Measuring the Bias of Technological Change Online Appendix

Transcription

1 Measuring the Bias of Technological Change Online Appendix Ulrich Doraszelski University of Pennsylvania Jordi Jaumandreu Boston University June 29, 206 Wharton School, University of Pennsylvania, Steinberg Hall-Dietrich Hall, 3620 Locust Walk, Philadelphia, PA 904, USA. Department of Economics, Boston University, 270 Bay State Road, Boston, MA 0225, USA.

2 OA Additions to Section 3: Data Table OA complements Table in the main paper. Columns ) and 2) document the extent of entry and, respectively, exit. Column 3) describes the demand shifter. Columns 4) 6) document the rate of growth of the prices of the various inputs. OA2 Additions to Section 4: A dynamic model of the firm Correction terms. In developing the correction term λ S T ) in the main paper we assume that the ratio W P W T = λ 0 is an unknown) constant. Table OA2 replicates the wage regression in Appendix E. To probe if the wage premium changes over time, we add an interaction of the share of temporary labor S T and a time trend t column 2)). In line with our assumption, this interaction is borderline significant in ust two industries and insignificant in the remaining industries. The remaining estimates columns ) and 3) 5)) are similar to those in columns 5) 8) of Table A2. In developing the correction term γ S O ) we assume that the ratio P I P O unknown) constant. Alternatively, we assume that P I of time t and treat ln Γ, γ 0 t) S O S O ) P O ) S O = γ γ 0 t) S O = γ 0 is an = γ 0 t) is an unknown) function as an unknown) function of γ 0 t)s O. In the simplest case, we set γt) = γ 0 + γ t with the normalization γ 0 =. As can be seen from column 2) of Table OA3, γ is significantly different from zero in three industries but very imprecisely estimated. Equation 7) yields lower estimates of column )) in five industries compared to our leading estimates in column 3) of Table 4; the estimates of are essentially unchanged in three industries. In the remaining two industries, the estimates of are either implausibly low industry 4) or high industry 8). Equation 20) becomes substantially more difficult to estimate. Compared to our leading estimates in columns ) and 2) of Table 7 the estimates of β K column 6)) are lower in six industries and essentially unchanged in two industries. The estimates of ν column 7)) are lower in one industry and essentially unchanged in seven industries. Comparing columns 5) and 0) of Table OA3 to column ) of Table 5 and, respectively, column ) of Table 8 shows that, on average, the growth of labor-augmenting productivity is higher in one industry, essentially unchanged in five industries, and lower in four industries. The growth of Hicks-neutral productivity is higher in two industries, essentially the same in four industries, and lower in two industries. Overall, our conclusions about technological change remain the same. An alternative model of outsourcing. If both in-house and outsourced materials are static inputs that the firm may combine in arbitrary proportions without incurring adust- Treating it as an unknown function of γ 0 t) S O S O instead of γ 0 t)s O introduces additional nonlinearities and considerably complicates estimation. 2

3 ment costs, then the Bellman equation becomes V t Ω ) = max K +,L P,L T,M I,M O,R P X ν expω H ), D ) X ν expω H )µ C I K + δ)k ) W P L P C LP L P, L P ) W T L T P I M I P O M O C R R ) + + ρ E t [V t+ Ω + ) Ω, R ], where Ω = K, L P, ω L, ω H, W P, W T, P I, P O, D ) is the vector of state variables. The corresponding first-order conditions for in-house and outsourced materials are νβ M µx νβ M µx ν + ) ν + ) exp ω H ) M ) exp ω H ) M ) M M I = M M O = P I ), OA) P ηp,d ) P O ). OA2) P ηp,d ) Equations OA) and OA2) imply that the mix of in-house and outsourced materials depends on their prices. We assume that P M = P I S O )+P O S O so that the price of materials is an appropriately weighted average of the prices of in-house and outsourced materials. We continue to assume that ΓM I, M O ) is linearly homogenous and normalize ΓM I, 0) = M I. This implies M = M P M P I Γ S O, P I P O S O ). Using Euler s theorem to combine equations OA) and OA2) yields νβ M µx ν + ) exp ω H ) M = PM P I Γ P M S O, P )) I S O P O ). OA3) P ηp,d ) PM and ln S O, P I P O S O )) = If P I P O = γ 0 is an unknown) constant, then P M P I = S O + S O γ 0 P I Γ γ 2 S O ) is an unknown) function of S O. Equation OA3) is thus indistinguishable from equation 4) in the main paper. ote that if S O = 0 and thus P M = P I and M = M I, then equation OA3) reduces to the first-order condition in a model without outsourcing. OA3 Additions to Section 6: Labor-augmenting technological change Additional checks: Lagged input prices. Table OA4 complements Table 4 in the main paper. Columns ) 3) show that our estimates of the elasticity of substitution are robust to purging the variation due to differences in the quality of labor from the lagged 3

