n How do Firms Respond to Cheaper Computers? Microeconometric Evidence for France Based on a Production Function Approach

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1 INSTITUT NATIONAL DE LA STATISTIQUE ET DES ETUDES ECONOMIQUES Série des Douments de Travail du CREST (Centre de Reherhe en Eonomie et Statistique) n How do Firms Respond to Cheaper Computers? Miroeonometri Evidene for Frane Based on a Prodution Funtion Approah P. BISCOURP 1 B. CRÉPON 2 T. HECKEL 3 N. RIEDINGER 4 Les douments de travail ne reflètent pas la position de l'insee et n'engagent que leurs auteurs. Working papers do not reflet the position of INSEE but only the views of the authors. 1 CREST-INSEE. 2 CREST. 3 CREST-INSEE. 4 CREST-INSEE.

2 How do Firms Respond to Cheaper Computers? Miroeonometri Evidene for Frane Based on a Prodution Funtion Approah Pierre Bisourp (CREST-INSEE), Bruno Crépon (CREST), Thomas Hekel (CREST-INSEE)*, Niolas Riedinger (CREST-INSEE) Abstrat We implement an original method based on the estimation of a prodution funtion, to investigate how the derease in the ost of omputers has affeted the marginal ost of firms, their aggregate labor demand and their skill struture. Using a panel of more than 5000 Frenh firms followed between 1994 and 1997, we find that the effets of the derease in the prie of omputers have been large both in terms of marginal ost redution and in terms of skill struture, although these effets exhibit some heterogeneity aross firms. In partiular, skill substitution effets have been larger in manufaturing industries. Keywords: labor demand, tehnologial bias, elastiity of substitution. JEL lassifiation: J21, J23, C33, J31, L60 * INSEE - timbre G Boulevard Gabriel PERI BP MALAKOFF CEDEX thomas.hekel@insee.fr We are indebted to John Van Reenen and Franis Kramarz for helpful omments. 1

3 I. Introdution For several deades, firms have benefited from the ontinuous tehnial progress ahieved by the produers of information tehnologies, as the data proessing power has grown faster than the retail pries of omputers. The resulting deline in the ost of omputer power may be viewed as exogenously driven by tehnial innovations 1. As a result firms have massively invested in omputers. In almost all OECD ountries, investment in information tehnologies grew at an average annual rate of 15% during the 90s (Colehia and Shreyer, 2001). A major onern for researhers has been to measure the global supply shok assoiated with this aumulation proess, as well as the effets on the demand for labor, with a partiular fous on the relative demand for skills. Maroeonomi studies have extensively disussed the magnitude of the supply shok (Oliner and Sihel, 2000; Gordon, 2000). They have also onsistently shown that the observed shift in labor demand away from unskilled workers and towards skilled workers, does not originate in the industries most exposed to international trade, thus putting forward the aumulation of omputers as the hief explanation. Miroeonometri studies on the other hand, have provided evidene of the effet of omputer aumulation on the supply of firms (Lehr and Lihtenberg, 1998), on their relative demand for skills (Bresnahan, Brynjolfsson and Hitt, 2002), as well as on the interation between information tehnology and work plae organization (Brynjolfsson and Hitt, 2000; Caroli and Van Reenen, 2001). The skill bias issue has usually been investigated in the literature by estimating labor demand equations where the stok of omputers is onsidered as a quasi-fixed input. We argue that it makes more sense to evaluate the impat of the deline in the ost of omputers diretly, rather than through the aumulation it has generated, if the deline in the ost of omputer is 2

4 the exogenous shok driving the aumulation proess. The fous of this paper is thus deliberately on the effets of the deline in the prie of omputers. The strong deline in the prie of omputers may be viewed as exogenous inasmuh as it is the result of tehnologial innovations that have ourred in a irumsribed set of ITproduing industries. Nonetheless, Aemoglu (1998) argues that these innovations have atually been spurred by an upwards shok on the relative supply of skill, enlarging the benefits of researh and developments in tehnologies omplementary with skilled labor. If this story is true, the deline in the prie of omputers is to some extent endogenous. However, this disussion lies upstream from our study sine the deline in the prie of omputers an still be onsidered exogenous at the firm level, whatever the nature of the truly exogenous maroeonomi shok. Fousing on the prie deline experiened by omputers is thus fine in priniple, yet proves triky in pratie, as the evolution of the purhase prie of omputers is idential for every firm at a given date. No diret identifiation of the impat of this exogenous shok is therefore possible from the estimation of fator demand equations. We develop an original methodology based on the primal approah to irumvent this limitation. We show that it is possible to measure omputer prie effets on both the marginal ost and the labor demand of firms, solely by estimating a prodution funtion. We take advantage of the fat that, given a tehnology and a level of output, the relative pries of inputs loally determine unique levels of inputs under the assumption of ost minimization. Therefore, the elastiities of fator demands to the pries of inputs an be expressed as funtions of the tehnology and the levels of inputs, without any additional information on fator osts being required. We derive suh relationships for the elastiities of aggregate labor demand as well as its omposition by skill, to the prie of omputers. In order 3

