Investment rates and the aggregate production function

European Economic Review 63 (2013) 150–169

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Investment rates and the aggregate production function Fernando García-Belenguer a,n, Manuel S. Santos b,1,2 a Departamento de Análisis Económico: T. Económica, Fac. CC. Económicas y Empresariales, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain b University of Miami, P.O. Box 248126, Coral Gables, FL 33124-6550, USA

a r t i c l e in f o

abstract

Article history: Received 11 January 2012 Accepted 29 June 2013 Available online 5 July 2013

In this paper we consider a simple version of the neoclassical growth model, and carry out an empirical analysis of the main determinants of aggregate investment across countries. The neoclassical growth model predicts that aggregate investment may be influenced by income growth, the capital income share, the relative price of capital, taxes, and other market distortions. We check these investment patterns for both OECD and non-OECD countries. We also decompose investment data into equipment and structures, and explore major factors affecting their relative prices. These empirical exercises shed light into the shape of the neoclassical production function. & 2013 Elsevier B.V. All rights reserved.

JEL classification: O41 O47 Keywords: Aggregate investment Aggregate production function Relative price of investment Factor income shares Market distortions

1. Introduction In this paper we are concerned with the determinants of aggregate investment across countries. We follow closely the analytical framework of the neoclassical growth model – a cornerstone in studies of economic growth since the early work of Solow (1956). Various quantitative exercises have singled out capital accumulation as a major factor in accounting for income levels (cf. Mankiw et al., 1992; Hall and Jones, 1999). There is, however, much more controversy about the influence of some other forces (e.g., Caselli, 2005; McGrattan and Schmitz, 1999) such as human capital and investments in technology adoption – which may affect total factor productivity (TFP). In most of this research the stock of physical capital is computed by a permanent inventory method using aggregate investment data as a primitive element in the analysis. Therefore, it is of great economic interest to delve into the ultimate reasons underlying world investment patterns. A basic tenet in the economic growth literature is that domestic investment rates are pretty constant across countries (cf. Summers and Heston, 1991; Hsieh and Klenow, 2007). Another well-known empirical regularity (cf. opt. cit.) is that there is a pronounced variability across countries in the relative price of capital which is inversely correlated with the income level. Thus, when adjusting GDP data by a common set of prices, real investment rates are much higher in rich countries. Consequently, rich countries display comparable nominal investment rates that get translated into higher real investment

n

Corresponding author. Tel.: +34 91 4972857; fax: +34 91 4978616. E-mail addresses: [email protected] (F. García-Belenguer), [email protected] (M.S. Santos). 1 Tel.: +1 305 284 3984; fax: +1 305 284 2985. 2 This research was partially funded by the Spanish Ministry of Education and Science through Research Project ECO2008-04073.

0014-2921/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.euroecorev.2013.06.007

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rates. This efficiency in capital accumulation is of course considered to be a major source of income disparity across countries. In spite of the low variability of nominal investment rates across countries, we cannot rule out the possibility that taxes and some other distortions matter for investment: There could be countervailing forces that make countries experience similar nominal investment rates. Indeed, taxes are usually higher in OECD countries, but non-OECD countries may endure further non-pecuniary distortions. Hence, the presumed stability of the share of nominal investment across groups of countries and time periods may conceal some other growth trends. For instance, when decomposing investment data into equipment and structures we find a rather weak correlation between these two sub-aggregates. We also observe substantial variation in the relative price of equipment across countries, but much less variation in the relative price of structures. Therefore, by analyzing investment subcategories and country groups we may be able to unmask some other patterns shaping the stability of the aggregate investment rate. We address all these empirical issues within a simple version of the neoclassical growth model. The model predicts that aggregate investment may be influenced by income growth, the capital income share, the relative price of capital, taxation, and other market distortions. The behavior of nominal investment rates and relative prices can actually shed light into the form of the neoclassical production function. As we depart from the Cobb–Douglas paradigm, our empirical exercise can capture the influence of external effects on the aggregate production function. Our results, however, support the Cobb–Douglas assumption for the aggregate production function. First, we find weak evidence of additional external effects coming from human capital, expenditures in R&D, and public investment. Second, the elasticity of substitution between aggregate capital and labor is slightly less than one, and so the Cobb–Douglas production function seems a good approximation. Third, by dividing aggregate investment into equipment and structures we try to unveil complementarities with labor, and the possibility of a nested production function. Again, this is rejected by the data. All this evidence works in favor of a simple Cobb–Douglas production function. But if the Cobb–Douglas assumption prevails, then capital income shares should be stable over time, and strongly correlated with nominal investment rates. Surprisingly, we find that there is a weak correlation between the nominal investment rate and the capital income share across countries. This is the most puzzling fact against the neoclassical production function. We also show that the observed weak connection between expenditures in equipment and structures cannot just be attached to the variability of the relative prices of equipment and structures. We later analyze the volatility of the relative prices of equipment and structures. These two prices are weakly correlated, and the relative price of equipment displays much more volatility than the relative price of structures. Hence, aggregation of these two prices into a single index may not be adequate. Early studies (Jones, 1994; DeLong and Summers, 1991; Restuccia and Urrutia, 2001) focus on the influence of relative prices on economic growth and development. Here, we are just concerned with the ultimate determinants of the relative prices of equipment and structures in order to enhance our understanding of the production of these two investment components. Hsieh and Klenow (2007) and Herrendorf and Valentinyi (2012) associate differences in relative prices with variations in sectoral TFPs. This would imply that the volatility of these sectoral TFPs is very large. We allow for other sources of price variability besides TFP. More precisely, we find that the factor income share of services is more pronounced in the production of structures, and the factor income share of goods is more pronounced in the production of equipment. The relative price of structures is not affected by the Balassa– Samuelson effect. This latter effect becomes prominent in the relative price of equipment. The paper is organized as follows. Section 2 lays out an extended version of the neoclassical growth model in which the efficiency of investment can vary across countries. Section 3 considers a balanced sample of 50 countries, and carries out an empirical implementation of this model. The original aggregate model is extended in Section 4 to include two types of capital goods. In Section 5 we test this latter model on various grounds. Section 6 presents a quantitative analysis of the relative prices of equipment and structures. Some concluding remarks are gathered in Section 7. 2. The model with aggregate investment This section puts forward a theoretical framework for assessing the determinants of investment rates. The model delivers three linear equations that will guide our empirical investigation. To simplify matters, we assume that each country operates in a competitive-markets setting of a closed economy. In each country there is a representative household supplying capital and labor. To this conventional version of the standard neoclassical growth model, we append a country-specific relative price of capital and various types of taxes and non-pecuniary distortions. The representative household is concerned with the optimization of a discounted stream of utility given by 1

∑ βt uðC t Þ

ð1Þ

t¼0

where Ct is the aggregate consumption, β is the discount factor, and uðC t Þ is a standard utility function. The production sector is represented by an aggregate technology as given by a C2 concave production function with aggregate capital and labor Y t ¼ At ðxt ÞFðK t ; Bt Lt Þ;

ð2Þ

where Kt denotes the total stock of physical capital in the country and At ðxt Þ denotes the level of TFP assumed to depend on a vector of variables xt. Function At ðxt Þ reflects external effects which may come from human capital, R&D, and public capital;

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e.g., see Aschauer (1989), Barro (1990) and Lucas (1988). Regarding the labor input, Bt is the average level of education or productive skills and Lt is the total labor supply. Hence, Bt Lt denotes the effective units of labor in the country. We will often refer to Bt as the average level of human capital, which grows according to the law of motion Bt ¼ B0 ð1 þ g b Þt for a given initial condition B0, a constant growth rate g b 4 0, and all t. At all times, output in the economy may be either consumed or invested subject to physical feasibility Y t ¼ C t þ qn I t :

ð3Þ

n

Observe that q represents the cost of transforming investment in terms of the aggregate consumption good. This relative price qn is allowed to vary across countries. Physical capital is subject to a constant depreciation rate δK , and follows the law of motion: K tþ1 ¼ I t þ ð1δK ÞK t :

ð4Þ

For convenience of the presentation, the various distortions affecting this competitive economy are gathered in the sequence of budget constraints of the representative household ð1 þ τC ÞC t þ φq qn ð1 þ τI ÞI t ¼ φR ð1τY ÞRt K t þ φw ð1τY Þwt Bt þ τY δK K t þ T t

all t≥0;