4 wage w. In contrast to the main paper, ŵ Q is the part of the wage that depends on the available data on the skill mix of a firm s labor force as well as on firm size. Firms R&D activities. Table OA5 complements Table 5 in the main paper. Column ) shows that firms that perform R&D have, on average, higher levels of labor-augmenting productivity than firms that do not perform R&D in nine industries. Columns 2) and 3) show that firms that perform R&D have, on average, higher rates of growth of laboraugmenting productivity than firms that do not perform R&D in seven industries. Firm turnover. Columns 4) 6) of Table OA5 show that survivors account for most of the output effect of labor-augmenting technological change. Skill upgrading. Columns 7) and 8) of Table OA5 document the increase in the share of engineers and technicians in the labor force between 99 and OA4 Additions to Section 8: Hicks-neutral technological change Elasticity of substitution: Lagrange-multiplier test. We replace the CES production function in equation 6) by the nested CES production function with β 0 = β L = ) Y = τ) τ β K K + [ ] expωl)l ) ) ) ) + β M M τ) τ ντ τ expω H ) expe ), where the additional parameter τ is the elasticity of substitution between capital and labor, respectively, materials. The first-order conditions for permanent and temporary labor become νµ νµ where X KLM X KLM ) + ντ ) + ντ τ ) X LM τ ) X LM ) ) τ) τ exp ωh) exp τ) τ exp ωh ) exp ωl ω L ) L ) L L P = ) L ) L = L T W P + ) OA4) ), P P ηp,d ) W T OA5) ), ηp,d ) X KLM X LM τ) τ = β K K + = expω L )L ) ) + β M M ) ), [ expωl)l ) ) ) ) + β M M ] τ) τ. Proceeding as in the main paper and using Euler s theorem to combine equations OA4) 4

5 and OA5) yields νµ X KLM ) + ντ τ ) X LM = W + ) P τ) τ exp ωh ) exp + W T S T W P S T ηp,d ) ) ) = ω L W ΛP ST,ST ) ) Λ T S T,S T ) + S T S T W P + S T W T S T P ηp,d ) L Λ S T, S T ) ) ), OA6) where the second equality follows from dividing equations OA4) and OA5) and solving for. The first-order condition for in-house materials becomes ) νµβ M X KLM + ντ τ ) X LM ) τ) τ exp ωh ) M ) dm = P I + P O Q M OA7) ), dm I P ηp,d ) where P I + P O Q M is the effective cost of an additional unit of in-house materials. Proceeding as in the main paper and rewriting equation OA7) yields νµβ M ) + X KLM ντ τ ) X LM ) τ) τ exp ωh ) M Γ, P I P O S O S O ) = P P M ηp,d ) OA8) ). From the labor and materials decisions in equations OA6) and OA8) we recover conveniently rescaled) labor-augmenting productivity ω L = )ω L and Hicks-neutral productivity ω H as ω L = γ L + m l + p M w ) λ 2 S T ) + )γ S O ) h L m l, p M w, S T, S O ), ω H = γ H + ) m + p M p ln ηp, D ) + + ντ ) x KLM + ) τ x LM + τ τ γ S O ) h KLM H k, m, S M, p, p M, D, S T, S O ), where X KLM X LM = β M M exp γ S O ))) [ τ) τ SM = β K K + β M λ S T ) + S M ) SM λ S T ) +, S M )] τ) τ M exp γ S O ))) τ) τ. Our first estimation equation 7) therefore remains unchanged and our second estima- 5

