MERIT-Infonomics Research Memorandum series. The Diffusion of Computers and the Distribution of Wages. Lex Borghans & Bas ter Weel

Transcription

1 MERIT-Infonomic Reearch Memorandum erie The Diffuion of Computer and the Ditribution of Wage. Lex Borghan & Ba ter Weel MERIT Maatricht Economic Reearch Intitute on Innovation and Technology PO Box MD Maatricht The Netherland T: F: International Intitute of Infonomic c/o Maatricht Univerity PO Box MD Maatricht The Netherland T: F:

2 The Diffuion of Computer and the Ditribution of Wage * Lex Borghan Reearch Centre for Education and the Labour Market (ROA) Maatricht Univerity P.O. Box 616, 6200 MD Maatricht The Netherland l.borghan@roa.unimaa.nl Ba ter Weel Maatricht Economic Reearch Intitute on Innovation and Technology (MERIT) Maatricht Univerity P. O. Box 616, 6200 MD Maatricht The Netherland b.terweel@merit.unimaa.nl November 2002 Abtract Thi paper model the impact of the diffuion of computer on the wage tructure, tarting from the obervation that computer ue increae individual productivity, but alo the upply of good. Thi latter effect negatively affect worker producing imilar good. If the productivity gain i proportional, and the cot of a computer are equal for everyone, worker with high wage are the firt to adopt, leading to within-group wage inequality. Ditinguihing killed and unkilled worker we how that between-group wage inequality fall when the firt killed worker adopt computer. When unkilled worker tart to ue computer, betweengroup wage inequality increae trongly becaue of the increaed upply of unkilled labor in term of efficiency unit. The maximum level of wage inequality depend mainly on parameter regarding the ditribution of the productivity of worker within and between group: A large initial level of wage inequality lead to a large hort term relative increae in wage inequality. In the long run, when all worker have adopted computer, both within-group and between-group wage inequality fall to a level depending on difference in productivity gain from uing computer. Empirically it i hown that the model i conitent with the pattern of wage inequality in the United State in the period The current pattern i mainly determined by the hort term determinant of wage inequality, making the long run implication difficult to identify and predict. Keyword: Wage Inequality; Wage Level and Structure; Computerization JEL Code: J31, O30 * We thank David Autor, Eve Caroli, Frank Cörver, Paul David, Machiel van Dijk, Arnaud Dupuy, Lui Garicano, Autan Goolbee, Andrie de Grip, Jonathan Guryan, Jim Heckman, Tom Hubbard, Boyan Jovanovic, Joeph Kaboki, Erzo Luttmer, Omer Moav, Kevin Murphy, Derek Neal, Lar Neheim, Paul Stoneman, Bob Topel, John Van Reenen, Gianluca Violante, Bruce Weinberg, and eminar participant at the Central Planning Bureau, the 2002 EALE in Pari, IZA, Maatricht Univerity, Ohio State Univerity, the Tinbergen Intitute, the Univerity of Chicago, the Univerity of Groningen, and ZEW for helpful comment. We acknowledge the Netherland Organization for Scientific Reearch (NWO) for financial upport.

3 1. Introduction It ha been well documented that wage inequality in the United State ha accelerated upon 1 the emergence of computer in the labor market. Several tudie have uggeted that the increae in wage inequality ince the early 1980 ha been caued by a complementary relationhip between computer and killed labor. Indeed, computer ue i more concentrated 2 among killed worker and aociated with higher earning. However, already in the early 1970 a non-negligible part of the workforce had acce to mainframe computer, which did not lead to wage inequality at that time (Brenahan, 1999). In addition, wage inequality decreaed until the early 1980 and although the diffuion of computer i till far from complete, the increae in wage inequality eem to be leveling off in the 1990 (Card and DiNardo, 2002). In thi paper we propoe a model which i able to explain thee obervation. We do o by explicitly taking into account the diffuion proce of computer, tarting from the imple obervation that computerization increae individual productivity but alo the upply of good. Computer ue by a particular group of worker therefore negatively affect worker in the ame group not uing a computer but producing a imilar good. The model contain three main feature. Firt, the diffuion of computer i baed on cot-benefit conideration 1 Greenwood and Yorukoglu (1997) argue that the mid-1970 are the waterhed in the acceleration of wage inequality becaue the price of computer equipment fell fater after 1974 than before, which foter adoption. Katz (2000) argue that wage inequality began to rie in the early 1980, jut after the invention of microcomputer. See alo Katz and Murphy (1992), Bound and Johnon (1992), Juhn, Murphy and Pierce (1993), Autor, Katz and Krueger (1998), Kruell, Ohanian, Río-Rull and Violante (2000); and Johnon (1997), Katz and Autor (1999), Acemoglu (2002), Aghion (2002), and Card and DiNardo (2002) for overview and criticim. 2 See for example Krueger (1993) for the eminal paper uggeting that computer uer earn higher wage becaue of kill advantage, explaining about one half of the widening of the educational wage tructure in the period Levy and Murnane (1996) and Autor, Levy and Murnane (2002) argue that the introduction of computer in a large U.S. bank ha induced ubtitution of unkilled for killed worker. Berman, Bound and Griliche (1994), Dom, Dunne and Troke (1997), Autor, Katz and Krueger (1998), Allen (2001), and Brenahan, Brynjolfon and Hitt (2002) oberve that higher level of computerization and invetment in computer equipment are aociated with higher level of kill and education in the workforce. -1-

