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Real rigidities and real exchange rate volatility
Journal of International Money and Finance 28 (2009) 135–147
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Real rigidities and real exchange rate volatility William D. Craighead* Department of Economics, Farmer School of Business, Miami University, 208 Laws Hall, Oxford, OH 45056, USA
a b s t r a c t JEL classification: E1 F4 Key words: Real exchange rates Intersectoral adjustment costs Distribution costs
This paper shows that certain real rigidities can help explain high volatility of real exchange rates relative to other macroeconomic aggregates. An international real business cycle model is used to demonstrate that real exchange rate volatility increases if (i) it is costly to move labor between sectors and (ii) the consumption of tradable goods requires distribution services. Model dynamics are generated by shocks to productivity and preferences based on sectoral output, employment and consumption data from G-7 countries. The introduction of intersectoral adjustment and distribution costs substantially increases the real exchange rate volatility generated by the model. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Real exchange rates are highly volatile relative to other macroeconomic variables. Table 1 reports the average annual percentage standard deviation of real exchange rates relative to output for the G-7 for the period 1970–2004. On average, the real effective exchange rate is 3.15 times as volatile as output. Economists have struggled to account for this ‘‘excess volatility.’’ In the words of Obstfeld and Rogoff (2000, p. 380), ‘‘exchange rates are remarkably volatile relative to any model we have of underlying fundamentals such as interest rates, outputs and money supplies.’’ Chari et al. (2002, p. 533) describe the volatility and persistence of real exchange rates as ‘‘the central puzzle in international business cycles.’’ One approach to this issue, pioneered by Dornbusch’s (1976) ‘‘overshooting’’ model, emphasizes nominal rigidities and monetary shocks. Chari et al. (2002) implement this idea in a calibrated, two-
* Tel.: þ1 513 529 2849; fax: þ1 513 529 8047. E-mail address: [email protected] 0261-5606/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jimonfin.2008.08.012
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Table 1 Standard deviations relative to output, 1970–2004a.
Canada France Germany Italy Japan United Kingdom United States G-7 average a
REER
RER vs. US
2.52 2.02 1.99 4.36 3.57 3.24 4.36 3.15
2.76 11.20 7.83 9.84 5.22 4.63 – 6.91
Data: OECD main economic indicators. All data are HP-filtered.
country dynamic general equilibrium model with sticky prices. They are able to match the volatility of the real exchange rate, but only by assuming a high degree of risk aversion. This paper explores an alternative approach based on real rigidities. It demonstrates that real exchange rates become considerably more volatile when it is costly to move factors of production between sectors, and when consumption of tradable goods requires nontradable distribution services. The international real business cycle framework developed by Backus et al. (1992) and extended by Stockman and Tesar (1995) is used to examine the effect of distribution costs and intersectoral labor mobility costs on the real exchange rate. Since the intuition is based entirely on relative prices and real costs, money and nominal rigidities are ignored, but the ideas explored here may be viewed as complementary to theories that rely on nominal rigidities. In addition to the standard productivity shocks, preference shocks are introduced to allow consideration of the effects of changes on the demand side of the economy in a nonmonetary framework. Introducing intersectoral labor mobility and distribution costs causes the standard deviation of the real exchange rate to more than double, increasing from 2.14% to 5.17%. The channels through which real exchange rate movements are affected by real rigidities are investigated by decomposing them into the portions due to the relative price of tradable goods between countries and the relative price of nontradable goods within each country. The effects of the individual shocks are examined by considering the impulse response functions generated by sectoral productivity and relative demand shocks. The intuition motivating the introduction of costly intersectoral factor movements is relatively simple. Real exchange rates are functions of relative prices. If it is costly to change quantities by reallocating inputs, relative prices will move more. To illustrate, consider a shock that increases the demand for tradable goods. The change in demand raises the relative price of tradables. In the absence of adjustment costs, factors of production would instantly move from the nontradable sector into the tradable sector, increasing the relative supply of tradables, and lowering the price. With adjustment costs, supply does not respond as much and the relative price of tradables remains elevated. Distribution costs also amplify relative price movements in an intuitively straightforward manner. With distribution costs, when consumers purchase goods, they are also purchasing nontradable services, like retailing. The retail price reflects both the good and service inputs. In order to achieve a given change in retail relative prices, the relative prices of the goods will need to change by a larger amount. Several strands of empirical research suggest that costs of reallocating labor between sectors may be substantial. The cost of adjusting labor inputs is reflected in the procyclical behavior of labor productivity known as ‘‘labor hoarding.’’ Based on surveys of employers, Fay and Medoff (1985) find that four percent of blue-collar hours should be classified as hoarded during downturns. Fair (1985) provides econometric estimates on aggregate US data consistent with Fay and Medoff’s evidence. Burgess and Dolado (1989) and Pfann and Palm (1993) estimate models of sluggish adjustment of labor inputs on UK data. Both find statistically significant adjustment costs. On the labor supply side, Lee and Wolpin (2006) estimate a dynamic model using survey data on individuals and find significant costs of moving between sectors.
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Two interesting applications of intersectoral adjustment costs in the international trade literature are Mussa (1978) and Davidson and Matusz (2004). Mussa (1978) analyzes the dynamics of the Hecksher–Ohlin–Samuelson model when it is costly to reallocate capital between sectors in response to a change in relative prices, which are taken as exogenous in his model. Davidson and Matusz (2004) examine the benefits of trade liberalization in the presence of intersectoral adjustment costs. They show that a significant portion of the benefits of liberalization may be offset by the costs associated with worker retraining. Several papers have examined real exchange rates in small open economy models with intersectoral adjustment costs. Gavin (1990) examines the dynamic response to a terms of trade shock in a model with nontradable goods and costs to reallocating capital. Capital adjustment costs play the same role of amplifying movements the price of tradable relative to nontradable goods as labor adjustment costs in this paper. Morshed and Turnovsky (2004) show that costs to moving capital between sectors generate persistent real exchange rate and current account dynamics in response to shocks to government expenditures and technology. de Cordoba and Kehoe (2002) employ intersectoral adjustment costs to help explain the movements of the real exchange rate and trade balance that occurred as Spain lifted restrictions on capital inflows after entering the European Community. Unlike those papers, the model presented here specifically addresses the standard deviation of the real exchange rate, and does so in the context of a two-country general equilibrium system where fluctuations in the terms of trade are generated endogenously from technology and preference shocks. Distribution costs are the other key feature of the model presented here. Burstein et al. (2003) argue that the nontradable components of tradable goods consumption are large. They use several sources of data to calculate the ‘‘distribution margin,’’ the difference between the retail and producer price, as a percentage of the retail price. For US personal consumption expenditures on tradable goods, they find a distribution margin of 43.4% using the input–output tables for 1997. For the other G-7 countries, the margin ranges from 35% (France) to 50% (Japan). In a model calibrated to match Argentina’s 1991 currency board, they show that accounting for distribution costs can help understand the movement of real exchange rates and relative prices following an exchange rate stabilization. Corsetti et al. (2008) use distribution costs to address the negative correlation between the terms of trade and relative consumption, which is contrary to international risk-sharing. They introduce distribution costs as a mechanism for reducing the share of imports in consumption and the elasticity of substitution between domestic and imported tradables. This allows their model to match the negative correlation between the terms of trade and relative consumption observed in the data.
