Online Appendices Practical Procedures to Deal with Common Support Problems in Matching Estimation
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1 Online Appendices Practical Procedures to Deal with Common Support Problems in Matching Estimation Michael Lechner Anthony Strittmatter April 30, 2014 Abstract This paper assesses the performance of common estimators adjusting for differences in covariates, like matching and regression, when faced with so-called common support problems. It also shows how different procedures suggested in the literature to tackle common support problems affect the properties of such estimators. Based on an Empirical Monte Carlo simulation design, a lack of common support is found to increase the root mean squared error (RMSE) of all investigated parametric and semiparametric estimators. Dropping observations that are off support usually improves their performance, although the amount of improvement depends on the particular method used. Keywords: Empirical Monte Carlo Study, matching estimation, regression, common support, outlier, small sample performance JEL classification: C21, J68 Address for correspondence: Michael Lechner, Swiss Institute for Empirical Economic Research (SEW), University of St. Gallen, Varnbüelstrasse 14, CH-9000 St. Gallen, Switzerland, Michael.Lechner@unisg.ch, Anthony Strittmatter, Swiss Institute for Empirical Economic Research (SEW), University of St. Gallen, Varnbüelstrasse 14, CH-9000 St. Gallen, Switzerland, anthony.strittmatter@unisg.ch. This project is part of the project Regional Allocation Intensities, Effectiveness and Reform Effects of Training Vouchers in Active Labor Market Policies, IAB project number This is a joint project of the Institute for Employment Research (IAB) and the University of Freiburg. We gratefully acknowledge financial and material support by the IAB. We thank Lorenzo Camponovo, Bernd Fitzenberger, and Andreas Steinmayr for helpful comments on a previous draft of the paper. The usual disclaimer applies. Swiss Institute for Empirical Economic Research (SEW),University of St. Gallen. Michael Lechner is also affiliated with CEPR and PSI, London, CESIfo, Munich, IAB, Nuremberg, and IZA, Bonn. Swiss Institute for Empirical Economic Research (SEW),University of St. Gallen. Anthony Strittmatter is also affiliated with the Albert-Ludwigs-University Freiburg.
2 A Detailed descriptive statistics Table A.1: Descriptive statistics in the full sample for the treatment award of vouchers for manufacturing and service workers (VMSW ). Variable Names Treated Non- Stand. Treatm. Dependent Variable Treated Diff. Prob. Earnings Months Empl. Employment mean mean in % Av. Marg. eff. in % Coef. Coef. Av. Marg. eff. in % (1) (2) (3) (4) (5) (6) (7) Constant 15, Female dummy , Age in years Age years , Age years Age years Age years , Lower secondary school degree Upper secondary school degree , University entry school degree , No vocational degree Vocational degree At least one child At least one child < 5 years , Single Married Beginning of unemployment Time to treatment in months Part-time job Craft, machine operators and related Service workers and clerks Technicians, associate professions, professionals, and managers Half-months employed in the last 24 months Number of employment spells in last 24 months Half-months unemployed in last 24 months Time since last unemployment in last months (half-months) No unemployment in last 24 months Unemployed 24 months before Number of unemployment spells in last months Any program in last 24 months Half-months out of labor force in last months Time since last out of labour force in last months Amount of unemployment benefit Remaining UI claim South Germany East Germany North Germany , West Germany Employed 4 years before Earnings 4 years before (daily, deflated) Cumulated duration employed 4 years before (half-months) Cumulated earnings 4 years before (defl., per , month, in