4 weighing the productivity benefit againt the cot of computer ue, which induce adoption among high-wage worker firt. Secondly, by ditinguihing two group of worker (killed and unkilled), each producing one imilar good, but with productivity difference between worker, we derive analytical reult for wage development both within and between different group of worker. Thirdly, we explicitly model the aignment of computer to worker. Due to productivity difference not all worker adopt at the ame time and limited ubtitution between killed and unkilled worker lead to different effect on wage within and between group. The main reult of the paper are the following. The pattern and tructure of wage over time predicted by the model how different effect for between-group and within-group wage inequality. Between-group wage inequality i falling when the firt killed worker adopt computer becaue the additional upply in efficiency unit depree average killed wage more than the productivity gain increae wage. When more killed worker adopt computer, and when unkilled worker tart to ue computer, between-group wage inequality will increae trongly becaue the productivity gain killed worker experience outweigh the additional upply of killed labor in efficiency unit. More importantly, the upply of additional efficiency unit of unkilled worker increae between-group wage inequality. When all worker have adopted computer, wage inequality fall to a level depending on difference in productivity gain between killed and unkilled worker. When killed (unkilled) worker benefit more, between-group wage inequality will be permanently higher (lower). However, the hort term effect on between-group wage inequality are much higher than the long term effect. We alo how that the maximum level of between-group wage inequality i higher the higher the level initial wage inequality. Within-group wage inequality for killed (unkilled) worker i increaing once the -2-

5 firt killed (unkilled) worker have adopted computer. Thi i the cae becaue all worker in a group uffer in term of wage from the additional upply of efficiency unit, but only the adopter benefit from the productivity gain from uing a computer. If all worker within a group have adopted computer, within-group wage inequality in that group fall to the level prior to computer adoption if the productivity gain for every worker within the ame group are the ame. Empirically, we how that the pattern of wage inequality predicted by the model i conitent with the pattern and timing of wage inequality in the United State in the period Uing CPS data, we find the productivity gain from uing computer to be between 15 and 40 percent, both for killed and unkilled worker. Thi i conitent with etimate of the cot of computer relative to annual wage. Becaue currently not all worker have adopted computer, the hort term effect of computer adoption are dominating the tructural long term productivity effect. Baed on pat and current development in the wage tructure, it i therefore hard to preciely point out whether killed or unkilled worker benefit mot in term of productivity gain. A a reult, the current development do not provide concluive information about the long run implication for wage inequality. The model i related to the older literature on the diffuion of new technologie, including the work of Griliche (1957), Manfield (1961), David (1969), Stoneman (1976), and Davie (1979), who argue that the cot of new technologie are important determinant 3 of adoption and diffuion. In thi paper, (endogenou) wage and productivity gain determine whether computer adoption i beneficial, wherea previou model treated the determinant of the diffuion proce motly exogenouly. The model i alo related to more recent tudie on technology adoption by Chari and Hopenhayen (1991), Galor and Tiddon 3 See Geroki (2000) for an overview of the technology diffuion literature. -3-

6 4 (1997), Caelli (1999), and Weinberg (2001). In thee paper, killed worker have a higher probability to work with new technologie than unkilled worker becaue new technologie can be more productively operated by killed worker, but they do not take into account the cot of new technologie. Violante (2002) aume noncompetitive labor market to explain wage inequality among ex ante equal worker in relation to the adoption of new technologie. The heterogeneity among worker i not generated by kill differential but by technological differential acro the machine of different vintage they are matched with. We are able to ditinguih between the timing of technology adoption and the productivity gain reulting from adoption in a competitive labor market. By ditinguihing productivity differential within the group of killed and unkilled worker, we alo differ from the above theorie, and the one developed by Greenwood and Yorukoglu (1997), Acemoglu (1998), and Kiley (1999), by explaining both between-group and within-group wage inequality, wherea the other tudie mentioned above only analyze wage inequality either within or between group. 5 Finally, with regard to the ditribution of productivity within the group of killed and unkilled worker, thi paper i related to the approache of Heckman, Lochner and Taber (1998), Galor and Moav (2000), Gould, Moav and Weinberg (2001), and Aghion, Howitt and Violante (2002). They alo ue ome (ability) ditribution to examine within-group inequality, which lead to the development and tranferability of technology-pecific kill driving wage inequality, wherea our mechanim of within-group inequality i determined by the cot of computer relative to the wage and the productivity gain from uing computer. Finally, the 4 The model predicting the adoption and diffuion of general purpoe technologie are alo conitent with our approach becaue computer ue i pervaive in a wide range of ector in way that change their mode of production (e.g., Brenahan and Trajtenberg, 1995 and Helpman and Trajtenberg, 1998). 5 Caroli and García-Peñaloa (2002) alo preent a model accounting for both between-group and within-group wage inequality uing difference in wage-etting behavior and wage intability in different tage of technological development. Their model i driven by the aumption that change in worker rik averion induce change in wage. -4-

7 pattern of wage inequality reulting from the diffuion of computer preented in thi paper i not necearily caued by a pervaive kill-biaed nature of computer, but driven by the adoption of computer at different point in time. The plan of the paper i a follow. Section 2 preent the pattern of wage inequality in the United State. Section 3 preent the baic model. Section 4 how the predicted pattern of wage inequality over time. Section 5 preent etimate of the model for wage inequality in the United State in the period Section 6 conclude. 2. Change in the U.S. Wage Structure, If computer adoption increae productivity, two factor influencing the wage tructure have to be ditinguihed. Firt, there will be an individual productivity increae for worker adopting computer. Secondly, increaed productivity alo increae the upply of good produced. Thi latter factor might influence the wage of all worker, depending on how ubtitutable the good they produce are. Hence, beide an individual effect, related to productivity, change in the wage tructure depend on the compoition of group of worker producing ubtitutable good. We define wage difference between worker with different productivity level producing imilar good a within-group wage inequality and define wage difference between worker in different product market group a between-group wage inequality. Since it i difficult to determine exactly the group of worker producing imilar good, we aume that the main ditinction in the good market can be made between phyical and cognitive good and ervice. We aume that phyical good are produced by unkilled worker, while cognitive good are produced by killed worker. Skilled worker are defined a thoe with a college degree or more, and unkilled worker a the one with a level of -5-