6 tion equation 20) becomes y = ντ τ xklm +g Ht h KLM H k, m, S M, p, p M, D, S T, S O ), R ) + ξ H + e. If τ =, then equation OA9) reverts to equation 20). OA9) This allows us to conduct a Lagrange-multiplier test for τ =, with fixed at our leading estimates in column 3) of Table 4. Firm turnover. Table OA6 complements Table 8 in the main paper. Columns ) 3) show that survivors account for most of Hicks-neutral technological change. Total technological change and its components. Column 4) of Table OA6 shows that the correlation between labor-augmenting productivity in output terms ϵ L 2 ω L and Hicks-neutral productivity ω H is positive in all industries. OA5 Additions to Section 0: Capital-augmenting technological change Table OA7 complements Table 0 in the main paper. Columns ) 3) present the results from estimating the analog to our first estimation equation 7) in the main paper: m k = p M p K ) )γ S O ) + g Kt h K m k, p M p K, S O ), R ) + ξ K. ω K in column 4) presents the implied rate of growth of a firm s effective capital stock expω K )K. Column 5) of Table OA7 documents the implausibly low elasticity of output with respect to the firm s effective capital stock that drives the output effect to zero when we plug our leading estimates from Section 5 into equation 24) in the main paper. OA6 Additions to Appendix C: Estimation Concentrating out. To reduce the number of parameters to search over in the GMM problems corresponding to equations 7) see also equation 2)) and 20) in the main paper, we concentrate out the parameters that enter it linearly Wooldridge 200, p. 435). To simplify the notation, in what follows we omit the subscripts L and H that distinguish these equations. 6

7 We exploit that the T vector of residuals ν θ) as a function of the P vector of parameters to be estimated θ can be written as ν θ) = y β) w β)γ, OA0) where β is a P vector of nonlinear parameters and γ is P 2 vector of linear parameters with θ = β, γ ) and P = P + P 2. y β) is a T vector and w β) is a T P 2 matrix of composite variables whose values depend on the nonlinear parameters β. The first-order conditions for the GMM problem min A z )ν θ) Ŵ A z )ν θ) θ OA) are A z )ν θ)), β A z )ν θ)) γ Ŵ A z )ν θ) = 0. This is a system of P equations. Equation OA0) implies Hence, the lower P 2 equations can be rewritten as A z )w β) Ŵ A z )y β) A z )ν θ)) γ A z )w β)γ = 0. = A z )w β). Solving yields the linear parameters as a function of the nonlinear parameters: γβ) = A z )w β) Ŵ A z )w β) A z )w β) Ŵ A z )y β). Plugging this back into the GMM problem in equation OA) concentrates out the linear parameters and reduces the GMM problem to a search over the nonlinear parameters. We estimate the asymptotic variance of θ = β, γ β) ) as Avar θ) = [Ĝ ] Ŵ Ĝ Ĝ Ŵ A z )ν θ)ν θ) A z ) [Ĝ Ŵ Ĝ Ŵ Ĝ ] if Ŵ is an arbitrary weighting matrix and as Avar θ) = Ĝ A z )ν θ)ν θ) A z ) Ĝ 7

8 if Ŵ is the optimal weighting matrix. Both expressions depend on Ĝ = A z )ν θ)) Using the fact that da z )ν θ)) dβ Ĝ = da z )ν θ)) dβ = A z )ν θ)) β + A z )w β) γβ) β, we compute A z )w β) γ β) β, A z )w β). θ. Correcting standard errors. We proceed as follows. Let w be a T vector of i.i.d. random variables and consider the functions g L w, θ L ) and g H w, θ H, θ L ) corresponding to equation 20) and, respectively, equation 7), where E[g L w, θ L0 )] = 0 and E[g H w i, θ H0, θ L0 )] = 0 at the true values θ L0 and θ H0. ote that our notation differs from that in the main paper to make explicit that some of the parameters in equation 20) reappear in equation 7). To estimate the parameters θ L and θ H we set up the GMM problems min θ L g L w, θ L ) Ŵ L g L w, θ L ) see also equation 2) in the main paper) and min θ H g H w, θ H, θ L ) Ŵ H g H w, θ H, θ L ). If E[ θl g H w, θ H0, θ L0 )] 0, then we have to correct the standard errors of θ H to ensure their consistency ewey & McFadden 994, Wooldridge 200). The first-order condition for θ H is θh g H w, θ H, θ L ) Ŵ H g H w, θ H, θ L ) = 0. Expanding g Hw i, θ H, θ L ) around θ H0 and substituting back into the first-order condition we have 0 = θh g H w, θ H, θ L ) Ŵ H g H w, θ H0, θ L ) + θh g H w, θ H, θ L ) Ŵ H θh g H w, θ H, θ L ) θ H θ H0 ), where θ H is the value that makes the expression exact according to the mean value theorem. Appropriately dividing and multiplying by and replacing θ H g H w, θ H, θ L ) by its 8

