The determinants of capiand the US

Dario Judzik a, Hector Sala a,b,a t Aut

; IZA, Germany.All rights re

http://dx.doi.org/10.1016/j.jjie.2014.10.003

Corresponding author at: Departament dEconomia Aplicada, Universitat Autnoma de Barcelona, Edici B, 08193Bellaterra, Spain.

E-mail addresses: dariojudzik@gmail.com (D. Judzik), hector.sala@uab.es (H. Sala).

J. Japanese Int. Economies 35 (2015) 7898

Contents lists available at ScienceDirect

Journal of The Japanese andInternational Economies0889-1583/ 2014 Elsevier Inc. All rights reserved.de Barcelona, Edici B, 08193 Bellaterra, Spain 2014 Elsevier Inc. served.Biased technological changeElasticity of substitutionCapacity utilization rateEmployment

in the capital deepening process of these economies, and lead us toconclude that demand-side drivers, quite relevant in the US, mayalso be relevant to account for different growth experiences. Aclose look at the nature of technological change is also neededbefore designing one-size-ts-all industrial, economic growth,and/or labor market policies. J. Japanese Int. Economies 35 (2015)7898. Departament dEconomia Aplicada, Universitat AutnomaDepartament dEconomia Aplicada, Universitab IZA, Germany

a r t i c l e i n f o

Article history:Received 4 April 2014Revised 15 September 2014Available online 18 November 2014

JEL classication:E22E24O33

Keywords:Capital intensitytal intensity in Japan

noma de Barcelona, Edici B, 08193 Bellaterra, Spain

a b s t r a c t

Judzik, Dario, and Sala, HectorThe determinants of capitalintensity in Japan and the US

We estimate the determinants of capital intensity in Japan and theUS, characterized by striking different paths. We augment anotherwise standard Constant Elasticity of Substitution (CES) modelwith demand-side considerations, which we nd especially rele-vant in the US. In this augmented setting, the elasticity of substitu-tion between capital and labor is placed between 0.74 and 0.90 inJapan, and around 0.30 in the US. We also nd evidence of biasedtechnical change, which is capital-saving in Japan but labor-savingin the US. These differences help us explain the diverse experiencejournal homepage: www.elsevier .com/locate/ j j ie

1. Introduction

Although capital intensity, i.e. the ratio of capital stock over employment, plays a central role ineconomic growth models, it is generally considered as an input variable. No effort is devoted to the

D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898 79empirical assessment of its determinants in spite, for example, of the contrasted trajectory of capitalintensity across countries, or in spite of the limitation that this imposes in growth accountinganalysis.1

This paper intends to ll this void by providing evidence on the determinants of capital intensity intwo economies with different trajectories: Japan and the United States. As shown in Fig. 1, the differ-ent time paths followed by the capital-per-worker ratio is itself calling for an empirical analysis of itscauses.

The progress of capital intensity was especially intense in Japan, where the amount of capital stockper employee grew almost sixfold between 1960 and 2011, in contrast to the US, where it less thandoubled (Fig. 1a). The origin of these differences lies in the very dynamic process of capital deepeninglinked to the industrialization process experienced by Japan in the 1960s and 1970s. However, afterpeaking in the rst half of the 1970s, the growth rate of capital intensity has evolved around a steadydownward path (Fig. 1b). On the contrary, the process of capital deepening in the US accelerated fromthe mid 1980s until 2009 when the Great Recession caused a sudden fall similar to those occurred inthe aftermath of the oil prices shocks.

To investigate on the determinants of capital intensity, we depart from a standard Constant Elas-ticity of Substitution (CES) model along the lines, among others, of Antrs (2004) and McAdam andWillman (2013) and relax the assumptions of perfect competition and perfect information. In thisway, we force rms to deal with product demand uncertainty, which they do by adjusting their degreeof factor utilization ex post, once investment decisions have already been made. In this context, capitalintensity is driven by supply-side factors (i.e., factor costs and technology) as well as by demand-sideconditions. The result is a model of capital intensity where the capital-per-worker ratio is explained bythe relative factor cost which is the main supply-side driver, relative factor utilization which is themain demand-side driver, and technological change which, as standard, is assumed to grow at a con-stant rate. Following related literature (e.g., Madsen, 2010; Hutchinson and Persyn, 2012), additionalempirical controls related to the tax system and the degree of exposure to international trade areconsidered.2

In this way, our paper contributes to the literature in three main dimensions. First of all, in consid-ering an extended CES model with demand-side considerations arising from the existence of imperfectcompetition and imperfect information. Second, in providing an empirical account of the determinantsof capital intensity in this wider than usual perspective, including updated estimates of the elasticityof substitution between capital and labor. Third, in identifying the different nature of factor-biasedtechnical change in Japan and the US, in response to the recent call for results by McAdam andWillman (2013, p. 698): . . . despite renewed interest in models of biased technical change, the cor-responding empirical effort to identify (i.e., measure) episodes from macro data has been lacking.

In a rst quantitative analysis, the estimated models are used to explore the explanatory power ofthe supply-side factors. We measure, in particular, the relative incidence of efciency and technology.We nd the latter to overwhelm the former in Japan, and to provide a close account of the facts whentaken together. In contrast, the relative incidence of these two factors in the US compensates oneanother. Hence, when their joint inuence is evaluated, wide space is left to demand-sidedeterminants.

In a second exercise we conduct dynamic accounting simulations. In each of them, the time path ofcapital intensity is evaluated as a result of different counterfactual scenarios that affect each empiricaldeterminant of capital intensity. As expected, we nd relative factor costs to be crucial in explaining

1 Madsen (2010), for example, points out that a problem associated with the traditional growth accounting framework is thelack of information about the factors responsible for the evolution of capital intensity.

2 A different way of looking into capital intensity is the one by Hasan et al. (2013) in a HecksherOhlin setup. They argue thatlabor and capital market regulations determine the industry-level capital stock per worker, and claim that restrictive labor laws

can curb rms ability to adjust their labor demand to shocks in demand, technology and trade.

300

4

5

00 =

196

0

e

Fig. 1. Capital intensity. Source: Ameco database.2. Analytical framework

We depart from a CES production function from which the factor demand equations are rstderived, and then combined into a single expression that accounts for the supply-side determinantsof capital intensity. This is along the lines of Antrs (2004) and McAdam and Willman (2013). Then,we add the possibility of product demand uncertainty in the spirit of Andrs et al. (1990a,b),Fagnart et al. (1999) and Bontempi et al. (2010). In this context, when expected demand is not metby its actual value, rms are likely to react by adjusting their use of the production factors eitherby hiring or ring workers, by changing the rate of capacity utilization, or by using both mechanisms.In other words, the uncertainty on the actual level of product demand creates a transmission channelby which the demand-side conditions affect the investment and hiring/ring decisions of the rms.the time-path of capital intensity in both countries. But, beyond that, we also nd that relative factorutilization, the demand-side determinant, accounts for a signicant chunk of its progress (or, better, ofits lack of progress) in the US. Finally, the different nature of the biased-technological change is shownto exert the opposite inuence on the progress of capital intensity. It has contributed to slow it downin Japan, due to its capital-saving nature, while it has boosted it quite intensively in the US because ofits labor-saving essence. Our simulations also point to growing openness to trade in Japan as a relevantfactor hindering the process of capital intensity.