thsd.) Cumulated duration of UI 4 years before (half-months) Cumulated UI benefits 4 years before (defl., per month, in thsd.) Female x Age in years Technicians and associate professions x Higher secondary school degree S i1 Professionals and managers x Higher secondary school degree S i2 Professionals and managers x University or college degree S i , Note: In columns (1) and (2) we show the first moments of all control variables in the treated and non-treated subpopulations. In column (3) we show the standardized differences of the first moments between these two groups. The standardized difference is defined as the difference of means normalized by the square root of the sum of estimated variances of the particular variables in both subsamples. In column (4) we report the estimated average marginal effects from the propensity score model. The propensity score is estimated using a probit model. Average marginal effects are based on discrete changes for binary variables and derivatives otherwise. Standard deviations of average marginal effects are estimated using the Delta method. In columns (5) - (6) we show the estimated coefficients from an OLS regression on the outcome variables earnings and months employed. In column (7) we report average marginal effects on employment. Bold indicates significant coefficients or marginal effects at 5% level. 2
3 Table A.2: Descriptive statistics in the full sample for the treatment award of vouchers for technicians (VTEC ). Variable Names Treated Non- Stand. Treatm. Dependent Variable Treated Diff. Prob. Earnings Months Empl. Employment mean mean in % Av. Marg. eff. in % Coef. Coef. Av. Marg. eff. in % (1) (2) (3) (4) (5) (6) (7) Constant 15, Female dummy , Age in years Age years , Age years Age years Age years , Lower secondary school degree Upper secondary school degree , University entry school degree , No vocational degree Vocational degree At least one child At least one child < 5 years , Single Married Beginning of unemployment Time to treatment in months Part-time job Craft, machine operators and related Service workers and clerks Technicians, associate professions, professionals, and managers Half-months employed in the last 24 months Number of employment spells in last 24 months Half-months unemployed in last 24 months Time since last unemployment in last months (half-months) No unemployment in last 24 months Unemployed 24 months before Number of unemployment spells in last months Any program in last 24 months Half-months out of labor force in last months Time since last out of labour force in last months Amount of unemployment benefit Remaining UI claim South Germany East Germany North Germany , West Germany Employed 4 years before Earnings 4 years before (daily,deflated) Cumulated duration employed 4 years before (half-months) Cumulated earnings 4 years before (defl., per , month, in thsd.) Cumulated duration of UI 4 years before (half-months) Cumulated UI benefits 4 years before (defl., per month, in thsd.) Female x Age in years Technicians and associate professions x Higher secondary school degree S i1 Professionals and managers x Higher secondary school degree S i2 Professionals and managers x University or college degree S i , Note: See note of Table A.1. 3
4 B Recovering the distributions of the outcome variables under effect heterogeneity As described in Section 5.3, we transform the outcome variables of the (pseudo) treated observations in order to introduce effect heterogeneity into the simulation process. In Section 5.3, we defined the transformed variable Ỹi, which is a function of the propensity score or the propensity score and the support variable S. However, the transformation of Ỹ i does not account for the semi-continuous, discrete, or binary distribution of the outcome variables. The outcome distribution equals Y i R + for earnings, Y i {0, 1,..., 12} for months employed, and Y i {0, 1} for the employment