5 to provide an assessment of the assoiated supply shok, we also derive the analog expression for the marginal ost of prodution. Implementing this strategy obviously requires assumptions on the funtional form of the prodution funtion, whose estimate enters the omputation of the parameters of interest. We estimate a translog prodution funtion, whih is flexible enough to aount for a wide variety of substitution patterns aross firms. The orresponding identifying restrition onsists in assuming the onstany aross time and a given subsample of firms used for estimation, of the first and seond order oeffiients of the translog (i.e. the homogeneity of the tehnology aross the firms involved in the estimation). Whether the prodution funtion framework is best suited for the purpose of modeling the hanges indued by omputerization is subjet to disussion. Athey and Stern (1995) suggest for instane an organizational design prodution funtion whih takes into aount the fat that organizational design praties may affet output by swithing from one prodution funtion to another. Suh a framework may be more appropriate sine omputers are said to affet the adoption of organizational design praties by lowering their ost. In this framework, our translog prodution funtion must be thought of as the best approximation available. Our approah allows to evaluate firm-speifi effets of the derease in the prie of omputers, as our measures of these effets depend on the level of inputs, whih may differ aross firms due to fator ost heterogeneity. This method thus yields a distribution aross firms of the quantitative effets of a fall in the prie of omputers on the marginal ost of prodution, as well as on labor demand and the relative demand for skills. 4

6 Data limitations have frequently been an important shortoming in studying the effet of omputer aumulation. Studies usually have at their disposal a small sample of firms followed for only one year. By ontrast, our evaluations are performed using a very large panel of firms (more than 5000) followed over the period This data set results from the merging of various soures of information whih provide us with a quantitative measure of the stok of omputers within the firm, as well as the struture by skill of its workfore and the orresponding wages. Our measure of the omputer stok orresponds to the Offie, Computing and Aounting Mahinery (OCAM) item of the balane sheet of firms. Our measures of employment and wage by skill within the firm, originate in a large amount of work performed at INSEE, whih has onsisted in aggregating at the firm level exhaustive soial seurity employee level files providing information on skill as well as labor ost. Our results point to a signifiant impat of omputerization on the marginal ost of prodution, labor demand and the relative demand for skills. The derease in the ost of omputer has indued a signifiant derease in the marginal ost of prodution. It has also shifted the relative demand of labor toward skilled workers at the ost of unskilled. The remainder of the paper is organized as follows. In the first setion, we define a set of parameters of interest relevant for assessing the impat of the fall in the prie of omputers on the marginal ost of prodution, the demand for labor and the skill struture. We derive their expression as funtions of the tehnology and the levels of inputs. The data are presented in the seond setion together with our estimates of the Translog tehnology of prodution. The third and last setion is devoted to the omputation of the firm-speifi parameters of interest, 5

7 using the prodution funtion estimates obtained in the seond setion. We disuss their signifiane when ompared to aggregate evolutions. 6

8 II. Measuring the eonomi effets of a derease in the prie of omputers We define a set of parameters measuring the effet of a fall in the prie of omputers on the marginal ost, the demand for aggregate labor and the relative demand for skills by the firm. We then show how to ompute them from the tehnology of prodution. Defining the parameters of interest Consider a prodution funtion y f ( x, x, x, x ) =, where x u and x s denote unskilled and u s o skilled labor, x is the stok of omputers, and x o is the stok of the apital goods other than omputers. The ost funtion assoiated with this tehnology is defined by : ( ) C p, p, p, p, y = min p x + p x + p x + p x u s o u u s s o o ( ) { xu, xs, x, xo} st.. y= f ( x, x, x, x ) u s o Denote x * the solution to the above program, onditional on the level of output y * and the initial vetor of fator osts p* { pu*, ps*, p*, po* } equal to x * =. Assume that fator demands are initially, and onsider an exogenous shok driving down the ost of omputers. We want to assess the effets of this shok on the new vetor x of fator demands, onditional on the tehnology f and the initial vetor of inputs x * interest: the one related to the effet on the marginal ost ( f, x* ) labor demand ( f, x* ) * η l and ( f, x ) ψ.. Table 1 defines our three parameters of χ and the two related to 7

9 All these parameters are defined all other input pries and output held onstant, and evaluated around the state defined by the initial level of fator demands. Notie that if initial fator pries (therefore initial states) differ aross firms, the parameters of interest are also firm-speifi. The first parameter χ is a measure of the supply shok assoiated with the redution in the prie of omputers. The derease in the ost of a partiular input affets the marginal ost of the firm, whih in turn indues for a given market struture a variation in the prodution prie and the demand addressed to the firm 2. The parameter χ enables us to ompute a ontribution of the derease in the prie of omputers to the redution in the marginal ost, simply equal to χ ln p. We assume that all firms fae the same hange ln p in the ost of omputers 3. The ontribution to the redution in marginal ost is nevertheless firm-speifi sine the parameter χ depends on the initial level of inputs whih is heterogeneous aross firms. χ ln thus provides an p assessment of the supply shok assoiated with omputerization, different from the one defined in the standard growth aounting framework 4. The last two parameters η l and ψ summarize the effets on the demand for labor inputs, whih result from substitution effets taking plae between all four inputs, onditional on a given level of output. As shown by Fuss and MFadden (1978), all above parameters an be expressed in the primal approah. Computing the parameters of interest as a funtion of tehnology and the initial state 8

