64 43.25 34.10 49.03 17.46 10.02 42.10 71.07 11.73 2.98 18.71 13.20 3.86 41.96 29.59 12.61 13.14 7.99 4.98
18.53 17.47 17.86 18.01 18.68 16.98 17.71 15.96 13.50 16.84 16.70 17.42 17.70 17.17 14.01 17.51 17.78 19.85 17.43 16.22 16.48 19.01 19.74 17.82 17.64
19.31 18.96 20.06 19.44 20.12 18.38 19.41 18.24 15.55 19.49 18.46 18.62 20.24 21.12 15.54 18.50 19.83 21.57 18.52 19.00 18.71 20.93 21.51 19.07 18.74
20.19 22.28 27.57 21.17 21.86 20.12 22.93 24.19 19.47 24.86 21.75 20.18 29.65 31.91 17.38 19.63 23.34 24.15 19.75 24.80 23.91 23.90 24.90 20.73 20.09
19.00 16.82 16.94 18.06 18.15 15.47 17.56 12.58 7.51 6.56 14.80 14.82 15.61 9.96 9.94 17.49 16.66 18.56 17.09 9.54 14.01 18.82 20.30 17.48 17.88
18.18 14.57 12.94 16.34 16.65 13.77 15.33 6.59 2.28 1.08 11.80 12.87 11.25 1.64 7.70 16.44 13.53 16.21 15.86 2.81 10.21 16.39 18.17 15.74 16.63
17.31 4.20 8.13 12.59 14.79 11.58 7.43 20.43 15.67 24.43 2.61 9.07 13.05 40.99 4.25 15.24 2.27 9.34 14.42 18.74 6.68 9.21 10.23 11.63 13.91
4.2. Sub-period analysis This section repeats the welfare comparison analysis on two different sub-periods. The motivation for the sub-period analysis is to account for structural breaks in the data. For instance, the literature identifies a decline of fluctuations in many countries from the mid-1980s. This phenomenon is referred to as the great moderation. Fig. 2, which plots the crosscountry unweighted average values of 10-year rolling estimates of the standard deviation of real consumption per capita growth, illustrates this. However, the data show that consumption volatility is still much higher in developing countries compared to their developed counterparts. In order to investigate the impact of the great moderation on the welfare comparison the following two sub-periods are considered: 1960–1985 and 1986–2003.22 For each of the sub-periods, I again carry out the lag-selection exercise and estimate the posterior distribution of l and z assuming g ¼ 5 and y ¼ 1:5. Tables 7 and 8 report summary results analogous to Table 3. See Appendices D and E for the detailed results. The results suggest that the time period under study plays an important role. Taking Belgium as an example, the credible interval for lz includes zero in the first sub-period while it has negative bounds in the second sub-period. This result could be explained by the fact that Belgium faced relatively smaller shocks in the second sub-period. In addition, the persistence of shocks has decreased in the second sub-period for Belgium. As a result, the welfare cost of fluctuations decreased in relative terms across the two periods. Overall, the welfare comparison differs across the two sub-periods. Moreover, the sub-sample analysis shows more inconclusive cases, especially for developing countries. These findings indicate larger uncertainty on earlier estimates obtained with small sample period data.
4.3. Other sensitivity analysis23 Finally, this section performs two other sensitivity analysis. First, given the recent inconsistency reported by Johnson et al. (2009) on GDP data across different versions of PWT I re-estimate welfare effects using data from two other versions of the database: PWT6.1 (1960–2003) and PWT6.3 (1960–2007). Tables 9 and 10 display summary results. Tables F1–F4 in Appendix F presents the median together with the 5th and 95th quantiles of the posterior distributions of l, z and lz, based on g ¼ 5:0 and y ¼ 1:5. In general, the qualitative results are comparable across different versions of PWT. However, there are differences in terms of macroeconomic priorities. From PWT6.2 to PWT6.1 there are only three moves: Brazil moves from inconclusive to growth; Cameroon moves from inconclusive to stabilization, and Jamaica from stabilization to 22 23
The break year of 1985 is also considered in other cross-country studies (see, for example, Kose et al., 2005). I thank the referees for drawing my attention to the points discussed in this section.