ð5Þ

where Rt is the marginal productivity of physical capital and wt is the competitive wage. We assume that the household offers one fixed unit of labor. Note that this budget set incorporates flat-rate taxes on consumption, τC , investment, τI , and income, τY . (Tax proceeds are rebated to the representative household as lump-sum transfers, T t ¼ τC C t þ qn τI I t þ τY ½ðRt δK ÞK t þ wt Bt .) Further, φq 4 1, and 0 o φR o1, 0 oφw o 1 represent some non-pecuniary costs inherent in the economic environment or legal restrictions. For instance, φq could stand for some non-tangible costs over the price of investment such as government permits, licenses, or property rights – the possibility of stealing or losing the property – and φR could stand for intangible costs of intermediation and misallocation of physical capital (cf. Hsieh and Klenow, 2009 and references therein). For the optimal investment decision of the household, what matters is the after-tax price of investment q ¼ qn ð1 þ τI Þ times φq . Our equilibrium conditions are then summarized in the following Euler equation: u′ðC t Þ φR ð1τY ÞRtþ1 þ τY δK ¼ þ 1δK : βu′ðC tþ1 Þ φq q Our analysis will be restricted to a stationary solution or balanced growth path (BGP) where Ct and Kt grow at constant rates. As is well known, the existence of a BGP imposes stringent conditions on the utility and production functions. We assume a CES utility function uðC t Þ ¼ C 1s =ð1sÞ, s 40, and consider that qt, At and Lt remain constant. Later we allow for t growth in A at the expense of a Cobb–Douglas production function, but we temporarily want to explore the implications of a more general technology. 2.1. A CES technology Let us assume a CES production function Y t ¼ An ½αK ρt þ ð1αÞðBt LÞρ 1=ρ , for 1o ρ≤1. As is well known, ρ ¼ 1 corresponds to a linear technology, ρ-0 corresponds to a Cobb–Douglas production function, and ρ-1 corresponds to a Leontief technology. Note that 1=ð1ρÞ is the so-called elasticity of substitution between capital and labor. Now, consider the income share of capital, γ t ¼ Rt K t =Y t . Then, letting the rental rate Rt equal the marginal productivity of capital3 we have γt ¼

1
 : 1α Bt L ρ 1þ α Kt

Observe that for the Cobb–Douglas case (ρ-0) we obtain the well known result that γ t ¼ α. Along the BGP the income share γ t is constant and given by
n ρ=ðρ1Þ R γ n ¼ α1=ð1ρÞ n A where Rn ¼

    1 1 q φ q  ð 1δ Þ τ δ : K Y K s φR ð1τY Þ βð1 þ g b Þ

The nominal investment rate is defined as st ¼ qIt =Y t . Then, imposing steady-state condition I n ¼ ðδK þ g b ÞK n in Eq. (4) and rearranging terms, we obtain  q sn ¼ δK þ g b γ n n : ð6Þ R 3

 ρ In the case of a CES production function Rt ¼ At ðxt Þα½α þ ð1αÞ Bt L=K t ð1ρÞ=ρ .

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Substituting out the previous values for Rn and γ n we have  sn ¼ δK þ g b qα1=ð1ρÞ ðAn Þρ=ð1ρÞ



 1=ðρ1Þ   1 1 q φ q  ð 1δ Þ τ δ : K Y K φR ð1τY Þ βð1 þ g b Þs

ð7Þ

If the income tax τY does not allow for depreciation so that the tax rebate τY δK K t is taken out of the budget constraint, then the above equation simplifies to  sn ¼ δK þ g b qρ=ðρ1Þ α1=ð1ρÞ ðAn Þρ=ð1ρÞ



 1=ðρ1Þ φq 1  ð 1δ Þ : K φR ð1τY Þ βð1 þ g b Þs

ð8Þ

These last two equations summarize the quantitative effects of distortions and other variables on the nominal investment rate. Let us simply consider Eq. (8). It follows that non-pecuniary frictions φq and φR have the expected sign and appear as a single variable φq =φR . Note that these two negative effects reinforce each other: an increase in the cost of investment (a higher φq ) and a drop in the marginal profitability of capital (a decline in φR ) decrease the nominal investment rate, s. Also, a rise in the income tax rate τY lowers s. Some other variables, however, have ambiguous effects on s depending on the value of parameter ρ. Thus, if the technology is close to linear, ρ 40, then an increase in the relative price q would have a negative influence on s. These effects reverse sign if the technology is close to the Leontief case, ρ o0. The productivity term An also has ambiguous effects albeit with the opposite sign. Therefore, q and An fade out of the investment equation as we approach the Cobb–Douglas case, where expression (8) reduces to sn ¼

ðδ þ g b Þα  K : φq 1  ð 1δ Þ K s φR ð1τY Þ βð1 þ g b Þ

Finally, the labor market friction, φw , and the flat-rate consumption tax, τC , remain neutral in all the scenarios considered.

2.2. Investment equations This analysis suggests the following empirical tests for the determinants of the nominal investment rate. 1st empirical formulation (EFM1). The first scenario originates from the definition of the nominal investment rate (6), after imposing steady-state conditions for the price-rental ratio q=Rn as determined by the interest rate and physical capital depreciation  1  φR ð1τY Þ 1 sn ¼ δK þ g b γ n  ð 1δ Þ : K s φq βð1 þ g b Þ Note that this formulation does not rely on the CES production function. Now, taking logs we get the following expression:
R     φ log sn ¼ log δK þ g b þ log γ n þ log q þ logð1τY Þlog r n þ δK ; ð9Þ φ where rn is the real interest rate. 2nd empirical formulation (EFM2). In the second scenario we substitute out the value of the capital income share γ n . Taking logs in Eq. (8) we get the following expression:    ρ ρ logðqÞ þ log An log sn ∝log δK þ g b þ ρ1 1ρ 
q   1 φ log R logð1τY Þ þ log r n þ δK : þ ρ1 φ

ð10Þ

3rd empirical formulation (EFM3). In the third scenario, TFP parameter A is allowed to grow. We assume that A is determined by the stocks of human capital, R&D, and public capital. Hence, this is an expanded version of the previous formulation that allows for other sources of growth besides labor-augmenting technological progress. This formulation requires a Cobb–Douglas production function FðK; BLÞ to insure existence of a BGP. For this Cobb–Douglas version of the model, the coefficients for human capital, R&D and public capital must be equal to zero. That is, if the estimated coefficients were to be significantly different from zero, then the Cobb–Douglas formulation could be ruled out. For a general functional form for the production function, letting A grow across countries might be inconsistent with the balanced growth path assumption. Hence, this exercise can be seen as an approximation for small changes in A. As shown below, the estimated coefficients are always close to zero, and so the Cobb–Douglas assumption prevails. Real investment rates. From these expressions we can also analyze the determinants of the real investment rate; that is, the nominal investment rate over the relative price of investment q. Technically, this entails to divide both sides of the equation by the same term. Therefore, our empirical work will just focus on the nominal investment rate with the understanding that one can also infer the behavior of the real investment rate.

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3. Empirical findings on aggregate investment In preparation for our empirical results, we first go over our sample of OECD and non-OECD countries, the available data variables that may best represent their model counterparts, and our econometric methods. Table A1 of Appendix lists notation and data sources. 3.1. Data sample Countries. Our empirical exercise covers the period 1960–2000 and includes a set of 50 countries. This group of countries has been selected on the grounds of data availability, data quality, and geographical and economic considerations. The time period rules out various Eastern European countries where data are roughly available after 1990. Among these countries we have the ex Soviet Republics, the Czech Republic, and those stemming from the former Yugoslavia. Our sample contains all countries graded A in the Penn World Table (PWT) but Luxembourg (with a population of less than one million), and all countries graded B in the PWT but Iceland (because of population size) and Israel (high military expenditure). Singapore has been kept in the sample as a B-graded country, even though this country only has one benchmark study from the International Comparison Program (ICP). We also selected several C-graded countries with reasonable data quality and at least two ICP benchmark studies. After all these considerations, we get a balanced sample of 26 major OECD countries and 24 major non-OECD countries as listed in Appendix. Economic variables. Notation and data sources for our variables are documented in Appendix. Some variables like the relative price of capital (q) and the rate of output growth (Ygr) are readily available from various international sources, whereas other variables do not have close counterparts in the data. We have constructed stocks for three types of capital: the human capital stock (HUM), the research and development capital stock (R&D), and the public capital stock (PUB). It is important to realize that there could be measurement errors, which may bias our results below. For instance, for taxes and non-pecuniary distortions, we use average rates rather than marginal rates. Moreover, the relative price of capital may not be well adjusted for quality. The size and cross-country variability of the capital income share ðγÞ has been an issue of great debate. Gollin (2002) argues that the usual calculation of income shares fails to account for labor income of the self-employed and other entrepreneurs. After proceeding with these adjustments, he finds that income shares are approximately constant across time and space. Unfortunately, for many of the non-OECD countries in our sample there is not enough data available to construct a panel under these adjustments. For the OECD countries, capital income shares are adjusted for self-employment. Our estimated values, however, are invariant to the choice of the data set. We consider an expanded version of Gollin's data taken from Bernanke and Gürkaynak (2001), and the corresponding coefficients ðγ BG Þ are not statistically significant when restricting the sample to the dates of their data set. Furthermore, these coefficients are again not statistically different from zero when considering the original Gollin data set. For taxes, we consider taxes on income, profits, and capital gains (TAXIN). Because of measurement errors, multicollinearity and endogeneity issues, it is well known (Levine and Renelt, 1992) that fiscal indicators are not robustly correlated with either growth or the investment share. Barro (1990) finds that government consumption is strongly correlated with investment. Hence, as a proxy for TAXIN we consider the share of government expenditures (GOVC). Our tax data are taken from the World Development Indicators (WDI) of the World Bank. For non-pecuniary distortions, variables φq and φR enter symmetrically in the above investment equations as φq =φR . Then, for this composite variable we include the economic freedom index (ECOF) from the Fraser Institute.4 We will sometimes introduce the degree of openness (OPEN), which is the ratio of exports plus imports to GDP. Of course, OPEN may reflect country size rather than non-pecuniary distortions. There exists a large literature on financial development and growth (e.g., King and Levine, 1993; Levine and Zervos, 1993). According to Benhabib and Spiegel (2000) these results are sensitive to country fixed effects. Thus, in order to understand the role played by financial distortions on investment decisions, we have considered the lending rate charged by banks (LEND) and the domestic credit to the private sector (CRED). As in most of this literature, the results are not conclusive, and will not be reported here. 3.2. Econometric method Panel data techniques have become increasingly popular in growth empirics since Islam (1995) implemented a panel data approach for studying growth convergence. A panel data structure can address the problem of unobserved timeinvariant individual heterogeneity. If there are omitted characteristics correlated with the dependent and independent variables, then regression estimates may be biased. Two types of data specifications are usually considered: fixed effects and random effects. The fixed-effects model removes the time-invariant idiosyncratic regressors. This specification is assumed to 4 As pointed out above, in the ratio φq =φR both distortions reinforce each other: a higher φq increases the price of investment and a lower φR reduces the returns to physical capital. The ratio φq =φR is approximated by the index of economic freedom (ECOF) of the Fraser Institute. As discussed in Appendix, this index aggregates over five components representing economic, legal and social structures of the countries. Therefore, ECOF gives a broader account of the non-pecuniary distortion φq =φR in our model.