dummy. Below we describe the modifications of Ỹi to recover these distribution. We define the auxiliary variable Y i and transform each of the three outcomes by Y i = d i Y i + (1 d i )Y i. For earnings, define the auxiliary variable Y i = max(0, Ỹi), which accounts for the fact that earnings cannot be negative. An additional bias could be introduced, if E[Y i d i = 1] E[Y i d i = 1]. To avoid this, we impose the restriction E[Y i Y i d i = 1] = 0. If this condition is violated, we multiply the outcome of (pseudo) treated individuals by a (positive) constant factor, such that it is satisfied. Accordingly, the average treatment effect in the sample is not affected by the described transformation. The manipulation for months employed needs to respect the discrete support. Therefore, define Y i = max(0, min(12, Ỹi)), where Y i is rounded to the closest integer. This adjustment respects the support of Y i {0, 1,..., 12}, but potentially affects the average treatment effect in the sample. Therefore, the additional constraint E[Y i Y i d i = 1] = 0 is imposed. If this condition is not satisfied, then Y i of pseudo treated observations is subsequently increased (decreased) by one integer, starting with the lowest (highest) Y i. In case of several observations with equal months of employment, we randomly choose the adjusted observations. Finally, the employment dummy is manipulated according to Y i = max(0, min(1, Ỹi)), where Y i is rounded to zero or one. To avoid an additional bias, we again impose the restriction E[Y i Y i d i = 1] = 0. If E[Y i Y i d i = 1] < 0, randomly chosen pseudo treated observations with Y i = 0 are increase by one. If E[Y i Y i d i = 1] > 0, randomly chosen pseudo treated observations with Y i = 1 are reduce to zero. 4
5 Figure B.1: Conditional potential outcome for the treated under treatment in the population for the treatment award of vouchers for manufacturing and service workers (VMSW ). (a) Earnings, effect heterogeneity 1 (b) Earnings, effect heterogeneity 2 (c) Months employed, effect heterogeneity 1 (d) Months employed, effect heterogeneity 2 (e) Employment, effect heterogeneity 1 (f) Employment, effect heterogeneity 2 Note: Conditional potential outcomes are estimated using Nadaraya-Watson estimators. We specify Epanechnikov kernels with Silverman s rule as bandwidth selector. Effect heterogeneity 1 is made dependent on the propensity score. Effect heterogeneity 2 depends on the propensity score stratified by the support variable S. See also descriptions in Sections 4.3 an
6 Figure B.2: Conditional potential outcome for the treated under treatment in the population for the treatment award of vouchers for technicians (VTEC ). (g) Earnings, effect heterogeneity 1 (h) Earnings, effect heterogeneity 2 (i) Months employed, effect heterogeneity 1 (j) Months employed, effect heterogeneity 2 (k) Employment, effect heterogeneity 1 (l) Employment, effect heterogeneity 2 Note: See note below Figure B.1. 6
7 C Normalization of performance measures To improve the comparability of the results, we rescale the simulated effect γ (see Section 6.1). In particular, we divide them by the standard deviations of γ in the specifications without support manipulations, which are estimated conditional on the type of estimator and different features of the DGPs. These features are the model specifications, treatment shares, types of effect heterogeneity, sample size, and type of voucher. Emphasizing that we rescale the treatment effects, we call measures for the quality of the different estimators normalized performance measures, i.e. normalized RMSE, normalized absolute bias, and normalized standard deviation. The regression coefficients of control dummies indicate by how many standard deviations the performance measure changes if this dummy turns on in comparison to the omitted category. 7