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R. Houssa / European Economic Review 59 (2013) 35–62
Table F4 Posterior quantiles of welfare effects in developing countries, PWT6.3. The numbers reported for Gabon, Nigeria and Zambia mean that welfare values explode. Countries
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippine Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
l
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
20.70 17.46 11.33 31.24 5.87 9.54 28.81 19.73 25.01 6.60 17.91 5.13 41.00 8.29 19.48 4.23 6.78 13.19 20.66 0.00 49.09 23.31 6.43 6.46 5.37 3.36 8.04 15.45 13.16 52.15 14.81 21.13 27.77 11.24 17.00 33.81 5.79 8.18 2.79 0.00 7.28 11.46 9.48 16.05 2.51 28.98 5.12 6.88 12.05 44.47 10.14 5.44 41.28 16.75 33.00 0.00 67.70
33.07 27.20 17.03 52.72 10.14 14.01 47.57 38.81 40.78 12.36 27.69 12.32 67.29 15.07 30.45 7.71 9.65 28.11 34.99 0.00 76.64 37.40 17.96 9.23 7.76 4.77 15.13 23.69 24.00 79.99 23.64 33.03 46.97 21.34 27.93 55.22 10.82 13.44 4.04 0.00 10.44 17.41 13.53 24.58 4.38 46.36 11.44 10.28 18.09 70.89 15.97 10.35 67.00 30.93 62.49 0.00 88.95
59.16 48.24 27.98 89.29 24.95 22.58 83.50 83.52 73.88 35.30 47.97 47.37 95.68 40.73 54.40 21.26 14.93 75.98 68.08 0.00 97.79 68.11 65.11 14.59 11.95 7.00 38.40 39.02 58.08 97.87 46.93 60.31 87.54 53.86 54.89 89.01 27.43 28.97 6.33 0.00 16.49 30.36 21.22 42.16 9.83 85.56 41.26 16.07 29.53 96.30 31.48 27.93 94.70 71.93 94.63 0.00 99.08
19.02 18.28 19.47 21.50 22.08 17.09 24.21 21.90 17.29 13.12 20.83 19.12 21.08 18.82 16.08 18.39 16.67 19.27 21.14 0.00 20.03 23.75 19.98 21.72 20.31 18.10 14.82 16.38 21.33 21.66 23.11 25.31 19.00 15.43 21.09 16.68 18.38 19.87 21.04 0.00 17.30 17.57 19.09 18.51 19.08 23.82 18.75 24.44 17.57 17.89 20.48 15.31 16.81 19.86 18.12 0.00 19.41
23.89 22.29 22.97 28.89 24.66 19.69 32.02 27.63 21.94 14.95 25.65 22.10 28.43 22.36 19.69 20.75 18.64 24.35 26.38 0.00 25.56 30.63 24.05 24.56 22.63 19.65 17.24 19.74 26.13 28.09 27.76 32.24 24.51 18.30 25.83 21.79 20.94 22.57 22.56 0.00 19.60 20.25 22.07 22.43 20.65 31.38 21.86 27.96 20.61 22.93 22.87 17.35 22.17 24.18 23.79 0.00 24.63
32.01 29.10 27.96 39.87 29.67 23.30 45.82 37.72 29.93 18.72 34.15 29.70 37.79 28.27 26.01 24.63 21.32 34.92 35.61 0.00 33.27 43.84 34.49 28.48 25.79 21.62 21.76 24.69 34.96 36.27 36.10 44.85 33.01 24.22 33.56 28.68 25.62 27.82 24.44 0.00 22.81 24.05 26.28 29.00 22.62 44.58 28.56 33.04 25.19 29.07 26.67 20.95 28.66 32.09 32.73 0.00 30.52
0.70 3.25 10.68 7.18 18.69 9.57 1.31 4.87 5.94 7.68 5.83 15.99 17.73 13.35 1.80 16.47 11.82 9.38 3.06 45.00 27.01 4.26 15.79 18.58 17.56 16.63 8.14 2.85 11.04 26.41 11.41 8.36 6.62 5.58 6.88 15.55 14.66 13.71 20.21 45.00 12.12 7.91 12.16 4.67 18.43 1.13 16.04 21.69 7.69 24.96 12.18 11.50 22.89 5.44 12.02 45.00 45.28
9.18 5.00 6.03 23.71 14.44 5.59 15.26 11.08 18.64 2.57 2.03 9.75 38.77 7.12 10.74 12.87 8.86 4.15 8.86 0.00 50.33 6.69 5.86 15.27 14.85 14.87 2.00 3.77 2.22 50.90 4.22 0.81 22.36 3.03 2.38 33.49 10.21 9.07 18.55 0.00 9.02 2.84 8.40 2.15 16.28 14.91 10.16 17.71 2.62 47.28 6.86 6.94 44.50 6.78 37.92 0.00 63.94
29.02 20.50 2.37 51.73 2.44 0.76 41.56 49.59 44.76 17.69 16.16 20.09 60.94 14.13 30.39 1.53 4.58 42.59 35.40 70.00 69.00 28.36 32.38 11.09 11.26 12.68 17.62 16.08 25.11 68.49 13.59 18.97 56.19 33.52 24.53 62.36 3.57 2.98 16.33 70.00 4.23 8.26 2.57 15.23 11.22 43.87 15.30 13.19 6.42 69.98 6.14 8.38 68.60 42.03 66.74 70.00 74.32
inconclusive. From PWT6.2 to PWT6.3 there are more movements24: for instance, Bolivia, Ecuador and Ireland move from the group of inconclusive to the one of growth; Benin, Madagascar, South Africa and Sri Lanka from growth to inconclusive; Burkina Faso and Malawi from growth to stabilization; Iran and Jamaica move from stabilization to inconclusive; and Venezuela from inconclusive to the one of stabilization. 24
This result could be related in part to new shocks that occurred in 2004–2007.