The rest of this paper is structured as follows. Section 2 presents the analytical framework. Section 3deals with empirical issues related to the data and the estimated models. Section 4 computes the elas-ticities of substitution between capital and labor, and evaluates technological change in Japan and theUS. Section 5 presents counterfactual simulations. Finally, Section 6 concludes.0

100

200

60 65 70 75 80 85 90 95 00 05 10

United StatesInde

x 1

-2

0

2

60 65 70 75 80 85 90 95 00 05 10

United States

Per

cThis e

2.1. Fa

Coinputsrm h

where(proxy(proxy00

00Japan

4

6

ntag

e600(a) Levels

8Japan

(b) Growth rates

80 D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898xplains why capital intensity is likely to depend both on supply-side and demand-side factors.

ctor demands and capital intensity

nsider an economy with f identical rms that supply a homogeneous good. These rms acquirein competitive markets and face a cost per unit of labor W, and a cost of capital use CC. Eachas a CES production technology so that:

Yt h ANt Nt b

1 h AKt Kt b 1=b

; 1

Y is output, N is employment, K is capital stock, AN is an index of labor-augmenting efciencying Harrod-neutral technological change), and AK is an index of capital-augmenting efciencying Solow-neutral technological change); the parameter h represents the factor share

0 < h

Neket byThis i

Thdemaminefor lab

D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898 81Along the lines of Fagnart et al. (1999) rms use a putty-clay technology. With productive capacityxed in the short-run, rms adjust the degree of factor utilization, and capital and labor are substitutesex ante. Ex post, once capacity choices have been made and idiosyncratic shocks are known, rmsactual demand is faced by adjusting the utilization intensity of the production factors; i.e., by hir-ing/ring workers, and by deciding on the capacity utilization rate. At this stage, production factorsmay be thought as complements to achieve a certain level of production. This model, therefore, allowsfor ex post rationing of factor utilization in contrast to the standard maximization problem.

The realization of the demand faced by rms depends on two factors: the price level (chosen byrms) and random shocks. The expected demand that rms consider in their prot maximizationproblem is the expected value of this realization YEt :

YE E Y P ;u ; 5e sequence of decisions is as follows. Firms maximize prots subject to their expectation ofnd in period t. In t 1, once the realization of the random (and unexpected) shocks that deter-the demand are known, the utilization rate of installed capacity and the corresponding demandor are adjusted accordingly.YE. Uncertainty about aggregate demand shapes rms investment decisions (Fagnart et al., 1999;Bond and Jenkinson, 2000; Bontempi et al., 2010) and allows for the inclusion of demand-sideconsiderations.xt, we relax the assumption of perfect competition and perfect information in the product mar-assuming that rms hold some market power and are subject to random unexpected shocks.

mplies that rms will now maximize prots based on an expectation of the stochastic demand1bthe degree of substitutability between both factors.

As standard (Antrs, 2004; Len-Ledesma et al., 2010), we assume that biased technological pro-gress grows at constant rates denoted, respectively, by kN and kK . We thus have A

Nt AN0 ekN t and

AKt AK0ekK t , where AN0 and AK0 are the initial values of the technological progress parameters, and tis a linear time trend. Note that kN kK > 0 would imply Hicks-neutral technical progress; kK > 0and kN 0 implies Solow neutrality; kN > 0 and kK 0 yields Harrod neutrality, while kN; kK > 0 butkN kK is indicative of factor-biased technical change.

Prot maximization in a perfectly competitive environment yields expressions for the factordemands (as a proportion of total output) that log-linearized can be written as

logKt=Yt aK r logCCt=Pt 1 rkKt; 2logNt=Yt aN r logWt=Pt 1 rkNt; 3

where P is the aggregate product market price; aK r log1 h r 1 logAK0 and aN r log hr 1 logAN0 are constants; and 1 r b1b. Subtraction of Eq. (3) from Eq. (2) yields the followingspecication for capital intensity:

logKt=Nt a r logCCt=Wt 1 rkN kKt; 4

where a aK aN .Eq. (4) is standard and corresponds, for example, to Eq. (30) in Antrs (2004, p. 19) and Eq. (5) in

McAdam andWillman (2013, p. 704). Following this expression, capital intensity depends on two sup-ply-side factors: (i) the relative cost of labor and capital and (ii) the direction of factor-biased technicalchange. In other words, there will be more capital intensity whenever real wages grow faster than theuser cost of capital, thus making labor relatively more expensive than capital; and whenever labor-efciency grows faster than capital-efciency kN > kK, provided that labor and capital are gross com-plements, i.e. r < 1.

2.2. Product demand uncertainty< 1; r 1 is the constant elasticity of substitution between capital and labor; and b denotest t1 t t

where E is the rational expectations operator, and u represents an idiosyncratic (stochastic) shockwith zero mean and a constant standard deviation greater than zero. In other words, rms produce(and decide their factor demands) accordingly to their expectation of product demand, which is afunction of the the aggregate product market price and the shocks.

tions

2.3. Mind the gap

Th2005;

capacable, w

among others, Graff and Sturm (2012). In this paper, however, we are also interested in Eq. (9) andrequirsameresponthe em

82 D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898relative to its total potential use (working-age population, Z).Accordingly, we re-write the factor demand equations as:

3 Although rms invest in capacity following their expectation on potential demand, they end up using it based on the actualdemand they face (this is the idea of ex post rationing) determining, in this way, their degree of capacity utilization (or capacity

utilizatie a specic proxy for the demand-pressures affecting the labor factor. For this, we follow thereasoning than the one normally used for Eq. (8).3 Thus, based on the fact that production issive to aggregate demand ex post, and installed capacity is rigid in the short run, we considerployment rate NR N=Z, which reects the actual use of the labor factor (employment, N)as a proxy of the ratio bY tYt .Regarding Eq. (8), the natural proxy is the standard capacity utilization rate CUR variable see,e bY tYt ratio is the transmission channel for business cycle effects (Fagnart et al., 1999; Nakajima,Planas et al., 2013). As such, it is directly related to the gap between total installed production

ity and the rate of capacity utilization of the production factors. However, since bY t is unobserv-e follow the literature and assume that the degree of factor utilization can be empirically usedt

Yt hr t

PtAN0 e

kN t 1b tYt

; 9

where the ratio bY tYt expresses the gap between potential aggregate demand bY and the actual level ofaggregate production Y, once factor demands have been adjusted ex post.ate demand level Y . Further addition of the ratio Yt 1 to the left-hand side of both equa-then yields:

KtYt

1 hr CCtPt

rAK0e

kK t b

1b bY tYt

; 8

N W r b bYUnder these assumptions, the prot-maximization problem of the rm corresponds to a standardmonopolistic competition case:

max p Kt ;Nt ; Pt PtYEt WtNt CCtKt ;

s:t: : YEt Et1 h AN0 ekN tNt b

1 h AK0ekK tKt b 1=b

;

where p stands for the rms prot function.Operating from the rst order conditions of this problem, the optimal levels of factor utilization rel-

ative to output are obtained as an inverse relation with respect to each factors cost:

KtYEt

1 hr CCtPt

rAK0e

kK t b

1b; 6

NtYEt

hr WtPt

rAN0 e

kN t b

1b: 7

Note that log-linearization of Eqs. (6) and (7) under perfect competition and perfect informationwould yield Eqs. (2) and (3).