10 Let us first define the elastiities of marginal ost to pries χ i and to output δ y : dln C = χ dln p + δ dln y y i i y i χ i and δ y may be expressed as funtions of the first and seond derivatives of the prodution funtion f, for a given level of inputs (see appendix 1): χ = i i i δ = y ff F ff 0 F [1] where F is the determinant of the bordered Hessian 5, and F 0 and F i are the o-fators of respetively 0 and f i in F. The intuition behind the expression of χ is not straightforward in the general ase. However, in the speial ase of homogeneity of the prodution funtion, the following simple relation holds between the elastiity of prodution to omputers ε = xf f and the elastiity of sale θ = ε + εo + εu + εs: χ = ε θ In order to examine the effet on labor demand of a derease in the prie of omputers, let us onsider the ompensated demand for inputs. It involves the prie elastiities η ij of fator i to fator prie p j and the elastiities to output µ iy : dln xi = η ijdln pj + µ iydln y [2] j Again, these elastiities an be expressed in the primal approah as funtions of the bordered Hessian F and its o-fators, for a given level of inputs (see appendix 1): η = ε σ θ µ Α ij j ij = ( f / x )( F F) iy i i [3] 9

11 A where σ xk fk xixj ( Fij F) ij = [4] are the Allen-Uzawa partial elastiities of k substitution (AUES) and F ij are the o-fators of f ij in F. The sensitivity of the aggregate labor demand and relative demand for skills an be expressed simply as linear ombinations of the two prie elastiities η u and η s. The elastiity of aggregate labor to the prie of omputers is simply a weighted sum of these two elastiities: η x η x = + η u s l u s xu + xs xu + xs [5] The sensitivity of the relative demand for skills is obtained by subtrating the equations of ompensated demand (equation [2]) for the two labor inputs. It is thus simply defined 6 as : ψ = ηs ηu [6] The fall in the prie of omputers is said to be biased toward skilled labor when ψ < 0, in other words when the Allen-Uzawa elastiity of substitution between unskilled labor and omputers is larger than that between skilled labor and omputers. Notie that the relative demand for skills an be expressed as ( s u ) σ Μ Μ us u σsu s ψ ψ o o ( µ sy µ uy ) dln x x = dln p dln p + dln p + dln p + dln y [7] σ Μ = ε σ σ θ are the Morishima elastiities of substitution (MES). 7 A A where ( ) ij j ij ii Another interesting parameter is the ratio ψ σ Μ us. Aording to equation [7], it represents the redution in unskilled labor ost required in order to ompensate a 1% derease in the omputer prie. In the following setion, we present the data and estimate the tehnology of prodution ˆf, first assumed to be homogenous aross all firms of our sample, then aross two subsamples 10

12 orresponding respetively to the manufaturing and non manufaturing industries. In the last setion, we use these prodution funtion estimates as well as the expressions given in this setion, to ompute the firm-speifi parameters of interest χ ( ˆ, * f x ), ( ˆ, * l f x ) ψ ( f ˆ, x * ) η,. Appendix 2 ontains the expressions of the main parameters defined in this setion under the translog speifiation, whih we adopt in our empirial work. 11

13 III. Data and estimation of the tehnology of prodution The data The dataset we use is obtained by merging two different soures, the Bénéfies Réels Normaux (BRN), an employer-level file, and the Délarations Annuelles des Données Soiales (DADS), an employee-level file. It overs the period and inludes ontinuing firms. The BRN onsists of firms' balane sheets and is olleted by the Diretion Générale des Impôts. It provides us with all the information needed to estimate prodution funtions : employment, apital stoks, value-added, as well as total wages. This file inludes around 600,000 firms in the private non finanial non agriultural setors eah year and overs around 80% of sales. Firms are identified through a speifi ode SIREN that allows to follow firms over time. Capital stoks are onstruted using information on fixed assets. In partiular the item Offie, Computing and Aounting Mahinery (OCAM) is used as a measure of the omputer stok. Information distinguishing the OCAM item from the other fixed assets are nevertheless not available for all firms submitted to the BRN regime. We have limited our study to the balaned sample of around 10,000 firms where this information is available over the period The OCAM item only provides a raw measure of the stok of omputers strito sensu, as it also ontains offie equipment (suh as typewriters, telephone handsets), as well as furniture (desks, hairs). We orret for this by taking only a fration of the OCAM item in measuring the stok of omputer apital. This fration has been set at 50% on the basis of national 12

14 aounts data 8. This orretion is not an important one when estimating the model. However it has an important effet when measuring the share of omputer in total ost. This share, a key parameter in the growth aounting framework, plays also for us the role of a benhmark to whih we will ompare our measure of the elastiity of prodution to omputer. A seond issue arises from the fat that fixed assets are valued in ompany aounts at the histori (aquisition) ost, whereas we need a measure of the volume of fixed assets at the replaement ost. In order to reover a apital stok in volume, we have performed a orretion whih onsists in deflating the initial measure by the investment prie index at the date onsidered, minus an estimated age of apital. This amounts to assuming that all the apital was aumulated through a lumpy investment. The age of apital is alulated from the ratio of depreiated asset to asset stok and multiplied by an assumed duration of servie life of 5 years. The prie index for omputer investment is the one ompiled by INSEE aording to the hedoni method. Quality improvements are therefore taken into aount in omputing the volume of omputer stok. The orretion from histori to replaement ost has also been used for the six other types of apital goods available in tax returns (onstrution, buildings, general and tehnial installations, transport equipment, reusable pakaging). These apital goods are then aggregated into a single Divisia index. The real value added is defined as the differene between prodution and materials divided by the value added prie index at the two digit level available from national aounts. We performed some elementary leaning over the ratios of inputs to value added. We imposed that their mean and standard error belong to the interval built from the median ± 5 times the differene between the upper and lower quartiles. The file at this stage has around firms over the period