R. Houssa / European Economic Review 59 (2013) 35–62
59
Table G1 Posterior quantiles of welfare effects in developed countries.
l
Australia Austria Belgium Canada Denmark Finland France Greece Hong Kong Iceland Ireland Israel Italy Japan Korea Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
0.86 2.14 2.96 1.63 2.05 3.53 1.88 6.01 9.26 12.93 4.31 4.19 3.53 8.86 5.48 1.50 3.09 2.86 2.02 10.13 4.54 2.52 1.83 2.01 1.16
1.23 4.63 8.59 2.83 2.91 5.05 4.15 14.04 18.51 22.85 8.57 6.32 8.43 25.15 8.05 2.11 6.01 5.01 2.90 19.43 10.27 4.93 4.06 3.72 2.07
1.83 20.42 44.13 6.33 4.39 7.67 15.75 54.01 54.05 55.62 25.40 10.97 35.57 78.23 12.63 3.15 15.94 12.25 4.32 53.78 36.27 14.59 16.17 10.18 5.33
18.43 16.84 17.37 18.21 18.20 16.51 16.88 15.61 13.52 16.29 16.72 16.63 16.54 15.94 13.66 16.84 17.64 20.19 17.33 15.61 16.87 19.30 18.81 17.66 17.45
19.28 18.33 19.99 19.77 19.73 18.12 18.50 18.05 15.94 19.10 18.86 17.90 18.92 20.09 15.08 17.87 19.63 22.09 18.53 18.58 19.59 21.47 20.73 19.12 18.61
20.22 22.15 29.98 21.54 21.41 20.01 21.71 24.61 21.39 24.74 23.16 19.46 26.29 30.56 17.06 19.01 22.99 24.85 19.92 25.16 26.77 25.17 24.57 21.34 20.14
18.93 15.94 16.07 18.57 18.38 14.95 16.53 11.15 5.33 4.98 14.34 13.77 14.50 8.50 9.35 16.82 16.65 19.42 16.90 7.23 14.27 19.17 18.98 17.23 17.80
18.04 13.59 11.14 16.87 16.79 13.04 14.27 3.94 2.67 3.80 10.27 11.50 10.39 4.84 7.01 15.74 13.68 17.00 15.63 0.92 9.37 16.40 16.55 15.35 16.49
17.05 0.94 14.80 13.39 14.96 10.49 4.47 28.99 32.61 32.16 4.99 7.32 9.49 48.90 3.09 14.45 4.49 10.76 14.03 29.97 10.65 8.23 6.55 9.66 13.39
Second, I investigate the role of unit root on estimates of welfare effects. For this purpose follow a two-step approach suggested by a referee. First, I perform the Bayesian unit root test of Phillips and Ploberger (1994) using the package developed by Ouliaris and Phillips (1994). The posterior odds in favor of a unit root (PICU25) suggests that unit root cannot be rejected in 38 cases. Moreover, trend stationary with serial correlation in consumption was only present in three cases. Second, I subsequently estimate welfare effects taking into account the outcome of the first step.26 Tables G1 and G2 in Appendix G present the median together with the 5th and 95th quantiles of the posterior distributions of l, z and lz, based on PWT6.2 and using g ¼ 5:0 and y ¼ 1:5. The summary results displayed in Table 11 show qualitatively similar results in terms of macroeconomic priorities as compared to the ones reported in Table 3. Moreover, only thee movements can be observed: Costa Rica, Peru and Venezuela.
