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Working Paper Series o 1175 / APRIL 2010 In Dubio pro CES Supply Estiation with Mis-Specified Technical Change by Miguel A. León-Ledesa, Peter McAda and Alpo Willan WORIG PAPER SERIES O 1175 / APRIL 2010

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Working Paper Series o 1175 / APRIL 2010 In Dubio pro CES Supply Estiation with Mis-Specified Technical Change by Miguel A. León-Ledesa, Peter McAda and Alpo Willan WORIG PAPER SERIES O 1175 / APRIL 2010 I DUBIO PRO CES SUPPLY ESTIMATIO WITH MIS-SPECIFIED TECHICAL CHAGE By Miguel A. León-Ledesa 1, Peter McAda 2, 3 and Alpo Willan 2 In 2010 all publications feature a otif taken fro the 500 banknote. OTE: This Working Paper should not be reported as representing the views of the European Central Bank (). The views expressed are those of the authors and do not necessarily reflect those of the. This paper can be downloaded without charge fro or fro the Social Science Research etwork electronic library at 1 Corresponding author: Departent of Econoics, eynes College, University of ent, Canterbury, ent, CT2-7P, United ingdo, 2 European Central Bank, aiserstrasse 29, Frankfurt a Main, Gerany, e-ail: 3 University of Surrey. Guildford, Surrey, GU2 7XH, United ingdo. European Central Bank, 2010 Address aiserstrasse Frankfurt a Main, Gerany Postal address Postfach Frankfurt a Main, Gerany Telephone Internet Fax All rights reserved. Any reproduction, publication and reprint in the for of a different publication, whether printed or produced electronically, in whole or in part, is peritted only with the explicit written authorisation of the or the authors. Inforation on all of the papers published in the Working Paper Series can be found on the s website, ecb.europa.eu/pub/scientific/wps/date/ htl/index.en.htl ISS (online) COTETS Abstract 4 on-technical suary 5 1 Introduction 6 2 Theory background 8 3 Soe possible pitfalls in supply estiation Mis-specified technical change: paraeter inference Mis-specified technical change: TFP estiates Identification aspects: Iso-shares 14 4 The specification bias: Monte Carlo evidence The Monte Carlo experient Monte Carlo results 19 5 CES estiation of the US econoy Data Specification Estiation results TFP estiates Robustness Soe lessons learnt 27 6 Conclusions 29 References 30 Tables and figures 34 3 Abstract Capital-labor substitution and total factor productivity (TFP) estiates are essential features of growth and incoe distribution odels. In the context of a Monte Carlo exercise ebodying balanced and near balanced growth, we deonstrate that the estiation of the substitution elasticity can be substantially biased if the for of technical progress is isspecified. For soe paraeter values, when factor shares are relatively constant, there could be an inherent bias towards Cobb-Douglas. The iplied estiates of TFP growth also yield substantially different results depending on the specification of technical progress. A Constant Elasticity of Substitution production function is then estiated within a noralized syste approach for the US econoy over 1960:1 2004:4. Results show that the estiated substitution elasticity tends to be significantly lower using a factor augenting specification (well below one). We are able to reject Hicks-, Harrod- and Solow-neutral specifications in favor of general factor augentation with a non-negligible capital-augenting coponent. Finally, we draw soe iportant lessons for production and supply-side estiation. JEL Classification: C15, C32, E23, O33, O51. eywords: Constant Elasticity of Substitution, Factor-Augenting Technical Change, Technical Progress eutrality, Factor Incoe share, Balanced Growth. 4 on Technical Suary Capital-labor substitution and overall productivity iproveents (total factor productivity, TFP) estiates are essential features of growth and incoe distribution odels. Both, however, in a production function fraework require the odelling of technical change. Technical change captures the degree to which the output contribution of factor inputs (capital and labor) changes over tie given fixed quantities of those factors in effect, it captures quality iproveents. The issue of the possible is-specification of the for of technical change and its iplications for the epirical estiates of the substitution elasticity and for TFP have been largely unexplored. We provide Monte Carlo (MC) evidence on the bias in the estiated substitution elasticity generated by is-specifying the nature of technical change. To best isolate the effect of such biases, we use the so-called \noralized syste approach. Although we find that the general factor augenting specification correctly identifies technical progress, alternative neutrality specifications only work well when they correspond to the true data generation process. For paraeter configurations that yield stable factor shares, the substitution elasticity is biased upwards (downwards), when its true value is below (above) unity. For plausible substitution values, this can often lead to biases in the estiated substitution elasticity towards unity. In the light of this, we then estiate a Constant Elasticity of Substitution production function is then estiated for the US econoy for the 1960:1-2004:4 period. Our results show that the estiated substitution elasticity tends to be significantly lower using a factor augenting specification and is well below one. We are able to reject Hicks-, Harrod- and Solow-neutral specifications in favor of general factor augentation with a non-negligible capital-augenting coponent. 