2. Model Stockman and Tesar (1995) show that incorporating nontradable goods and taste shocks into a twocountry real business cycle model improves its ability to match certain empirical regularities such as cross-country output correlations and the correlation between trade balances and output. The model presented below builds on their framework by incorporating intersectoral labor adjustment costs and distribution costs. Two countries, ‘‘home’’ and ‘‘foreign,’’ each produce tradable and nontradable goods. Foreign variables are denoted with an asterisk. Capital letters denote consumption bundles and price indexes, and lower-case letters represent consumption and prices of specific goods. For simplicity, the preferences and technology for home are presented here; foreign is symmetric. Each country has a representative household that maximizes expected lifetime utility from consumption and leisure. The utility function has the form
E
N X t ¼0
bt
1 g C 1 ð1 Nt Þ1m ; 1g t
(1)
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Table 2 Baseline parameterization. Parameter
Value
Definition
b g m q s u h aN aT d
0.96 2 4.17 0.44 1.5 0.55 0.69 0.44 0.39 0.1
Discount factor Intertemporal elasticity of substitution (consumption) Intertemporal elasticity of substitution (labor) Elasticity of substitution between tradables and nontradables Elasticity of substitution between domestic and imported tradables Share of tradables in consumption bundle Share of domestic goods in tradable consumption Capital share (nontradable sector) Capital share (tradable sector) Depreciation rate
where N denotes labor and the consumption bundle, C, is a constant elasticity of substitution aggregate of tradable and nontradable goods,
i h ðq1Þ=q ðq1Þ=q q=ðq1Þ C ¼ ð1 uÞ1=q cN þ u1=q CT :
(2)
Tradable goods consumption, CT, is an aggregate of home-produced and imported tradable goods
i h ðs1Þ=s ðs1Þ=s ðs1Þ=s CT ¼ h1=s cT þ ð1 hÞ1=s cT :
(3)
The elasticity of substitution between tradable and nontradable goods is q; s is the elasticity of substitution between domestically produced and imported tradables; u is the weight on tradables in the consumption bundle; h is the weight on domestically produced tradables. The representative household allocates fractions sT and sN of its labor respectively to the tradable and nontradable sectors, with sT þ sN ¼ 1. Output in each sector is produced according to the function
yjt
¼
zjt
2 aj 1aj y sjt sjt1 j j kt st Nt ; 2 sjt
j ¼ T; N;
(4)
where z is technology, k is capital and sN is the total labor employed in the sector. The second term represents the cost of reallocating labor between sectors, with y governing the degree of costliness.1 The cost takes the form of lost output when the share of labor allocated to the sector is changed. Note that the cost is associated with changing the sectoral allocation rather than the overall amount of labor. Capital is sector-specific and each sector produces its own capital. Capital is accumulated according to j
j
j
ktþ1 ¼ it þ ð1 dÞkt ;
j ¼ T; N;
(5)
where i is investment and d is the depreciation rate. Distribution costs are introduced by assuming tradable consumption is a combination of a goods input produced by the tradable sector, and a service input produced by the nontradable sector. Distribution services take place in the same country as consumption. Home’s tradable sector produces
1 The functional form is chosen to be consistent with the existence of a large number of identical competitive firms in each sector. If there are M identical firms indexed by i,
2 M X y sit sit1 y ðst st1 Þ2 ¼ : 2 2 st sit i¼1
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Table 3 Share of tradable goods in consumptiona.
Canada, 1970–2003 France, 1978–2004 Germany, 1991–2004 Italy, 1970–2004 Japan, 1980–2003 United Kingdom, 1970–2001 United States, 1970–2003 a
Beginning
End
Average
0.59 0.66 0.61 0.68 0.56 0.70 0.55
0.49 0.53 0.53 0.50 0.43 0.52 0.40
0.54 0.59 0.56 0.61 0.50 0.61 0.47
Data: OECD annual national accounts.
goods for domestic and foreign consumption and the home nontradable sector produces nontradable consumption goods as well as the service input into home consumption of home- and foreignproduced tradables. One unit of tradable consumption is comprised of 4 units of goods and 1 4 units of services. The market-clearing conditions can be rewritten as and
yT ¼ 4cT þ 4cT
(6)
yN ¼ cN þ ð1 4ÞcT þ ð1 4ÞcT :
(7)
A complete set of state-contingent claims is assumed to be available for international asset trade, allowing the model to be solved as a social planner’s problem.
3. Parameterization The parameters used are reported in Table 2. The capital share parameters for the tradable and nontradable sectors and the depreciation rate are taken from Stockman and Tesar (1995). The levels of the technology parameters, z, are normalized so that all relative prices are unitary in the steady state. The discount factor and the utility curvature parameters are also taken from Stockman and Tesar (1995); the curvature on leisure, m, is set so that 20% of the time endowment is devoted to labor in the steady state. The consumption bundle includes two elasticities. The elasticity of substitution between tradables and nontradables is estimated by Stockman and Tesar (1995) to be 0.44. Based on an examination of relevant empirical literature, Backus et al. (1994) choose a value of 1.5 for the elasticity between domestic and imported tradables; this value is also used by Chari et al. (2002). The weighting parameters in the consumption bundles are chosen based on OECD annual national accounts data. This database includes household final consumption broken into services, durable and nondurable goods components. Table 3 reports the shares of tradable goods in consumption for the G7; the average share is 0.55, which is used for the weighting parameter u. The share of imports in tradable consumption is proxied by multiplying imports of goods by the share of GDP devoted to household consumption and dividing by total household consumption of durable and nondurable goods. The average of the import shares reported in Table 4 is 0.31; h is set to 0.69 to match this in the model. 2 A process for the demand shocks is derived using some properties of the CES structure of the consumption bundles. The functional form implies that total home expenditure on imported tradable goods, xT , is
2 The share of tradables (i.e. durable and nondurable goods) in consumption has fallen while the import share has risen. Because the model is stationary, these dynamics are not accounted for here, but the effects of these trends may merit consideration in future research.
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Table 4 Share of imports in tradable goods consumptiona.
Canada, 1970–2003 France, 1978–2004 Germany, 1991–2004 Italy, 1970–2004 Japan, 1980–2003 United Kingdom, 1970–2001 United States, 1970–2003 a
Beginning
End
Average
0.27 0.24 0.38 0.18 0.22 0.23 0.07
0.59 0.39 0.55 0.39 0.19 0.46 0.29
0.45 0.32 0.43 0.28 0.15 0.36 0.19
Data: OECD annual national accounts.
1s p xT ¼ ð1 hÞ T XT ; PT
(8)
where XT is total expenditure on tradables. Log-linearization gives
b x T ¼
h 1h
b h þ ð1 sÞ bp T Pb T þ Xb T ;
(9)
where the carets denote percentage deviations. This can be rearranged to yield an equation for the deviation in the share of domestic goods in the tradable bundle,
1 hh
b h ¼
h
i b X b : b x T ð1 sÞ b p T P T
(10)
Similarly, expenditure on nontradable goods, xN, is related to total consumption expenditure, X, by
p 1q xN ¼ ð1 uÞ N X: P
(11)
This can be log-linearized and rearranged to give
b ¼ u
1 uh
u
i b X b : b x N ð1 qÞ b pN P
(12)
Expenditure on durable and nondurable goods is used for XT. Nontradable expenditure, xN, is expenditure on services, xT is imports of goods, and X is household final consumption expenditure. Prices are the corresponding deflators. The data are from the OECD annual national accounts. The series are HP-filtered and the percentage deviations from trend are applied to the above formulas. Data are available to estimate preference shock processes for Canada and the US for the period 1970–2003, Italy (1970–2004)3 and France (1978–2004). The average estimated process is
bt u b ht
¼
0:494 0:019
0:279 0:459
"
#
b t1 u þ 3t ; b h t1
(13)
where
3t wN ½0;
1 0:069 1000 0:034
0:034 0:605
:
(14)
In the model, home and foreign preference shocks are assumed to be independent and to behave according to this process.4
3
Several outlier observations at the beginning of the series were discarded. It would be preferable to jointly estimate a US and European process; however, the requisite data are not available for two of four European G-7 economies. 4
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Table 5 Standard deviations of selected aggregates, 1970–2004a.
Output Labor Consumption Investment Tradable output Tradable labor Tradable consumption Nontradable output Nontradable labor Nontradable consumption Terms of trade REER RER vs. US
Canada
France
Germany
Italy
Japan
UK
US
2.57 1.91 2.79 6.37 7.43 3.41 3.86 2.08 1.67 2.10 3.41 6.50 7.09
1.45 1.23 1.66 5.46 2.81 1.84 1.99 1.69 1.11 1.45 3.75 2.93 16.24
2.17 1.43 2.36 5.24 3.24 3.33 – 1.76 1.08 – 3.74 4.31 16.99
1.51 1.44 2.04 4.50 4.13 2.15 2.51 1.51 1.86 1.14 5.37 6.59 14.59
2.54 1.11 2.32 6.51 4.19 1.96 2.53 2.42 1.23 1.81 10.01 9.08 13.02
2.42 2.19 3.18 6.55 4.36 3.62 – 3.32 2.16 – 4.03 7.83 10.63
2.12 1.69 2.09 6.70 3.92 3.19 1.84 2.33 1.53 1.39 3.82 9.25 –
a Data: OECD annual national accounts (output, consumption, investment, tradable consumption, nontradable consumption, terms of trade), OECD STAN database (labor, tradable output, tradable labor nontradable output, nontradable labor), OECD main economic indicators (real effective exchange rate, real exchange rate vs. US).