5. Conclusion This paper has proposed a framework for inference on welfare effects of consumption fluctuations and growth. The literature has thus far produced only point estimates. Moreover, the empirical analysis here examines data from 82 developed and developing countries while most existing studies focus on the USA. In addition, the data cover a relatively long time period (1960–2003), and it is shown how the results evolve across sub-periods. The results show large credible intervals on the welfare cost of consumption fluctuations, which suggest great uncertainty as regards previously reported point estimates. Thus, while the literature shows conflicting point estimates of welfare effects across different models, this paper finds that estimates obtained from a particular model economy can display considerable uncertainty. As such, one should account for this uncertainty in the comparison between the welfare gain from consumption stabilization and the welfare gain from growth. Credible intervals for the difference between the welfare gain from consumption stabilization and the welfare gain from growth include zero in many developed and developing countries. Sub-period and sensitivity analysis support these results. These findings suggest the need for caution in drawing strong policy conclusions from point estimates. The framework proposed in this paper can be extended to account for uncertainty about the risk aversion parameter and IES implied by data on consumption. 25
The unit root specification is preferred if PICU 4 1. P In the case of stationary process the ARð‘Þ consumption growth process in Eq. (1) is modified as g t ¼ f0 þ ‘i ¼ 1 fi g ti þ et , where g t ¼ C t =g1 C t1 1, and g1 is derived from the following AR(1) model lnðC t Þ ¼ g0 þ g1 lnðC t1 Þ þ xt at each draw of the MCMC. The normalized value function analogous to the 1g ð1yÞ=ð1gÞ y b½Eðc one in Eq. (6) is vðct Þ ¼ ð1 þ g1 Þ. t þ 1 vðct þ 1 Þ9c t Þ 1 26
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R. Houssa / European Economic Review 59 (2013) 35–62
Table G2 Posterior quantiles of welfare effects in developing countries.
l
Argentina Barbados Benin Burkina Faso Bolivia Brazil Burundi Cameroon Chile China Cote d’Ivoire Colombia Congo Costa Rica Dominican. Rep. Ecuador Egypt El Salvador Ethiopia Gabon Gambia Ghana Guatemala Guinea Honduras India Indonesia Iran Jamaica Jordan Kenya Madagascar Malawi Malaysia Mali Mauritius Mexico Morocco Nepal Nigeria Pakistan Panama Paraguay Peru Philippine Rwanda South Africa Senegal Sri Lanka Syria Tanzania Thailand Trinidad Uruguay Venezuela Zambia Zimbabwe
z
lz
0.005
0.50
0.95
0.005
0.50
0.95
0.005
0.50
0.95
15.86 16.24 8.75 8.20 6.42 8.48 31.78 24.67 30.09 5.92 14.57 5.26 50.10 7.38 20.85 5.26 5.65 12.92 20.47 52.05 52.89 25.59 5.11 7.44 5.56 3.67 8.60 29.91 18.17 50.67 19.15 8.51 7.74 12.11 14.93 28.89 6.18 10.35 3.05 47.91 6.85 12.41 8.66 18.51 2.36 44.38 3.68 8.87 8.08 48.69 6.21 5.91 25.45 16.85 23.57 47.86 66.19
25.17 25.72 13.29 12.32 11.57 12.43 53.50 50.33 51.07 10.71 22.52 12.10 78.19 10.85 33.18 10.30 8.30 28.18 34.92 79.53 80.23 42.36 13.97 10.91 8.05 5.25 16.02 49.83 36.81 80.01 32.53 12.72 11.90 22.40 24.27 47.55 11.15 17.80 4.53 74.97 9.94 19.88 12.77 28.50 4.15 70.74 7.38 13.29 11.85 76.32 11.90 11.02 41.54 31.53 47.60 75.82 88.13
43.95 46.03 21.93 20.36 30.17 20.30 89.10 92.10 87.03 28.02 38.33 50.28 97.65 17.38 62.36 31.22 12.82 75.73 69.64 98.12 97.76 78.06 58.14 17.43 12.37 7.85 44.08 87.11 82.88 98.10 64.45 20.67 20.99 57.31 44.25 85.40 28.35 42.42 7.42 96.14 15.82 34.72 20.38 51.98 9.37 96.09 23.26 21.69 18.42 96.54 35.46 33.49 77.44 76.46 89.12 97.50 98.91