Through aggregation of the f rms, the overall expected demand can be replaced by the potentialaggreg b Yton rate).

Kt 1 hr CCt r

AK0ekK t

b1bhCURt; 10

Log-linearization of Eqs. (10) and (11), and subtraction of the second one from the rst one yieldsan exp

logKt a r log CCt log Wt 1 r kN kK t

menting in medium-run transitions away from the BGP. With an elasticity of substitution betweenlabor and capital different from unity, this pattern allows for long-run asymptotic stability of factor

showntively

@K=N> 0 if r < 1; 13

kN < kK , there is a fall in capital intensity.Th

Chirin(2013

4 Conand NR

D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898 83is situation of r < 1 is empirically endorsed in the works of Antrs (2004), Chirinko (2008),ko et al. (2011), Len-Ledesma et al. (2010), Klump et al. (2012), and McAdam and Willman).

sistently with the rest of the variables, we assume that the log-linearization of h yields a linear function of the logs of CUR@AN=AK

which, in terms of Eqs. (4) and (12), takes place whenever kN > kK . On the contrary, with r < 1 andby McAdam and Willman (2013, p. 703), this implies that capital intensity grows with a rela-higher growth of labor-augmenting technical change:shares and, also, for a non-stationary evolution in the medium-run, which we actually observe inreality.

In the context of our model, let us consider a situation in which the elasticity of substitutionbetween labor and capital is below unity (and the production factors are gross complements). AsNt Pt Pt cK cN log CURt log NRt : 12

Note that the only difference with respect to Eq. (4) is the last term, which results from theassumption of stochastic behavior of aggregate product demand allowing for ex post rationing of factorutilization.

2.4. Factor-biased technical change

The empirical measurement of factor-biased technological change is a critical issue see, amongmany others, Antrs (2004), Len-Ledesma et al. (2010, 2014), and McAdam and Willman (2013). Inthis context, making a priori assumptions about the form of technical progress (e.g. assuming Hicksneutrality) is likely to misguide the insights on the effect of technical progress, for example, on capitalintensity. This is the reason why it is worth paying close attention to the second term in the right-hand-side of Eq. (12).

Achieving a balanced growth path (BGP) in standard models of economic growth implies that themain macro variables converge to a common growth rate, the underlying ratios (factor income sharesand factor to GDP ratios) remain constant as described by Kaldor (1961), and technical change issolely labor augmenting (i.e., Harrod neutral). Acemoglu (2003) and McAdam and Willman (2013)suggest that although technical progress is labor-augmenting along the BGP, it can be capital-aug-ression for capital intensity and its determinants4:

Yt PtNtYt

hr WtPt

rAN0 e

kN t b

1bhNRt; 11

where h are monotonically increasing functions of CURt and NRt (see Andrs et al., 1990a, p. 88).as presented in Eq. (12).

3. Empirical issues

3.1. Estimated models

We augment the base-run Eq. (12) with two sets of control variables related to capital intensity:the degree of exposure to international trade and the scal system. Since capital intensity, the degreeof substitution between capital and labor, and globalization are deeply intertwined (Hutchinson andPersyn, 2012), inclusion of the degree of trade openness op is a must. Regarding the scal system, akey variable for rms decisions is direct taxes on business, which is crucial in dening, for example,investment decisions. This has been studied in Bond and Jenkinson (2000), Edgerton (2010) andMadsen (2010), where the decelerating effect of corporate taxation on capital deepening is explainedas a disincentive to rm-level investment. Because we originally have one expression per productionfactor, we consider both direct taxes on business sb and direct taxes on households sh to capture, ifany, the specic impact of taxes on each factor. Of course, payroll taxes is another crucial element ofthe tax system, but its relevance is more related to the wage bargaining process between rms andworkers. Since this is implicitly taken into account through the wage variable in the user cost of capital(total compensation, which includes social security contributions), no further control is required.

Following this reasoning, the rst model we estimate is a straightforward augmented version of Eq.(12):

knt b0 b1cct wt b2curt nrt b3t b4opt b5sb b6sh u1t ; 14where knt logKt=Nt, cct logCCt=Pt,wt logWt=Pt, curt logCURt, nrt logNRt and u1t rep-resents a standard error term with zero mean and constant standard deviation. This is called Model 1in Tables 25. Note, also, that detailed denitions of the additional controls, op; sb, and sh (and also of

n Employment

84 D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898kn Capital intensity k nz Working-age populationnr Employment rate n zcur Capacity utilization ratew Real compensation per employeehr Hours of work per employeeY GDPX Exports of goods and servicesM Imports of goods and servicesop Trade openness = log([X +M]/Y)c Constantp GDP deatorpi Investment deatord Depreciation ratei Nominal interest ratecc Real user cost of capital pip i d DpiTB Direct taxes on businessTH Direct taxes on householdssb Direct taxes on business (TB) as % GDP = log(TB/Y)sh Direct taxes on households (TH) as % GDP = log(TH/Y)t Linear time trendD Difference operatork Real net capital stockthe rest of the variables) are given in Table 1.We consider a second model because the choice of demand-side drivers in factor demand equa-

tions is still an open issue, and we want to know how robust their inclusion is. This is the reasonwhy, on top of the relative degree of factor utilization logCURt logNRt, we follow An-Hign

Table 1Denitions of variables.Note: All variables used in the econometric analysis are expressed in logs.

(2007) and consider the variation in worked hours per employee as an alternative aggregate proxy ofdemand-side pressures (we take the growth rate because this proxies the business cycle in terms of

for the perception of the rm of the economic reality, which reects on its expectations on aggregatedemaintensment rate widens.

D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898 85Given the assumption of constant rates of technical progress, the coefcients b3=c3 1 rkN kK measure an asymmetric progress in the efciency of each production factor. If b^3=c^3 > 0and r^ < 1, there is evidence that labor-augmenting efciency grows faster than capital-augmentingefciency (the same holds in case of opposite signs in both estimates). If, on the contrary, theb^3=c^3 > 0 are positive and r^ > 1, the conclusion is that capital-augmenting efciency grows fasterthan labor-augmenting efciency. In both cases, therefore, there is evidence of biased technologicalchange, something that in the standard CobbDouglas framework, where r^ 1, cannot be measured.

