STEM Occupations in the German Labor Market
C.2. Gelbach’s Decomposition
C.2. Gelbach’s Decomposition
To quantify the contribution of unobserved worker and firm effects as well as observed time-varying worker characteristics to the unadjusted STEM premium, I apply Gelbach’s decomposition to a linear wage equation. In the following, I illustrate the working of Gelbach’s standard decomposition approach for model (4.5) in analogy to Gelbach (2016) and Cardoso et al. (2016). The application of the approach to my auxiliary wage model (4.8) can be conducted analogously and will be discussed briefly at the end of this section.
In general, Gelbach’s decomposition links the change of a coefficient of interest between abasic modeland afull modelusing the formula of omitted variable bias (OVB).4Notably, in the present study, the coefficient of interest is a (time constant) STEM dummy which captures the unadjusted STEM premium in a basic model and is absorbed in the full model.
I start by defining a full model as a linear wage equation of the following form:
wit =αi+ψJ(i,t)+x0itβ+rit, (C.2) wherewit is the log wage of an workeriin yeart,αi is a worker fixed effect (absorbing the time constant STEM dummy), ψJ(i,t) is a firm fixed effect, andβ captures the effect of observable time-varying worker characteristics. The idea is to interpret the estimated coefficient on the STEM dummysiin a basic model of the form:
wit =γBsi+rit (C.3)
as a biased estimator of returns to STEM jobs.5 Using the formula of omitted variable bias (OVB), Gelbach’s approach allows for an unequivocal quantification of the portion of the difference in the STEM premium between the basic model and the full model (γˆB) due to worker effects, firm effects, and a time-varying covariate index. To show this formally, I rewrite the stacked system of model (C.2) in matrix notation:
W=Lα+Dψ+Xβ+r, (C.4)
whereWis a(N×1)vector of log wages,Lis a(N×N)design matrix for the worker effects, Dis a (N×F) design matrix for the firm effects, andX is a(N×k)matrix containing observed time-varying worker characteristics, and r is a (N×1)vector of disturbances (assumed to be orthogonal to the design matrices due to the exogenous mobility assumption).
4The omitted variable bias formula is based on a least-squares identity that links estimates of a base specificationY =X1β1base+εbaseand a full specificationY=X1β1f ull+X2β2+εf ullvia the formulaβˆ1base= βˆ1f ull+ (X10X1)−1X10X2βˆ2. To this end, standard results imply thatβ1f ullis a consistent estimate forβ1“without assuming anything about eitherβ2or the correlation betweenX1andX2, since allX2variation is partialed out in the full specification” and, accordingly,β1baseis biased in the traditional sense of an omitted variable bias (Gelbach 2016).
5Note thatγˆBcorresponds to the average unadjusted STEM premium for the periods underlying the estimation of the model.
141
Further, I rewrite equation (C.4) in terms of fitted values:
W =Lαˆ +Dψˆ +Xβˆ+r.ˆ (C.5) Likewise, the stacked system of model (C.3) can be written as:
W=γBS+r, (C.6)
whereSis a (N×1)vector that indicates the assignment of workers to the occupational group of STEM or non-STEM workers. Next, I plug equation (C.6) into equation (C.5) and left-multiply both sides byMS≡(S0S)−1S0. GivenMsis orthogonal torˆdue to the assumed exogenous mobility, this yields:
ˆ
γB=MSLαˆ +MSDψˆ +MSXβˆ, (C.7) or written in the notation of Cardoso et al. (2016):
ˆ
γB=δˆα+δˆψ+δˆβ, (C.8)
whereδˆα=MSLαˆ is the contribution of worker effects,δˆψ =MSDψˆ is the contribution of firm effects, andδˆβ =MSXβˆ is the contribution of the covariate index. Empirically, the three terms on the RHS of equation (C.8) are coefficients of regressions ofLα,ˆ Dψˆ, andXβˆ on the vectorS, wherebyLα,ˆ Dψˆ, andXβˆ are obtained as predicted values from model (C.4).