21.00 19.69 20.11 20.59 22.13 15.35 23.26 21.48 17.70 13.49 20.03 18.94 20.74 18.70 16.79 18.29 16.80 18.09 20.07 13.12 22.40 24.43 19.98 21.61 20.94 17.96 14.74 20.31 18.70 20.75 15.83 27.91 18.94 15.71 19.01 16.11 17.71 16.51 20.70 13.33 16.95 16.30 18.30 15.48 19.30 21.89 19.44 23.31 16.10 15.55 22.51 15.15 18.17 20.84 19.75 25.74 11.34
26.01 24.20 23.44 24.02 25.00 17.67 31.49 28.06 23.36 15.25 24.39 21.88 28.17 21.62 20.67 21.18 18.79 23.19 25.13 18.16 29.55 32.53 23.89 24.72 23.52 19.71 17.10 26.60 24.71 28.07 22.99 33.03 21.56 18.78 23.15 20.94 20.54 19.16 22.48 20.46 19.19 19.37 21.12 19.59 20.87 29.49 21.96 27.44 18.40 20.47 25.58 17.36 23.30 25.40 26.20 34.67 17.48
33.88 31.99 28.09 28.88 30.87 20.74 44.19 39.04 31.93 18.63 31.68 30.77 37.47 25.67 28.38 26.62 21.35 33.14 34.30 24.32 37.94 46.67 35.42 29.20 26.93 21.79 22.05 36.64 35.58 37.79 33.28 41.08 25.48 25.34 29.10 28.96 25.35 24.67 24.79 29.56 22.24 23.94 25.24 26.03 22.89 39.41 26.87 33.42 21.52 26.42 31.90 21.60 32.31 34.04 37.15 46.82 24.72
8.22 6.48 14.24 15.64 18.28 8.87 5.15 0.10 10.44 8.99 8.52 15.56 25.93 14.42 2.20 15.54 13.12 8.24 2.19 36.66 27.55 2.89 17.30 17.45 18.49 16.43 7.57 7.25 4.06 24.30 2.94 25.70 13.54 5.45 6.96 11.07 14.06 7.86 19.90 28.97 12.26 6.08 12.19 0.17 18.83 18.96 18.22 18.49 9.93 31.17 19.03 10.94 5.32 6.72 1.14 17.99 49.94
0.87 1.58 10.29 11.51 13.50 5.13 21.68 22.13 27.63 4.49 1.74 9.73 49.34 10.75 12.52 10.73 10.52 4.92 9.73 60.88 49.82 9.92 9.53 13.83 15.41 14.42 1.13 22.83 11.43 50.85 9.69 20.22 9.74 3.53 1.19 26.38 9.27 1.61 18.00 53.98 9.17 0.62 8.37 8.95 16.71 40.40 14.53 14.11 6.50 55.33 13.50 6.28 18.24 6.40 20.72 39.57 69.86
12.97 15.97 3.76 5.88 1.13 1.04 48.91 58.26 57.65 10.04 9.53 21.07 67.13 5.52 36.00 6.31 6.45 45.24 37.60 78.32 66.33 34.32 24.96 8.91 11.60 11.96 23.89 52.84 51.58 69.13 37.50 14.34 2.06 33.40 18.45 57.67 4.78 19.00 15.14 74.52 4.38 13.04 2.52 27.75 11.91 62.62 1.62 8.15 0.82 74.25 5.11 12.25 47.56 44.02 56.98 59.78 82.58
Acknowledgments I am grateful to the editor and the referees for their their constructive comments and suggestions. I thank Luc Bauwens, Ales Bulir, Raouf Boucekkine, Geert Dahene, Paul De Grauwe, Hans Dewachter, Lennart Erickson, Andrew Feltenstein, Ayhan Kose, David Liedo, Chris Marsh, Chris Otrok, Michel Robe, Marijke Verpoorten, and Remco Zwinkels for valuable comments and suggestions. In addition, I thank participants at the 2007 Meeting of the EEA in Budapest, the May 2006
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Spring Meeting of Young Economists in Seville, the February 2005 Doctoral Workshop in UCL, and seminar participants at IMF, at the Nijmegen University, and at CES for useful comments. The usual disclaimer applies. Appendix A. OLS estimation of the AR process OLS estimates of the AR process in developed and developing countries are given in Tables A1 and A2. Appendix B. Higher risk aversion level Posterior quantiles of welfare effects in developed and developing countries are given in Tables B1–B3. Appendix C. Higher intertemporal elasticity of substitution Posterior quantiles of welfare effects in developed and developing countries are given in Tables C1–C3. Appendix D. First sub-period: 1960–1985 Posterior quantiles of welfare effects in developed and developing countries are given in Tables D1–D3. Appendix E. Second sub-period: 1986–2003 Posterior quantiles of welfare effects in developed and developing countries are given in Tables E1–E3. Appendix F. Welfare effects with PWT6.1 and PWT6.3 Posterior quantiles of welfare effects in developed and developing countries, PWT6.1 and PWT6.3 are given in Tables F1–F4. Appendix G. The role of unit root Posterior quantiles of welfare effects in developed and developing countries are given in Tables G1 and G2. References Agenor, P.