8 education below a college degree. Worker are aumed to be fully ubtitutable within thee two group, and ubtitutable in a limited way or complementary between group. Figure 1 how three picture of relative annual wage in the United State in the 6 period uing the March CPS file. Each picture provide annual wage relative to th the annual wage of the worker at the 10 percentile of the unkilled wage ditribution. Comparion of Panel A and B reveal information about the pattern of within-group wage inequality for killed worker. The figure reveal that within-group wage inequality for killed worker i increaing throughout the whole period but that the behavior of the top and bottom percentile i rather different. Panel C how within-group wage inequality for unkilled worker. Thi picture how a rather modet increae until 1980 and an acceleration afterward. To examine between-group wage inequality between killed and unkilled worker, Panel A and B have to be compared with Panel C of Figure 1. Thi comparion yield that the wage of the top earner among the killed worker are teadily increaing over time, but that the wage of the bottom earner among the killed worker are firt falling and then riing again. INSERT FIGURE 1 OVER HERE To how the crucial ditinction between the development of between-group and within-group wage inequality, we compare worker from both group earning the ame wage 7 th th in We have taken the annual wage of the killed worker at the 40 and 50 percentile and looked for the unkilled worker earning the ame annual wage. It turn out that thee are th th the wage of the unkilled worker at the 75.7 and 83.9 percentile of the unkilled wage 6 See Appendice A.1-A.5 for detail concerning the data. 7 We are grateful to Kevin Murphy for hi uggetion to perform thi analyi. -6-

9 8 ditribution. Figure 2 how the wage differential between both group keeping the relative poition within each group contant at thee percentile. The picture reveal that wage differential rie omewhat and are poitive until the early From then on until the mid the wage for unkilled worker are higher. Around 1980 there i a turning point in the wage differential in favor of killed worker. Figure 2 reveal that worker with the ame productivity in 1963, but who differ with repect to the group they belong to, have experienced a different pattern of wage over time. 9 INSERT FIGURE 2 OVER HERE 3. Baic Model Analyzing thee imple picture ugget that wage are both determined by individual productivity level within each group of worker and by difference between the two group of worker. Thee two effect have a different impact on the wage tructure over time and 10 need to be analyzed eparately. To do o, conider a competitive economy producing a homogeneou good Y. The good i produced by a labor input coniting of killed and unkilled worker. Becaue of productivity difference among killed and unkilled worker, we define the upply in term of efficiency unit a S and U. 8 Thee percentile of the wage ditribution of both group are taken becaue at thee percentile there exit a great deal of overlap between the wage of both group of worker. The percentile do not exactly match th th becaue not all poible value of wage are preent in the ample. Actually the 75.7 and 83.9 percentile of the th th unkilled wage ditribution are omewhat above the 40 and 50 percentile of the killed wage ditribution. 9 Thi pattern of between-group wage inequality i conitent with the figure preented by Katz and Murphy (1992) uing imilar data for the period , and the analyi of Kruell, Ohanian, Río-Rull and Violante (2000) for the period Such argument have alo been put forward by Card and DiNardo (2002). They argue that the effect of computer adoption on the wage tructure need to be different for different group of worker at different point in time to be able to connect the tructure of wage over the lat 50 year to computerization. -7-

10 Production Production occur according to a CES production function and equal (1) Y ((χs) ρ (ψu) ρ ) 1/ρ, where ρ 1, and the elaticity of ubtitution between S and U equal σ=1/(1-ρ). The wage give a tandard relative demand equation: w eu w eu (2) w eu u w eu u w eu ψu χs w eu u correponding wage in efficiency unit are and for S and U, and competitive For convenience, i normalized to 1, o 1/σ. w eu (χs/ψu) 1 ρ. Heterogeneity among Worker Productivity level differ not only between group, but alo within both group. Thi might be due to unoberved heterogeneity, but individual productivity level might alo differ from year to year due to on-the-job learning, aging, ector hift and other influence, which need not be pecified further. We aume that worker are perfectly ubtitutable within both group, o any productivity difference i reflected in wage. 11 Productivity depend on the parameter a i [α,α] with α > α for killed worker i and b j [β,β] with β > β for unkilled worker j. Productivity parameter of killed and unkilled worker can only be compared when wage in efficiency unit are taken into account. We allow the wage interval of both group to overlap. Thi i conitent with the empirical obervation that the wage of the mot productive unkilled worker are higher than 11 Gould, Moav and Weinberg (2001), Aghion, Howitt and Violante (2002), and Violante (2002) alo explain difference in the development of within-group and between-group wage inequality in the United State. They aume worker to differ in their adaptability to new technologie a a reult of random hock or aignment, and Violante (2002) alo aume that technologie differ in their productivity or quality to generate temporary within-group wage inequality. Aghion, Howitt and Violante (2002) ue an overlapping generation model to get imilar effect of technology adoption on wage. Caroli and García-Peñaloa (2002) build a model in which they ue different attitude toward rik to generate heterogeneity between worker. -8-