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be consistent; nonetheless, if the time-invariant characteristic is not correlated with the independent regressors the random-effects model is more efficient. In our empirical investigation we have considered both specifications. We then run a Hausman test to determine the appropriate specification. Furthermore, we have also checked OLS estimates for various benchmark years, and the OLS estimates do not differ significantly from our panel data results. Besides, in our data set some of the independent regressors (e.g., capital income shares) are quite stable over time; hence, some coefficients may be underestimated under the fixed-effects model. As argued below, none of our results is driven by the choice of the econometric model. A second issue is the structure of the error term. If there are only two dates available, the fixed effects estimator becomes equivalent to the estimator in first differences. For more than two dates, the fixed effects estimator is more efficient under the assumption of serially uncorrelated error terms. Moreover, as our focus is on long-run relationships, estimation based on the level variables is preferred to first differences. The first-difference estimator is more efficient if the error term follows a random walk. But if some of the variables are nearly constant over time or have already been differenced (growth rates), then first differencing can give imprecise estimates. Thus, in order to check the robustness of our results the error term is allowed to follow a general autoregressive process. The results are consistent with those of the fixed-effects specification. More recently, researchers have become acquainted with pooled cointegration methods. Coe et al. (2009) apply panel cointegration techniques to assess the importance of international R&D spillovers. This seems a valid application of these techniques because their capital stocks are cointegrated. Our analysis, however, focus on investment rates which appear quite constant for the last forty years for many countries in our sample. Pooled cointegration methods may nevertheless be of interest to study long transition and postwar periods observed in some economies. Finally, all variables considered in our exercise are computed over 5-year moving averages to filter business cycle effects. In all regressions, a level variable y is expressed as logðyÞ and a rate variable g is expressed as logð1 þ gÞ. 3.3. Results EFM1: The role of income growth, capital income shares, and distortions. Table 1a and b displays our results for the nominal investment rate as the dependent variable for the OECD and the non-OECD, respectively. It is worth pointing out that OECD data present less variability but appear to be of much better quality. Note that EMF1 comes from Eq. (9) which includes output growth, the capital income share, and distortions. From this equation we should expect the output growth rate (Ygr) to have a positive effect on the nominal investment rate. This is actually confirmed for both the OCDE and non-OECD samples since Ygr is highly significant with a sizable coefficient. The positive correlation between nominal investment rates and economic growth has been amply documented in the literature; see Edwards (1996) and references therein. Following (9), an increment in the capital income share ðγÞ should bring a linear increase in the nominal investment rate. Surprisingly, the OECD coefficient is close to zero and the non-OECD coefficient is not statistically significant. As already discussed, the coefficient is also not statistically different from zero when considering the capital income share ðγ BG Þ from Bernanke and Gürkaynak (2001). As this is a more restricted set of data, we report estimates for ordinary least squares. Regarding taxes, the evidence is less clear. Again, this could be blamed to our data set. Taxes on income (TAXIN) should be a good proxy for taxes on capital rents; the problem is that TAXIN does not appear to be statistically significant. Given that data quality for TAXIN may be low, we have included government consumption (GOVC) as a proxy for expected income taxes. Observe that GOVC displays the expected sign for the OECD group, and has no clear effect for the non-OECD group. Finally, to capture the effects of the non-pecuniary distortion variable logðφq =φR Þ we consider separately the degree of economic freedom (ECOF), and the degree of openness to international trade (OPEN). Mauro (1995) analyzes a set of indices of corruption in a cross-section of countries and finds negative effects on investment and economic growth. To exploit the advantages of panel data we use ECOF, which is only statistically significant for the non-OECD group. Hence, lack of economic freedom seems to be a much bigger barrier for investment in less developed countries. Also, OPEN seems to matter for the non-OECD group. Levine and Renelt (1992) argue that the correlation between OPEN and investment is quite robust. It should be remarked that this correlation appears to be quite dubious for the OECD group. EFM2: The role of relative prices. Table 1a and b also presents our estimated values for EFM2. Recall that under this specification the steady-state value for the capital income share γ n is replaced by primitive elements. Now, the relative price q appears in the investment equation. It can be observed that for both the OECD and the non-OECD sample the slope estimate for q is statistically significant with positive sign; that is, higher investment prices lead to higher nominal investment rates. From these values we can get estimates for the elasticity of substitution between capital and labor, since in Eq. (10) the slope estimate for q is given by ρ=ðρ1Þ. Duffy and Papageorgiou (2000) find evidence of an elasticity of substitution between capital and labor considerably greater than unity. Our estimated value for ρ=ðρ1Þ is 0.02 for the OECD and 0.06 for the non-OECD. This entails ρ ¼ 0:02 for the OECD and ρ ¼ 0:064 for the non-OECD. Hence, the Cobb–Douglas assumption of a unit elasticity of substitution is rejected for both samples. Our implied value for ρ yields an elasticity of substitution between capital and labor less than one, but quite close to this benchmark case. From our analysis below, there could be further misspecification and aggregation problems. The volatility of investment prices is not well understood: the price of equipment is much more volatile than the price of structures, and these two prices are weakly correlated. Hence, investment prices may affect nominal investment rates through other channels not

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Table 1 Aggregate investment rate at domestic prices. Explanatory variables (a) OECD Ygr

EFM1

EFM1

EFM1(OLS)

EFM2

EFM3

EFM3

EFM3

0.469 (7.08) 0.014 (1.93)

0.445 (6.87) 0.015 (2.04)

1.202 (2.07)

0.484 (7.58)

0.560 (7.76)

0.015 (0.41)  0.138 (  2.18)  0.431 (  2.77)

0.017 (0.87)  0.520 (  6.52)

0.022 (0.87)  0.620 (  4.64)

0.055 (2.05)  0.485 (  3.42)

0.015 (0.67)  0.620 (  4.65)

0.023 (2.04)

0.024 (1.47) 0.135 (1.65)  0.194 (  0.52)  0.057 (  1.30) 0.236

0.154 (2.16) 0.475 (1.35) 0.029 (0.70) 0.336

EFM3

EFM3

a

γ γ BG ECOF

0.003 (0.14)  0.510 (  6.32)

GOVC OPEN

 0.487 (  5.81) 0.041 (1.48)

q

0.566 (7.90)

R2

0.306

0.330

0.527

0.312

0.009 (0.62) 0.138 (1.82) 0.448 (1.26) 0.034 (0.80) 0.337

Explanatory variables

EFM1

EFM1(OLS, 15o.)

EFM2

EFM2

EFM3

0.651 (8.07) 0.006 (0.54)

0.927 (1.60)

0.599 (10.64)

0.578 (10.87)

0.705 (9.64)

0.007 (0.21) 0.180 (3.73)  0.021 (  0.06)

0.047 (3.22) 0.083 (1.31)

0.0352 (2.55) 0.017 (0.28) 0.159 (8.61) 0.068 (6.97)

0.039 (1.91)  0.167 (  2.00)

0.049 (2.13)  0.371 (  4.10)

0.039 (1.83)  0.168 (  1.97)

0.059 (4.24)  0.050 (  0.60)  2.046 (  2.212) 0.031 (0.84) 0.400

0.063 (3.98) 0.031 (0.33)  3.487 (  3.39)  0.080 (  2.06) 0.237

 0.118 (  1.41)  1.115 (  1.21) 0.002 (0.04) 0.368

HUM R&D PUB

(b) Non-OECDb Ygr γ γ BG ECOF GOVC

0.053 (0.45) 0.192 (5.15)

OPEN q

0.066 (6.45)

HUM R&D PUB R2

0.424

Explanatory variables (c) Whole sample Ygr γ

GOVC OPEN q HUM

0.337

0.412

EFM1

EFM1(OLS)

EFM2

EFM2

EFM3

EFM3

0.466 (9.74) 0.010 (1.75)

1.009 (2.47)

0.639 (15.79)

0.585 (15.20)

0.699 (14.34)

0.641 (13.23)