-R., McDermott, J., Prasad, E., 2000. Macroeconomic fluctuations in developing countries: some stylized facts. World Bank Economic Review 14 (2), 251–285. Aghion, P., Saint-Paul, G., 1998a. Virtues of bad times interaction between productivity growth and economic fluctuations. Macroeconomic Dynamics 2 (3), 322–344. Aghion, P., Saint-Paul, G., 1998b. Uncovering some causal relationships between productivity growth and the structure of economic fluctuations a tentative survey. LABOUR 12 (3), 279–303. Atkeson, A., Phelan, P., 1994. Reconsidering the costs of business cycles with incomplete markets. NBER Working Papers 4719, National Bureau of Economic Research. Barlevy, G., 2004. The cost of business cycles under endogenous growth. American Economic Review 94 (September (4)), 964–990. Barlevy, G., 2005. The cost of business cycles and the benefits of stabilization. Economic Perspectives 29 (1), 32–49. Blackburn, K., 1999. Can stabilization policy reduce long-run growth? Economic Journal 109 (452), 67–77. Blackwell, D., 1965. Discounted dynamic programming. The Annals of Mathematical Statistics 36 (1), 226–235. Caballero, R., Hammour, M., 1994. The cleansing effect of recessions. American Economic Review 84 (5), 1350–1368. Campbell, J.Y., Mankiw, N.G., 1989. Consumption, income and interest rates: reinterpreting the time series evidence. In: NBER Macroeconomics Annual 1989, vol. 4. NBER Chapters. National Bureau of Economic Research, pp. 185–246. Cooley, T.F., Ogaki, M., 1996. A time series analysis of real wages, consumption, and asset returns. Journal of Applied Econometrics 11 (2), 119–134. Dolmas, J., 1998. Risk preferences and the welfare cost of business cycles. Review of Economic Dynamics 1 (2), 646–676. Eichenbaum, M., 1991. Real business-cycle theory: wisdom or whimsy? Journal of Economic Dynamics and Control 15 (October (4)), 607–626. Epstein, L.G., Zin, S.E., 1989. Substitution, risk aversion and the temporal behavior of consumption and asset returns: a theoretical framework. Econometrica 57 (4), 937–969. Francois, P., Lloyd-Ellis, H., 2006. Growth, cycles and welfare: a schumpeterian perspective. Working Papers 1090, Queen’s University, Department of Economics, September. Geweke, J., 1991. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Staff Report 148, Federal Reserve Bank of Minneapolis. Giannone, D., Reichlin, L., 2005. Euro area business cycle: stylized facts and measurement issues. In: Reichlin, L. (Ed.), Euro Area and US Recessions, 1970–2003, C.E.P.R, London, pp. 83–93. Hall, R.E., 1988. Intertemporal substitution in consumption. Journal of Political Economy 96 (2), 339–357. Heston, A.R., Summers, R., Aten, B., 2006. Penn world table version 6.2. Technical Report, Center for International Comparisons at the University of Pennsylvania (CICUP). Imrohoroglu, A., 2008. Welfare costs of business cycles. In: Durlauf, S.N., Blume, L.E. (Eds.), The New Palgrave Dictionary of Economics, Palgrave Macmillan, Basingstoke. Imrohoruglu, A., 1989. Cost of business cycles with indivisibilities and liquidity constraints. Journal of Political Economy 97 (December (6)), 1364–1383. Johnson, S., Larson, W., Papageorgiou, C., Subramanian, A., 2009. Is newer better? Penn world table revisions and their impact on growth estimates. Working Papers 191, Center for Global Development, November.
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