11 the wage of the leat productive unkilled worker, i.e. βw eu u > αw eu. To make thi overlap of productivity level conitent with rational individual chooling deciion, it ha to be aumed that productivity doe not only depend on year of chooling. Difference in innate ability, talent for either phyical or cognitive tak, or age and experience all provide plauible argument for thi aumption. P (a) 1 1 ρ p P u (b) 1 1 ρ p u p σ 1 1 form: and, where and p u σ 1 σ To enable an analytical olution of the model, the ditribution of the productivity parameter for killed and unkilled worker i aumed to take the following 1 β σ 1 β σ 1 1 ρ a 2ρ 1 1 ρ b 2ρ 1 σ α σ 1 α σ 1 are obtained from olving the integral for the ditribution of productivity parameter of both type of worker. If σ=2, the aumed ditribution i uch that the wage bill i uniformly ditributed over the productivity parameter a and b. 12 Productivity Each worker productivity level depend on hi productivity parameter and whether or not he ue a computer. Productivity equal q i a i and q u j b j without uing a computer and q i a i θ and q u j b j θ u u when uing a computer, where θ, θ >1 i the proportional productivity gain from working with a computer. We aume that within both group the productivity gain from uing a computer i the ame, while between both group it i allowed to differ, and for all worker there exit ome computer application, which make production 13 more efficient. Thee aumption are jutified becaue within each group, worker are 12 For the production function ued here, a different elaticity of ubtitution between killed and unkilled worker could lead to a lightly different ditribution of the productivity parameter. 13 The alternative aumption would be a complementary relationhip between the productivity parameter a and b and θ. Auming uch a relationhip lead to earlier adoption of computer (given the cot of adoption) for i j u worker with a proportional productivity gain θ >θ and θ >θ and to a later adoption for worker experiencing u proportional productivity gain maller than θ and θ. A will be hown below, uch an aumption would lead to a imilar pattern of diffuion but to a permanently higher level of within-group wage inequality. -9-

12 producing the ame product. Wage In a competitive labor market, each efficiency unit of labor receive the ame return and the individual wage equal the productivity parameter multiplied by the return to an efficiency unit of labor. In uch a etting, employer are indifferent between employing a worker who ue a computer and one who doe not becaue they pay the ame wage for each efficiency unit of labor. Thi mean that both the productivity gain and the cot of the computer are paed on to worker. Hence, wage equal w i a i w eu and w u j b j for a worker who doe not ue a computer and w i a i w eu θ V and w u j b j θ u V for one who doe, where V repreent the cot of the computer. Note that V i (implicitly) expreed in term of w eu u. Wage and Computer Adoption The deciion to adopt a computer can be written a a trade-off between the increaed 14 productivity θ and the cot of the computer V, given the worker productivity. The break- even productivity for computer adoption for both type of worker then equal (3a) and (3b) a be i b be j V (θ 1)w eu V (θ u 1). Equation (3) how that the break-even productivity at which it become beneficial to adopt a computer fall when (i) the cot of the computer fall, (ii) the productivity gain become 14 Note that the adoption deciion may be different for each individual worker within a firm. Thi i conitent with the literature invetigating inter- and intra-firm technology diffuion howing that the diffuion of new technology within firm i imilar to the diffuion between firm (e.g., Karhena and Stoneman, 1993 and Stoneman and Kwon, 1996). Hence, it i unlikely that firm adopt computer for all worker at once. -10-

13 larger, and (iii) the wage per efficiency unit of labor i higher. Auming that the cot of the computer are the ame for each worker and fall exogenouly and continuouly over time, the productivity gain and the wage in term of efficiency unit determine the adoption of the 15 computer. Hence, computer cot relative to wage determine whether or not it i beneficial for a worker to adopt a computer while difference in computer ue between killed and unkilled worker alo depend on difference in the proportional productivity gain from uing a computer. 16 Supply of Efficiency Unit The upply of efficiency unit of labor conit of two component: (i) the um of all productivity parameter repreenting total productivity before computerization, and (ii) the productivity gain worker experience from uing a computer, which equal S S e α a i P da i S e α (θ 1)a i P da i U U e β b j P u db i U e β and (θ u 1)b j P u db j, α a be β i b be j e e where S and U are defined a the upply of killed and unkilled worker in peron. Solving thee equation reult in the following two expreion for the upply of efficiency unit of labor: (4a) and S S e p (α σ α σ ) (θ 1) α σ V (θ 1)w eu σ 15 The development of computer might alo be endogenized by directing a certain fraction of production toward the development of computer. The allocation of labor to R&D then lead to falling cot and higher quality. However, endogenizing the development of computer doe not yield additional inight in explaining wage inequality. David and Olen (1986) develop uch a diffuion model in which the development of new technology i endogenized. Earlier attempt to endogenize the development of new technologie can be found in e.g., Griliche (1957, 1958), and Manfield (1961, 1965). 16 If, all thing being equal, θ 1>θ u 1, killed worker gain more in term of productivity from uing a computer, which i equivalent to arguing that they are more efficient in uing the computer. Chennell and Van Reenen (1997), Entorf and Kramarz (1997), and Entorf, Gollac and Kramarz (1999) interpret their finding for the United Kingdom and France of high-wage worker uing a computer a reult in favor of uch an explanation. -11-