5 Decisions to invest in new capacity are inuenced by the cost and availability of capital and the target rates of return sought byrms and nancial institutions. The dependence on bank loans is an important factor limiting expansion and the user cost of

capitalnd. Since the expansion of capacity drives investment, we expect a positive effect on capitality when the wedge between a higher degree of capacity utilization rate and a higher employ-time-varying demand-side pressures). The reasoning behind this choice is that worked hours peremployee reect simultaneously the increase in the usage intensity in both capital stock and labor.Moreover, the average annual amount of hours worked per employee is likely to avoid the endogene-ity problems that would entail considering variations in output (since the dependent variable isindeed made of capital and labor), which is the natural alternative in the literature.

Following this reasoning, in Model 2 we substitute relative factor utilization, curt nrt , by thechange in worked hours per employee Dhr:

knt c0 c1cct wt c2Dhrt1 c3t c4opt c5sb c6sh u2t; 15

where u2t represents a standard error term with zero mean and constant standard deviation. Note thatthe coefcient on hours is lagged once to help avoiding endogeneity problems. In contrast, the termcapturing demand-side pressures in Eq. (14) is not lagged to maintain coherence with respect tothe theoretical model. We have assumed a putty-clay technology and argued that short-run capitalstock adjustments take place through changes in the degree of capacity utilization. This implies thatdemand changes foreseen in t 1 are accommodated through changes in investment, not throughchanges in cur which can only respond in period t.

A crucial remark is that these empirical models are estimated as dynamic equations to take intoaccount the adjustment costs potentially surrounding all variables involved in the analysis (endoge-nous and exogenous). The lagged structure of the estimated relationships is therefore a strict empiricalmatter.

The coefcients b1=c1 are associated to the relative cost of production factors, and a negative sign isexpected. As the wedge between the cost of factors cc w increases, capital becomes relatively morecostly than labor, and a deceleration in the growth capital intensity is expected.5 The crucial feature ofthese coefcients is their correspondence with the constant elasticity of substitution between capital andlabor r.

The coefcients b2=c2 are associated to the role of demand-side pressures, and a positive sign isexpected. A rise in the wedge between the relative intensity in factor utilization cur nr implies thattightness in the capital side is larger than in the labor side. Firms, therefore, are expected to react byinvesting more intensively than embarking in new hirings. As a consequence, capital intensity isexpected to accelerate.

Firms decisions to expand capacity through investment are based to a large extent on their assess-ment of their future sales, which we assumed to be uncertain. Managers are naturally cautious aboutoverestimating future sales, as the penalty for doing so tends to be much greater than for losing poten-tial business by failing to expand (Smith, 1996). In our model, the capacity utilization rate is a proxyis a crucial factor in the expected net return to investment by rms.

3.2. Data

We use annual data obtained from various sources. From the European Commissions Ameco data-base we take long-time series on net capital stock.6 Data on the capacity utilization rate is obtainedfrom Ministry of Economy, Trade and Industry for Japan, and from the Board of Governors of the Federal

86 D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 78983.3. Estimation procedure

Time series estimates need to ensure that the long-run estimated relationships between capitalintensity and its determinants are non-spurious. Of course, if k;n; cc;w; cur; z; TB; TH, and Y certainlybehaved as I1 variables we could argue, since we work with these variables in ratios(kn; cc w; cur nr; X M=Y; TB=Y and TH=Y), that we end up dealing with I0 variables and coin-tegration issues are of no concern.

However, unit root tests show that some of these ratios behave as I1 variables (see Table A1 in theappendix for the tests results). This is why our estimation is conducted following the bounds testingapproach, or ARDL (AutoRegressive Distributed Lag) approach, which yields consistent short- andlong-run estimates irrespective of whether the regressors are I1 or I0. This approach, which wasdeveloped by Pesaran and Shin (1999) and Pesaran et al. (2001), provides an alternative econometrictool to the standard Johansen maximum likelihood, and the Phillips-Hansen semi-parametric fully-modied Ordinary Least Squares (OLS) procedures. The main advantage of the bounds testingapproach is the possibility of avoiding the pretesting problem implicit in the standard cointegrationtechniques. It also yields consistent long-run estimates of the equation parameters even for small sizesamples and under potential endogeneity of some of the regressors (see Harris and Sollis, 2003).

We proceed as follows. We rst estimate our models by OLS, and select equations that are dynam-ically stable and satisfy the conditions of linearity, structural stability, no serial correlation, homosce-dasticity, and normality of the residuals. Then, among the models that meet these requirements, weselect the dynamic specication of each equation by relying on the optimal lag-length algorithm ofthe Schwartz information criterion (Table A2 in the appendix shows that these standard diagnostictests are all passed at conventional signicance levels). Then, to make sure that we have obtainednon-spurious relationships between potential non-stationary variables, we verify that the residualsresulting from our estimated models are indeed stationary (see Table 4).

Finally, we estimate the selected specications by Two Stages Least Squares (TSLS) so as to controlfor potential endogeneity biases in the estimated effect of the relative factor costs cc w, in relativefactor utilization cur nr or hours, and in direct taxes on business. The instruments are statisticallysignicant and we nd the OLS and the TSLS results to be relatively alike, thus supporting the robust-ness of the estimated relationships.7

4. Results

4.1. Estimated equations

We present the estimation results for Eqs. (14) and (15) in Table 2, for Japan, and Table 3, for the US.

6 The net capital stock at constant prices is computed as OKNDt OKNDt1 OIGTt UKCTt : PIGTt 100, where OIGT = grossxed capital formation at constant prices; UKCT = consumption of xed capital at current prices; and PIGT = price deator grossxed capital formation; and OIGT = gross xed capital formation at constant prices in construction; equipment; products ofagriculture, forestry, sheries and aquaculture; and other products.

7 Although, the DurbinWuHausman test of exogeneity is rejected by a short margin in Model 2 for Japan, this is not affectingReserve System for the US. The rest of the variables is gathered from the OECD Economic Outlook.Table 1 provides the concrete denitions of the empirical variables used. All of them are standard

and the only clarication refers to the denition of the user cost of capital, which is constructed aspi

p i d Dpi

assuming a constant depreciation rate, d, equal to 0.1. All variables will be used in logsso as to allow an unambiguous interpretation of the estimated coefcients as elasticities.our empirical conclusions because our simulation exercises are based on Models 1 estimates.

D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898 87Table 2Japan, 19802011.