The technology shock process is estimated using annual data from the OECD STAN database for industrial analysis for 1978–2003. The two countries are US and Europe, where Europe is a weighted average of Germany (0.31), France (0.23), Italy (0.23) and the UK (0.23). The tradable sector is proxied by total manufacturing (ISIC 15–37) and total services (ISIC 50–99) is used to represent nontradables.The productivity shock for each sector is
b ð1 aÞb bz ¼ Y L:
(15)
Volume indexes of value added are used for output. Labor is total employment in each sector.5 Capital stock data are not available for all countries, so they are omitted.6 The technology shock process is estimated on HP-filtered data. Terms of the estimated process are averaged to give the symmetric process used in to generate the moments of the model:
2
3 T b z 6 t 7 6 bN 7 6 zt 7 6 T 7 ¼ 6 bz t 7 4 5 bz N t
2
0:494 6 0:085 6 4 0:113 0:359
0:035 0:503 0:099 0:029
3 2 3 bT z 0:113 0:099 6 t1 7 6 bN 7 z 0:359 0:029 7 7 76 þ 3t ; 6 t1 T 7 5 0:494 0:035 6 b 7 z 5 4 t1 0:085 0:503 N b z t1
(16)
where
0
2 0:452 B 6 0:092 1 6 3t wNB @½0; 10004 0:132 0:011
0:092 0:123 0:011 0:018
0:132 0:011 0:452 0:092
31 0:011 C 0:018 7 7C: 5 0:092 A 0:123
(17)
4. Results The steady state is found numerically and the first-order conditions of the social planner’s problem are log-linearized around it. The resulting system of 28 linear difference equations7 is solved using the
5
Data on hours worked are not available for all countries. Backus et al. (1992) also omit capital from the calculation of technology shocks. They argue that this ‘‘is probably not a serious problem. Experience indicates that the short run variability of the capital stock is small and orthogonal to the cycle’’ (p. 759). 7 A technical appendix with the complete system is available from the author upon request. 6
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Table 6 Model standard deviations.
Output Consumption Labor Investment Tradable output Tradable labor Tradable consumption Nontradable output Nontradable labor Nontradable consumption Terms of trade Real exchange rate
Data (G-7 average)
4 ¼ 1, y ¼ 0
4 ¼ 1, y ¼ 24
4 ¼ 0.572, y ¼ 0
4 ¼ 0.572, y ¼ 24
2.11 2.35 1.57 5.90 4.30 2.79 2.54 2.16 1.52 1.58 4.87 6.64
3.02 2.37 1.93 5.54 4.12 2.93 3.19 2.59 2.58 2.66 3.32 2.14
3.06 2.43 1.96 5.56 3.78 2.21 3.14 2.63 2.03 2.69 3.38 2.71
2.91 2.27 1.84 5.18 4.22 3.60 2.81 2.74 1.96 2.98 6.43 4.65
2.96 2.39 1.89 5.25 3.86 2.63 2.90 2.82 1.84 3.01 6.42 5.17
method of King and Watson (2002). This algorithm automates the process of reducing a large, singular system to a solvable nonsingular system in a subset of the variables and solving it. For a given distribution of the exogenous variables – the technology and preference shocks – the moments of the endogenous variables as well as other variables that are functions of them can be found from the statespace form of the solution. Table 6 reports selected moments of the model. For comparison, Table 5 reports moments from annual data from the G-7 countries, over the period 1970–2004. Model moments are reported for four cases: (i) no labor mobility or distribution costs, (ii) labor mobility costs only, (iii) distribution costs only and (iv) both labor mobility and distribution costs. There is no obvious empirical counterpart to y, the parameter governing labor mobility costs. The value used to generate the results in Table 6 (y ¼ 24), is based on Lee and Wolpin’s (2006) estimate that the cost to a worker of changing sectors is $9655, in 1983 dollars (the midpoint of their sample). In 1983, US per capita GDP was approximately $20,300, which implies a cost to an individual of changing sectors of 48% of a year’s income. Using the data on sectoral employment, the OECD average standard deviation of the fraction of the labor force in the tradable sector is 1.8%. If 1.8% of the population is changing sectors on average, this implies an overall annual loss of output of 0.855%, which is replicated in the model when y ¼ 24.8 With no distribution or labor mobility costs, the model generates a standard deviation of the real exchange rate of 2.14%, which is significantly less than the model’s output volatility of 3.02%. Introducing the labor mobility cost increases the volatility of the real exchange rate by 27%, to 2.71%, without significantly changing the behavior of the other aggregates. With distribution costs only, the standard deviation of the real exchange rate is 4.65%, and with both distribution and labor mobility costs, it is 5.17%, which is 1.75 times the volatility of output. More insight into the effects of these costs can be gained by examining the behavior of the component parts of the real exchange rate, which depends on several relative prices. Engel (1999) proposes the decomposition
b x2; q ¼ b x1 þ b
(18)
where x1 is the relative price of tradable goods between the two countries,
b P bT; b x1 ¼ b eþP T and x2 is proportional to the difference between countries in the relative price of nontradables,
8
Because of the uncertainty about this parameter, a much higher value is used in a robustness check below.
(19)
W.D. Craighead / Journal of International Money and Finance 28 (2009) 135–147
143
Table 7 Standard deviations of real exchange rate components.
x1 x2
4 ¼ 1, y ¼ 0
4 ¼ 1, y ¼ 24
4 ¼ 0.572, y ¼ 0
4 ¼ 0.572, y ¼ 24
1.26 1.28
1.28 2.22
3.77 0.96
3.97 1.38
b x 2 ¼ ð1 uÞ
h
i b b bT : b pN P pN P T
(20)
Engel (1999) argues that movements in real exchange rates are primarily due to movements in x1. Burstein et al. (2005) point out that Engel’s measures fail to separate the distribution cost component of tradable goods prices. When import and export price indexes are used to remove the influence of distribution costs in traded goods prices, they find that roughly 50% of real exchange movements at cyclical frequencies are attributable to x2. The results reported in Table 7 show that labor mobility costs increase real exchange rate volatility by increasing the volatility of the cross-country difference in relative price of nontradables (x2). The distribution costs act on the relative price of tradables between countries (x1). When both costs are present, both components contribute to real exchange rate volatility, but the contribution of the x1 component is larger. Introducing distribution costs actually dampens movements in x2, the component associated with the price of nontradable relative to tradable goods. This is because distribution costs introduce a nontradable component into the tradable goods price. To examine the sources of real exchange rate movements in response to particular shocks, the responses over 10 periods of the real exchange rate, x1 and x2 to each type of shock are presented in Figs. 1–4. In each figure, the upper left-side panel represents the case of no costs, the upper right-side panel is intersectoral adjustment costs only, the lower left-side panel is distribution costs only and the lower right-side panel is both costs.
0.50 0.40 0.30 0.20 0.10 0.00 -0.10
Percent
0.25 0.20 0.15 0.10 0.05 0.00 -0.05
Case 2: Intersectoral Adjustment Costs Only
1
2
3
4
5
6
7
8
9
10
0.30 0.25 0.20 0.15 0.10 0.05 0.00
1
2
3
4
5
6
7
8
9
10
Year
Year
Case 3: Distribution Costs Only
Case 4: Intersectoral Adjustment and Distribution Costs 0.50
Percent
Percent
Percent
Case 1: No Costs
1
2
3
4
5
6
7
8
9
0.40 0.30 0.20 0.10 0.00
10
1
2
3
4
Year
5
6
Year q
x1
x2
Fig. 1. Response to 1% home tradable sector productivity increase.
7
8
9
10
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W.D. Craighead / Journal of International Money and Finance 28 (2009) 135–147
0.50 0.40 0.30 0.20 0.10 0.00
Percent
0.25 0.20 0.15 0.10 0.05 0.00 -0.05
Case 2: Intersectoral Adjustment Costs Only
1
2
3
4
5
6
7
8
9
10
1
0.25 0.20 0.15 0.10 0.05 0.00
1
2
3
4
5
6
7
8
9
10
Year
Year
Case 3: Distribution Costs Only
Case 4: Intersectoral Adjustment and Distribution Costs Percent
Percent
Percent
Case 1: No Costs
2
3
4
5
6
7
8
9
10
0.50 0.40 0.30 0.20 0.10 0.00
1
2
3
4
Year
5
6
7
8
9
10
Year q
x1
x2
Fig. 2. Response to 1% home nontradable sector productivity increase.
Fig. 1 presents responses to a one-percent home tradable sector productivity increase. In the absence of adjustment costs, home will reallocate some labor to nontradable goods production, since tradable and nontradable goods are complements. When adjustment costs impede the reallocation of resources, the relative price movement is larger, generating a larger movement in x2, which can be seen by comparing the left-side panels to the right-side panels. Comparing upper
0.10 0.08 0.06 0.04 0.02 0.00
Percent
0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -0.02
Case 2: Intersectoral Adjustment Costs Only
1
2
3
4
5
6
7
8
9
10
1
0.25 0.20 0.15 0.10 0.05 0.00 -0.05
1
2
3
4
5
6
7
8
9
10
Year
Year
Case 3: Distribution Costs Only
Case 4: Intersectoral Adjustment and Distribution Costs Percent
Percent
Percent
Case 1: No Costs
2
3
4
5
6
7
8
9
10
0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00
1
2
3
4
Year
5
6
Year q
x1
x2
Fig. 3. Response to 1% home tradables relative demand (u) shock.