14 (4b) U U e p u (β σ β σ ) (θ u 1) β σ V σ (θ u 1) Equation (4) how that the upply of efficiency unit of labor depend poitively on the ize of the ditribution of the productivity parameter a and b, the productivity gain from uing a computer θ, and the elaticity of ubtitution between killed and unkilled worker σ, and negatively on the cot of the computer V.. Relative Wage after Complete Diffuion with No Computer Cot To olve the equilibrium relative wage in efficiency unit, equation (4) are ubtituted into the relative demand equation (2). Before turning to the equilibrium wage, conider relative wage after the complete diffuion of computer and V=0: w θ (5). w u θ u w 0 u u ρ Equation (5) how that relative wage after diffuion have changed with a factor (θ /θ ). ρ w 0 u Wage inequality will be higher if θ <θ and killed and unkilled worker are complement u (ρ<0) and if θ >θ and killed and unkilled worker are ubtitute (ρ>0). While the empirical literature eem to point at ρ>0, the model leave open both alternative. Computer cot Of coure, the cot of uing a computer are not negligible relative to the wage. The cot of 17 See e.g., Katz and Murphy (1992) and Johnon (1997) for U.S. etimate, Angrit (1995) for etimate for Irael, and Hamermeh (1993) for an overview. 18 An intance at which ρ<0, often pointed at, i the complementarity between the manager and the ecretary. If u θ <θ the ecretary benefit more from computer ue than the manager. Thi mean that, given the amount of work, the demand for ecretarie will fall. -12-

15 the computer hould be interpreted a the cot of the entire deal, i.e. hardware, oftware, network, and technical aitance. In dollar term, a back-of-the-envelope calculation etimate the annual cot of uing a computer to be $6,567 in 1997, which account for about 21 percent of the average worker real annual wage in the United State. Thi figure i computed a follow. Firt, uing the invetment in information proceing equipment and oftware data collected by NIPA and dividing thi number by the computer uing workforce in full-time equivalent yield computer cot of $4,530. Secondly, regreing the relative number of 21 worker in computer related job (cw) to computer uer (c) per ector of indutry, uing the October 1997 School Enrollment Supplement to the CPS, and weighing by indutry ize, yield (tandard error in bracket) cw = 1.38 (.003) (.005) c. To obtain a conervative etimate for the cot of technical aitance, we left out the ector of indutry with relatively 22 high fraction of computer related job. Since the average monthly wage of worker in 19 Full-time equivalent employee equal the number of employee on full-time chedule plu the number of employee on part-time chedule converted to a full-time bai. The number of full-time equivalent employee in each indutry i the product of the total number of employee and the ratio of average weekly hour per employee for all employee to the average weekly hour per employee on full-time chedule. 20 Autor, Katz and Krueger (1998) report computer invetment per full time equivalent worker to be $2,545 in 1990, which i equivalent to about $5,000 per full time equivalent computer uer. Figure for 1960, 1970 and 1980 yield comparable invetment per full-time equivalent computer uer. Computer ue i taken from the October 1997 School Enrollment Supplement to the CPS. There i likely to be meaurement error in the NIPA data becaue the Bureau of Economic Analyi doe often not directly meaure information proceing equipment and oftware at high frequency, but impute thee data. See Gorman, Mugrave, Silvertein and Comin (1985), Berndt and Morrion (1995), and Autor, Katz and Krueger (1998) for a dicuion. See alo Allen (2001) for a more detailed treatment of computer invetment and invetment in cience and technology related to the wage tructure in the United State. 21 Thee occupation are Computer ytem analyt and cientit (CPS Occupational Claification Code for Detailed Occupational Categorie 064), Operation and ytem reearcher and analyt (065), Computer cience teacher (129), Computer programmer (229), Tool programmer, numerical control (233), Computer operator (308), Peripheral equipment operator (309), Data-entry keyer (385), Data proceing equipment repairer (525), and Office machine repairer (538). 22 Sector of indutry with more than 10 percent computer related employment are Computer and data proceing ervice (CPS Indutry Claification Code for Detailed Indutry 732), Telegraph and micellaneou communication ervice (442), Not pecified utilitie (472), Computer and related -13-

16 computer related job equal $2,692, we etimate the cot of aitance for each individual worker to be equal to $2,037. It ha been well documented that the price of computer equipment ha been falling extremely rapidly over time, which induced diffuion (e.g., Jorgenon and Stiroh, 1999 and Jorgenon, 2001). Figure collected by NIPA ugget that invetment in computer equipment are only ome percent of total invetment in information proceing equipment and oftware over the Invetment in oftware account for ome percent, while other invetment make up ome percent of total invetment. The quality-adjuted price of oftware (e.g., Jorgenon, 2001, Figure 2), and other computer related invetment have hardly been falling over time. The overall annual decline in the cot of information 23 proceing equipment and oftware ha been 2.1 percent over the period Thee figure ugget that the adoption rate of computer at work i likely to be lower than the rate of fall in the price of computer equipment, and that the cot of computer are non-negligible relative to the worker wage. Difference in the quality of computer ued by different worker are not explicitly conidered in the model. When conidering different vintage of computer in a perfectly competitive market, the mot productive worker would be aigned to the mot recent vintage. In addition, the cot of the computer might alo be different for different worker. For example, large firm might have an advantage in maintenance and technical aitance, which lead to lower computer cot per worker. Next to that, ome worker need a le expenive computer than other, which induce earlier adoption, all other thing equal. equipment (322), Electrical repair hop (752), Profeional and commercial equipment and upplie (510), and Radio, TV, and computer tore (633). 23 Thee number and calculation are baed on NIPA figure and conitent with the number and calculation preented by Jorgenon (2001). -14-