15 The DADS is an exhaustive dataset available sine , ontaining information about all employees of all firms. The data soure onsists in mandatory employer reports of the gross earnings of eah employee subjet to Frenh payroll taxes. This file inludes around 15 millions workers per year. Note that workers an only be followed for two adjaent years. We have at our disposal files overing all suessive ouples of years between 1994 and 1997 : , , and The identifying ode of workers hanges from one file to the other. The files provide information on working days, working hours, wages and various harateristis of the employee (sex, age, oupation) for all firms in the private setor. It also inludes the identifying ode of the firm SIREN. Labor osts were first omputed from wages by applying the payroll taxes rule (this omplex rule has hanged during the overed period, espeially through the introdution of a redution in payroll taxes for low wage workers). Employee level information was then aggregated at the firm level into two broad ategories of oupations : offie and manual workers (unskilled labor hereafter) are opposed to business heads, senior exeutives and intermediate oupations (skilled labor hereafter). For eah ategory, the number of days and hours worked as well as the labor osts are available. Note that unskilled labor represents more than 50% of total labor so that our definition of unskilled does not only over the population of low wage workers (see Figure 1). The two files were merged using the identifying ode SIREN for the year 1994 to The quality of the math is not perfet. The reason for this remains unlear up to now. This redued the size of the data set to a balaned sample of 5112 firms over the period It overs all setors of manufaturing and servies. Table 2 displays some simple desriptive statistis. 14

16 Estimation of the prodution funtion We estimate a prodution funtion speified as a Translog funtion, that is for firm n at period t: 1 ln y = α + α ln x + β ln x ln x + u + u with β = β nt 0 i int ij int jnt n nt ij ji i 2 ij This speifiation is general enough in the sense that it is a seond order approximation to any tehnology of prodution. It has the desirable property that AUES are allowed to differ from unity and to be heterogeneous aross inputs. The derivatives of this prodution funtion with respet to the levels of inputs, whih are needed for the omputation of the parameters of interest, are simple funtions of the { i, ij} α β and the levels of inputs. The estimation of prodution funtions has been the fous of a large amount of eonometri work, beause of the strong biases involved when the estimation is arried out using simple OLS. Grilihes and Mairesse (1995) (GM) explain the nature of these biases at length. Apart from measurement errors and omitted variables, the main soure of bias is the existene of simultaneity between unobserved terms and the quantities of inputs : some shoks either permanent or transitory experiened by firms are taken into aount while deiding on the levels of inputs to be used. Part of the unobserved term is thus transmitted to inputs in the GM terminology. The indued orrelation between the error term of the prodution funtion and the explanatory variables, leads to biased OLS estimates. Permanent shoks orrespond to fixed effets u n appearing in the tehnology of prodution : estimations arried out in the within dimension or in differenes are unbiased. When transitory shoks our, however, the within and differene transformations no longer protet 15

17 against biased estimates. The traditional way of dealing with this problem is the use of instrumental variables in the GMM setting. More preisely, writing the speifiation of the prodution funtion as ynt = xntb+ un + unt the basi GMM estimator proposed by Arellano and Bond (1991) is based on the identifying restritions : E u x = s< t H1: ( ) 0 nt ns whih lead to the well known set of orthogonality onditions : E u x = 0 s< t 1 S1: ( ) nt ns The restrition of no serial orrelation in the time varying perturbations may be imposed further : E u u = t s H2: ( ) 0 nt ns Under this assumption, the following orthogonality ondition may be used for estimation in addition to S1 : E u y = 0 s< t 1. S2: ( ) nt ns In other words, moment onditions involving lagged values of the endogenous variable may be added to the set of moment onditions based on lagged regressors. However, the lassial Arellano and Bond estimator, where lagged levels are used to instrument a first-differened model, usually performs poorly as instruments are only weakly orrelated with explanatory variables. An alternative speifiation is the Arellano and Bover (1995) estimator, based on the additional assumption that the orrelation between the fixed effet and the explanatory variables is onstant over time: H3: E( u x ) n ns = δ Under this stationarity assumption, the following orthogonality onditions hold : 16

18 ( n nt ns) 0 E u + u x = s< T, S3: ( ) as well as ( n nt ns) 0 E u + u y = s< T S4: ( ) under assumption H2. Estimators based on the sets of moment onditions S1 to S3 or S1 to S4 are known as System estimators. As usual in GMM estimation, a test of the onsisteny of the extended set with the set S1 is provided by a Sargan test of overidentifiation. Blundell and Bond (1998) deals with the ase of a time varying perturbation exhibiting autoorrelation, modeled as a simple AR(1) proess : u = ρu + ε. nt nt 1 nt The quasi-differened model an be written as: ( ) ( ) y y b x x u nt = ρ nt 1+ nt ρ nt ρ n + εnt Blundell and Bond (1998) shows that the assumptions H1 to H4 an be extended to the quasidifferened model and lead to a set of orthogonality onditions S1 to S4 in whih u nt is replaed by ε nt. Notie that the validity of the orthogonality onditions set S4 (based on lagged values of y ) requires the additional assumption that the proess generating the data started a long time before the first observation of the data, so that the orrelation between the instrument and the fixed effet an be negleted. Two speifi estimation problems must be addressed in order to estimate the tehnial oeffiients α i and β ij onsistently. The first problem is the presene of measurement errors, the seond is non linearity. Both are onneted. 17