5 1 Introduction Balanced growth defines a situation in which the capital-output ratio and factor incoe shares are constant (stationary). In ters of neoclassical growth theory, Uzawa (1961), it requires that technical progress should be Harrod eutral or that production should be Cobb Douglas (i.e., a unitary elasticity of factor substitution). Although balanced growth is often considered a reasonable description of any econoies, these two conditions underlying balanced growth are widely disputed. For instance, there is now ounting evidence that aggregate production ay be better characterized by a non-unitary substitution elasticity (e.g., Chirinko et al. (1999), lup et al. (2007), León-Ledesa et al. (2010), Duffy and Papageorgiou (2000)). Further, Chirinko (2008) s survey suggests that, across any different studies, evidence favors elasticities ranges of for the US. Likewise, that all technical change ust be labor augenting is extreely restrictive. One perspective (Aceoglu (2003, 2007)) ay be that while technical progress is asyptotically labor-augenting, it ay becoe capital-biased in transition reflecting incentives for factor-saving innovations. Such odels of biased technical change attept to reconcile historically-observed fluctuations in factor incoe shares with their apparent secular stability. However, whatever its plausibility, disissing the purely Harrod eutral case risks the finding that any developental pattern can be fitted by soe suitable cobination of technical progress and non-unitary substitution. Indeed, Diaond and McFadden (1965) (see also Diaond et al. (1978)) faously asserted that the elasticity and biased technical change could not be siultaneously identified. To counter this ipossibility theore researchers coonly ake a priori assuptions about the direction of technical change (typically Hicks or Harrod neutral). lup et al. (2007) and León-Ledesa et al. (2010) also argued that using the syste approach (i.e., estiating the production function and capital and labor first order conditions jointly) with its iplied cross-equation restriction vastly iproved identification (an additional consideration, following the seinal work of La Grandville (1989) and lup and de La Grandville (2000), was estiation in noralized for). otwithstanding, a priori restrictions on the direction of technical change still iply a is-specification error of soe proportion. Understanding the iplications of that is-specification in a noralized context is the subject of this paper. We provide Monte Carlo (MC) evidence on the bias in the estiated substitution elasticity generated by is-specifying the nature of technical change. To best isolate 6 the effect of such biases, we follow lup et al. (2007) and León-Ledesa et al. (2010) and use the noralized syste approach for estiation which was shown to doinate linear and nonlinear single equation approaches. 1 Although we find that the general factor augenting specification correctly identifies technical progress, alternative neutrality specifications only work well when they correspond to the true data generation process (DGP). For paraeter configurations that yield stable factor shares, the substitution elasticity is biased upwards (downwards), when its true value is below (above) unity. For plausible substitution values, this can often lead to biases in the estiated substitution elasticity towards unity. In the light of this, we then estiate the supply syste for the US econoy for the 1960:1 2004:4 period under general factor-augenting, Hicks-, Harrod-, and Solow-neutral specifications. Following the MC, we estiate a relatively siplified but ost coonly used fraework where growth in technical progress is constant (and without structural breaks) and where we abstract fro tie-varying factor utilization. 