9 probability limit G H = E [ θh g H w, θ H0, θ L0 )], replacing ŴH by its probability limit W H, and solving for θ H θ H0 ) yields θh θ H0 ) = [ G ] HW H G H G H W H g H w, θ H0, θ L ) + o p ). OA2) Expanding g Hw, θ H0, θ L ) around θ L0 we have g H w, θ H0, θ L ) = g H w, θ H0, θ L0 ) + θl g H w, θ H0, θ L0 ) θ L θ L0 ) = g H w, θ H0, θ L0 ) + G HL θl θ L0 ) + o p ), OA3) where G HL = E[ θl g H w, θ H0, θ L0 )]. Because θ L is a GMM estimator, it has a similar representation to the one derived for θ H in equation OA2): θl θ L0 ) = [ G ] LW L G L G L W L g L w, θ L0 ) + o p ), OA4) where G L = E [ θl g L w, θ L0 )]. Plugging equation OA4) into equation OA3), we have g H w, θ H0, θ L ) = [ ] g H w, θ H0, θ L0 ) G HL G L W L G L G L W L g L w, θ L0 ) + o p ). Plugging equation OA5) into equation OA2), we have OA5) θh θ H0 ) = [ G ] HW H G H G [ [ ] ] H W H g H w, θ H0, θ L0 ) G HL G L W L G L G L W L g L w, θ L0 ) + o p ). Defining g H w, θ H0, θ L0 ) = g H w, θ H0, θ L0 ) G HL [ G L W L G L ] G L W L g L w, θ L0 ) and D = E[ g H w, θ H0, θ L0 ) g H w, θ H0, θ L0 ) ], 9

10 we finally have Avar θ H ) = [G H W HG H ] G H W HDW H G H [G H W HG H ]. The asymptotic variance can be estimated by replacing the probability limits by estimates and the matrix D by an estimate based on g H w, θ H, θ L ) and g L w, θ L ). References ewey, W. & McFadden, D. 994), Large sample estimation and hypothesis testing, in R. Engle & D. McFadden, eds, Handbook of Econometrics, orth-holland, Amsterdam, pp Wooldridge, J. 200), Econometric analysis of cross section and panel data, 2nd edn, MIT Press, Cambridge. 0

11 Table OA: Descriptive statistics. Rates of growth a Entry Exit Demand shifter PK W PM Industry %) %) s. d.) s. d.) s. d.) s. d.) ) 2) 3) 4) 5) 6). Metals and metal products ) 5.8) 0.344) 0.073) 0.63) 0.067) 2. on-metallic minerals ) 4.) 0.337) 0.00) 0.44) 0.034) 3. Chemical products ) 9.4) 0.330) 0.22) 0.38) 0.065) 4. Agric. and ind. machinery ) 9.0) 0.352) 0.09) 0.50) 0.038) 5. Electrical goods ) 4.8) 0.353) 0.086) 0.68) 0.044) 6. Transport equipment ).8) 0.372) 0.082) 0.62) 0.048) 7. Food, drink and tobacco ) 9.5) 0.33) 0.04) 0.70) 0.058) 8. Textile, leather and shoes ) 24.8) 0.343) 0.092) 0.78) 0.044) 9. Timber and furniture ) 2.6) 0.338) 0.8) 0.66) 0.039) 0. Paper and printing products ) 8.7) 0.324) 0.092) 0.39) 0.076) a Computed for 99 to 2006.

12 Table OA2: Wage regression. Time trend Temp. temp. White Engin. Tech. Industry s. e.) s. e.) s. e.) s. e.) s. e.) R 2 ) 2) 3) 4) 5) 6). Metals and metal products ) 0.00) 0.096) 0.297) 0.094) 2. on-metallic minerals ) 0.0) 0.58) 0.28) 0.80) 3. Chemical products ) 0.05) 0.074) 0.37) 0.099) 4. Agric. and ind. machinery ) 0.02) 0.05) 0.227) 0.24) 5. Electrical goods ) 0.02) 0.073) 0.264) 0.087) 6. Transport equipment ) 0.04) 0.07) 0.300) 0.69) 7. Food, drink and tobacco ) 0.008) 0.053) 0.264) 0.54) 8. Textile, leather and shoes ) 0.008) 0.083) 0.406) 0.243) 9. Timber and furniture ) 0.00) 0.089) 0.38) 0.64) 0. Paper and printing products ) 0.08) 0.083) 0.202) 0.26)