7
8
9
10
W.D. Craighead / Journal of International Money and Finance 28 (2009) 135–147
Case 1: No Costs
Case 2: Intersectoral Adjustment Costs Only
0.05 0.00
1
2
3
4
5
6
7
8
9
10
Percent
Percent
0.10
-0.05 -0.10
0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15
1
2
3
4
5
6
7
8
9
10
Year
Year
Case 3: Distribution Costs Only
Case 4: Intersectoral Adjustment and Distribution Costs
1
2
3
4
5
6
7
8
9
10
Percent
Percent
-0.15
0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08
145
0.08 0.06 0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08
1
2
Year
3
4
5
6
7
8
9
10
Year q
x1
x2
Fig. 4. Response to 1% home domestic tradables relative demand (h) shock.
with lower panels shows that distribution costs amplify the change in the relative price of tradable goods between countries (x1) and this is the main source of the real exchange rate movement. The responses to a one-percent home nontradable sector productivity increase are shown in Fig. 2. Without distribution costs, the main source of real exchange rate dynamics is the movement in x2 because the relative price of nontradables falls in home. Introducing distribution costs leads to an increase in x1 because the change in the relative price of home nontradables affects the distribution component of the home tradables. Distribution costs nearly double the magnitude of the real exchange rate response to the shock. Fig. 3 shows that, without distribution costs, the increase in the real exchange rate following a one-percent increase in the weight on tradables (u) in the home consumption bundle is driven by x2. The movement in x2 due to the larger relative demand change when it is costly to reallocate labor between sectors. Comparing upper to lower panels shows that the effect of distribution costs dampening the movement in x2 is strong enough to reduce the overall response of the real exchange rate to the shock. The real exchange rate movement resulting from a one-percent increase in the weight on domestic tradables (h) in the home tradable consumption aggregate is quite small, as shown in Fig. 4. The main effect of the increase in demand for the home tradable good is to increase the price of tradables in home. The negative effect of this on x1 and the positive effect on x2 partially cancel Table 8 Model standard deviations, productivity shocks only.
Output Consumption Labor Real exchange rate x1 x2
4 ¼ 1, y ¼ 0
4 ¼ 1, y ¼ 24
4 ¼ 0.572, y ¼ 0
4 ¼ 0.572, y ¼ 24
2.99 2.36 1.92 2.07 0.98 0.95
3.03 2.42 1.95 2.59 0.91 1.76
2.89 2.25 1.83 4.59 3.69 0.93
2.95 2.38 1.88 5.13 3.92 1.25
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Table 9 Model standard deviations, s ¼ 3.
Output Consumption Labor Real exchange rate x1 x2
4 ¼ 1, y ¼ 0
4 ¼ 1, y ¼ 24
4 ¼ 0.572, y ¼ 0
4 ¼ 0.572, y ¼ 24
2.95 2.30 1.89 1.57 0.71 1.18
3.02 2.39 1.94 2.42 0.71 2.20
2.77 2.00 1.73 3.44 2.68 0.83
2.90 2.24 1.83 4.53 3.23 1.39
each other out. Note that the presence of distribution costs does lead to a bigger movement in both components. 5. Robustness Dynamics in real business cycle models are traditionally generated with productivity shocks. Table 8 reports some of the standard deviations of the model without the preference shocks. Since the technology shocks generate most of the model dynamics, the results are similar when the preference shocks are excluded. There is little consensus in the literature regarding the elasticity of substitution between domestic and imported tradables (s). A value of 1.5 was used above, following earlier literature. However, as discussed in Anderson and van Wincoop (2004), estimates at a less aggregated level generally find a higher elasticity. To test the effect of increasing the elasticity, the model properties are reexamined with s ¼ 3. The results reported in Table 9 show that increasing the elasticity reduces real exchange rate volatility, but does not alter the basic result regarding the effects of intersectoral labor mobility costs and distribution costs. As discussed above, it is unclear how costly it is to reallocate labor between sectors. Table 10 reports model moments with a much higher degree of intersectoral adjustment costs (y ¼ 1000). This change results in a significant increase in real exchange rate volatility. 6. Conclusion The volatility of real exchange rates has acquired the status of a ‘‘puzzle’’ in macroeconomics. This paper demonstrates that a two-country general equilibrium model generates substantially more real exchange rate volatility when two plausible types of rigidity – intersectoral adjustment costs and distribution costs – are included. The examination of impulse responses for productivity and preference shocks illustrates that the mechanism depends on the type of shock. It is beyond the scope of this research to take a position on the true nature of the shock process driving the economy. Certainly, a natural extension would be to incorporate intersectoral adjustment and distribution costs into a framework which includes monetary shocks. The significant increase in real exchange rate volatility when the costs are included suggests that real exchange rate volatility may be less puzzling than previously thought.
Table 10 Model standard deviations, y ¼ 1000.
Output Consumption Labor Real exchange rate x1 x2
4¼1
4 ¼ 0.572
3.09 2.54 2.00 3.48 1.21 3.10
3.05 2.64 1.98 6.22 4.40 1.97
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Acknowledgements This paper is based on a chapter of my Ph.D. dissertation at the University of Virginia. It benefited from numerous suggestions by my advisors, Christopher Otrok and Eric van Wincoop. I am also grateful to Marco Cagetti, George Davis, Ben Keen, Norm Miller, Gregor Smith, Frank Warnock and an anonymous referee as well as seminar participants at Miami University, Ohio Wesleyan University, Sewanee, the U.S. Treasury Department, the University of Virginia, Western Washington University and the Southern Economic Association for their comments. Any errors are my own, of course. Financial support from the Bankard Fund for Political Economy at the University of Virginia is gratefully acknowledged. References Anderson, J.E., van Wincoop, E., 2004. Trade costs. Journal of Economic Literature 42, 691–751. Backus, D.K., Kehoe, P.J., Kydland, F.E., 1992. International real business cycles. Journal of Political Economy 100, 745–775. Backus, D.K., Kehoe, P.J., Kydland, F.E., 1994. Dynamics of the trade balance and the terms of trade: the J-curve? American Economic Review 84, 84–103. Burgess, S.M., Dolado, J.J., 1989. Intertemporal rules with variable speed of adjustment: an application to U.K. manufacturing employment. Economic Journal 99, 347–365. Burstein, A.T., Neves, J.C., Rebelo, S., 2003. Distribution costs and real exchange rate dynamics during exchange rate-based stabilizations. Journal of Monetary Economics 50, 1189–1214. Burstein, A.T., Eichenbaum, M., Rebelo, S., 2005. The importance of nontradable goods prices in cyclical real exchange rate fluctuations. NBER Working Paper 11699. Chari, V.V., Kehoe, P.J., McGrattan, E.R., 2002. Can sticky price models generate volatile and persistent real exchange rates? Review of Economic Studies 69, 533–563. de Cordoba, G.F., Kehoe, T.J., 2002. Capital flows and real exchange rate fluctuations following Spain’s entry into the European Community. Journal of International Economics 51, 49–78. Corsetti, G., Dedola, L., Leduc, S., 2008. International risk sharing and the transmission of productivity shocks. Review of Economic Studies 75, 443–473. Davidson, C., Matusz, S.J., 2004. Should policy makers be concerned about adjustment costs? In: Mitra, D., Panagariya, A. (Eds.), The Political Economy of Trade, Aid and Foreign Investment Policies. Elsevier, pp. 31–68. Dornbusch, R., 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84, 1161–1176. Engel, C., 1999. Accounting for U.S. real exchange rate changes. Journal of Political Economy 107, 507–538. Fair, R.C., 1985. Excess labor and the business cycle. American Economic Review 75, 239–245. Fay, J.A., Medoff, J.L., 1985. Labor and output over the business cycle: some direct evidence. American Economic Review 75, 638–655. Gavin, M., 1990. Structural adjustment to a terms of trade disturbance: the role of relative prices. Journal of International Economics 28, 217–243. King, R.G., Watson, M.W., 2002. System reduction and solution algorithms for singular linear difference systems under rational expectations. Computational Economics 20, 57–86. Lee, D., Wolpin, K.I., 2006. Intersectoral labor mobility and the growth of the service sector. Econometrica 74, 1–46. Morshed, A.K.M.M., Turnovsky, S.J., 2004. Sectoral adjustment costs and real exchange rate dynamics in a two-sector dependent economy. Journal of International Economics 63, 147–177. Mussa, M., 1978. Dynamic adjustment in the Hecksher–Ohlin–Samuelson model. Journal of Political Economy 86, 775–791. Obstfeld, M., Rogoff, K., 2000. The six major puzzles in international economics: is there a common cause? NBER Macroeconomics Annual 15, 339–390. Pfann, G.A., Palm, F.C., 1993. Asymmetric adjustment costs in non-linear labour demand models for the Netherlands and U.K. manufacturing sectors. Review of Economic Studies 60, 397–412. Stockman, A.C., Tesar, L.L., 1995. Tastes and technology in a two-country model of the business cycle: explaining international comovements. American Economic Review 85, 168–185.