0.001 (0.07) 0.039 (0.86)  0.367 (  3.73) 0.050 (2.03)

0.035 (3.15)  0.084 (  1.79)

0.027 (2.57)  0.097 (  2.18) 0.171 (12.20) 0.063 (9.73)

0.053 (3.75)  0.238 (  4.01)

0.060 (4.34)  0.205 (  3.54) 0.124 (6.38) 0.037 (4.26)  0.049 (  0.98)

EFM3

EFM3

EFM3

0.700 (14.21)

0.642 (13.11)

0.044 (3.12)  0.245 (  4.09)

0.051 (3.67)  0.212 (  3.62) 0.123 (6.25)

 0.050 (  0.96)

 0.043 (  0.85)

c

γ BG ECOF

0.665

0.712 (9.52)

0.063 (5.05)  0.343 (  5.56) 0.112 (5.42)

0.065 (9.50)

0.036 (4.07)  0.056 (  1.09)

0.072 (4.72)  0.315 (  4.96) 0.173 (8.17) 0.374 (3.91) 0.037 (0.67)

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157

Table 1 (continued ) R&D PUB R2

0.320

Explanatory variables

(d) OECD Ygr γ ECOF GOVC

0.555

0.366

Random effects

0.295 (0.90)  0.008 (  0.33) 0.361

 0.133 (  0.37)  0.109 (  4.38) 0.219

0.066 (0.20)  0.005 (  0.19) 0.314

0.355 (1.07)  0.029 (  1.25) 0.347

Fixed Ef. with AR(1) disturb.

EFM1

EFM2

EFM1

EFM2

0.533 (7.34) 0.020 (2.88)  0.062 (  2.93)  0.329 (  4.252)

0.519 (7.46)

0.617 (10.26) 0.003 (0.23)  0.002 (  0.04)  0.628 (  3.453)

0.574 (10.01)

d

q R2

0.289

0.005 (0.02) 0.017 (0.70) 0.328

0.323

 0.019 (  0.93)  0.342 (  4.616) 0.072 (4.29) 0.341

0.311

0.014 (0.34)  0.592 (  3.394) 0.087 (4.42) 0.338

a Estimates for the fixed-effects model with the aggregate investment rate s as dependent variable. For the definitions of all variables see Table A1; for sources, time span, and country list, see Appendix. Sample: OECD countries. t-statistics in parentheses. b Estimates for the fixed-effects model with the aggregate investment rate s as dependent variable. For the definitions of all variables see Table A1; for sources, time span, and country list, see Appendix. Sample: Non-OECD countries. tstatistics in parentheses. c Estimates for the fixed-effects model with the aggregate investment rate s as dependent variable. For the definitions of all variables see Table A1; for sources, time span, and country list, see Appendix. Sample: all countries. t-statistics in parentheses. d Estimates for both the fixed-effects and the random-effects model with the aggregate investment rate s as dependent variable. For the definitions of all variables see Table A1; for sources, time span, and country list, see the Appendix. tstatistics in parentheses. n OECD countries without Mexico and Turkey.

discussed in this paper. For instance, q may have an impact on the nominal investment rate via the capital and labor income shares. We have already established the empirical weakness of this channel, as income shares do not affect nominal investment rates. EFM3: The role of external effects. EFM3 allows for externality effects for A(x). These effects are embedded in the stocks of human capital, R&D, and public capital.5 Indeed, previous research has emphasized the importance of external effects coming from these capital stocks. Aschauer (1989) finds evidence of external effects from infrastructure capital, while Coe et al. (2009) conclude that R&D and human capital have a strong influence on TFP. From Eq. (10) the coefficient attached to A(x) is ρ=ð1ρÞ, which has the opposite sign of the coefficient of q. Thus, for ρ o 0 the A-coefficient has to be negative, and for ρ-0 this coefficient equals zero. As already pointed out, human capital parameter Bt has no influence on the nominal investment rate. From an analysis of US time series 1948–1998, Antràs (2004) contends that restricting the growth process to Hicksneutral technological change A necessarily biases the estimates of the production function to Cobb–Douglas. Of course, the existence of a BGP under growth in TFP parameter A requires a Cobb–Douglas production function. Our cross-country study is very convenient to address the functional form of the utility function because it avoids the problem of comparing capital stock qualities at very distant dates. It seems more plausible to suppose that countries with related income levels may be linked to similar technologies and factor qualities. Our measure HUM is adjusted for quality across countries. Hence, we now let parameter A grow over time, and test if there is evidence of external effects on investment as a proof of statistically significant departures from the Cobb–Douglas production function. Turning to the estimates of Table 1a and b we find some evidence of external effects of HUM for the OECD countries and some evidence of external effects of R&D and PUB for the non-OECD countries. This evidence is not robust. The statistical significance of these coefficients is only present in some regressions. It should be stressed that in one of these specifications output growth Ygr is taken out of the equation to avoid a possible multicollinearity with HUM, R&D and PUB. Therefore, the influence of external effects on the nominal investment rate seems rather dubious. This is a further check that the aggregate production function is close to Cobb–Douglas, since the implied A-coefficient appears to be close to zero.

5

Data for the R&D and public capital stocks are limited to the period 1980–2000.

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EFM4: Cross-country regressions for the whole country sample. Table 1c reports the same exercises for the whole country sample. The results are in line with those obtained for the two groups of countries. Output growth has a similar coefficient, the capital income share has no influence, tax variables have a negative impact, while ECOF and OPEN have positive effects. The coefficient for q is positive although not far from zero. Regarding externality effects, it turns out that now public capital decreases the nominal investment rate, which entails positive external effects on aggregate productivity. In summary, when pooling all these countries into a single group we get that both taxes and non-pecuniary distortions are statistically significant; whereas in reality taxes mostly matter for the OECD group, and non-pecuniary distortions mostly matter for the non-OECD group. Therefore, this aggregation is masking certain differences between the OECD and non-OECD groups. 3.4. Robustness checks From the above results, we can now summarize our main findings: (i) factor shares are not statistically significant for both OECD and non-OECD countries, (ii) the relative price of investment has positive slope but very close to zero for both groups, (iii) income taxes seem to have a negative effect on investment for the OECD and seem to have no influence for nonOECD countries, and (iv) economic freedom and openness seem to matter for non-OECD countries. To insure that these results are not dependent on our econometric techniques we now run a few robustness checks whose results are displayed in Table 1d. These tests build on the following assumptions. (1) Steady state. It could be argued that some of the countries in our sample are not in the steady state for most of the period considered in our sample. To check that our results are invariant to the choice of our sample, in Table 1d we present the results when considering the OECD sample without Mexico and Turkey. We also considered several other scenarios. (2) Random-effect formulation. As already mentioned, some of our variables (e.g., the capital income share) are quite stable over time. In order to check that the low significance of these variables is not driven by the removal of the fixedeffects term, the first two columns of Table 1d report the results obtained when using the random-effects formulation. (3) Correlated error term. In the last two columns of Table 1d we provide estimates under a non-white noise error term. More precisely, this is the fixed-effects formulation with an AR(1) disturbance term. As it is clear from the estimates in Table 1d, none of our previous findings is affected by any of the alternative specifications introduced in these regressions. Note that all other tables belong to the fixed-effects formulation. 4. The model with equipment and structures In order to make further progress on some of the issues raised above, we now proceed to a more detailed modeling of the investment sector. As in the previous framework the representative household is concerned with the optimization of a discounted stream of utility (1). The aggregate production function contemplates a fixed TFP parameter A, two types of capital, and qualified labor Y t ¼ AFðK et ; K st ; Bt Lt Þ;

ð11Þ

where Ket denotes the stock of physical capital in equipment and Kst denotes the stock of physical capital in structures. At all dates, output in the economy may be either consumed or invested Y t ¼ C t þ qne I et þ qns I st : qne

ð12Þ qns

reflects the cost of transformation of equipment using the aggregate consumption good and reflects the cost Note that of transformation of structures. These two prices may vary across countries. As before, these prices are not allowed to depend on t to insure existence of a BGP under a CES production function. Capital stocks, Ke and Ks are subject to constant depreciation rates, δe ; δs 4 0, and follow the laws of motion K etþ1 ¼ I et þ ð1δe ÞK et ;

ð13Þ

K stþ1 ¼ I st þ ð1δs ÞK st :

ð14Þ

The individual budget constraint now includes two taxes on investment, τIe and τIs , and non-pecuniary distortions for prices, φqe and φqs , and for rental rates, φRe and φRs , affecting capital in equipment and structures ð1 þ τC ÞC t þ φqe qne ð1 þ τIe ÞI et þ φqs qns ð1 þ τIs ÞI st ¼ φRe ð1τY ÞRet K et þφRs ð1τY ÞRst K st þ φw ð1τY Þwt Bt þ τY δe K et þ τY δs K st þ T t :

ð15Þ

Here, Ret and Rst represent the marginal productivities of the stocks of equipment and structures, respectively. Let qe ¼ qne ð1 þ τIe Þ and qs ¼ qns ð1 þ τIs Þ. From the first-order conditions we can derive the following two Euler equations associated with state variables, Ke and Ks over an interior solution: u′ðC t Þ φRe ð1τY ÞRetþ1 þ τY δe ¼ þ ð1δe Þ; βu′ðC tþ1 Þ φqe qe