2 Many of the lessons drawn fro the MC find an echo in these epirical estiates. Although results yield very different values for the substitution elasticity, in all cases, our tests support the general factor-augenting specification. Using the latter, the substitution elasticity for the US is around We then derive estiates of Total Factor Productivity (TFP) growth and show and otivate relevant differences between specifications. Our preferred general factor-augenting syste captures a productivity acceleration during the second half of the 1990s consistent with that found in other studies (see Basu et al. (2003), Fernald and Ranath (2004) and Jorgenson (2001)). The iportance of our subject atter is worth recalling. The shape of the production function (as captured by the substitution elasticity) plays a key role in odels analyzing growth and convergence; incoe distribution; technical efficiency; labor-arket outcoes, etc (e.g., see lup and de La Grandville (2000), La Grandville (2009), Sato (2006), Rowthorn (1999), Chirinko (2008)). Moreover, 1 oralization essentially iplies representing the production function in consistent indexed nuber for (see La Grandville (1989), lup and de La Grandville (2000)). Without noralization the paraeters of the production function have no econoic interpretation since they are dependent on the noralization point and the elasticity of substitution. This feature significantly underines estiation and coparative static exercises. Moreover noralization avoids the otherwise unusual situation whereby capital and labor output shares approach one half in the Leontief case. 2 For attepts to odel non-constant growth in technical change, see lup et al. (2007). On the second point, naely tie-varying factor utilization rates, this is essentially not probleatic under the reasonable assuption of stationarity in such rates. 7 easureent of potential output is a key indicator for stabilization policy. 3 Likewise, changes in the direction of technical bias over tie have contributed to our understanding of, e.g., labor-arket inequality and the skills preia (Aceoglu (2002)) 4 ; factor incoe share oveents (McAda and Willan (2008)) and the welfare consequences of new technologies (Marquetti (2003)) etc. Finally, of course, since Solow (1957), the calculation of total factor productivity (TFP) growth has been a key application of production estiation. The paper is organized as follows. In section 2 we present soe relevant background on the ore general Constant Elasticity of Substitution (CES) production function and in section 3 discuss the potential biases arising fro is-specification of technical change. In Section 4 we present the Monte Carlo setup and discuss the results. Section 5 present epirical results using US data. Section 6 concludes. 2 Theory Background The CES production function allows the elasticity of capital and labor with respect to their relative price to be any constant between zero and infinity. This special type of production functions was forally introduced into econoics by Arrow et al. (1961) and spawned a vast supporting literature (e.g., David and van de lundert (1965), enta (1967), Berndt (1976), Chirinko (2002), lup et al. (2007)). Furtherore, following the seinal work of La Grandville (1989) and lup and de La Grandville (2000), the function is often expressed in noralized (or indexed) for since its paraeters then have a direct econoic interpretation. 5 oralization also turns out to be iportant for estiation as ephasized by León-Ledesa et al. (2010). The noralized CES takes the for: Y t = F ( [ ( ) σ 1 ( ) σ 1 ] σ σ 1 ) Γ Γ t t, Γ σ t t = Y0 π t t Γ σ 0 +(1 π Γ 0 ) t t 0 0 Γ 0 0 (1) 3 Orphanides (2003) suggest is-easureent of potential output in real tie has been a historical constraint and tension for US onetary policy 4 See also Greenwood et al. (1997) and russel et al. (2000). 5 See also lup and Preissler (2000), lup and de La Grandville (2000), lup and Saa (2008), and La Grandville (2009) for an analysis of the relevance of noralized production functions for growth theory. For any legitiate CES function, the value of the substitution elasticity depends on (i) a given level of capital deepening, (ii) a given arginal rate of substitution and (iii) a given level of per-capita production. Different CES functions are considered to be in the sae faily if they share coon baseline values but differ only in their elasticity values and one point of tangency characterized by the given baseline values. lup and de La Grandville (2000) then show how, given this noralization procedure, coparative statics on the elasticity substitution can be legitiately ade. 8 where the point of tie t = 0 represents the point of noralization, Y t represents real output, t is the real capital stock and t is the labor input. The ters Γ t and Γ t capture capital and labor-augenting technical progress. To circuvent probles related to the Diaond-McFadden ipossibility theore, researchers usually assue specific functional fors for technical progress, e.g., Γ t =Γ 0 e γt and Γ t =Γ 0 e γ t where γ i denotes growth in technical progress associated to factor i, t represents a tie trend. This technical progress is alternatively Hicks neutral (γ = γ 0), Harrod neutral (γ =0,γ 0) or, ore seldo, Solow-eutral (γ 0,γ = 0). Hence a general factor-augenting case (γ 0 =γ 0) is typically by-passed. The capital incoe share at the point of noralization is π 0 = r 0 0 Y 0 (r denotes the real user cost of capital) and the elasticity of substitution between capital and labor inputs is given by the percentage change in factor proportions due to a change in the factor price ratio along an isoquant: σ (0, ) = d log (/) d log (F /F ) (2) CES production function (1) nests Cobb-Douglas when σ = 1; the Leontief function (i.e., fixed factor proportions) when σ = 0; and a linear production function (i.e., perfect factor substitutes) when σ. 6 The higher is σ, the greater the siilarity between capital and labor. Thus, when σ 1, factors are gross copleents in production and gross substitutes when σ 1. Thus, it can be shown that with gross substitutes, substitutability between factors allows both the augentation and bias of technological change to favor the sae factor. 