Model 1 Model 2

OLS TSLS OLS TSLS

c 0.224 0.218 c 0.179 0.017[0.023] [0.033] [0.077] [0.922]

knt1 0.950 0.947 knt1 0.953 0.958[0.000] [0.000] [0.000] [0.000]

cct wt 0.035 0.039 cct wt 0.035 0.038[0.000] [0.000] [0.000] [0.006]

Dcct wt 0.020 0.019 Dcct wt 0.021 0.025[0.001] [0.000] [0.000] [0.007]

Dcct1 wt1 0.016 0.017 Dcct1 wt1 0.018 0.023[0.002] [0.000] [0.001] [0.000]

curt nrt 0.001 0.0004 Dhrt1 0.033 0.069[0.910] [0.965] [0.400] [0.154]

Dcurt nrt 0.014 0.013[0.116] [0.223]

Dsbt 0.015 0.015 Dsbt 0.014 0.012Japans estimation includes several dummy variables: d8090; d9102; d0311, and d97, which take valueone, respectively, in 19801990, 19912002, 20032011, and 1997. The rst three are designed tocapture the deceleration in the time-path of capital intensity since the 1970s, while d97 accountsfor the turmoil brought by the East-Asian crisis. The latter helps to achieve better results in termsof the misspecication tests (displayed in Table A2).

The estimated coefcient associated to the rst lag of capital intensity is large in all estimatedequations. This high persistence is to be expected since productive capacity is not easily changed inthe short run. Relative factor costs in Japan are highly signicant and with the expected negative signin both models. Regarding the demand-side proxies, hours worked in Model 2 have greater statisticalsignicance than the employment rate in Model 1. Direct taxes, both on businesses and households,exert the expected decelerating effect on capital intensity in the two models, as also does the degreeof openness to international trade.

Finally, the estimated coefcients associated to the time trends are negative. Although the short-run estimates are similar for the 1980s and the lost decade, they reveal signicant differences whentranslated into long-run elasticities. Note also, that the largest impact of technological change on cap-ital intensity takes place in 20032011, coinciding with the years in which the progress of capitalintensity has been the slowest in the whole sample period. In any case, the negative effect of techno-logical change in the three cases, combined with a lower-than-one elasticity of substitution, is

[0.000] [0.001] [0.001] [0.102]Dsht1 0.008 0.007 Dsht1 0.010 0.009

[0.140] [0.194] [0.047] [0.106]opt 0.031 0.033 opt 0.032 0.044

[0.000] [0.000] [0.000] [0.000]

D8090 t=100 0.045 0.043 D8090 t=100 0.045 0.047[0.000] [0.000] [0.000] [0.000]

D9102 t=100 0.041 0.040 D9102 t=100 0.042 0.044[0.000] [0.000] [0.000] [0.000]

D0311 t=100 0.060 0.058 D0311 t=100 0.060 0.057[0.000] [0.000] [0.000] [0.000]

D97 0.010 0.010 D97 0.010 0.010[0.000] [0.000] [0.000] [0.002]

LL 175.3 173.4Obs 32 32 32 32

Notes: LL = log-likelihood; p-values in brackets; Instruments: knt1 cct1 wt1 Dcct1 Dwt1 curt1 nrt1 opt1 Dsht1 Dsbt Dsbt1D9102 D

83 D97 t Dhrt1 Dhrt2.DurbinWuHausman test [prob]: Model 1 [0.95]; Model 2 [0.04].

Table 3US, 19702011.

Model 1 Model 2

OLS TSLS OLS TSLS

c 0.345 0.327 c 0.136 0.286[0.401] [0.516] [0.772] [0.582]

knt1 0.951 0.941 knt1 0.973 0.965[0.000] [0.000] [0.000] [0.000]

Dknt1 0.292 0.308 Dknt1 0.215 0.288[0.015] [0.038] [0.241] [0.176]

cct wt 0.010 0.016 cct wt 0.013 0.011[0.094] [0.132] [0.058] [0.443]

curt nrt 0.083 0.126 Dhrt1 0.310 0.204[0.139] [0.192] [0.317] [0.572]

Dcurt nrt 0.182 0.170 Dhrt2 0.526 0.547[0.000] [0.001] [0.027] [0.026]

sbt 0.019 0.035 sbt 0.018 0.008[0.069] [0.114] [0.115] [0.699]

sht 0.002 0.003 sht 0.014 0.011 ][0.899] [0.862] [0.366] [0.535

Dopt 0.099 0.069 Dopt -0.149 0.206[0.024] [0.382] [0.002] [0.002]

t 0.001 0.001 t 0.0002 0.0004[0.079] [0.191] [0.655] [0.492]

LL 161.2 155.5Obs. 42 42 42 42

Notes: LL = log-likelihood; p-values in brackets; Instruments: knt1 Dknt1 cct1 wt1 curt1 nrt1 Dcurt1 Dnrt1sb sb sh sh Dop t Dhrt1 Dhrt2.

88 D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898indicative that capital-associated efciency grows at a higher rate than labor-associated efciency (adetailed discussion on this issue is provided in Section 4.2).

As for the US, the coefcients associated to relative factor cost are also negative and signicant.And, in contrast to Japan, not only Dhrt1 presents statistical signicance, but also the relative factorutilization. Direct taxes and openness are also detrimental for capital intensity, with the latter enter-ing the equation in differences. This implies a long-run elasticity of capital intensity with respect tothe level of openness cannot be computed. We interpret this as a reection of a more conjuncturalthan structural type of inuence in a context of a closed economy, in contrast to Japan.

The estimated coefcient associated to the time trend is positive. Taking into account that the esti-mated elasticity of substitution for the US is lower than unity, this is indicative of labor-saving biasedtechnical change resulting from faster growth rates of labor-efciency than those of capital-efciency(details in Section 4.2).

Beyond the use of the ARDL methodology, we further ensure the validity of the estimated long-runrelationships (with the key ones presented in Table 5) by testing for the existence of unit roots in theresiduals of the estimated equations. For this, we use the Augmented DickeyFuller test (ADF, withthe null hypothesis of non-stationarity) and the KwiatkowskiPhillipsSchmidtShin test (KPSS, withthe null hypothesis of stationarity). The results of these tests are presented Table 4 and reject, in allcases and by large, the existence of a unit root in the ADF test, and fail to reject the hypothesis ofstationarity in the KPSS test. We thus conclude that the residuals are stationary and we can safelycompute the key long-run relationships.

4.2. Elasticities of substitution, technology and efciency

Directed technical change is a consequence of a production factor becoming relatively more scarce,more expensive, or both. Innovation is then directed towards technologies that would save on the rel-atively more expensive factor. The bias in technical change may have a saving effect on one factor and

t t1 t t1 t1DurbinWuHausman test [prob]: Model 1 [0.92]; Model 2 [0.73].

an augmenting effect on the other one. The degree of substitutability between labor and capital is clo-sely related to this phenomenon. They are, together, key variables in economic growth models, with

Eqs. (4) or (12). More precisely, in case of Models 1 estimates for Japan, we use r 0:74 andeLRkntren

Table 4Unit root tests on the residuals of Eqs. (14) and (15).