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159

u′ðC t Þ φRs ð1τY ÞRstþ1 þ τY δs ¼ þ ð1δs Þ: βu′ðC tþ1 Þ φqs qs Inspection of these two equations reveals a linear relationship between the rental rates Retþ1 and Rstþ1 over the BGP and transitional dynamics. This is a simple consequence of the postulated linear accumulation process for both types of capital as given by Eqs. (12)–(14) and the linear tax rate. Hence, Iet and Ist should be highly correlated. As a matter of fact, for a CES production function the linear relationship between the rental rates Ret and Rst translates into a linear relationship between the capital stocks, Ket and K st . We now explore the determinants of the ratio of these expenditures. 4.1. Symmetric elasticity of substitution with labor Let us first consider the following family of aggregate production functions: 1=ρ

Y t ¼ Afα½μK εet þ ð1μÞK εst ρ=ε þ ð1αÞðBt LÞρ g

:

Note that the elasticity of substitution between the capital stocks is equal to 1=ð1εÞ. As in the previous model, the elasticity of substitution between the nested capital aggregate and labor is equal to 1=ð1ρÞ. Let γ et denote the equipment income share, γ et ¼ Ret K et =Y t . From the first-order conditions of the maximization problem we get αμ

γ et ¼ " α þ ð1αÞ

!ρ #

Bt L ðμK εet þ ð1μÞK εst Þ1=ε




μ þ ð1μÞ

K st K et

ε  :

Let set denote the nominal investment rate of equipment, set ¼ qe I et =Y t . Imposing the steady-state condition I ne ¼ ðg b þ δe ÞK ne and rearranging terms, we then have  q sne ¼ g b þ δe γ ne en : Re Plugging in the steady-state value γ ne in terms of the marginal productivities of equipment Rne and structures Rns , we obtain (  ε=ð1εÞ )ðερÞ=εðρ1Þ  ð1μÞRne sne ¼ qe g b þ δe ðαμÞ1=ð1ρÞ ðAÞρ=ð1ρÞ ðRne Þ1=ðρ1Þ μ þ ð1μÞ : ð16Þ μRns Following a similar procedure we obtain the nominal investment rate of structures: (  ε=ðε1Þ )ðερÞ=εðρ1Þ  ð1μÞRne sns ¼ qs g b þ δs ½αð1μÞ1=ð1ρÞ ðAÞρ=ð1ρÞ ðRns Þ1=ðρ1Þ ð1μÞ þ μ : μRns

ð17Þ

From these two equations we can see that both sne and sns depend on qe and qs since in the Euler equations Rne and Rns are determined by qe and qs, respectively. Also, A cancels out as we consider the expenditure ratio sne =sns ; hence, the level of TFP and associated external effects will have no bearing on sne =sns . The Cobb–Douglas/CES case. As in Section 2, from the first-order conditions we can substitute for the steady state-values Rne and Rns in expressions (16) and (17), and assume no depreciation allowances for the income tax. For ε-0 we have a Cobb– Douglas production function nested into a CES-technology ρ ρ Y t ¼ AfαðK μet K 1μ st Þ þ ð1αÞðBt LÞ g

1=ρ

:

Then, the ratio sne =sns simplifies to   q  1 φs μ g b þ δe s ð1δs Þ n se βð1 þ g b Þ φRs i q : ¼  h 1 φe sns ð1μÞ g b þ δs βð1þg Þs ð1δe Þ φRe

ð18Þ

b

It follows that in the Cobb–Douglas/CES case the relative prices qe and qs do not enter into the expression sne =sns . Again, there are non-separate effects of non-pecuniary distortions. Only the ratios φRe =φRs and φqe =φqs appear in this expression. 4.2. Asymmetric elasticity of substitution with labor There is a second family of functions in which equipment and structures do not have the same degree of substitution with labor. It is often postulated in the literature that equipment is complementary with qualified labor (cf. Heckman et al., 1998; Krusell et al., 2000). In our simple framework, this type of complementarity would take the form Y t ¼ AfαK ρet þ ð1αÞ½μK εst þ ð1μÞðBt LÞε ρ=ε g

1=ρ

:

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For the purposes of our analysis we could also allow for complementarities between structures and a nested aggregate of equipment and qualified labor 1=ρ

Y t ¼ AfαK ρst þ ð1αÞ½μK εet þ ð1μÞðBt LÞε ρ=ε g

:

In the sequel we just present the nominal investment rates for the first of these two production functions. Interchanging the roles of equipment and structures one can readily compute the results for the remaining production function. Following the same steps as in (16)–(17), we must have: sne ¼ qe ðg b þ δe Þα1=ð1ρÞ ðAÞρ=ð1ρÞ ðRne Þ1=ðρ1Þ 8 (" 9ðερÞ=ðρð1εÞÞ )1
n ρ=ð1ρÞ # < = Re 1 ε=ð1εÞ n 1=ðε1Þ 1=ð1εÞ ðAÞ ðRs Þ α α þ 1α : ss ¼ qs g b þ δs ½ð1αÞμ : ; 1α αA n



ð19Þ

ð20Þ

Note that now the TFP variable A has differential effects on equipment and structures. The Cobb–Douglas/CES case. From the first-order conditions we can substitute for the steady state-values Rne and Rns in expressions (16) and (17), and assume no depreciation allowances for the income tax. Again, letting ε-0 we get the following production function: 1=ρ

Y t ¼ AfαK ρet þ ð1αÞ½K μst ðBt LÞ1μ ρ g

:

Then, the investment simplify to  ρ=ðρ1Þ 1=ð1ρÞ ρ=ð1ρÞ α ðAÞ sne ¼ g b þ δe qe



 1=ðρ1Þ 1 φq e s ð1δe Þ βð1 þ g b Þ ð1τY ÞφRe

(   ρ=ðρ1Þ )  1 φqe qe ð Þ μ g b þ δs 1α1=ð1ρÞ ðAÞρ=ð1ρÞ  1δ e βð1 þ g b Þs ð1τY ÞφRe   sns ¼ : qs 1 φ s ð1δs Þ R s βð1 þ g b Þ ð1τY Þφ It follows that the relative price of structures does not alter any of the steady-state nominal investment rates, sne and sns ; only the relative price of equipment influences these rates. 4.3. Summary of main results Before embarking on our empirical investigation let us gather our main results on the predictions of our twosector model: (1) Nominal investment rates. Nominal investment rates of equipment and structures, se and ss, are linearly correlated. This robust result mainly stems from our linear technology for capital accumulation. (2) Relative prices. The coefficients of the relative prices of equipment and structures, qe and qs ; may uncover deviations from the Cobb–Douglas assumption, and asymmetries in the elasticities of substitution between the two types of capital and labor. (3) Distorsions. Taxes and non-pecuniary distortions, φqe =φRe and φqs =φRs , may have differential effects on se and ss. (4) Economic growth. Even though economic growth has often been linked to investment in equipment (DeLong and Summers, 1991), it follows from the above equations that output growth rate gb should have positive effects on both se and ss. 5. Empirical findings on nominal investment rates of equipment and structures The countries and years considered are the same as before contingent upon data availability. We also make use of the panel data techniques described above. In the national accounts aggregate investment (gross fixed capital formation) is divided into producers’ durable goods and construction. Producers’ durable goods is composed of transportation and machinery; we group these two entries into equipment investment. Construction includes residential, non-residential, and other construction; we group all these latter items into structures investment.6 In our analysis we deal with both investment rates and prices of investment. Although the United Nations National Accounts provide disaggregated data for residential and non-residential construction, the benchmark studies do not provide data for the prices of non-residential construction for all the benchmark years considered in our work. As a matter of fact, there is no disaggregated data for residential and non-residential construction prices in the 1996 benchmark study; this benchmark year is the most comprehensive. 6 Depending on the year and country sometimes the entries land improvement and plantation and orchard development and breeding stock, draught animals, dairy cattle and the like are available. We have included these items whenever possible although their size is relatively small.

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161

The modeling of aggregate investment rests upon the basic presumption that investments in equipment and structures share similar statistical properties. This turns out not to be true in the data. Nominal investment rates of equipment are not highly correlated with those of structures. Fig. 1 plots the nominal investment rate in equipment against the nominal investment rate in structures from the 1996 ICP benchmark study. We see considerable deviations from the possible fit of a straight line. DeLong and Summers (1991) present similar scatter plots for earlier periods, and Bems (2008) finds a lack of cross-country correlation between investments in tradable and non-tradable sectors. Below, we regress investment in equipment against investment in structures. The slope coefficient is about 0.2895 for the OECD and 0.2978 for the nonOECD countries. These coefficients are statistically significant, but are a long way from the linear correlation suggested by our neoclassical growth model. Nominal investment rates of equipment and structures are hardly correlated with income levels (cf. Eaton and Kortum, 2001; Hsieh and Klenow, 2007). We now explore the effects of relative prices on these investment patterns. Table 2 shows the coefficient of variation (standard deviation over the mean) of both investment rates and relative prices. For investment rates, we see more variation in the non-OECD group. Surprisingly, for both the OECD and non-OECD groups we find much more volatility in the ratio se =ss , which confirms the lack of correlation between these two categories of investment. Regarding relative prices, as expected we see from the table that the volatility in the relative price of equipment in terms of the consumption good is three times greater than that of structures. We also see more volatility in the relative prices of the non-OECD group. Moreover, as reported below when the nominal ratio se =ss is regressed against the price ratio qe =qs we get a slope coefficient of 0.0904 for OECD countries and 0.2973 for non-OECD countries; these univariate coefficients usually

THA

MYS

Investment rates in equipment 1996

.2 TUN

CHN SGP

.15

KEN MAR

KOR JPN

IND

LKACHL TUR AUSPHL NZL PRT EGY ITA COL HUN FRA ESP PAK NLD SWEGBR USA CHE PERAUT DNKPOL MEX PAN FIN NOR DEU IRLGRC ECU VEN ARG BRA CAN URY BEL

.1

HKG

IRN

IDN

.05 .05

.1

.15

.2

Investment rates in structures 1996 Fig. 1. Nominal investment rates for benchmark year 1996. Source: UN National Accounts.