The approach can be applied analogously to alternative wage equations. Notably, in the present study, I use an auxiliary wage model that has the following form:
wit =αi+
20
∑
q=2
˜
ψqFJq(i,t)+x0itβ+rit, (C.9) wherewit is the log daily real wage,αi is a worker fixed effect, eachFJq(i,t)forq=2, ..., 20 represents a dummy variable that is 1 if an individuali’s weighted CHK firm effect falls into theqth 5%-percentile of the weighted CHK firm effects and 0 otherwise (with the 1st 5%-percentile as the reference category), andxit is a covariate index. While the contribution of the firm effects in model (C.2) are obtained by regressing the predicted firm effects on the STEM dummy, the contribution of the firm effects in the auxiliary model (C.9) are obtained by regressing each of firm dummy covariate on the STEM dummy and then summing over the estimated coefficients or equivalently by summing over the series of firm dummy covariates for each worker, and regressing the compound covariate index on the STEM dummy (see notes to Table 4.4).
C.3. APPENDIXTABLES
C.3. Appendix Tables
Table C.1.: Overview of Occupations Classified as STEM
Empl. Empl. %-Change Log Mean Log Mean %-Change
Share Share in Empl. Wage Wage in Log
in 1980 in 2010 Share in 1980 in 2010 Mean Wage
(1) (2) (3) (4) (5) (6)
...on total employment
Non-STEM 0.91 0.87 −0.04 4.11 4.21 0.11
STEM 0.09 0.13 0.04 4.57 4.76 0.20
...on STEM employment Engineers
Architects, civil engineers 0.06 0.04 −0.02 4.74 4.65 −0.09
Electrical engineers 0.06 0.06 0.00 4.79 5.07 0.28
Mechanical, motor engineers 0.06 0.06 0.00 4.81 5.02 0.21
Survey engineers until other engineers 0.05 0.10 0.05 4.79 4.92 0.13
Computer scientists 0.00
Computer scientists 0.07 0.20 0.12 4.58 4.75 0.17
Technicians
Biological, physical and math specialists 0.03 0.01 −0.01 4.28 4.50 0.23 Chemical until photo laboratory assistants 0.03 0.02 −0.01 4.22 4.54 0.32 Electrical engineering and building techn. 0.10 0.08 −0.02 4.49 4.66 0.17
Foremen, master mechanics 0.10 0.04 −0.06 4.58 4.76 0.18
Manufacturing technicians 0.06 0.03 −0.03 4.46 4.56 0.09
Mechanical engineering technicians 0.06 0.04 −0.02 4.57 4.73 0.16
Other technicians 0.14 0.13 −0.01 4.48 4.68 0.20
Technical draughtspersons 0.07 0.04 −0.03 4.17 4.38 0.20
Math, Physics, Chemistry, Economics 0.00
Chemists, physicists, mathematicians 0.02 0.02 0.00 4.82 5.00 0.18 Economics, social scientists, statisticians, 0.00 0.00 0.00 0.00 0.00 0.00 humanities, and other natural scientists1 0.03 0.05 0.02 4.70 4.67 −0.03 Medical workers
Physicians and Pharmacists 0.06 0.08 0.02 4.80 4.885 0.09
Notes:Table lists the occupations defined as STEM.1Humanities as a non-STEM occupation within the aggregated occupation category ofEconomics, social scientists, statisticians, humanities, and other natural scientistsconstitutes a share of about 1 to 2% of all STEM workers between 1980 and 2010 (based on frequency counts of the SIAB 7510.). Data source: SIAB-R 7510.
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Table C.2.: Shift-Share Decomposition of Changes in Share of Employment due to Changes in Industry Shares and Changes in Occupational Shares Within Industries
Decade Change Total Change 1980-1990 1990-2000 2000-2010 1980-2010
(1) (2) (3) (4)
Panel A: Men Non-STEM
Total∆ −1.79 −1.86 −1.17 −4.82
Industry∆ −0.46 −0.39 −0.72 −1.41
Occupation∆ −1.32 −1.48 −0.45 −3.41
STEM
Total∆ 1.79 1.86 1.17 4.82
Industry∆ 0.46 0.39 0.72 1.41
Occupation∆ 1.32 1.17 0.45 3.41
Panel B: Women Non-STEM
Total∆ −1.29 −1.24 −1.22 −3.75
Industry∆ −0.07 −0.11 −0.13 −0.27
Occupation∆ −1.22 −1.13 −1.09 −3.48
STEM
Total∆ 1.29 1.24 1.22 3.75
Industry∆ 0.07 0.11 0.13 0.27
Occupation∆ 1.22 1.22 1.09 3.48
Notes:Each set of three rows presents the change in the share of employment in percentage points in the indicated occupational group and time interval and decomposes this change into between and within-industry components. The decom-position is based on 120 occupations and 13 industry groups. See section 4.3 for additional details. Data source: SIAB-R 7510.