19 Our measurement of the omputer stok is partiularly likely to be affeted by large errors sine it is based on the item OCAM, as explained in the data setion. Computers strito sensu are only one part of this item, so that the true stok of omputers one would wish to have aess to is : * Knt =Θ ntocamnt =Θnt Θ Knt, where Θ nt is the individual share of omputer stok in the OCAM item, Θ the average share used for all firms (here 50%) and K nt the measure of the omputer stok we have used. In logarithms one obtains k = k + θ where * nt nt nt θ = Θ Θ. The shares may exhibit persistent heterogeneity aross individuals. Let us nt log ( ) nt model these shares, as a first approximation, as θ nt = θ n + η nt, and assume away serial orrelation in the η nt terms. These assumptions are suffiient to deal with the measurement issue properly using GMM in the ase of a linear speifiation like a Cobb-Douglas prodution funtion, as the firm-speifi terms θ n always drop off either in instruments or in the differened equation itself, and the assumption of no serial orrelation of the remaining term insures that the estimators will be onsistent. Similarly, the within or long differene estimators eliminate the firm speifi omponent, whih leaves either ( η η ) the only part of the perturbation linked to the measurement issue. or ηnt as nt n. The seond estimation issue is non linearity. Crossed terms are diffiult to estimate, espeially in the presene of measurement errors for whih no simple instrumental variable strategy is available (Hausman, Newey and Powell, 1995; Hausman, 2001). To see this onsider the following simple model: y x u * 2 n = γ n + n Assume the standard measurement model: x = x + e * n n n The model based on the observable variables is then written : 18

20 y = γ x + u 2γ e x γ e 2 * 2 n n n n n n An instrumental variable for the measurement error problem is usually a variable orrelated with the true measure but independent of the measurement error. It is this way at least that GMM estimation solves the measurement error problem, assuming these errors not orrelated through time (Grilihes and Hausman, 1986). In this ase suh an instrument would not be suitable, sine : * ( n γ n n γ n n) γ ( n n) γ ( n) E u 2 e x e z = E e z = E e 0 Even standard GMM panel estimator would not be onsistent. Reduing this bias requires a proedure that insures that the variane of the measurement error is small 10. As the firmspeifi omponent of the residual variane enountered in miroeonometri studies is usually the most important, an appropriate proedure should not be a speifiation involving the equation in levels, suh as the Blundell and Bond estimator. Using within or long differene estimators is one way to redue this bias, as suh estimators remove the permanent omponent in the residuals due to measurement errors and its square. The Arellano and Bond estimator has the same desirable property, as well as that of orreting for simultaneity and measurement error biases. However, we show that it yields impreise estimates, probably due to the weak instruments issue. Turning to the estimation, we present traditional methods dealing with the orrelated effet (within and long differenes) as well as two nonlinear GMM estimators based on the quasi differentiated model of Blundell and Bond (1998). The first GMM estimator relies on the sets of orthogonality onditions S1 and S2 based on the quasi-differentiated model (hereafter GMMDIFQD). The seond GMM estimator is the orresponding system estimator (hereafter GMMSYSQD). We also present the between estimator as a benhmark. 19

21 We measure the volume of labor by the number of days worked, using the number hours worked per day as an additional ontrol variable, possibly interated with other inputs. Ignoring the latter variable would indue to an omitted variable bias sine the elastiity of prodution with respet to days may differ from the elastiity to hours. The number of hours per day is also likely to adjust more quikly than the other regressors and thus apture simultaneity biases. All inputs have been entered at the mean of the sample before omputing ross-produts so that first order oeffiients an be interpreted as average elastiities. Table 3a displays the estimation results using the whole sample for the within estimator, the long differene estimator, the two GMM estimators and finally the between estimator. Separate estimations are then arried out for the manufaturing and non manufaturing industries, as shown in table 3b (within, GMMDIFQD and GMMSYSQD). Table 3a shows strong differenes in first order oeffiients aross estimators. The average elastiity of prodution to omputer is very high (around 0.15) for estimators that involve levels, namely between and GMMSYSQD. The average elastiity is muh lower with GMMDIFQD, within and long differenes that abstrat from levels. The average elastiity for the within and long differene estimators are very lose, around 0.03, and signifiantly different from zero. GMMDIFQD yields a negative but strongly impreise average elastiity. This result is learly not in favor of the level estimations. Indeed, as will be further disussed later, one puzzle assoiated with the estimation of prodution funtions involving omputer stoks is the existene of exess returns to omputers ompared to their share in total ost (whih is usually evaluated around a few perents). From this point of view, within 20

22 and long differene perform better than between and GMMSYSQD that lead to average elastiity too large to be onsistent with plausible orders of magnitude. Estimates of the elastiity of sale are very lose for all estimators exept GMMDIFQD (that yields a dubious value of 1.46), ranging from 0.88 to Notie that using the numbers of hours worked per day (by ategory of workers) as additional ontrols has little effet on the estimated parameters. The elastiity of sale however tends to be higher : the within estimator obtained by omitting these ontrols leads to an average elastiity of sale of 0.80 (unreported regressions). 11 Table 3b displays the analog results based on two subsamples restrited to the manufaturing and the non manufaturing industries respetively. The piture is quite similar to the one obtained from the pooled estimation. The within estimate of the elastiity to omputers averages the onsistent value of 0.03 for both manufaturing and non manufaturing industries, while it is muh higher for GMMSYSQD (0.09 and 0.19 respetively). The seond order oeffiients usually exhibit the same pattern aross estimators but with some notieable exeptions. We mainly look at rossed terms involving omputers. The rossed term unskilled workers*omputer stok is usually negative, only signifiantly so for the between and within estimators. GMMSYSQD yields a positive but insignifiant value. This negative rossed effet is obtained at the industry level for all estimators. It is signifiantly negative in the manufaturing industry. By ontrast, the rossed term skilled worker*omputer stok is generally positive. It is only negative with GMMSYSQD and not signifiantly so in the industry regressions (table 3b). Fousing on the within estimator, the rossed term is signifiantly positive in the pooled estimation (table 3a) and in the manufaturing industry. 21