Table 2 Volatility of investment and relative prices in 1996. Explanatory variables

All countries

OECD

Non-OECD

Investment rates se ss se =ss

0.338 0.361 0.739

0.191 0.288 0.278

0.386 0.421 0.877

Relative prices qe qs qe =qs

0.622 0.279 0.553

0.314 0.129 0.277

0.541 0.316 0.551

Coefficients of variation for investment rates and relative prices. For the definitions of all variables see Table A1; for sources, time span, and country list, see Appendix. Coefficient of variation: standard deviation over mean.

.25

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become smaller upon the introduction of other regressors. These results confirm small departures from the Cobb–Douglas production function for the OECD group. Therefore, the relative prices of equipment and structures cannot account for the cross-country variability in the nominal investment rates. We are now in a position to analyze differential effects of distortions on equipment and structures as they appear in the above investment equations, as well as the effects of economic growth and relative prices. Our results are displayed in Table 3 for both OECD and non-OECD countries. Note that the dependent variable could be se or ss, or the ratio se =ss . As already discussed, the correlation between se and ss is positive, but much less than one, for both univariate and expanded regressions. Regarding the effects of the relative prices of equipment and structures, they all point out to small departures from the Cobb–Douglas assumption. For the OECD countries, investment in equipment is generally affected by the price of structures, and investment in structures is affected by the price of equipment but with the opposite sign. For the non-OECD countries, the coefficient of the price of structures is usually smaller than that of the price of equipment. These estimates suggest that for the OECD sample the most adequate production function is the one in which both investments appear as part of a nested capital aggregate, whereas for the non-OECD countries the most adequate production function would be the Table 3 Equipment and structures investment rates at domestic prices. Explanatory variables

Dependent variable se =ss

(a) OECDa qe =qs

se =ss

se

se

se

se

ss

ss

ss

0.016 (1.80) 0.022 (3.67) 0.284 (6.02) 0.153 (3.14)

0.005 (0.68) 0.018 (3.12) 0.339 (7.45) 0.198 (4.10)

 0.050 (  6.85) 0.005 (0.73) 0.339 (6.76)

 0.040 (  4.50) 0.004 (0.65) 0.321 (6.30)

 0.049 (  6.71) 0.005 (0.70) 0.348 (6.81)

0.290 (10.47)

0.005 (0.68) 0.018 (3.14) 0.339 (7.56) 0.198 (4.11)

0.023 (1.22)  0.397 (  5.59)

0.023 (1.19)  0.365 (  4.99) 0.013 (1.93)

0.019 (0.94)  0.403 (  5.65)

0.090 (1.33)

qe

0.379 (4.42) 0.103 (1.36)

qs Ygr ss ECOF

 0.001 (  0.02)

GOVC γ

0.091 (1.29) 0.016 (2.50)

OPEN

 0.001 (  0.01)

0.495 (8.72) 0.539

0.473 (8.12) 0.542

 0.023 (  0.92) 0.493 (8.64) 0.540

 0.019 (  2.32) 0.015 (2.83) 0.285 (5.16)

 0.017 (  2.09)  0.020 (  3.01) 0.305 (5.17)

 0.013 (  1.74) 0.026 (5.12) 0.283 (5.60)

 0.012 (  0.65) 0.173 (2.16)

 0.021 (  1.26) 0.435 (2.25)  0.025 (  2.91)

0.001 (0.02)  0.013 (  0.17)

0.002 (0.11)

se R2

0.296

0.338

0.175

0.264

0.256

0.264

0.025 (3.82)  0.014 (  3.42) 0.269 (6.23) 0.079 (1.66) 0.061 (4.63)  0.042 (  0.65)

0.005 (0.48)  0.011 (  1.31) 0.099 (1.43) 0.260 (2.95) 0.068 (3.72) 0.048 (0.21) 0.021 (1.96)

0.020 (3.15)  0.008 (  1.71) 0.270 (7.04) 0.011 (0.20)

b

(b) Non-OECD qe =qs

0.297 (5.27)

qe

0.538 (5.48)  0.195 (  2.97)

qs Ygr ss

0.298 (10.04)

ECOF GOVC γ OPEN

 0.084 (  1.31)

0.073 (3.85)

se R2 a

0.240

0.258

0.392

0.390

0.608

0.367

0.453 (5.13) 0.292

0.684 (6.71) 0.632

0.173 (8.06) 0.142 (1.59) 0.409

Estimates for the fixed-effects model for investment rates of equipment se and structures ss. For the definitions of all variables see Table A1; for sources, time span, and country list, see Appendix. Sample: OECD countries. t-statistics in parentheses. b Estimates for the fixed-effects model for investment rates of equipment se and structures ss. For the definitions of all variables see Table A1; for sources, time span, and country list, see Appendix. Sample: Non-OECD countries. t-statistics in parentheses.

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one in which equipment and labor are complements. At any rate, these coefficients are small, and hence the elasticities of substitution 1=ð1εÞ and 1=ð1ρÞ are close to one. More clear-cut evidence appears for the correlation between nominal investment rates and economic growth. Both the one-sector and two-sector models imply that at the BGP the growth variable gb has a positive influence on nominal investment rates. DeLong and Summers (1991) focus on equipment investment as a potential key factor for growth. Jones (1994) has pointed out that a negative strong relationship emerges in the data between the relative price of machinery and economic growth, whereas the relative price of nonmachinery enters insignificantly in growth regressions. We see from Table 3 that the growth variable has a positive influence on both equipment and structures. Finally, for economic policy it becomes of interest to see how our distortion variables may have differential effects on these investment components. As discussed in Section 3, for the OECD countries TAXIN has a weak effect on investment, and GOVC has a more robust influence. Table 3 shows that for the OECD sample GOVC has a negative effect on structures, but not on the equipment investment rate. Again, the capital income share ðγÞ has minor effects on both components of investment. Regarding the non-OECD sample, we see from this table that ECOF has a positive effect on equipment investment but not on investment in structures. This result suggests that barriers and non-pecuniary distortions are detrimental to equipment investment, which is usually related to trade, technology, and innovation. This influence, however, is not apparent in OECD countries. Likewise, OPEN is not statistically significant for both components of investment in OECD countries, but it is significant for both components of investment in non-OECD countries. 6. Relative prices of investment goods There is a low correlation between expenditures in equipment and structures, as well as between the relative prices of equipment and structures. From Table 2, the relative price of equipment displays much more variability than that of structures. We now inquire into the sources of this volatility. Fig. 2 plots the relative price of equipment against the relative price of structures from the 1996 ICP benchmark study. We can observe considerable dispersion between these relative prices. The sources of this dispersion cannot easily be explained from the existing literature. For instance, regarding the relative price of equipment, Eaton and Kortum (2001) summarize the evidence as follows: “while the relative price of equipment is substantially lower in rich countries, the reported price of equipment itself is, if anything, higher in rich countries … The ICP measure of equipment certainly varies across countries, but the numbers do not show that it is systematically higher in the net importers than in the net exporters.” That is, the relative price of equipment seems to vary because of the variability of the price of consumption. The relative price of consumption also appears in the computation of the relative price of structures. Then, one should expect a simple connection between the relative prices of equipment and structures. The data, however, shows that both prices are only mildly correlated. Hsieh and Klenow (2007) and Herrendorf and Valentinyi (2012) infer cross-country levels of sectoral productivities from the relative prices of consumption and investment goods. If sectoral productivities can be tied down to relative prices, then we must conclude that there is a lot of cross-country volatility in these productivities. Hence, general statements about sectoral TFPs among groups of countries (e.g., rich vs. poor nations) must take into account the existence of a pronounced within-group variability. In our view, the main shortcoming of the model of Hsieh and Klenow (2007) is to consider the same factor income shares for the production of consumption and investment goods. In their framework this assumption implies that price volatility can only come from variation in sectoral TFPs. It seems worth considering more general production functions. 6.1. The production of equipment and structures We now study the volatility of the relative prices of equipment and structures in a much richer framework. This extended model incorporates two separate production processes for equipment and structures. Let us assume the following Cobb– Douglas production function for equipment investment: αe

αe

I e ¼ Ae K αs s Le l Ge g e

where Ae is the level of TFP for the production of equipment, Ks is the stock of structures in the production of equipment, Le is the amount of services or labor input, and Ge is the amount of goods consumed in the production process. We assume constant-returns to scale so that the sum of the production coefficients, α, equals one. That is, αes þ αel þ αeg ¼ 1. Likewise, let αs

αs

I s ¼ As K αe e Ls l Gs g s

be the production function for structures in a given country. Again, we assume constant-returns to scale so that αse þ αsl þ αeg ¼ 1. Note that in this simple setting there is an asymmetry in the production of the two investment goods. The stock of structures Ks enters into the production of equipment whereas the stock of equipment Ke enters into the production of structures.