17 Finally, ome worker perform tak on the bai of ready-made application, wherea for other with higher wage and higher productivity gain no application i available yet. However, for implicity, we make the aumption that the cot of the computer are given to the worker and are equal for all worker. Equilibrium Relative Wage in Efficiency Unit With an exogenouly falling price of computer, the benefit of adopting a computer are changing over time for all worker. Since the productivity level of both killed and unkilled worker i concentrated on the interval parameter [α,α] and [β,β], different tage in the adoption proce will occur. The order of thee tage depend on both the level of wage and break-even wage of killed and unkilled worker. Since a diffuion pattern in which the mot productive killed worker are the firt to adopt followed by the mot productive unkilled worker, the leat productive killed worker, and finally the leat productive unkilled worker eem to be conitent with the actual pattern of adoption, our analye focu on thi equence of adoption. 24 Equilibrium wage in efficiency unit are computed in each of the five tage in the 25 diffuion proce: (i) no computer ue, (ii) the high-wage killed worker adopt computer, (iii) both type of worker adopt computer, (iv) all killed and a fraction of the unkilled worker adopt computer, and (v) all worker ue computer. Table 1 how the relative 24 Thi aumption i conitent with the figure on computer ue for 1984, 1989, and 1993 preented by Autor, Katz and Krueger (1998). They how that computer ue i higher for more educated worker but it i riing among all different educational group. 25 Note that it i poible that certain tage of diffuion will never become effective becaue of the overlapping productivity parameter between killed and unkilled worker. For example, given wage, proportional productivity gain and the ditribution of productivity parameter, an unkilled worker with productivity β could reach the break-even point for computer ue later than a killed worker with productivity α, which would induce computer ue among unkilled worker when all killed worker already have one. Therefore, in theory, the order of the tage could be different. -15-

18 wage in efficiency unit in each of the five tage. When there i no computer ue, relative wage depend on the upply of efficiency unit, the ditribution of productivity parameter and the elaticity of ubtitution between killed and unkilled labor. In the other four tage, relative wage in efficiency unit alo depend on θ, V, and the additional unit of upply of efficiency unit. Note that relative wage in efficiency unit do not change anymore once every worker ha adopted a computer, even when V>0. Thi i becaue the upply of the number of efficiency unit of labor, once all worker have adopted a computer, remain contant and i independent of V, e.g. equation (4). INSERT TABLE 1 OVER HERE Table 2 how individual wage for two worker with productivity parameter a and 1 a relative to worker j with productivity 2 β. The level of the wage in efficiency unit and the ize of the proportional productivity gain are aumed in uch a way that the adoption of computer i aumed to take place in the following order: α, a 1, β, α, β and α, β, a 2, α, β. From Table 2 it become clear that the wage of all worker are influenced once the firt worker adopt a computer. In addition, once every worker ha adopted a computer, it i not until V=0 that wage do not change any more (tage 6). 26 INSERT TABLE 2 OVER HERE 4. Pattern of Relative Wage over Time Within-Group Wage Inequality The individual wage in Table 2 can be ued to analyze the propertie of within-group wage inequality over time. Figure 3 provide the wage pattern that reult from the model for killed 26 The equilibrium wage for other killed worker with different productivity parameter follow traightforwardly from the reult preented in Table 2. In addition, the derivation of the wage for unkilled worker i imilar to the derivation of the equilibrium wage hown here. -16-

19 (Panel A) and unkilled (Panel B) worker. Since no worker ha adopted a computer yet, in the firt tage of the model all wage differential remain the ame. The wage tructure tart to change when V i ufficiently low for the mot productive killed worker to adopt a computer. In thi econd tage (which lat until the mot productive unkilled worker adopt a computer), the wage of killed worker change when killed worker l adopt a computer ( a l (θ 1)w eu V) according to (6a) w k / V a k 1 a k a σ 1 l θ θ α σ α σ for killed worker k who already adopted a computer ( a k a l ), and according to (6b) w m / V a σ 1 l a m θ α σ α σ for killed worker m who did not yet adopt ( a m <a l ). From equation (6) a number of model feature become apparent. Firt, once it become beneficial for worker l to adopt a computer hi wage increae relative to the wage of worker m leading to wage inequality within the group of killed worker becaue w l / V a l > w m / V a m 27. The wage for the non-adopter change, but only proportionally, and there i no increae in wage inequality between non-adopter. Since the term 1/ak i larger for lower value of a k there i wage convergence within the group of computer uer, leading to 27 If θ i high relative to V, adoption of the whole group will occur at earlier tage. It will alo lead to a higher αθ 1 V α > αθ maximum level of within-group wage inequality becaue V α if θ >θ. The maximum level of wage inequality will be experienced earlier becaue the leat productive worker will reach the break-even point of adoption earlier on. On the other hand, V become negligible relative to the wage cot earlier on, which lead to a fater drop in within-group wage inequality. If V fall fater over time, the adoption of computer and the effect on the wage tructure will occur fater and earlier on. The maximum level of within-group wage inequality will remain the ame becaue thi only depend on α α and θ. -17-