C.3. APPENDIXTABLES
Table C.3.: Food, Cleaning, Security and Logistics Occupation Codes in KldB 1988 and SIAB-R
KldB1988 SIAB-R Ambiguous
Occ. Occ. Occ. Occ.
Type Label Code Code Code
Food Restaurant, inn, bar keepers, hotel proprietors, catering trade dealers
911 115
Food Waiters, stewards 912 115
Food Others attending on guests 913 116
Food Cooks 411 40
Food Ready-to-serve meals, fruit, vegetable preservers, preparers
412 40
Cleaning Other housekeeping attendants 923 117 921,922
Cleaning Household cleaners 933 119
Cleaning Glass, buildings cleaners 934 119
Cleaning Vehicle cleaners, servicers 936 120 935
Cleaning Machinery, container cleaners and related occupations 937 120
Security Factory guards, detectives 791 96
Security Watchmen, custodians 792 96
Security Doormen, caretakers 793 97
Logistics Motor vehicle drivers 714 81
Logistics Warehouse managers, warehousemen 741 84
Logistics Transportation equipment drivers 742 85
Logistics Stowers, furniture packers 743 86
Logistics Stores, transport workers 744 86
Notes:Table lists occupations defined as food, cleaning, security and logistics (FCSL) occupations using the KldB 1988classification and the SIAB-R classification. The definition of FCSL occupations in theKldB 1988 classification results from Table A-3 of the Appendix to Goldschmidt and Schmieder (2017).
145
Table C.4.: Estimation Results of OLS Regressions of CHK Worker Effects on Estimates of Worker Effects Based on SIAB-R
Men Women
1985-1991 2002-2009 1985-1991 2002-2009
(1) (2) (3) (4)
Beta 1.02 0.94 0.94 0.97
(se x100) (0.03) (0.02) (0.04) (0.03)
T-test 3,405 4,593 2,315 2,849
R-squared (adjusted) 0.88 0.93 0.88 0.91
Worker-year observations 1,587,636 1,702,954 757,302 817,475 Notes:Table shows results from OLS regressions of Card et al. (2013)’s estimated worker effects (provided in the supplementary IAB data) on own predictions of worker effects as given by empirical model (4.8) using the SIAB-R. Data sources: SIAB-R 7510 and supplementary IAB data on CHK effects.
C.4. APPENDIXFIGURES
C.4. Appendix Figures
Figure C.1.: Distribution of CHK Worker Effects
A. Men, 1985-1991 B. Women, 1985-1991
C. Men, 2002-2009 D. Women, 2002-2009
Notes:Figure shows densities of worker effects by 5%-percentiles in the first and last subinterval. The histograms are based on all worker-year observations. Data sources: SIAB-R 7510 and supplementary IAB data on CHK effects.
147
Figure C.2.: Distribution of CHK Firm Effects
A. Men, 1985-1991 B. Women, 1985-1991
C. Men, 2002-2009 D. Women, 2002-2009
Notes:Figure shows densities of weighted firm effects by 5%-percentiles in the first and last subinterval. The histograms are based on all worker-year observations in a given subinterval. Data sources: SIAB-R 7510 and supplementary IAB data on CHK effects.
C.4. APPENDIXFIGURES
Figure C.3.: Distribution of CHK Firm Effects for FCSL Occupations
A. Men, 1985-1991 B. Women, 1985-1991
C. Men, 2002-2009 D. Women, 2002-2009
Notes:Figure shows densities of weighted firm effects by 5%-percentiles for FCSL workers in the first and last subinterval. The histograms are based on all worker-year observations in a given subinterval. Data sources:
SIAB-R 7510 and supplementary IAB data on CHK effects.
149
Figure C.4.: Evolution of Adjusted and Unadjusted Mean Differences in Log Real Wages Between STEM and non-STEM Occupations Using Alternative Imputation Method
A. Men B. Women
Notes:Figure shows annual estimates of the coefficient on the STEM dummysitas well as the 95% confidence interval from OLS estimates of the model (4.1) controlling for linear, quadratic and cubic terms in age fully interacted with skill groups. Estimates based on right censored (non-imputed) wages are plotted with pluses and crosses. Estimates based on imputed wages following the ’normal, no heteroscedasticity’ method (baseline sample) are plotted with dots and diamonds. Estimates based on wages following the ’normal, full heteroscedas-ticity’ method are plotted with squares and triangles. See Appendix C.1.1 for additional details. Data source:
SIAB-R 7510.
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