Contents lists available at ScienceDirect
Journal of International Money and Finance journal homepage: www.elsevier.com/locate/jimf
Real rigidities and real exchange rate volatility William D. Craighead* Department of Economics, Farmer School of Business, Miami University, 208 Laws Hall, Oxford, OH 45056, USA
a b s t r a c t JEL classification: E1 F4 Key words: Real exchange rates Intersectoral adjustment costs Distribution costs
This paper shows that certain real rigidities can help explain high volatility of real exchange rates relative to other macroeconomic aggregates. An international real business cycle model is used to demonstrate that real exchange rate volatility increases if (i) it is costly to move labor between sectors and (ii) the consumption of tradable goods requires distribution services. Model dynamics are generated by shocks to productivity and preferences based on sectoral output, employment and consumption data from G-7 countries. The introduction of intersectoral adjustment and distribution costs substantially increases the real exchange rate volatility generated by the model. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Real exchange rates are highly volatile relative to other macroeconomic variables. Table 1 reports the average annual percentage standard deviation of real exchange rates relative to output for the G-7 for the period 1970–2004. On average, the real effective exchange rate is 3.15 times as volatile as output. Economists have struggled to account for this ‘‘excess volatility.’’ In the words of Obstfeld and Rogoff (2000, p. 380), ‘‘exchange rates are remarkably volatile relative to any model we have of underlying fundamentals such as interest rates, outputs and money supplies.’’ Chari et al. (2002, p. 533) describe the volatility and persistence of real exchange rates as ‘‘the central puzzle in international business cycles.’’ One approach to this issue, pioneered by Dornbusch’s (1976) ‘‘overshooting’’ model, emphasizes nominal rigidities and monetary shocks. Chari et al. (2002) implement this idea in a calibrated, two-
* Tel.: þ1 513 529 2849; fax: þ1 513 529 8047. E-mail address: [email protected] 0261-5606/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jimonfin.2008.08.012
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Table 1 Standard deviations relative to output, 1970–2004a.
Canada France Germany Italy Japan United Kingdom United States G-7 average a
REER
RER vs. US
2.52 2.02 1.99 4.36 3.57 3.24 4.36 3.15
2.76 11.20 7.83 9.84 5.22 4.63 – 6.91
Data: OECD main economic indicators. All data are HP-filtered.
country dynamic general equilibrium model with sticky prices. They are able to match the volatility of the real exchange rate, but only by assuming a high degree of risk aversion. This paper explores an alternative approach based on real rigidities. It demonstrates that real exchange rates become considerably more volatile when it is costly to move factors of production between sectors, and when consumption of tradable goods requires nontradable distribution services. The international real business cycle framework developed by Backus et al. (1992) and extended by Stockman and Tesar (1995) is used to examine the effect of distribution costs and intersectoral labor mobility costs on the real exchange rate. Since the intuition is based entirely on relative prices and real costs, money and nominal rigidities are ignored, but the ideas explored here may be viewed as complementary to theories that rely on nominal rigidities. In addition to the standard productivity shocks, preference shocks are introduced to allow consideration of the effects of changes on the demand side of the economy in a nonmonetary framework. Introducing intersectoral labor mobility and distribution costs causes the standard deviation of the real exchange rate to more than double, increasing from 2.14% to 5.17%. The channels through which real exchange rate movements are affected by real rigidities are investigated by decomposing them into the portions due to the relative price of tradable goods between countries and the relative price of nontradable goods within each country. The effects of the individual shocks are examined by considering the impulse response functions generated by sectoral productivity and relative demand shocks. The intuition motivating the introduction of costly intersectoral factor movements is relatively simple. Real exchange rates are functions of relative prices. If it is costly to change quantities by reallocating inputs, relative prices will move more. To illustrate, consider a shock that increases the demand for tradable goods. The change in demand raises the relative price of tradables. In the absence of adjustment costs, factors of production would instantly move from the nontradable sector into the tradable sector, increasing the relative supply of tradables, and lowering the price. With adjustment costs, supply does not respond as much and the relative price of tradables remains elevated. Distribution costs also amplify relative price movements in an intuitively straightforward manner. With distribution costs, when consumers purchase goods, they are also purchasing nontradable services, like retailing. The retail price reflects both the good and service inputs. In order to achieve a given change in retail relative prices, the relative prices of the goods will need to change by a larger amount. Several strands of empirical research suggest that costs of reallocating labor between sectors may be substantial. The cost of adjusting labor inputs is reflected in the procyclical behavior of labor productivity known as ‘‘labor hoarding.’’ Based on surveys of employers, Fay and Medoff (1985) find that four percent of blue-collar hours should be classified as hoarded during downturns. Fair (1985) provides econometric estimates on aggregate US data consistent with Fay and Medoff’s evidence. Burgess and Dolado (1989) and Pfann and Palm (1993) estimate models of sluggish adjustment of labor inputs on UK data. Both find statistically significant adjustment costs. On the labor supply side, Lee and Wolpin (2006) estimate a dynamic model using survey data on individuals and find significant costs of moving between sectors.
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Two interesting applications of intersectoral adjustment costs in the international trade literature are Mussa (1978) and Davidson and Matusz (2004). Mussa (1978) analyzes the dynamics of the Hecksher–Ohlin–Samuelson model when it is costly to reallocate capital between sectors in response to a change in relative prices, which are taken as exogenous in his model. Davidson and Matusz (2004) examine the benefits of trade liberalization in the presence of intersectoral adjustment costs. They show that a significant portion of the benefits of liberalization may be offset by the costs associated with worker retraining. Several papers have examined real exchange rates in small open economy models with intersectoral adjustment costs. Gavin (1990) examines the dynamic response to a terms of trade shock in a model with nontradable goods and costs to reallocating capital. Capital adjustment costs play the same role of amplifying movements the price of tradable relative to nontradable goods as labor adjustment costs in this paper. Morshed and Turnovsky (2004) show that costs to moving capital between sectors generate persistent real exchange rate and current account dynamics in response to shocks to government expenditures and technology. de Cordoba and Kehoe (2002) employ intersectoral adjustment costs to help explain the movements of the real exchange rate and trade balance that occurred as Spain lifted restrictions on capital inflows after entering the European Community. Unlike those papers, the model presented here specifically addresses the standard deviation of the real exchange rate, and does so in the context of a two-country general equilibrium system where fluctuations in the terms of trade are generated endogenously from technology and preference shocks. Distribution costs are the other key feature of the model presented here. Burstein et al. (2003) argue that the nontradable components of tradable goods consumption are large. They use several sources of data to calculate the ‘‘distribution margin,’’ the difference between the retail and producer price, as a percentage of the retail price. For US personal consumption expenditures on tradable goods, they find a distribution margin of 43.4% using the input–output tables for 1997. For the other G-7 countries, the margin ranges from 35% (France) to 50% (Japan). In a model calibrated to match Argentina’s 1991 currency board, they show that accounting for distribution costs can help understand the movement of real exchange rates and relative prices following an exchange rate stabilization. Corsetti et al. (2008) use distribution costs to address the negative correlation between the terms of trade and relative consumption, which is contrary to international risk-sharing. They introduce distribution costs as a mechanism for reducing the share of imports in consumption and the elasticity of substitution between domestic and imported tradables. This allows their model to match the negative correlation between the terms of trade and relative consumption observed in the data.