20 le wage inequality among computer uer in the ame group. Secondly, it i not necearily the cae that the wage of computer adopter rie immediately after adoption. Wage fall, relative to worker j with productivity β, for the w α α 1 ασ θ firt adopter becaue. However, the wage for the worker not V adopting a computer fall by more becaue θ α σ α σ <0 a σ k θ (θ α σ α σ )<a σ 1 k a l, o it i rational to adopt a computer at the break-even point (e.g., equation (3)). In thi tage of the diffuion proce, wage rie immediately after adoption only if equation (6a) i poitive. Thi ituation might never occur in thi tage but i more likely to occur if α α 28 i relatively large. w al 1 a l σ θ If 0 wage for worker l rie immediately after adoption. Note V θ α σ α σ that, becaue 1/a k <1/a l, the wage for worker k are till falling, relative to β, at thi point in time. Wage of computer uer and non-uer are till diverging, but at a lower pace, becaue when killed and unkilled worker are ubtitute (σ 1) decreae. a l σ 1 decreae when α l In the third tage, when unkilled worker tart to adopt computer ( b(θ u 1)w eu V ), the wage development of killed worker when worker l adopt a computer ( a l (θ 1)w eu V) can be decribed by u (7a) w k / V a k 1 a k a σ 1 l θ ψu e u p θ α σ α σ χs e p θ 1 θ u 1 σ 1 a σ 1 l θ θ α σ α σ for killed worker k who already adopted a computer ( a k a l ), and by 28 The pattern and length of time of within-group wage inequality alo depend on the productivity differential α α, the cot of the computer relative to the productivity gain, and the peed at which V i falling over time. The maximum level of within-group wage inequality only depend on α α and θ. When the initial productivity differential i maller, or the productivity gain relative to the computer cot i higher, or V i falling more rapidly over time, the length of time of increaing and overall within-group wage inequality i horter. A higher productivity differential and a higher proportional productivity gain will induce a higher maximum abolute level of within-group wage inequality. -18-

21 (7b) w m / V a σ 1 l a ψu e u p m θ α σ α σ χs e p θ 1 θ u 1 σ 1 a σ 1 l θ α σ α σ for killed worker m who did not yet adopt ( a m <a l ). If killed and unkilled labor are ubtitute, both the killed computer uer and the killed non-uer benefit from the increaed productivity among unkilled worker, reflected in additional term in equation (7) when compared to equation (6). Due to the increaed productivity of killed computer uer, thee worker gain more in relative term than the killed non-uer. Computer ue among unkilled worker therefore timulate the increaing within-group wage inequality among killed worker. Note that the development of relative wage of two computer uer or of two non-uer are not affected by computer adoption among unkilled worker. In the fourth tage, all killed worker have adopted the computer. Until adoption i completed among unkilled worker (tage 5), the wage development for killed worker are decribed by (8) w k / V a k 1 a k (θu 1) (θ 1) 1 σ ψu e p u θ σ 1 be a. χs e p θ (α σ α σ ) From equation (8) it follow that if all killed worker have adopted a computer, but not all unkilled worker have adopted one yet, there will be wage convergence within the group of 1 α < 1 α killed worker becaue. If all worker have adopted computer, w k / V a k 1 a k, o it follow traightforwardly that wage inequality within the group of killed worker behave imilarly to the previou ituation. Finally, if V=0, wage inequality within the group of killed worker i back at it -19-

22 level prior to computerization. INSERT FIGURE 3 OVER HERE A imilar pattern of wage inequality within the group of unkilled worker can be obtained. The only difference i that the timing of the different tage of adoption i different. Eentially, the wage tructure within both group i characterized by only three phae: (i) no computer ue, (ii) ome computer ue, and (iii) every worker ue a computer. Only when unkilled worker tart to adopt computer, the adoption proce of killed worker, and therefore within-group wage inequality accelerate becaue of the increae in killed worker efficiency wage. Such increaing wage are equivalent to fater decreaing computer price, ince the wage/computer price ratio determine the adoption proce. Between-Group Wage Inequality Defining the wage ratio of the worker with productivity α and β a between-group wage inequality, it follow from equation (6) that thi ratio i falling when the firt killed worker adopt a computer, leading to a lower level of between-group wage inequality. Between-group wage inequality continue to fall until 0, where α>a V i or until the firt unkilled worker adopt a computer. Between-group wage inequality then increae w ai becaue of two effect. The firt effect reult from benefit of the falling cot of computer ue for killed worker, and the econd effect reult from the increaing upply of efficiency unit of unkilled labor after computer adoption, which depree the unkilled wage in u efficiency unit. Note that thee effect do not depend on difference between θ and θ. The development of between-group wage inequality in each tage of computer adoption and diffuion i diplayed in Figure 4. The figure reveal that between-group wage inequality i not likely to increae after the firt worker have adopted computer. Only when -20-

23 a non-negligible group of killed worker or the firt unkilled worker adopt computer, between-group wage inequality tart to rie. Thi i conitent with Brenahan (1999) concern about many worker already uing computer without any ubtantial rie in wage inequality a a reult of computer adoption in the The figure alo how that the pattern of between-group wage inequality i leveling off at the end of tage 3 and again at the end of tage 4. At the end of tage 3 almot all killed worker have adopted computer, which eem to be the cae in the late And at the end of tage 4 all worker have adopted computer. The leveling off of between-group wage inequality in the mid-1990, pointed at by Card and DiNardo (2002) i therefore conitent with our model. Final wage inequality (when V=0) i decribed by equation (5). Between-group wage inequality reache it maximum level at the point where the leat productive unkilled worker i jut about to adopt a computer. At that point, the wage of the worker with productivity α equal (9) w c α 1 β ψu e p u θ u (β σ β σ ) χs e p θ (α σ α σ ) 1 σ αθ β(θ u 1) compared to (10) w nc α α β ψu e p u (β σ β σ ) χs e p (α σ α σ ) 1 σ before computerization. The ratio of thee two wage equal (11) w c α w nc α θu θ 1 σ θ β(θu 1). w nc α -21-