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5

Relative prices of equipment 1996

EGY

4

3

KEN TUN

2

IRN HUN

MAR

LKA

TUR POL PHL VEN MEX PAN PAK CHL URY PRT ARG BRA GRC AUS NZL GBR IRL ITA ESP USA FIN CAN DEU DNK NLD HKG FRA AUT SWE BEL KORNOR JPN CHE SGP

THA

IDN

ECU PER

1

0 0

.5

1

1.5

2

Relative prices of structures 1996 Fig. 2. Relative prices of equipment and structures for benchmark year 1996. Source: ICP benchmark studies.

We shall assume competitive behavior in all input markets. Then, the prices of equipment and structures will be derived from the unitary cost functions. Let us start with the cost of producing one unit of equipment. Let Ω ¼ ðωs ; ωl ; ωg Þ be the vector of input prices: ωs is the rental price of one unit of structures, ωl is the price of one unit of services, and ωg is the price of one unit of goods. Then, the cost function for producing one unit of equipment takes on the form ce ðΩÞ ¼

Δe αes αel αeg ω ω ω Ae s l g

where Δe is a constant term, Δe ¼ ½ðαes Þαs ðαel Þαl ðαeg Þαg . Also, the cost function for producing one unit of structures takes on the form e

cs ðΩ′Þ ¼

e

e

Δs αse αsl αsg ω ω ω As e l g

where Δs ¼ ½ðαse Þαe ðαsl Þαl ðαsg Þαg . In a competitive setting, the prices of equipment and structures will be determined by cost functions ce ðΩÞ and cs ðΩ′Þ, respectively. These two equations will be the starting point of our empirical investigation. As these cost functions are homogeneous of degree one, we can take one of the inputs as the numeraire commodity. For instance, dividing these expressions over the price of services ωl and taking logs we obtain


 ωg ce ðΩÞ ωs ∝logðAe Þ þ αes log þ αeg log : ð21Þ log ωl ωl ωl s

log

s

s




 ωg cs ðΩ′Þ ωe ∝logðAs Þ þ αse log þ αsg log : ωl ωl ωl

ð22Þ

As shown later, in these equations the appropriate choice of the numeraire commodity will be dictated by economic considerations. 6.2. Empirical results Now we present the results obtained under the framework laid out above. Price data are collected from the benchmark studies of 1980, 1985 and 1996; these are the most recent years for which these studies are available. The 1996 benchmark includes 30 goods categories, which we aggregate into our four subaggregates: equipment, structures, goods and services. Further details are provided in Appendix. As there are at most three observations for each country, we use OLS estimation with a dummy variable for each year. It should be stressed that these benchmark studies report final prices that include taxes and other distortions, whereas our cost functions deal with producer prices; hence, these distortions may bias our estimates. We define the relative price of equipment over the price of services as qe=l ¼ ωe =ωl , the relative price of structures over the price of goods as qs=g ¼ ωs =ωg ; and so on. Also, what appears in our demand functions are the rental prices of equipment ωe and structures ωs rather than

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the final prices. Indeed, rental prices are not available in the benchmark studies but should be commensurate with final prices. Table 4a and b reports the estimated coefficients of our empirical formulations (21) and (22) for the OECD and the nonOECD groups. For the price of equipment as the dependent variable in the OECD, the price of services is not statistically significant, and thus the relevant formulation takes the price of services as the numeraire. For the three other cases (structures and non-OECD equipment) our preferred specification takes the price of goods as numeraire. Therefore, the relevant inputs for the production of equipment in the OECD are goods and structures, and for equipment in the non-OECD are services and structures. By the homogeneity of degree one of the cost function, the estimated coefficients in our regressions are independent of the numeraire commodity. As a matter of fact, in all our numerical exercises the estimated coefficients are not affected by the choice of the normalization. The estimated shares are 0.7 and 0.4 for the OECD and slightly lower for the non-OECD. For the production of structures the significant variables are services and equipment in both subsamples. The estimated shares are now 0.65 and 0.45 for the OECD and 0.5 and 0.35 for the non-OECD. In all the cases we cannot reject the constant-returns to scale assumption. From the results above we have that the production function for equipment differs for the OECD and the non-OECD. In the case of structures, the inputs, equipment and services, are the same for the two groups. To test if the share for these two inputs is equal for both groups we perform a Chow test. The results show that the coefficients αse and αsl are not statistically different for the two subsamples. When we introduce income per worker (Y) in our equations (Table 4a and b, columns two and four), we obtain two further results: (i) the so-called Balassa–Samuelson effect appears to be present in equipment for both country groups but it is not present in structures (as a matter of fact the coefficients are positive for structures and the OECD coefficient is significant) and (ii) the coefficients of the factor income shares for the OECD go down and so the assumption of a constantreturns to scale technology clearly prevails. In summary, our analysis suggests that the volatility of the relative prices of equipment and structures can be affected by the prices of goods and services in a setting of different factor shares as well as sectoral TFPs. In this more general framework, there is not a univocal correspondence between fluctuations in the relative price of investment and sectoral TFP. As a matter of fact, the positive correlation between the level of income and TFP is lost when it comes to the production of structures in which the Balassa–Samuelson effect may be reversed. Hence, an adequate modeling of investment may require different factor shares for the production of equipment and structures, and the introduction of intermediate goods and services.

Table 4 Relative prices of equipment and structures. Explanatory variables

Dependent variable qe=l

qe=l

qs=g

qs=g

(a) OECD qg=l

0.733

0.547

qs=l

(7.48) 0.394

(4.62) 0.462

ql=g

(2.15)

(2.80) 0.653

0.479

qe=g

(8.32) 0.449

(5.86) 0.558

(3.03)

(3.85) 0.189 (4.95) 0.633

a

0.681

 0.202 (  2.23) 0.734

0.586

0.403

0.588

0.517

0.395

(2.38)

(3.20)

(2.76) 0.353

(1.80) 0.427

(2.37)

(2.66)

0.278

0.277

(2.49)

(2.46)  0.285 (  2.51) 0.494

0.352

0.119 (1.13) 0.352

Y R

2 b

(b) Non-OECD ql=g qe=g qs=g Y R

2

0.385

a Pooled OLS regression for the relative prices of equipment qe and structures qs. Dummy variables for each benchmark year: 1980, 1985, 1996. For the definitions of all variables see Table A1; for sources and country list, see Appendix. Sample: OECD countries. t-statistics in parentheses. b Pooled OLS regression for the relative prices of equipment qe and structures qs. Dummy variables for each benchmark year: 1980, 1985, 1996. For the definitions of all variables see Table A1; for sources and country list, see Appendix. Sample: Non-OECD countries. t-statistics in parentheses.