13 Table OA3: Elasticity of substitution, distributional parameters, and elasticity of scale. GMM GMM γ χ 2 df) p val. ωl β K ν χ 2 p val. ωh Industry s. e.) s. e.) s. e.) df) ) 2) 3) 4) 5) 6) 7) 8) 9) 0). Metals and metal products ) 7.592) 38) 0.07) 0.028) 8) 2. on-metallic minerals ) 0.009) 38) 0.042) 0.087) 8) 3. Chemical products ) 0.04) 38) 0.047) 0.048) 8) 4. Agric. and ind. machinery a ) ) 38) 5. Electrical goods ) 0.030) 38) 0.026) 0.035) 0) 6. Transport equipment b ) 6.262) 38) 0.580) 0.0) 7. Food, drink and tobacco ) 0.054) 38) 0.357) 0.08) 8) 8. Textile, leather and shoes a ) 2.897) 38) 9. Timber and furniture c 0.095) 56.8) 38) 0.545) 0.592) 8) 0. Paper and printing products ) 2.27) 38) 0.58) 0.589) 8) All industries a We have been unable to compute the first-step GMM estimate for equation 20). b We have been unable to compute the second-step GMM estimate for equation 20). c We trim values of ω H below 0.25 and above 0.5. This amounts to trimming around one third of observations.

14 Table OA4: Elasticity of substitution. GMM with qualitycorrected wage as instr. a χ 2 df) p val. Industry s. e.) ) 2) 3). Metals and metal products ) 38) 2. on-metallic minerals ) 38) 3. Chemical products ) 38) 4. Agric. and ind. machinery ) 38) 5. Electrical goods ) 38) 6. Transport equipment ) 38) 7. Food, drink and tobacco ) 38) 8. Textile, leather and shoes ) 38) 9. Timber and furniture ) 38) 0. Paper and printing products ) 38) a ŵ Q based on firm size in addition to skill mix.

15 Table OA5: Labor-augmenting technological change. Firms R&D activities Firm turnover Share of ωl ωl Contributions to ϵl, 2 ωl eng. and tech. Industry R&D-o R&D R&D o R&D Survivors %) Entrants %) Exitors %) ) 2) 3) 4) 5) 6) 7) 8). Metals and metal products ) 9.5) 0.0) 2. on-metallic minerals ) 3.2) -9.7) 3. Chemical products ) 50.0) 0.0) 4. Agric. and ind. machinery ) 6.3) 9.4) 5. Electrical goods ) 9.5) 4.8) 6. Transport equipment ) 6.7) 3.3) 7. Food, drink and tobacco ) 0.0) 0.0) 8. Textile, leather and shoes ) 0.0) 0.0) 9. Timber and furniture ) -50.0) 0.0) 0. Paper and printing products ) -8.3) 0.0) All industries ) 0.25) 0.063)

16 Table OA6: Hicks-neutral technological change. Firm turnover Contributions to ωh Industry Survivors %) Entrants %) Exitors %) corrϵl, 2ωL, ωh) a ) 2) 3) 4). Metals and metal products ) 5.9) 9.) 2. on-metallic minerals ) 20.0) -60.0) 3. Chemical products ) 0.0) 5.3) 4. Agric. and ind. machinery ) 0.0) 4.6) 5. Electrical goods ) -5.0) -40.0) 6. Transport equipment ) 23.8) -26.2) 7. Food, drink and tobacco Textile, leather and shoes ) -50.0) 8.3) 9. Timber and furniture 0.03 b b b ) 28.6) 4.3) 0. Paper and printing products All industries ) -2.4) -4.3) a Without replication and weighting. b We trim values of ω H below 0.25 and above 0.5. This amounts to trimming around one third of observations.

17 Table OA7: Capital-augmenting technological change. GMM χ 2 df) p val. Industry s. e.) ωk ϵk, 2 ) 2) 3) 4) 5). Metals and metal products ) 38) 2. on-metallic minerals ) 38) 3. Chemical products ) 38) 4. Agric. and ind. machinery ) 38) 5. Electrical goods ) 38) 6. Transport equipment ) 38) 7. Food, drink and tobacco ) 38) 8. Textile, leather and shoes ) 38) 9. Timber and furniture ) 38) 0. Paper and printing products ) 38) All industries -0.87