ADF test KPSS test

Model 1 u1t Model 2 u2t Model 1 u1t Model 2 u2tOLS TSLS OLS TSLS OLS TSLS OLS TSLS

Japan 6.09 5.70 5.27 5.37 0.056 0.107 0.071 0.216US 4.17 6.18 6.41 6.89 0.054 0.042 0.081 0.083

Note: ADF test critical value is 3.60 at the 1% level.KPSS test critical values are 0.739 at the 1% level, and 0.463 at the 5% level.

D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898 89) kK kN 3:1%:This result implies that there is factor-biased technical change in Japan (kK kN > 0, that is, kK kN)and the direction, in this case, is capital saving.

Table 5 shows the calculations for both countries using the instrumental variables estimation ofModels 1 and 2.

As noted, we nd the elasticity of substitution between capital and labor to be below 1 in Japan.This value is larger than in other studies, which place it between 0.2 and 0.4 (Rowthorn, 1999,Klump et al., 2012). However, neither the sample period nor the methodology is common to theone followed here.Table 5Elastici

Japa198019912003

Aver

US

Notes: ecapitald 0:81% to compute the value of kK kN using:0:81% 1 0:74kN kKspecial inuence in medium-run dynamics as explained in McAdam and Willman (2013).Table 5 shows the elasticity of substitution between factors implied by our empirical models r^,

together with the long-run impact on capital intensity of the constant rate of technological progresseLRkntrend

. Given that the estimated models are dynamic, the elasticity of substitution is computedas the long-run elasticity of kn with respect to cc w. Taking the example of Japan using Model 1,we have 0:039=1 0:947 0:74 r^. In turn, the long-run impact of the constant rate technologicalchange in 19801990 is eLRkntrend 0:043=1 0:947 0:81%.

These two values are used to compute the implied rate of biased technological change following^ties of substitution and technological change.

Model 1 Model 2

Technical progress Technical progress

r^ eLRkntrend (%) Type Rate (%) r^ eLRkntrend (%) Type Rate (%)

n1990 0.74 0.81 Capital saving 3.1 0.90 1.12 Capital saving 11.22002 0.75 2.9 1.05 10.52011 1.09 4.2 1.36 13.6age 0.88 3.4 1.18 11.8

0.27 1.69 Labor saving 2.3 0.31 1.14 Labor saving 1.7

LRkdtrend denotes the long-run elasticity of capital intensity with respect to constant technical change; technical change issaving whenever kK > kN and labor saving whenever kN > kK .

We nd the long-run impact of technological change to be between 0.75% and 1.36%, dependingon the model and period of reference. This implies that a rise in the rate of technological progress istranslated, in the long-run and ceteris paribus, to a fall in capital intensity. This result is critical tounderstand the deceleration in the process of capital deepening experienced by Japan since the mid1970s. Together with the estimated elasticity of substitution, it provides evidence of a substantial biasin technological change, which is capital saving, and evolves at a rate around 3% according to Models 1estimahigher

90 D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898This is consistent with the path followed by the process of capital deepening in Japan, with a hugeincrease in capital accumulation in the expansionary decades of 1960 and 1970, and a steep and con-tinuous decrease in the 1980s, 1990s and 2000s. On this account, let us recall that our sample periodfor Japan starts in 1980. Not only this prevents us to have noise from the structural break occurred inthe Japanese economic growth model, but it also allows us to capture more precisely this extraordi-nary long period of continuous deterioration in the ratio of capital stock to employment.

Regarding the US, our analysis yields an elasticity of substitution between capital and labor around0.3, a value in the lower range of the estimates provided by the literature. In particular, althoughChirinko (2008) nds a r between 0.4 and 0.6, and Len-Ledesma et al. (2010) and Klump et al.(2007) present values in the 0.50.7 range, it is important to emphasize Chirinkos et al. (2011) indi-cation that the use of time series data at annual frequencies may lower the estimation of r.8 Chirinkoet al. (1999), for example, provide an estimation of the elasticity of substitution rather low for the US ofaround 0.25.

We also nd a long-run impact of technological change on capital intensity between 1% and 2%.This implies that a rise of 1 percentage point in the rate of technological progress is translated, inthe long-run, in at least a 1% increase in capital intensity. In terms of biased technological change,we nd consistent evidence (since Models 1 and 2 yield similar results) of a labor-saving bias (i.e.,labor-related efciency grows at a faster rate in the US, kK < kN). This may contribute to explain thesecular process of industrial rms delocalization of the US economy including the growing relevanceof phenomena such as offshoring and outsourcing.

It is important to remark that our estimates between 1.7% and 2.3% of biased technological changein the US are fully aligned with those supplied by the literature and summarized in Klump et al.(2012), Table 1. The reported range of values obtained from many studies is placed between 0.27%and 2.2%, with the exception of Antrs (2004) where it is placed slightly above 3%.

Once provided with information on r, and on the nature and extent of technological change, it isinteresting to check the capacity of the base-run model to account for the actual trajectories of capitalintensity in each economy. This is done for illustrative periods running from the year in which thegrowth rate of capital intensity attained its maximum (1983 in both Japan and the US), to the yearin which this value was the lowest (1997 in Japan, 2005 in the US). Moreover, by disaggregatingthe two supply-side drivers, this exercise yields a quantitative evaluation of the relative incidenceof efciency and technology in shaping the deceleration of the growth rate of capital intensity. Note,nally, that this exercise is also an implicit test on the relevance of our augmented theoretical setup.The reason is that the unexplained portion of this evolution may be ascribed to demand-side forces,which turn to be relevant in the US (see Section 5).

Differentiating the base-run Eq. (4) with respect to time, and rearranging, yields the followingequation:

dKN

r cW cCC 1 rkN kK; 16

8 Chirinko et al. (2011) argue that time series variations of investment spending largely reect adjustments to transitory shocks;then, because rms respond less to temporary than to permanent shocks, an elasticity estimated with time series data will tend to

be lowetes and 12% if we take Model 2 as reference. The capital-saving effect comes from the fact that arate of capital related efciency growth (i.e., kK > kN) reduces the pace of capital stock growth.r than the true long-run elasticity.

Table 6Supply-side forces: technology vs. efciency.

Japan US

Fall in cc w (%) 56.6 Max to min 116.6 Max to minAnnual average (%) 3.8 (19831997) 5.1 (19832005)

D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898 91where x^ dx=dtx and x represents either logKt=Nt or logCCt=Wt. The rst term is a technology termdepending on the relative cost of the production factors, while the second one is an efciency termdepending on the relative technical progress of those factors.