23 Our onlusion at this stage is that within and long differene estimators yield the most onvining estimations. Of ourse within and long differene do not solve all the problems assoiated with the prodution funtion estimation. However the GMMSYSQD does not solve all problems either as shown above beause of the measurement errors and the non linearity of the Translog prodution funtion. Besides, it does not pass the Sargan speifiation test and leads to unreasonably high elastiities of prodution to omputers. GMMDIFQD, whih is a priori more reliable but subjet to the weak instruments issue, gives very impreise results. Furthermore, the additional ontrol variables we have introdued (hours worked per day) an apture and redue the simultaneity bias in the within and long differene estimations. In the rest of the paper, we therefore work with the traditional within estimation. 12 The features of the estimated tehnology of prodution are further disussed in the next setion by looking at the parameters of interest defined in the first setion. 22

24 IV. Assessing empirially the effets of a derease in the prie of omputers Reall from the first setion that the parameters of interest χ ( ˆ, f x), η ( ˆ, l f x) ( f ˆ, x) ψ are fully defined by the parameters { i, ij}, and α β and the initial level of inputs x *. It is therefore possible to ompute them from one of the previously estimated prodution funtion { ˆ α, ˆ β } i ij fˆ =, onditional on some initial level of inputs x *. As argued in the previous setion, we favor here the within estimator. Besides, a natural hoie for the level of inputs is the individual average of fator levels over time x. Sine the average fator levels differ aross firms, these parameters are firm speifi. We onsider suessively the effet on the marginal ost (parameter χ ) and on labor demand (parameters η l and ψ ). We first display the values of the parameters of interest omputed on the basis of the prodution funtion estimation arried out using the whole sample of 5112 firms, i.e. assuming the homogeneity of the tehnology aross the whole eonomy. We omment on the maroeonomi signifiane of these results. Reall however that the prodution funtion estimates arried out separately on manufaturing and non manufaturing industries, differ somewhat as far as the magnitude and statistial signifiane of the seond order oeffiients involving omputer apital are onerned. We thus omment on the robustness of the previous results when manufaturing and non manufaturing industries are onsidered separately. Effet on the marginal ost 23

25 We find the supply shok assoiated with the derease in the prie of omputers to be large and quite heterogeneous aross the sample. Table 4 displays the 25%, 50% and 75% fratiles of the distribution of χ. The median value is 0.05 : all other input pries and output being held onstant, a derease in the prie of omputer by 15% (about the average annual hange in the Frenh hedoni prie over the period ) should indue a derease in the marginal ost of the median firm by 0.75%. This represents a substantial ontribution, given that the prie of value-added has atually dereased by 1.4% a year relatively to the average labor ost between 1990 and The effet of the deline in omputer ost is sizeable even at the bottom of the distribution : the first quartile of the parameter is equal to 0.04, whih orresponds to a marginal ost derease by about 0.6%. Another way of assessing the extent of the supply shok is to ompare χ to the ratio ε of the elastiity of prodution to omputers divided by the elastiity of sale, and to the shareπ of the remuneration of omputers in total ost. Reall that under the assumption of homogenous prodution funtion of degree θ, χ should be equal to ε θ θ. Besides, if firms are prie-takers on the inputs markets and optimize orretly, ε θ must equal the share π. Table 4 however shows the former to be muh larger than the latter. This result is supported by reent studies (Lehr and Lihtenberg, 1998; Stolarik, 1999; Brynjolfsson and Hitt, 2000). It may point to exess returns of omputers and thus under investment. An alternative explanation is that the effet of omputers aptures something larger than returns to omputers strito sensu, as the stok of omputer apital is bound to be orrelated with unobserved omplementary inputs suh as software or with omplementary workplae organization proesses. In this ase, the prie elastiities we ommented on are elastiities not to the omputer prie but to the prie of an aggregate of all the inputs for whih omputers serve as a proxy. 24

26 Effets on labor demand We analyze here the effet of the omputer prie derease on the struture of the demand of firms with a partiular fous on the two labor inputs. Table 5 presents the AUES that sum up to some extent the pattern of substitutability of the estimated tehnology. However, we omment diretly on omputer prie elastiities (see their sample quartiles in table 6) rather than the orresponding AUES. 14 The primary effet of a derease in the prie of omputers is an aumulation of omputer apital whose magnitude depends on its degree of substitutability with other inputs. We find that the three quartiles of its own prie elastiity are not signifiantly different from -1, whih means that, apart from volume effets, a derease in omputer pries should lead to an inrease in omputer stoks by roughly the same proportion. Notie that with a Cobb-Douglas speifiation the prie elastiity would have been ( ε θ) whih is lose to 1 given the 1 small magnitude of the elastiity of prodution to omputer stok. Thus the more flexible pattern of substitutability aross inputs implied by the translog prodution funtion does not play a major role here. Given that output is held onstant, the aumulation of omputer apital must be neessarily ompensated by a derease in the use of at least one of the three other inputs. One of the most striking features of our results is that this is only the ase for unskilled labor. Indeed, the elastiity of unskilled labor to the prie of omputers appears to be signifiantly positive, with a median value of By ontrast, the estimated quartiles of the prie elastiities of skilled labor are negative with a median value of 0.8. The elastiity of the other apital goods is also negative but not signifiantly so. We an therefore onsider that the derease in the prie of omputers leads firms to inrease the intensity of prodution in 25