2. Model Stockman and Tesar (1995) show that incorporating nontradable goods and taste shocks into a twocountry real business cycle model improves its ability to match certain empirical regularities such as cross-country output correlations and the correlation between trade balances and output. The model presented below builds on their framework by incorporating intersectoral labor adjustment costs and distribution costs. Two countries, ‘‘home’’ and ‘‘foreign,’’ each produce tradable and nontradable goods. Foreign variables are denoted with an asterisk. Capital letters denote consumption bundles and price indexes, and lower-case letters represent consumption and prices of specific goods. For simplicity, the preferences and technology for home are presented here; foreign is symmetric. Each country has a representative household that maximizes expected lifetime utility from consumption and leisure. The utility function has the form
E
N X t ¼0
bt
1 g C 1 ð1 Nt Þ1m ; 1g t
(1)
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Table 2 Baseline parameterization. Parameter
Value
Definition
b g m q s u h aN aT d
0.96 2 4.17 0.44 1.5 0.55 0.69 0.44 0.39 0.1
Discount factor Intertemporal elasticity of substitution (consumption) Intertemporal elasticity of substitution (labor) Elasticity of substitution between tradables and nontradables Elasticity of substitution between domestic and imported tradables Share of tradables in consumption bundle Share of domestic goods in tradable consumption Capital share (nontradable sector) Capital share (tradable sector) Depreciation rate
where N denotes labor and the consumption bundle, C, is a constant elasticity of substitution aggregate of tradable and nontradable goods,
i h ðq1Þ=q ðq1Þ=q q=ðq1Þ C ¼ ð1 uÞ1=q cN þ u1=q CT :
(2)
Tradable goods consumption, CT, is an aggregate of home-produced and imported tradable goods
i h ðs1Þ=s ðs1Þ=s ðs1Þ=s CT ¼ h1=s cT þ ð1 hÞ1=s cT :
(3)
The elasticity of substitution between tradable and nontradable goods is q; s is the elasticity of substitution between domestically produced and imported tradables; u is the weight on tradables in the consumption bundle; h is the weight on domestically produced tradables. The representative household allocates fractions sT and sN of its labor respectively to the tradable and nontradable sectors, with sT þ sN ¼ 1. Output in each sector is produced according to the function
yjt
¼
zjt
2 aj 1aj y sjt sjt1 j j kt st Nt ; 2 sjt
j ¼ T; N;
(4)
where z is technology, k is capital and sN is the total labor employed in the sector. The second term represents the cost of reallocating labor between sectors, with y governing the degree of costliness.1 The cost takes the form of lost output when the share of labor allocated to the sector is changed. Note that the cost is associated with changing the sectoral allocation rather than the overall amount of labor. Capital is sector-specific and each sector produces its own capital. Capital is accumulated according to j
j
j
ktþ1 ¼ it þ ð1 dÞkt ;
j ¼ T; N;
(5)
where i is investment and d is the depreciation rate. Distribution costs are introduced by assuming tradable consumption is a combination of a goods input produced by the tradable sector, and a service input produced by the nontradable sector. Distribution services take place in the same country as consumption. Home’s tradable sector produces
1 The functional form is chosen to be consistent with the existence of a large number of identical competitive firms in each sector. If there are M identical firms indexed by i,
2 M X y sit sit1 y ðst st1 Þ2 ¼ : 2 2 st sit i¼1
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Table 3 Share of tradable goods in consumptiona.
Canada, 1970–2003 France, 1978–2004 Germany, 1991–2004 Italy, 1970–2004 Japan, 1980–2003 United Kingdom, 1970–2001 United States, 1970–2003 a
Beginning
End
Average
0.59 0.66 0.61 0.68 0.56 0.70 0.55
0.49 0.53 0.53 0.50 0.43 0.52 0.40
0.54 0.59 0.56 0.61 0.50 0.61 0.47
Data: OECD annual national accounts.
goods for domestic and foreign consumption and the home nontradable sector produces nontradable consumption goods as well as the service input into home consumption of home- and foreignproduced tradables. One unit of tradable consumption is comprised of 4 units of goods and 1 4 units of services. The market-clearing conditions can be rewritten as and
yT ¼ 4cT þ 4cT
(6)
yN ¼ cN þ ð1 4ÞcT þ ð1 4ÞcT :
(7)
A complete set of state-contingent claims is assumed to be available for international asset trade, allowing the model to be solved as a social planner’s problem.
3. Parameterization The parameters used are reported in Table 2. The capital share parameters for the tradable and nontradable sectors and the depreciation rate are taken from Stockman and Tesar (1995). The levels of the technology parameters, z, are normalized so that all relative prices are unitary in the steady state. The discount factor and the utility curvature parameters are also taken from Stockman and Tesar (1995); the curvature on leisure, m, is set so that 20% of the time endowment is devoted to labor in the steady state. The consumption bundle includes two elasticities. The elasticity of substitution between tradables and nontradables is estimated by Stockman and Tesar (1995) to be 0.44. Based on an examination of relevant empirical literature, Backus et al. (1994) choose a value of 1.5 for the elasticity between domestic and imported tradables; this value is also used by Chari et al. (2002). The weighting parameters in the consumption bundles are chosen based on OECD annual national accounts data. This database includes household final consumption broken into services, durable and nondurable goods components. Table 3 reports the shares of tradable goods in consumption for the G7; the average share is 0.55, which is used for the weighting parameter u. The share of imports in tradable consumption is proxied by multiplying imports of goods by the share of GDP devoted to household consumption and dividing by total household consumption of durable and nondurable goods. The average of the import shares reported in Table 4 is 0.31; h is set to 0.69 to match this in the model. 2 A process for the demand shocks is derived using some properties of the CES structure of the consumption bundles. The functional form implies that total home expenditure on imported tradable goods, xT , is
2 The share of tradables (i.e. durable and nondurable goods) in consumption has fallen while the import share has risen. Because the model is stationary, these dynamics are not accounted for here, but the effects of these trends may merit consideration in future research.
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Table 4 Share of imports in tradable goods consumptiona.
Canada, 1970–2003 France, 1978–2004 Germany, 1991–2004 Italy, 1970–2004 Japan, 1980–2003 United Kingdom, 1970–2001 United States, 1970–2003 a
Beginning
End
Average
0.27 0.24 0.38 0.18 0.22 0.23 0.07
0.59 0.39 0.55 0.39 0.19 0.46 0.29
0.45 0.32 0.43 0.28 0.15 0.36 0.19
Data: OECD annual national accounts.
1s p xT ¼ ð1 hÞ T XT ; PT
(8)
where XT is total expenditure on tradables. Log-linearization gives
b x T ¼
h 1h
b h þ ð1 sÞ bp T Pb T þ Xb T ;
(9)
where the carets denote percentage deviations. This can be rearranged to yield an equation for the deviation in the share of domestic goods in the tradable bundle,
1 hh
b h ¼
h
i b X b : b x T ð1 sÞ b p T P T
(10)
Similarly, expenditure on nontradable goods, xN, is related to total consumption expenditure, X, by
p 1q xN ¼ ð1 uÞ N X: P
(11)
This can be log-linearized and rearranged to give
b ¼ u
1 uh
u
i b X b : b x N ð1 qÞ b pN P
(12)
Expenditure on durable and nondurable goods is used for XT. Nontradable expenditure, xN, is expenditure on services, xT is imports of goods, and X is household final consumption expenditure. Prices are the corresponding deflators. The data are from the OECD annual national accounts. The series are HP-filtered and the percentage deviations from trend are applied to the above formulas. Data are available to estimate preference shock processes for Canada and the US for the period 1970–2003, Italy (1970–2004)3 and France (1978–2004). The average estimated process is
bt u b ht
¼
0:494 0:019
0:279 0:459
"
#
b t1 u þ 3t ; b h t1
(13)
where
3t wN ½0;
1 0:069 1000 0:034
0:034 0:605
:
(14)
In the model, home and foreign preference shocks are assumed to be independent and to behave according to this process.4
3
Several outlier observations at the beginning of the series were discarded. It would be preferable to jointly estimate a US and European process; however, the requisite data are not available for two of four European G-7 economies. 4
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Table 5 Standard deviations of selected aggregates, 1970–2004a.
Output Labor Consumption Investment Tradable output Tradable labor Tradable consumption Nontradable output Nontradable labor Nontradable consumption Terms of trade REER RER vs. US
Canada
France
Germany
Italy
Japan
UK
US
2.57 1.91 2.79 6.37 7.43 3.41 3.86 2.08 1.67 2.10 3.41 6.50 7.09
1.45 1.23 1.66 5.46 2.81 1.84 1.99 1.69 1.11 1.45 3.75 2.93 16.24
2.17 1.43 2.36 5.24 3.24 3.33 – 1.76 1.08 – 3.74 4.31 16.99
1.51 1.44 2.04 4.50 4.13 2.15 2.51 1.51 1.86 1.14 5.37 6.59 14.59
2.54 1.11 2.32 6.51 4.19 1.96 2.53 2.42 1.23 1.81 10.01 9.08 13.02
2.42 2.19 3.18 6.55 4.36 3.62 – 3.32 2.16 – 4.03 7.83 10.63
2.12 1.69 2.09 6.70 3.92 3.19 1.84 2.33 1.53 1.39 3.82 9.25 –
a Data: OECD annual national accounts (output, consumption, investment, tradable consumption, nontradable consumption, terms of trade), OECD STAN database (labor, tradable output, tradable labor nontradable output, nontradable labor), OECD main economic indicators (real effective exchange rate, real exchange rate vs. US).