Eq. (4) can be used, together with the actual values of the variables and the estimatedparameters, to give values to these terms. Then, the portion of the growth in capital intensitynot related neither to technology nor to efciency may be thought as a residual essentiallyconnected to the demand-side factor. Table 6 summarizes the results of this calculation for Japanand the US.9

It is important to remark that the magnitude of both the technology and efciency terms dependson r. Thus, given the larger value in Japan (between 0.74 and 0.90) relative to the one in the US(between 0.27 and 0.31), we expect the rst term to play an specially important role in Japan. Andit does. The technology term accounts for an annual increase between 2.8% and 3.5% in capital inten-sity, which is diminished by the negative impact on capital intensity from efciency gains (0.8% or1% annually, depending on the model). In other words, the effect of labor-saving technologiesoverwhelms the one of efciency gains. This is an important phenomenon that took place in the1970s and 1980s in Japan due to strong wage-hike pressures from the workers side. The responsefrom most Japanese rms was a strategy to introduce more labor-saving technologies instead of

Model 1 Model 2 Model 1 Model 2

r 0.74 0.90 0.27 0.31Technology term (TT): [TT = Annual average r] 2.8% 3.5% 1.4% 1.6%Efciency term (ET): [ET=ABTC (1 r)] 0.8% 1.0% 1.7% 1.2%Total [=TT + ET]: 2.0% 2.5% 0.3% 0.4%Capital intensityActual change (19831997 or 19832005) 3.1% 3.1% 1.3% 1.3%Percent accounted by model 64.5 80.6 23.2a 31.4

Notes: ABTC is the average biased technical change in 19801990 and 19912002 (see Table 5).a The negative sign here indicates that supply-side forces were pushing capital intensity upwards.improving their efciency.10

On the contrary, the technology term in the US explains an annual progress in capital intensity ofaround 1.41.6%, much lower than in Japan. Furthermore, this stimulus is essentially counterbalancedby the inuence of the efciency term which, under Models 1 estimates, is even larger than the onefrom technology.

The addition of both components is also very informative when compared to the actual progress ofcapital intensity. In Japan they account for between 2.0 and 2.5 percentage points of the actual 3.1%annual growth rate. This means that, in 19831997, between 64% and 81% of the evolution of capitalintensity in Japan is explained by supply-side forces. The standard base-run model, therefore, is able toaccount reasonably well for the facts. On the contrary, supply-side drivers account, at most, for a thirdof the actual evolution of capital intensity in the US, which grows much slower than in Japan (asshown in Fig. 1). This leaves space for examining the role of demand-side forces, which is what we

9 The upper block of Table 6 shows the actual evolution of cc w in the periods of interest (19831997, and 19832005), whichis then used to compute the technology term (TT) in the lower block. Note, also, that the calculation of the efciency term (ET) forJapan takes into account the average of the two estimated trends covering years 19831997.10 We owe this point to an anonymous referee to which we are grateful for suggesting us this decomposition and theinterpretation connected to the actual experience of the Japanese economy as just discussed.

do next using the whole sample period and the complete models thus letting all explanatoryvariables compete to explain the facts.

5. Counterfactual simulations

Takahashia et al. (2012) show that capital intensity has been crucial in Japan and other OECDeconomies postwar growth. Few efforts, however, have been made to assess the determinants of

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165.9the economiess capital intensity in such long-run perspective. To contribute to such importantmatter, we now use our estimated models to perform dynamic accounting exercises.

For each country, the estimated Model 1 is solved in two scenarios. The rst one is a baselinescenario in which all exogenous variables take their actual values. In the second scenario, each ofthe exogenous variables (one at a time) is kept constant at its value at the beginning of the sampleperiod (1980 for Japan, 1970 for the US). We call this a counterfactual simulation because thedifference between the tted values of capital intensity obtained with the actual and the simulatedvalues of the explanatory variables reveals how much of its actual trajectory can be explained bythe factor kept constant in the simulation.

Note we are not claiming that the tted values from the simulated scenarios are the true valuesthat capital intensity would have taken had some particular variable remained constant. It is just adynamic accounting exercise to assess which have been the main driving forces of capital intensityin the two examined economies.

Fig. 2 plots the results. The scale in all graphs is based on a 100 index for the rst year of the sampleperiod. To evaluate these results it is helpful to take into account the evolution of the exogenous vari-ables which is plotted in Figs. A1 and A2 in the appendix.

The actual path of capital intensity is represented by the continuous line. With a 98.9% growth, italmost doubled in Japan between 1980 and 2011, while in the US it grew by 65.9% over the 1970 to2011 period.

Following our simulations, had relative factor costs (cc w) remained unchanged at thebeginning of the sample, these growth rates would have been between 30% and 40% (34.2% in

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Fig. 2 (continued)

94 D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898Japan and 40.2% in the US). This is the outcome of the decline in the relative cost of factors thatboth countries have experienced in last decades. This implies that the fall in the relative factorcosts, with capital becoming secularly cheaper, has been a relevant source of capital accumulationand, thus, of progress in capital intensity. This is specially so in Japan, where the differencebetween the two scenarios amounts to 50 percentage points of growth, half the actual progressin capital intensity.

In contrast to Japan, in the US it is the evolution of relative factor utilization what explains mostof the progress. This is the outcome of the estimated coefcients recall that the demand-side driv-ers had a stronger explanatory power in the US than in Japan, but also of the trajectories of the var-iable cur nr (depicted in Figs. A1 and A2). In Japan its has an oscillatory evolution, with a fall in the1990s and a steep rise over the 2000s whereas in the US it is more homogeneous, with a downwardtrend over the sample period that ends up explaining a signicant portion of the evolution of capitalintensity. In the absence of this downward trend, capital intensity would have grown by 176.8%rather than by 65.9% (Fig. 2b). This means that steady demand-side pressures may be notably inu-ential in the process of economic growth. Therefore, the fact that pressures on the rate of capacityutilization have been systematically less binding than pressures on the employment rate (as uncov-ered by the steady fall in the relative factor utilization variable cur nr) appears as a clear-cut dis-incentive for US rms to keep investment at the same path than the Japanese rms, where this wasnot occurring.

Another interesting result arises when technology is not allowed to progress. The outcome of thissimulation clearly uncovers the dramatic opposite inuence of a factor-biased technological changethat is capital saving in Japan, but labor-saving in the US (Fig. 2c). This implies that capital intensityhas been hindered by technical progress in Japan had it not been there, capital intensity would havegrown by 138%, rather than by 98.9%, and has been boosted in the US, where the absence of labor-sav-ing progress in technology would have left capital intensity virtually unchanged.

One of the critical changes experienced by the Japanese economy in last decades has been aglobalization process by which the degree of openness to trade, which had already increased inthe 1960s and 1970s, doubled between 1980 and 2011. Our simulations show that this processhas been as inuential as the evolution of relative costs in shaping the trajectory of capital intensityduring this period, but in the opposite sense (Fig. 2d): in the absence of such opening process,capital intensity in Japan would have progressed by 142% (instead of close to 100%). The resultsfor the US are not comparable, since they are based on keeping the growth rate of openness atits large 1970 value (6.5%) relative to an average growth rate of 2.8% during the sample period.The result from this simulation is that had the exposure to international trade kept growing sorapidly, capital intensity would have been lower. Thus, the negative impact of trade on capitalintensity is a common feature of Japan and the US.