7 For gross copleents, however, a capital-augenting technological change, for instance, increases deand for labor (the copleentary input) ore than it does capital, and vice versa. By contrast, when σ = 1 an increase in technology does not produce a bias towards either factor (factor shares will always be constant since any change in factor proportions will be offset by a change in factor prices). Thus, the question of whether σ is above or below unity is arguably as iportant as its nuerical value. 6 Going back to Hicks (1932), the value of the substitution elasticity is often viewed as reflecting econoic flexibility and thus deep institutional factors such as labor bargaining power, the taxation burden, degree of econoic openness, the characteristics of national education syste, etc. Accordingly, soe view changes in the substitution elasticity as potential drivers of endogenous growth and potentially even ore iportant than traditionally-studied growth factors such as savings and technical progress, La Grandville (2009), Yuhn (1991). See also Baira (1991). 7 In other words, if σ 1 and γ i γ j this iplies that F i F j plus that there is a relative rise in the incoe share of factor i. Hence we can say that technical change related to factor i favors factor i in the gross copleents case. 9 3 Soe Possible Pitfalls In Supply Estiation The CES function and the first-order conditions for a highly nonlinear syste. This points to the advantage of Monte Carlo ethods in detecting and quantifying is-specification issues. However, before that, we discuss the general issues at stake and analytically derive soe potential estiation probles. First, in sections (3.1) and (3.2), we consider the particular ipact of isspecification of technical progress on the estiation of the elasticity of substitution, and then on TFP estiates and its decopositions. Second, in section (3.3) we touch on the possibility of observational equivalence; the properties of the CES function in aditting gross substitutes / copleents in production can iply a siilar evolution of, for instance, factor incoe shares across distinct technical paraeters. These exaples, note, are eant to be priarily otivational: they usefully highlight any of the issues that will becoe apparent in both the MC and data estiation sections. 3.1 Mis-Specified Technical Change: Paraeter Inference The capital-to-labor incoe share, given a copetitive goods arket and profit axiization, can be expressed as, Θ t = r t w t t t = π 0 1 π 0 ( Γ t t / 0 Γ t t / 0 ) σ 1 σ (3) Whilst Θ is observed, neither the substitution elasticity nor technical change are. For Θ to be constant requires the failiar balanced growth cases of σ =1or Harrod neutrality. But can dθ 0 when we purposefully depart for these two restrictive assuptions? And what would be the likely estiation consequences? Equation (3) shows that if we assue Hicks neutrality, stable factor shares would require σ 1 to offset the trend in capital deepening. 8 Antràs (2004) uses this arguent to rationalize Berndt (1976) s widely-cited finding of Cobb-Douglas for US anufacturing. The sae is true of Solow neutrality. Another possibility, for factor-augenting technical progress, is that stable factor shares hold if the growth of technical bias offsets that of capital deepening. Likewise, independent fro the size of σ, Θ would reain broadly constant outside the balanced growth path if r t absorbs soe of the trend in capital aug- 8 Capital deepening, /, grows at the sae rate as labor-augenting technical progress plus population growth. Thus, li t / t. t 10 entation. This, though, violates our priors that the real interest rate (and thus the real user cost) is stable. 9 However, we can show that this trend absorption need only be odest. If the user cost only partially absorbs the capital-augenting technical progress, there will be trends also in the factor incoe shares, but these ay be weak when coupled with a oderate pace of capital augentation. 10, 11 Hence, the relative stability of factor incoe shares is not a sufficient condition for the correctness of either Cobb Douglas or Harrod neutrality. We have seen that the assuption of Hicks neutrality can bias σ towards unity when the true DGP is Harrod-neutral. Correspondingly, we can show that quite generally (although not universally) also the Harrod-neutral specification can result in σ estiates that are either upwards or downwards biased when the true DGP contains capital-augenting technical progress. The lhs of equation (4) below corresponds to the true DGP

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