The technology shock process is estimated using annual data from the OECD STAN database for industrial analysis for 1978–2003. The two countries are US and Europe, where Europe is a weighted average of Germany (0.31), France (0.23), Italy (0.23) and the UK (0.23). The tradable sector is proxied by total manufacturing (ISIC 15–37) and total services (ISIC 50–99) is used to represent nontradables.The productivity shock for each sector is
b ð1 aÞb bz ¼ Y L:
(15)
Volume indexes of value added are used for output. Labor is total employment in each sector.5 Capital stock data are not available for all countries, so they are omitted.6 The technology shock process is estimated on HP-filtered data. Terms of the estimated process are averaged to give the symmetric process used in to generate the moments of the model:
2
3 T b z 6 t 7 6 bN 7 6 zt 7 6 T 7 ¼ 6 bz t 7 4 5 bz N t
2
0:494 6 0:085 6 4 0:113 0:359
0:035 0:503 0:099 0:029
3 2 3 bT z 0:113 0:099 6 t1 7 6 bN 7 z 0:359 0:029 7 7 76 þ 3t ; 6 t1 T 7 5 0:494 0:035 6 b 7 z 5 4 t1 0:085 0:503 N b z t1
(16)
where
0
2 0:452 B 6 0:092 1 6 3t wNB @½0; 10004 0:132 0:011
0:092 0:123 0:011 0:018
0:132 0:011 0:452 0:092
31 0:011 C 0:018 7 7C: 5 0:092 A 0:123
(17)
4. Results The steady state is found numerically and the first-order conditions of the social planner’s problem are log-linearized around it. The resulting system of 28 linear difference equations7 is solved using the
5
Data on hours worked are not available for all countries. Backus et al. (1992) also omit capital from the calculation of technology shocks. They argue that this ‘‘is probably not a serious problem. Experience indicates that the short run variability of the capital stock is small and orthogonal to the cycle’’ (p. 759). 7 A technical appendix with the complete system is available from the author upon request. 6
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Table 6 Model standard deviations.
Output Consumption Labor Investment Tradable output Tradable labor Tradable consumption Nontradable output Nontradable labor Nontradable consumption Terms of trade Real exchange rate
Data (G-7 average)
4 ¼ 1, y ¼ 0
4 ¼ 1, y ¼ 24
4 ¼ 0.572, y ¼ 0
4 ¼ 0.572, y ¼ 24
2.11 2.35 1.57 5.90 4.30 2.79 2.54 2.16 1.52 1.58 4.87 6.64
3.02 2.37 1.93 5.54 4.12 2.93 3.19 2.59 2.58 2.66 3.32 2.14
3.06 2.43 1.96 5.56 3.78 2.21 3.14 2.63 2.03 2.69 3.38 2.71
2.91 2.27 1.84 5.18 4.22 3.60 2.81 2.74 1.96 2.98 6.43 4.65
2.96 2.39 1.89 5.25 3.86 2.63 2.90 2.82 1.84 3.01 6.42 5.17
method of King and Watson (2002). This algorithm automates the process of reducing a large, singular system to a solvable nonsingular system in a subset of the variables and solving it. For a given distribution of the exogenous variables – the technology and preference shocks – the moments of the endogenous variables as well as other variables that are functions of them can be found from the statespace form of the solution. Table 6 reports selected moments of the model. For comparison, Table 5 reports moments from annual data from the G-7 countries, over the period 1970–2004. Model moments are reported for four cases: (i) no labor mobility or distribution costs, (ii) labor mobility costs only, (iii) distribution costs only and (iv) both labor mobility and distribution costs. There is no obvious empirical counterpart to y, the parameter governing labor mobility costs. The value used to generate the results in Table 6 (y ¼ 24), is based on Lee and Wolpin’s (2006) estimate that the cost to a worker of changing sectors is $9655, in 1983 dollars (the midpoint of their sample). In 1983, US per capita GDP was approximately $20,300, which implies a cost to an individual of changing sectors of 48% of a year’s income. Using the data on sectoral employment, the OECD average standard deviation of the fraction of the labor force in the tradable sector is 1.8%. If 1.8% of the population is changing sectors on average, this implies an overall annual loss of output of 0.855%, which is replicated in the model when y ¼ 24.8 With no distribution or labor mobility costs, the model generates a standard deviation of the real exchange rate of 2.14%, which is significantly less than the model’s output volatility of 3.02%. Introducing the labor mobility cost increases the volatility of the real exchange rate by 27%, to 2.71%, without significantly changing the behavior of the other aggregates. With distribution costs only, the standard deviation of the real exchange rate is 4.65%, and with both distribution and labor mobility costs, it is 5.17%, which is 1.75 times the volatility of output. More insight into the effects of these costs can be gained by examining the behavior of the component parts of the real exchange rate, which depends on several relative prices. Engel (1999) proposes the decomposition
b x2; q ¼ b x1 þ b
(18)
where x1 is the relative price of tradable goods between the two countries,
b P bT; b x1 ¼ b eþP T and x2 is proportional to the difference between countries in the relative price of nontradables,
8
Because of the uncertainty about this parameter, a much higher value is used in a robustness check below.
(19)
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Table 7 Standard deviations of real exchange rate components.
x1 x2
4 ¼ 1, y ¼ 0
4 ¼ 1, y ¼ 24
4 ¼ 0.572, y ¼ 0
4 ¼ 0.572, y ¼ 24
1.26 1.28
1.28 2.22
3.77 0.96
3.97 1.38
b x 2 ¼ ð1 uÞ
h
i b b bT : b pN P pN P T
(20)
Engel (1999) argues that movements in real exchange rates are primarily due to movements in x1. Burstein et al. (2005) point out that Engel’s measures fail to separate the distribution cost component of tradable goods prices. When import and export price indexes are used to remove the influence of distribution costs in traded goods prices, they find that roughly 50% of real exchange movements at cyclical frequencies are attributable to x2. The results reported in Table 7 show that labor mobility costs increase real exchange rate volatility by increasing the volatility of the cross-country difference in relative price of nontradables (x2). The distribution costs act on the relative price of tradables between countries (x1). When both costs are present, both components contribute to real exchange rate volatility, but the contribution of the x1 component is larger. Introducing distribution costs actually dampens movements in x2, the component associated with the price of nontradable relative to tradable goods. This is because distribution costs introduce a nontradable component into the tradable goods price. To examine the sources of real exchange rate movements in response to particular shocks, the responses over 10 periods of the real exchange rate, x1 and x2 to each type of shock are presented in Figs. 1–4. In each figure, the upper left-side panel represents the case of no costs, the upper right-side panel is intersectoral adjustment costs only, the lower left-side panel is distribution costs only and the lower right-side panel is both costs.
0.50 0.40 0.30 0.20 0.10 0.00 -0.10
Percent
0.25 0.20 0.15 0.10 0.05 0.00 -0.05
Case 2: Intersectoral Adjustment Costs Only
1
2
3
4
5
6
7
8
9
10
0.30 0.25 0.20 0.15 0.10 0.05 0.00
1
2
3
4
5
6
7
8
9
10
Year
Year
Case 3: Distribution Costs Only
Case 4: Intersectoral Adjustment and Distribution Costs 0.50
Percent
Percent
Percent
Case 1: No Costs
1
2
3
4
5
6
7
8
9
0.40 0.30 0.20 0.10 0.00
10
1
2
3
4
Year
5
6
Year q
x1
x2
Fig. 1. Response to 1% home tradable sector productivity increase.
7
8
9
10
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0.50 0.40 0.30 0.20 0.10 0.00
Percent
0.25 0.20 0.15 0.10 0.05 0.00 -0.05
Case 2: Intersectoral Adjustment Costs Only
1
2
3
4
5
6
7
8
9
10
1
0.25 0.20 0.15 0.10 0.05 0.00
1
2
3
4
5
6
7
8
9
10
Year
Year
Case 3: Distribution Costs Only
Case 4: Intersectoral Adjustment and Distribution Costs Percent
Percent
Percent
Case 1: No Costs
2
3
4
5
6
7
8
9
10
0.50 0.40 0.30 0.20 0.10 0.00
1
2
3
4
Year
5
6
7
8
9
10
Year q
x1
x2
Fig. 2. Response to 1% home nontradable sector productivity increase.
Fig. 1 presents responses to a one-percent home tradable sector productivity increase. In the absence of adjustment costs, home will reallocate some labor to nontradable goods production, since tradable and nontradable goods are complements. When adjustment costs impede the reallocation of resources, the relative price movement is larger, generating a larger movement in x2, which can be seen by comparing the left-side panels to the right-side panels. Comparing upper
0.10 0.08 0.06 0.04 0.02 0.00
Percent
0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -0.02
Case 2: Intersectoral Adjustment Costs Only
1
2
3
4
5
6
7
8
9
10
1
0.25 0.20 0.15 0.10 0.05 0.00 -0.05
1
2
3
4
5
6
7
8
9
10
Year
Year
Case 3: Distribution Costs Only
Case 4: Intersectoral Adjustment and Distribution Costs Percent
Percent
Percent
Case 1: No Costs
2
3
4
5
6
7
8
9
10
0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00
1
2
3
4
Year
5
6
Year q
x1
x2
Fig. 3. Response to 1% home tradables relative demand (u) shock.