Finally, direct taxation has negative effect on the evolution of capital per worker. As shown inFigs. A1 and A2, taxes have not grown in last decades. Had they stayed at their 1970 and 1980 values,capital intensity would have grown around 8 percentage points less in each country (i.e., 91% in Japan,rather than 99%, and 58% in the US, rather than 66%).

6. Concluding remarks

This paper focuses on a generally unattended issue: the determination of capital intensity. Thecapital-per-worker ratio is usually considered as an input in growth accounting, and the empiricalassessment of its determinants has been a rather neglected topic.

We develop an analytical setting that extends, with demand-side considerations, the models inAntrs (2004) and McAdam and Willman (2013). In this setting, we estimate empirical models forcapital intensity that include supply- and demand-side determinants, technology, and relevantcontrols related to international trade and the tax system.

We conrm the relative cost of production factors as a main supply-side driver of capital intensityyielding, also, plausible estimates of the elasticity of substitution between capital and labor. The

two proxies accounting for the demand-side pressures are also found relevant in the US, and partly so

Along the lines of recent works stressing the relevance factor-specic efciency growth Acemoglu (2003), Klump et al. (2012), McAdam and Willman (2013), the different nature of

supply-side considerations. On the supply-side, our ndings call for a careful design of policies

D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898 95affecting rms decisions on investment and hiring. The reason is that these policies crucially affectthe procyclical behavior of the ratio between the rates of capacity utilization and (the use of)employment, since in economic expansions the capacity utilization rate tends to increaseproportionally more than the employment rate, probably because in the very short run it is lesscostly to use already installed capacity than to hire new workers. From this point of view, thedesign and implementation of labor market reforms should be closely connected to investmentpolicies, a conclusion already obtained in Sala and Silva (2013) in their analysis of laborproductivity.

In general, demand-side forces are not included in economic growth models. Nonetheless, ourresults reveal the incidence of demand-side pressures on the evolution of capital intensity,specially in the US, where the growth path of capital intensity could have been much steeperwithout the fall in the relative factor utilization rate. Considering that capital intensity is a keygrowth driver, this result has important policy implications in the elds of economic growthand development.

To conclude, there are several sources of potential improvements in this analysis. The rst one isthe introduction of imperfect competition in factor markets. There is work done regarding the labormarket (Raurich et al., 2012), but nancial markets, and the associated mark-up over the marginalproduct of capital, should simultaneously be evaluated. The second one, as explained in Len-Ledesma et al. (2010), is to block potential identication problems by moving from single-equationestimates of the elasticity of substitution to multi-equation systems in which output and all factordemands are modeled. The third avenue for improvement is to relax the assumptions on technologicalchange and devote further effort in modeling efciency progress by explicitly considering R&D andinnovation. The fourth one is to embark into a disaggregated analysis by industries, along the linesof Young (2010, 2013), and obtain detailed sectoral information on how the processes of structuralchange and capital intensication are intertwined. Future research will have to face these compellingchallenges.

Acknowledgments

We gratefully acknowledge the insightful comments and suggestions received by an anonymousreferee. Dario Judzik is grateful to the Spanish Ministry of Education for nancial support throughFPU grant AP2008-02662. Hector Sala is grateful to the Spanish Ministry of Economy and Competitive-ness for nancial support through grant ECO2012-13081.

Appendix A

See Figs. A1, A2 and Tables A1, A2.technological change in Japan and the US has been also uncovered. As we have argued, thisdifference provides an explanation of the contrasted evolution of capital intensity in theseeconomies, and even of their diverse growth models; Japan having been, traditionally, one ofthe great world net exporters and the US having been, and being, one of the greatest net importingeconomies.

Policywise, our results warn about a simplistic design of policies exclusively based onin the case of Japan. This calls for a wider than usual approach when working with productionfactor demands and, as we have done in this study, when examining the determinants of capitalintensity.

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96 D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898

D. Judzik, H. Sala / J. Japanese Int. Economies 35 (2015) 7898 97Table A2Misspecication tests.

Japan US

Model 1 Model 2 Model 1 Model 2

OLS TSLS OLS TSLS OLS TSLS OLS TSLS

Table A1Unit root tests of main variables.

Japan US

ki cc w cur nr op Dhrs ki cc w cur nr op DhrsADF 0.33 0.71 1.11 0.03 4.80 3.18 0.94 2.45 0.25 4.95

I(1) I(1) I(1) I(1) I(0) I(1) I(1) I(1) I(1) I(0)KPSS 0.72 0.70 0.20 0.61 0.13 0.78 0.54 0.75 0.81 0.23

I(1) I(1) I(0) I(1) I(0) I(1) I(1) I(1) I(1) I(0)Result I1 I1 I1 I1 I1 I1 I1 I1 I1

ADF = Augmented DickeyFuller test. Hypothesis of unit root. 1% and 5% critical values = 3.66 and 2.96 respectively.KPSS = KwiatkowskiPhillipsSchmidtShin Test. Hypothesis of stationarity. 1% and 5% critical values = 0.739 and 0.463respectively.References

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SC v21 0.90 0.14 0.04 0.001 0.52 0.003 0.01 2.17[0.343] [0.709] [0.838] [0.981] [0.470] [0.960] [0.916] [0.141]

HET v2a 0.54 0.63 0.32 0.51 10.9 9.98 10.2 9.03[0.777] [0.691] [0.977] [0.803] [0.615] [0.696] [0.602] [0.700]

ARCH v21 0.56 0.49 1.08 0.18 1.95 1.61 0.16 0.06[0.443] [0.475] [0.298] [0.678] [0.163] [0.204] [0.693] [0.801]

NOR JB 1.36 1.24 7.59 1.42 0.47 1.62 0.45 1.25[0.506] [0.539] [0.023] [0.490] [0.791] [0.445] [0.799] [0.534]

Notes: p-values in brackets.SC = Lagrange multiplier test for serial correlation of residuals; HET = White test for Heteroscedasticity; NOR = JarqueBera testfor Normality; ARCH = Autoregressive Conditional Heteroscedasticity; a = number of coefcients in estimated equation(intercept not included).

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The determinants of capital intensity in Japan and the US1 Introduction2 Analytical framework2.1 Factor demands and capital intensity2.2 Product demand uncertainty2.3 Mind the gap2.4 Factor-biased technical change

3 Empirical issues3.1 Estimated models3.2 Data3.3 Estimation procedure

4 Results4.1 Estimated equations4.2 Elasticities of substitution, technology and efficiency

5 Counterfactual simulations6 Concluding remarksAcknowledgmentsAppendix A References