27 omputers and skilled workers, and simultaneously derease the use of unskilled workers, keeping the stok of other apital goods unhanged. The effet on aggregate labor demand of a derease in the prie of omputers, measured by η l, involves the two opposite effets on unskilled labor and skilled labor (doumented by the prie elastiities η u and η s in table 6). Table 7 displays the quartiles of the global effet as defined in equation [5]. It has a median value of 0.07 and a 5% onfidene interval of [0.03,0.11]. This value is fairly stable aross quartiles, ranging from 0.06 to Our result an thus be summarized by the statement that omputer aumulation is biased towards apital against labor. Aording to these results, the yearly deline in the omputer prie by about 15% over the period has been assoiated with a negative shift in labor demand for the median firm equal to 1% with a 5% onfidene interval of [-1.6%,-0.4%]. Notie that this does not imply that employment dereased. Indeed the total effet inludes the positive impat assoiated with the redution in marginal ost whih should have fostered the ativity and input levels with a magnitude depending on the demand prie elastiity. The effet on the relative demand for skills of the derease in the ost of omputers, is measured by ψ = ηs ηu. Table 7 shows this elastiity to be unambiguously negative : it has a median value of Besides, it is quite heterogeneous aross the sample, with the first quartile around Table 7 also shows that no suh impat on the relative demand for skills is signifiant for the other forms of apital : the quartiles of the elastiity ψ o do not differ signifiantly from zero. Considering the median value of the parameter ψ, a derease in the omputer prie by 15% should indue a shift in the relative demand for skills by ψ ln( p ) equal to 3.9% with a 5% 26

28 onfidene interval of [1.5%, 6.0%]. In other words, aording to our results, the shift in the relative demand for skills therefore lays between 1.5% and 6.0%. At the aggregate level, this M shift an be measured as ln ( x x ) σ ln ( p p ). In Frane, the relative ost of skilled s u u, s u s to unskilled workers dereased on average by 0.03% a year on average between 1990 and 1999 whereas the ratio of skilled to unskilled labor inreased by 2.2% a year (see figure 1). Sine the median Morishima elastiity of substitution between unskilled and skilled labor is 3.2, the shift in the relative demand for skills an be evaluated at around 2.1%. This figure lies within our onfidene interval. Our results are therefore onsistent with the maroeonomi evolution. They also indiate that omputerization does matter as far as the skill struture is onerned. The parameter ψ ln( p ) represents the median hange in the ratio of skilled to unskilled employment if the relative labor supply is assumed perfetly elasti and held onstant. Under the polar assumption of perfet inelastiity of the relative labor supply, the skill premium M would inrease by ψ σ, ln( p ) whih is found to be rather onentrated around 1.3%. u s As has been heavily stressed above, we fous on the impat of the derease in the prie of omputers, whih we onsider to be the true exogenous shok. This leads us to investigate the issue of biased tehnologial hange through the parameter ψ. We now relate this parameter to alternative measures used in the literature. Studies looking at the skill bias generally rely on the diret estimation of an equation of the form: ( ) D ( ) dln x x = σ dln p p + ϕ dln x + ϕ dln x + λ dln y [8] s u us u s o o y This equation represents the relative demand for skills with quasi-fixed apital stoks 15. The elastiity ϕ measures the response in the demand for skills to a hange in the quantity of 27

29 omputers x, quantities of other apital and output being held onstant. In the framework of equation [8], the aumulation of omputer apital is said to be biased toward skilled labor when ϕ > 0. Most miro-eonometri studies indeed find a positive orrelation between skilled intensity and omputer use 16. Let us show that this popular onept of tehnologial bias ( ϕ ) holds a simple relation with ours ( ψ ), and an also be derived from the estimation of the tehnology of prodution and the level of inputs 17. More generally, the parameters ( ϕ, ϕ ) an be related to ( ψ, ψ ) through the own- and ross- prie elastiities of apital stoks to their pries 18 : that is to say : ( ) ( ) ( ) ( ) o ( ) ( ) ln xs xu ln xs xu ln k,ln ko = ln p,ln p ln k,ln k ln p,ln p o pu, ps, y o pu, ps, y o pu, ps, y ( ψ ψ ) ( ϕ ϕ ) η η o o = o ηo ηoo This last equation shows that, unlike ϕ whih is omputed assuming that apital stoks are onstant, the elastiity ψ takes into aount the substitution effets between omputers and the other forms of apital 19. As the own prie elastiity of omputers is lose to 1 and the ross prie elastiity between omputers and the other forms of apital is not signifiantly different from zero, both measures are lose within our framework. This is obvious when omparing estimates of ψ in table 7 and estimates of ϕ in table 8 for the median firm. o Table 8 also shows that the prodution funtion based estimate of parameter ϕ is relatively homogenous aross our sample of firms. It therefore makes sense to ompare this estimate with the value provided by the diret estimation of equation [8]. 28