7
8
9
10
W.D. Craighead / Journal of International Money and Finance 28 (2009) 135–147
Case 1: No Costs
Case 2: Intersectoral Adjustment Costs Only
0.05 0.00
1
2
3
4
5
6
7
8
9
10
Percent
Percent
0.10
-0.05 -0.10
0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15
1
2
3
4
5
6
7
8
9
10
Year
Year
Case 3: Distribution Costs Only
Case 4: Intersectoral Adjustment and Distribution Costs
1
2
3
4
5
6
7
8
9
10
Percent
Percent
-0.15
0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08
145
0.08 0.06 0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08
1
2
Year
3
4
5
6
7
8
9
10
Year q
x1
x2
Fig. 4. Response to 1% home domestic tradables relative demand (h) shock.
with lower panels shows that distribution costs amplify the change in the relative price of tradable goods between countries (x1) and this is the main source of the real exchange rate movement. The responses to a one-percent home nontradable sector productivity increase are shown in Fig. 2. Without distribution costs, the main source of real exchange rate dynamics is the movement in x2 because the relative price of nontradables falls in home. Introducing distribution costs leads to an increase in x1 because the change in the relative price of home nontradables affects the distribution component of the home tradables. Distribution costs nearly double the magnitude of the real exchange rate response to the shock. Fig. 3 shows that, without distribution costs, the increase in the real exchange rate following a one-percent increase in the weight on tradables (u) in the home consumption bundle is driven by x2. The movement in x2 due to the larger relative demand change when it is costly to reallocate labor between sectors. Comparing upper to lower panels shows that the effect of distribution costs dampening the movement in x2 is strong enough to reduce the overall response of the real exchange rate to the shock. The real exchange rate movement resulting from a one-percent increase in the weight on domestic tradables (h) in the home tradable consumption aggregate is quite small, as shown in Fig. 4. The main effect of the increase in demand for the home tradable good is to increase the price of tradables in home. The negative effect of this on x1 and the positive effect on x2 partially cancel Table 8 Model standard deviations, productivity shocks only.
Output Consumption Labor Real exchange rate x1 x2
4 ¼ 1, y ¼ 0
4 ¼ 1, y ¼ 24
4 ¼ 0.572, y ¼ 0
4 ¼ 0.572, y ¼ 24
2.99 2.36 1.92 2.07 0.98 0.95
3.03 2.42 1.95 2.59 0.91 1.76
2.89 2.25 1.83 4.59 3.69 0.93
2.95 2.38 1.88 5.13 3.92 1.25
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Table 9 Model standard deviations, s ¼ 3.
Output Consumption Labor Real exchange rate x1 x2
4 ¼ 1, y ¼ 0
4 ¼ 1, y ¼ 24
4 ¼ 0.572, y ¼ 0
4 ¼ 0.572, y ¼ 24
2.95 2.30 1.89 1.57 0.71 1.18
3.02 2.39 1.94 2.42 0.71 2.20
2.77 2.00 1.73 3.44 2.68 0.83
2.90 2.24 1.83 4.53 3.23 1.39
each other out. Note that the presence of distribution costs does lead to a bigger movement in both components. 5. Robustness Dynamics in real business cycle models are traditionally generated with productivity shocks. Table 8 reports some of the standard deviations of the model without the preference shocks. Since the technology shocks generate most of the model dynamics, the results are similar when the preference shocks are excluded. There is little consensus in the literature regarding the elasticity of substitution between domestic and imported tradables (s). A value of 1.5 was used above, following earlier literature. However, as discussed in Anderson and van Wincoop (2004), estimates at a less aggregated level generally find a higher elasticity. To test the effect of increasing the elasticity, the model properties are reexamined with s ¼ 3. The results reported in Table 9 show that increasing the elasticity reduces real exchange rate volatility, but does not alter the basic result regarding the effects of intersectoral labor mobility costs and distribution costs. As discussed above, it is unclear how costly it is to reallocate labor between sectors. Table 10 reports model moments with a much higher degree of intersectoral adjustment costs (y ¼ 1000). This change results in a significant increase in real exchange rate volatility. 6. Conclusion The volatility of real exchange rates has acquired the status of a ‘‘puzzle’’ in macroeconomics. This paper demonstrates that a two-country general equilibrium model generates substantially more real exchange rate volatility when two plausible types of rigidity – intersectoral adjustment costs and distribution costs – are included. The examination of impulse responses for productivity and preference shocks illustrates that the mechanism depends on the type of shock. It is beyond the scope of this research to take a position on the true nature of the shock process driving the economy. Certainly, a natural extension would be to incorporate intersectoral adjustment and distribution costs into a framework which includes monetary shocks. The significant increase in real exchange rate volatility when the costs are included suggests that real exchange rate volatility may be less puzzling than previously thought.
Table 10 Model standard deviations, y ¼ 1000.
Output Consumption Labor Real exchange rate x1 x2
4¼1
4 ¼ 0.572
3.09 2.54 2.00 3.48 1.21 3.10
3.05 2.64 1.98 6.22 4.40 1.97
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Acknowledgements This paper is based on a chapter of my Ph.D. dissertation at the University of Virginia. It benefited from numerous suggestions by my advisors, Christopher Otrok and Eric van Wincoop. I am also grateful to Marco Cagetti, George Davis, Ben Keen, Norm Miller, Gregor Smith, Frank Warnock and an anonymous referee as well as seminar participants at Miami University, Ohio Wesleyan University, Sewanee, the U.S. Treasury Department, the University of Virginia, Western Washington University and the Southern Economic Association for their comments. Any errors are my own, of course. Financial support from the Bankard Fund for Political Economy at the University of Virginia is gratefully acknowledged. References Anderson, J.E., van Wincoop, E., 2004. Trade costs. Journal of Economic Literature 42, 691–751. Backus, D.K., Kehoe, P.J., Kydland, F.E., 1992. International real business cycles. Journal of Political Economy 100, 745–775. Backus, D.K., Kehoe, P.J., Kydland, F.E., 1994. Dynamics of the trade balance and the terms of trade: the J-curve? American Economic Review 84, 84–103. Burgess, S.M., Dolado, J.J., 1989. Intertemporal rules with variable speed of adjustment: an application to U.K. manufacturing employment. Economic Journal 99, 347–365. Burstein, A.T., Neves, J.C., Rebelo, S., 2003. Distribution costs and real exchange rate dynamics during exchange rate-based stabilizations. Journal of Monetary Economics 50, 1189–1214. Burstein, A.T., Eichenbaum, M., Rebelo, S., 2005. The importance of nontradable goods prices in cyclical real exchange rate fluctuations. NBER Working Paper 11699. Chari, V.V., Kehoe, P.J., McGrattan, E.R., 2002. Can sticky price models generate volatile and persistent real exchange rates? Review of Economic Studies 69, 533–563. de Cordoba, G.F., Kehoe, T.J., 2002. Capital flows and real exchange rate fluctuations following Spain’s entry into the European Community. Journal of International Economics 51, 49–78. Corsetti, G., Dedola, L., Leduc, S., 2008. International risk sharing and the transmission of productivity shocks. Review of Economic Studies 75, 443–473. Davidson, C., Matusz, S.J., 2004. Should policy makers be concerned about adjustment costs? In: Mitra, D., Panagariya, A. (Eds.), The Political Economy of Trade, Aid and Foreign Investment Policies. Elsevier, pp. 31–68. Dornbusch, R., 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84, 1161–1176. Engel, C., 1999. Accounting for U.S. real exchange rate changes. Journal of Political Economy 107, 507–538. Fair, R.C., 1985. Excess labor and the business cycle. American Economic Review 75, 239–245. Fay, J.A., Medoff, J.L., 1985. Labor and output over the business cycle: some direct evidence. American Economic Review 75, 638–655. Gavin, M., 1990. Structural adjustment to a terms of trade disturbance: the role of relative prices. Journal of International Economics 28, 217–243. King, R.G., Watson, M.W., 2002. System reduction and solution algorithms for singular linear difference systems under rational expectations. Computational Economics 20, 57–86. Lee, D., Wolpin, K.I., 2006. Intersectoral labor mobility and the growth of the service sector. Econometrica 74, 1–46. Morshed, A.K.M.M., Turnovsky, S.J., 2004. Sectoral adjustment costs and real exchange rate dynamics in a two-sector dependent economy. Journal of International Economics 63, 147–177. Mussa, M., 1978. Dynamic adjustment in the Hecksher–Ohlin–Samuelson model. Journal of Political Economy 86, 775–791. Obstfeld, M., Rogoff, K., 2000. The six major puzzles in international economics: is there a common cause? NBER Macroeconomics Annual 15, 339–390. Pfann, G.A., Palm, F.C., 1993. Asymmetric adjustment costs in non-linear labour demand models for the Netherlands and U.K. manufacturing sectors. Review of Economic Studies 60, 397–412. Stockman, A.C., Tesar, L.L., 1995. Tastes and technology in a two-country model of the business cycle: explaining international comovements. American Economic Review 85, 168–185.