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7. Concluding remarks Guided by the neoclassical growth model, in this paper we inquire into the determinants of investment rates across countries. This question is of fundamental interest for studies of economic growth since physical capital accumulation appears to be a major factor in accounting for income levels. We first explore the determinants of the nominal investment rate. Then, the real investment rate is to be found as the nominal investment rate over the relative price of capital. We also explore the determinants of the relative price of capital. Moreover, from the sensitivity of investment to relative prices we can draw inferences about the shape of the neoclassical production function. The nominal investment rate is barely correlated with the level of income, which accords with the basic prediction of the neoclassical growth model without market distortions. But this does not mean that no other factor can account for investment. Indeed, from our analysis of the neoclassical growth model we can uncover certain trends. First, we find that income growth has a positive effect on the nominal investment rate whereas some market distortions have negative effects. As is well known income growth is uncorrelated with the income level, and so it can have a positive influence on the nominal investment rate when integrated in our empirical analysis. Regarding market distortions, taxes seem to matter in OECD countries whereas non-pecuniary distortions seem to matter in less developed countries. There is a second category of factors including the relative price of capital and the capital income share that are inversely correlated with the level of income. Hence, one would expect these forces to have a small effect on the nominal investment rate, since the nominal investment rate is barely correlated with the level of income. The small effect of the relative price of capital supports the Cobb–Douglas assumption for the aggregate production function, which entails stable capital income shares moving in tandem with nominal investment rates. What is puzzling for our theory is that for both OECD and nonOECD countries, the capital income share is a weak explanatory factor of nominal investment rates. Our paper calls attention to some of the pitfalls of cross-county studies of aggregate investment. As all countries are included in our sample we find that both taxes and non-pecuniary distortions affect nominal aggregate investment. But as already stressed, taxes are mostly relevant for OECD countries, whereas non-pecuniary distortions are mostly relevant for non-OECD countries. Moreover, in contrast to the predictions of our neoclassical growth model, expenditures in equipment and structures are weakly correlated. There is also a great variability of the relative prices of equipment and structures. We find, however, that these scattered investment patterns cannot be accounted for by the relative prices of equipment and structures. This lack of influence of relative prices points at a Cobb–Douglas production function with two aggregate capitals and labor. In the OECD, income taxes appear to affect structures but not equipment. For non-OECD countries, our measure of economic freedom has a significant influence on the quantity of equipment goods but not on structures. The empirics of the relative prices of equipment and structures is hard to explain: both prices are barely correlated, and the relative price of equipment displays much more variability than the relative price of structures. According to Eaton and Kortum (2001), equipment goods share roughly the same absolute price across countries. Building upon this idea, Hsieh and Klenow (2007) relate cross-country changes in relative prices to changes in sectoral productivities. Their analysis derives from a calibration exercise in which factor income shares are assumed to be equal across sectors. In contrast, in our empirical exercise these factor income shares are left unrestricted, and are estimated from input price data. We find that the production functions for equipment and structures appear to be quite different. Hence, the weak correlation between the prices of equipment and structures across countries may come from changes in sectoral TFPs as well as from changes in the relative prices of production factors (intermediate goods and services) and different input shares in the production of equipment and structures. Moreover, the Balassa–Samuelson effect appears to be present in equipment but not in structures. Related empirical studies of economic growth on physical capital accumulation (e.g., Edwards, 1996; Kormendi and Meguire, 1985; Levine and Renelt, 1992) do not follow as closely the analytical framework of the neoclassical growth model, and do not distinguish between OECD and non-OECD countries, and between investment in equipment and structures. These other studies consider a wide range of financial and monetary variables, but there is no conclusive evidence that such variables may have a robust influence on investment. Of course, testing more general models of economic growth with monetary and financial variables – together with life cycle considerations and intergenerational transfers – should be worth further investigation. Acknowledgment The authors would like to thank two anonymous referees and an editor for their helpful comments and suggestions. Appendix Countries. Our sample contains all countries graded A in the PWT but Luxembourg that has a population of less than one million. It also includes all countries graded B in the PWT but Iceland (because of population size) and Israel (high military expenditure). Singapore has been kept in the sample, even though this country only has one ICP benchmark. Our sample contains most countries graded C in the PWT with at least two ICP benchmarks. For several reasons, the following C-rated countries with at least two ICP benchmark studies were not included: (a) Bahamas, Barbados, Botswana, Grenada, St. Lucia, Trinidad & Tobago, and Mauritius have populations of less than one million. (b) Benin, Bangladesh, Congo

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Republic, Ivory Coast, Madagascar, Mali, and Senegal are missing investment data for the subcategories of equipment and structures. Although these countries have either two or three benchmarks, their investment data does not expand for all years in the sample. Along the same lines, (c) Ethiopia, Malawi, Nepal, and Swaziland do not seem to have good investment data for these two subcategories. (d) Cameroon, Sierra Leone, Tanzania, Zambia and Zimbabwe have been engaged in major confrontations over the period 1960–2000. Finally, (e) Bolivia, Jamaica, Nigeria, Romania (data starting 1970) and Syria show very low quality data for the National Accounts. Besides, Nigeria is not in the Barro-Lee data set (cf. Barro and Lee, 1996), which is an input of our human capital series. After these considerations, the following countries do comprise our sample: (i) OECD-group. Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hungary (data starting 1970), Ireland, Italy, Japan, Korea, Mexico, Netherlands, New Zealand, Norway, Poland (data starting 1970), Portugal, Spain, Sweden, Switzerland, Turkey, UK, and USA.

Table A1 Definitions. Description s se ss q qe qs Y Ygr γ γ BG CRED

ECOF

GOVC

HUM

LEND OPEN PUB R&D TAXGS

TAXIN

Gross fixed capital formation over GDP at domestic prices. Source: National Accounts Statistics (UN) Producers' durable goods over GDP at domestic prices. Source: National Accounts Statistics (UN) Total construction over GDP at domestic prices. Source: National Accounts Statistics (UN) Price of investment over price of consumption. Source: ICP benchmark studies (UN) and PWT Price of equipment over price of consumption. Source: ICP benchmark studies (UN) Price of structures over price of consumption. Source: ICP benchmark studies (UN) Real GDP per worker (RGDPW) measured at international prices of year 2000. Source: PWT Growth rate of Y. Source: PWT The capital income share for the OECD countries comes from the OECD statistics. For the non-OECD countries factor shares have been computed with data from the UN National Accounts Statistics Capital income share from Bernanke and Gürkaynak (2001) (% of GDP) Domestic credit to private sector refers to financial resources provided to the private sector, through loans, purchases of nonequity securities, and trade credits and other accounts receivable, which establish a claim for repayment. For some countries these claims include credit to public enterprises Source: World Development Indicators (World Bank) The economic freedom index aggregates over the following five components: (i) The size of government, which includes government consumption, transfers and subsides, marginal tax rates and government enterprises. (ii) The legal structure and the security of property rights, which includes judicial independence, impartial courts, protection of intellectual property, military inference and integrity of the legal system. (iii) The access to sound money, which includes the growth rate of the money supply, inflation variability, inflation rates and freedom to own foreign currency. (iv) The freedom to exchange with foreigners, which includes taxes on international trade, regulatory trade barriers, the actual size of trade sector, the difference between the official exchange rate and the black market rate and international capital market controls. And finally, (v) the regulation of credit, labor and business, which includes credit market regulation, such as the ownership of banks and competition; labor market regulations, such as minimum wages, hiring and firing practices and unemployment benefits; and business regulations such as price controls, administrative conditions, irregular payments and time with government bureaucracy. Source: Fraser Institute (% of GDP) Includes all government current expenditures for purchases of goods and services (including compensation of employees). It also includes most expenditures on national defense and security, but excludes government military expenditures that are part of government capital formation. Source: World Development Indicators (World Bank) Level of human capital. These series are adjusted for quality and have been computed with data on investment in education constructed by the authors. Enrollment by categories of education has been obtained from the UNESCO Statistical Yearbooks Rate charged by banks on loans to favored customers. Source: World Development Indicators (World Bank) Exports plus imports to GDP at current international prices. Source: PWT The public capital stock has been computed with data on public investment available at the Government Finance Statistics Yearbook (IMF) The Research and Development capital stock has been computed with data on R&D investment expenditure available at the UNESCO Statistical Yearbooks (% of GDP) Taxes on goods and services include all taxes and duties levied by the central government on the production, extraction, sale, transfer, leasing, or delivery of goods and rendering of services, or on the use of goods or permission to use goods or perform activities. These include value added taxes, general sales taxes, single-stage and multistage taxes (where “stage” refers to stage of production or distribution), excise taxes, and motor vehicle taxes, and taxes on the extraction, processing, or production of minerals or other products. Source: World Development Indicators (World Bank) (% of GDP) Taxes collected by the central government on income, profits, and capital gains as levied on wages, salaries, tips, fees, commissions and other compensation for labor services; interest, dividends, rent, and royalties; capital gains and losses; and profits of businesses, estates, and trusts. Social security contributions based on gross pay, payroll, or number of employees are not included, but taxable portions of social security, pension, and other retirement account distributions are included. Source: World Development Indicators (World Bank)

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(ii) Non-OECD group. Argentina, Brazil, Chile, China (data starting 1975), Colombia, Ecuador, Egypt, Hong Kong, India, Indonesia, Iran, Kenya, Malaysia, Morocco, Pakistan, Panama, Peru, Philippines, Sri Lanka, Singapore, Thailand, Tunisia, Uruguay, and Venezuela. Therefore, our sample comprises 50 countries over the period 1960–2000 with 26 countries that belong to the OECD. This makes a balanced representation of all major economic areas. Some further non-OECD countries could be added to this sample at the cost of lowering our data quality demands. Economic variables. In our empirical investigation we use the nominal investment rate and its two components: equipment and structures. These rates are computed at domestic prices using the data and definitions available in the UN National Accounts Statistics. Equipment includes electrical and non-electrical machinery as well as transportation equipment, while structures comprises residential, non-residential and other construction. The relative prices of aggregate investment are taken from PWT 6.2 while the disaggregated values are provided by the ICP benchmark studies. For our period of analysis, we have ICP benchmark studies for years 1970, 1975, 1980, 1985, 1990, and 1996. Various sources have been used for the explanatory variables (see Table A1). Output per worker measured at international prices is taken from the PWT. Capital income shares for the OECD countries are taken from the OECD statistics, whereas for the non-OECD countries we have used data available at the UN National Accounts Statistics. The stocks of human capital, R&D, and public capital were constructed in our previous work (García-Belenguer and Santos, 2010). The R&D and public capital stocks are computed as a share of GDP. Many of the variables representing the economic environment and economic policies are from the WDI of the World Bank. The WDI contains various kinds of data, but many of those did not turn out to be significant and are not reported. These variables include the consumer price index, the exchange rate, the interest rate spread, and the share of import duties to GDP. Aggregates for relative prices. We aggregate the categories of the 1996 benchmark study into our four categories: equipment, structures, goods and services. The category of goods includes fuel and power, furniture coverings and repair, other household goods, household appliances and repairs, and personal transportation equipment. The category of services comprises gross rent and water charges, medical and health services, operation of transportation equipment, purchased transport services, communication, recreation and culture, education, restaurants, cafes and hotels, and other goods and services. Structures and equipment are taken as defined in Section 5. 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