30 Diret estimates of equation [8] based on three different estimators are displayed in the right hand side sub-table of table 8. The within estimator points to a signifiant shift in labor demand toward skilled workers, muh weaker however than the one obtained through the prodution funtion approah : the diret estimate of ϕ (0.02) is ten times lower than the median value (0.23) of its estimate based on the prodution funtion. Our approah therefore leads to a muh larger extent of the skill bias than the traditional approah followed in the literature. Estimating equation [8] raises endogeneity issues related to both relative wage and apital stoks. Indeed, relative employment and relative wages are determined at equilibrium. Moreover firms simultaneously hoose apital stoks. The diretion of the resulting estimation bias on the parameter ϕ is in general unlear. GMM estimations, aimed at orreting for simultaneity biases by means of internal instruments, perform poorly. The oeffiients are very impreise when the equation is estimated in levels and instrumented by lagged first-differenes. The Arellano and Bond approah (first-differened model instrumented by lagged levels) leads to poor overidentifiation tests as well as oeffiients inonsistent with the previous estimation. The GMM approah proves here fully inonlusive, when it omes to explaining the disrepany observed in the measure of ϕ aording to the prodution funtion and the diret approah. The lak of external instruments is a reurrent problem in this study, whih we have not been able to overome. Assuming however that simultaneity biases are of limited magnitude when the estimation is arried out in the intra-individual dimension, one may interpret the disrepany between the diret and the prodution funtion approahes in terms of imperfet information from the 29

31 managers side. The latter may indeed not be fully aware of the true tehnologial omplementarities between labor and omputers. Firms may onsequently not have exhausted all the possibilities of substitution allowed by omputerization. Comparing the manufaturing and non manufaturing industries Table 9 displays the results based on the within prodution funtion estimations arried out for the manufaturing and non manufaturing setors separately(table 3b). There are some differenes between both subsamples. The median value of the supply effet (parameter is 4% in both sets of industries. The first and third quartiles are however 0% and 7% in the former against 2% and 4% in the latter. As a rule, effets are stronger and more dispersed in manufaturing than in non manufaturing setors. The omputer prie elastiities of skilled and unskilled labor demand (not reported) have higher median values for firms belong to the manufaturing industries, but also higher interquartiles spread. The omputer prie elastiity of skilled labor demand is also no longer signifiantly negative in the non manufaturing setor. This results in the skill bias parameter ψ being larger in manufaturing than in non manufaturing, where it is insignifiant (table 9). χ ) 30

32 V. Summary and onlusions In this paper, we have developed a methodology enabling us to measure at the firm level the effet of a derease in the prie of omputers on various important firm harateristis : the marginal ost of prodution, the demand for aggregate labor and the skill struture. This methodology is based on the estimation of a prodution funtion from whih we derive the elastiities of the above variables of interest to the prie of omputers. We find that the observed fall in omputer pries onstitutes a large supply shok. We also find large effets on the demand for inputs. The aumulation of omputers indued by the fall in their pries appears to be biased towards apital against labor, and within labor biased against unskilled labor toward skilled labor. The fall in the prie of omputers is thus assoiated with an upward shift in the demand for skilled workers while it is assoiated with a negative shift in the demand for unskilled ones. This appears to be very speifi to omputers. Analog effets have been investigated for the prie of usual apital goods. No pattern of substitutions similar to that found for omputers may be identified. Our approah leads to larger effets on the relative demand for skills than the ones usually found in the literature and based on the diret estimation of a labor demand equation. Our results all for further developments. Comparing the elastiity of prodution to omputers to their ost share suggests that some omplementary input orrelated with omputer stoks, suh as organizational hange, may matter as muh as omputers themselves. The existene of suh unobserved inputs may explain why the elastiity of prodution to omputers is higher than their ost share. It may also imply that the effets on the skill struture speifially assoiated with the aumulation of omputers, may have been overestimated if organizational hange also affets skilled and unskilled workers differently. Making this link 31

33 expliit between omputerization and organizational hange is thus partiularly important sine it is a pre-requisite if we are to assess the influene of future dereases in the prie of omputer power. If the tehnologial bias atually reflets the existene of an organizational bias, omputerization may indeed beome skill-neutral when assoiated opportunities of reorganizations are exhausted. 32

34 Referenes Aemoglu D., Why do new tehnologies omplement skills? Direted tehnial hange and wage inequality, The Quarterly Journal of Eonomis (November 1998), Arellano, M. and Bond, S., Some tests of speifiation for panel data: Monte-Carlo evidene and an appliation to employment equation, Review of Eonomi Studies 58 (1991), Arellano, M. and Bover, O., Another look at the instrumental variable estimation of erroromponents model, Journal of Eonometris 68 (1995), Blundell, R. and Bond S. GMM estimation with persistent panel data: an appliation to prodution funtions IFS Working Paper 99/4 (1998). Bresnahan, T., Brynjolfsson, E. and Hitt, L., Information Tehnology, Workplae Organization and the Demand for Skilled Labor : Firm-level Evidene, The Quarterly Journal of Eonomis forthoming (february 2002). Brynjolfsson, E. and Hitt, L., Computing produtivity : Firm-level evidene, MIT Working paper (2000) Caroli, E. and Van Reenen, J., Skills and organizational hange : evidene from British and Frenh establishments in the 1980s and 1990s, Quarterly Journal of Eonomis vol 116 n 4 (2001). 33