24 Equation (11) ha a number of intereting propertie. Firt, the ratio of wage i increaing in w nc α meaning that a higher level of initial wage inequality between the mot and leat productive worker lead to a higher peak in between-group wage inequality. Secondly, it i alo increaing in θ for ρ>0, which mean that a higher productivity gain for killed worker lead to a higher maximum level of between-group wage inequality. Thirdly, the derivative of 1 σ θ θ u ρ β w nc α u u equation (11) with repect to θ equal, which i increaing in θ if β i σ 1 θ σ u mall or if θ /θ i large. Finally, if β 0, equation (11) equal θ u. Now, the effect of 1 σ an increae in θ i larger if σ>2 and β>0 increae thi effect. After the leat productive worker ha adopted a computer, between-group wage inequality fall becaue w α / V α < w β / V β back at i level prior to computerization.. Finally, if V=0, between-group wage inequality i INSERT FIGURE 4 OVER HERE 5. Empirical Analyi 5.1. Data and Contruction of Variable We ue the March Demographic Supplement to the CPS from 1964 to 2001 for information about the tandard labor market variable and to contruct labor upply in the period The October School Enrollment Supplement to the CPS from 1984, 1989, 1993, and 1997 are ued for information about computer ue at work. The Appendix provide a detailed overview of the contruction of labor upply, annual wage, and computer ue in the period uing thee data. Important data that i miing from the CPS i ytematic information on computer ue. Computer ue i only available in four year (1984, 1989, 1993, and 1997) and ha been imputed conitent with the break-even wage approach of the model, uing the figure from -22-

25 the March and October CPS file (ee Appendix A.4 and A.5 for more detail). The imputed fraction of killed and unkilled worker uing computer are diplayed in Figure 5. The pattern of diffuion how a S-haped diffuion pattern, which i conitent with other evidence on the diffuion of new technologie (e.g., David, 1969 for an overview). From Figure 5 it can be read that computer ue for killed worker ha rien rather rapidly ince the early 1970 and that computer ue for unkilled worker tarted to increae around While thi imputation i far from ideal, it ugget that IT-related technological change ha been going on ince at leat the early 1970 and ha continued throughout later decade. Thi i conitent with everal figure brought together by Card and DiNardo (2002, Section II.A) on the diffuion of IT at the workplace and Brenahan inference that a non-negligible fraction of U.S. worker were employed in firm with computer acce from the early 1970 onward (Brenahan, 1999). INSERT FIGURE 5 OVER HERE 5.2. Econometric Specification of the Model To etimate between-group wage inequality we etimate the log of labor demand equation (2), allowing for a time trend. To do o, the upply and wage in term of efficiency unit of both type of labor have to be determined. Thi yield the following equation for etimating between-group wage inequality: (12) ln w w u ln γ 0 w eu w u (θ u 1)w u be C u w u γ 0 (θ 1)w eu C (θ 1) w be w u C, U e U e (θ u 1)F u w eu u where and F and F are the wage-bill hare of the computer S e S e (θ 1)F 1/σ e γ 1 t uer within both group. Thi equation ha been etimated by non-linear leat quare with θ, -23-

26 u θ, γ 0, and γ 1 a the unknown parameter. The derivation of the equation for etimation i given in Appendix A.6. Note that if not all ubgroup of killed worker are equally ubtitutable with unkilled worker and vice vera, the etimate for between-group wage inequality will underetimate the productivity gain from computer ue, becaue the productivity gain will not have affected the other group a would have been the cae if we obtained the perfect diviion of the labor force into group of killed and unkilled worker. Since our diviion of killed and unkilled worker into two group manufacturing different good might not be the bet plit of the ample, we expect the etimate to be relatively low compared to the withingroup etimate of the proportional productivity gain from computer ue. For within-group wage inequality the following two equation have been etimated: (13a) ln w 90 th w 10 th ln γ 0 γ 0 (θ 1)C 90 th (θ 1) w be C w 10 th 90 th for killed worker, and (13b) ln w u 90 th w u 10 th ln γ 0 γ 0 (θ u 1)C u 90 th (θ u 1) w be C w u 10 th u 90 th for unkilled worker. Thee equation have alo been etimated by non-linear leat quare u with θ, θ, and γ a the unknown parameter. Again, the derivation of thee equation i 0 hown in Appendix A.6. Note that if there i heterogeneity in the quality of the computer equipment, the etimate for within-group wage inequality i likely overetimate the average productivity gain from computer ue becaue it meaure the productivity gain of the worker at the 90 th -24-

27 th percentile relative to the worker at the 10 percentile. If the allocation of computer i optimal, the mot productive worker will get the bet computer. In addition, all difference between worker within one group are addreed to difference in computer ue. In all likelihood there might be other difference between thee worker, which will now be included in the etimate for the proportional productivity gain from uing a computer. Hence, we regard the etimate for the proportional productivity gain to be the cloe to the upper bound of the expected productivity gain from computer ue Etimation Reult Table 3 report the reult from etimating equation (12). Firt we have ran a regreion without taking into account the additional upply created by computer ue and the proportional productivity gain from uing a computer. The regreion reult are reported in the firt column and comparable to the etimate reported by Katz and Murphy (1992) for the 29 period They obtain an etimate for σ of 1.41 for a comparable but different definition of killed and unkilled worker, compared to 1.82 here. The ue of weighted erie doe not lead to a ignificantly different etimate (ee Appendix A.3 for detail about controlling for change in the compoition of the U.S. labor force). The annual increae in the demand for killed labor i about 2.4 percent, which i omewhat lower than the 3.3 percent obtained by Katz and Murphy (1992). Thi model i conitent with the explanation that the increae in the killed worker wage i caued by a lowdown in the growth rate of the upply of killed worker ince the early It hould be noted that we are aware of the erial correlation in the data and we conider the etimate in thi ection a evidence 29 It i alo conitent with the etimate without the incluion of capital of Kruell, Ohanian, Río-Rull and Violante (2000) for the period See Acemoglu (2002, Table 2, p. 30). -25-