8 D Additional results without support manipulations Table D.1: Influence of all procedures to handle support problems on the performance of different estimators in terms of normalized RMSE in specifications without support restrictions for the treatment award of vouchers for manufacturing and service workers (VMSW ). Manufacturing and Service Workers WA *** 0.003** ** [0.004] [0.005] [0.001] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] B *** ** 0.329*** 0.297*** 0.293*** 0.967*** 0.911*** 0.850*** [0.004] [0.005] [0.002] [0.046] [0.038] [0.035] [0.154] [0.117] [0.109] B * *** *** 0.220*** 0.187*** 0.188*** 0.701*** 0.640*** 0.611*** [0.004] [0.005] [0.002] [0.050] [0.040] [0.037] [0.163] [0.124] [0.115] WB *** ** 0.329*** 0.297*** 0.293*** 0.967*** 0.911*** 0.850*** [0.004] [0.005] [0.002] [0.046] [0.038] [0.035] [0.154] [0.117] [0.109] WB * *** *** 0.220*** 0.187*** 0.188*** 0.701*** 0.640*** 0.611*** [0.004] [0.005] [0.002] [0.050] [0.040] [0.037] [0.163] [0.124] [0.115] C [0.004] [0.003] [0.002] [0.009] [0.006] [0.005] [0.023] [0.017] [0.016] C *** 0.019*** 0.011*** [0.004] [0.003] [0.002] [0.008] [0.006] [0.005] [0.023] [0.017] [0.016] WC ** 0.004*** ** [0.004] [0.005] [0.001] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] WC *** *** ** [0.004] [0.005] [0.002] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] D *** 0.007*** *** [0.004] [0.003] [0.004] [0.009] [0.006] [0.005] [0.023] [0.017] [0.016] D [0.004] [0.003] [0.002] [0.009] [0.006] [0.005] [0.023] [0.017] [0.016] WD *** *** ** [0.004] [0.004] [0.004] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] WD *** ** [0.004] [0.005] [0.002] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] E *** *** ** [0.004] [0.003] [0.003] [0.010] [0.006] [0.006] [0.024] [0.017] [0.016] E ** *** *** *** [0.004] [0.006] [0.004] [0.011] [0.008] [0.007] [0.024] [0.019] [0.017] E *** *** 0.070*** 0.027** 0.058*** 0.242*** 0.182*** 0.186*** [0.007] [0.008] [0.005] [0.015] [0.012] [0.011] [0.031] [0.024] [0.020] WE *** ** *** ** ** [0.004] [0.004] [0.003] [0.010] [0.007] [0.006] [0.024] [0.017] [0.016] WE * *** *** *** [0.004] [0.006] [0.004] [0.011] [0.009] [0.007] [0.024] [0.019] [0.017] WE *** *** 0.072*** 0.028** 0.059*** 0.242*** 0.182*** 0.186*** [0.008] [0.008] [0.005] [0.015] [0.012] [0.010] [0.031] [0.024] [0.020] F *** 0.052*** ** 0.039*** [0.003] [0.004] [0.002] [0.008] [0.007] [0.005] [0.024] [0.016] [0.016] F *** 0.082*** 0.033*** 0.068*** 0.069*** 0.028*** 0.055** 0.055*** 0.045*** [0.004] [0.004] [0.002] [0.008] [0.006] [0.005] [0.023] [0.017] [0.016] F *** 0.328*** 0.227*** 0.374*** 0.320*** 0.243*** 0.338*** 0.308*** 0.251*** [0.006] [0.013] [0.010] [0.009] [0.008] [0.007] [0.023] [0.017] [0.016] WF *** 0.047*** *** 0.034*** [0.003] [0.003] [0.001] [0.007] [0.007] [0.005] [0.024] [0.016] [0.016] WF *** 0.086*** 0.036*** 0.078*** 0.072*** 0.033*** 0.055** 0.055*** 0.045*** [0.004] [0.005] [0.002] [0.007] [0.006] [0.005] [0.023] [0.017] [0.016] WF *** 0.331*** 0.230*** 0.388*** 0.328*** 0.249*** 0.338*** 0.308*** 0.251*** [0.007] [0.014] [0.010] [0.011] [0.009] [0.008] [0.023] [0.017] [0.016] G *** 0.019*** *** *** [0.003] [0.003] [0.003] [0.009] [0.006] [0.006] [0.024] [0.017] [0.016] G *** 0.013*** *** 0.014* 0.017*** [0.003] [0.004] [0.002] [0.009] [0.007] [0.006] [0.024] [0.019] [0.017] G *** 0.103*** 0.065*** 0.157*** 0.104*** 0.087*** 0.135*** 0.097*** 0.083*** [0.005] [0.005] [0.003] [0.011] [0.011] [0.008] [0.025] [0.020] [0.017] WG *** 0.009*** *** [0.003] [0.003] [0.003] [0.008] [0.006] [0.006] [0.024] [0.017] [0.016] WG *** 0.015*** *** 0.013* 0.019*** [0.003] [0.003] [0.002] [0.009] [0.007] [0.006] [0.024] [0.019] [0.017] WG *** 0.105*** 0.066*** 0.161*** 0.106*** 0.088*** 0.135*** 0.097*** 0.083*** [0.005] [0.005] [0.003] [0.010] [0.010] [0.008] [0.025] [0.020] [0.017] < table continues on next page > 8
9 Table D.1: < continued > Manufacturing and Service Workers H *** 0.063*** 0.009*** 0.027*** 0.040*** [0.004] [0.006] [0.002] [0.008] [0.007] [0.005] [0.023] [0.016] [0.016] H *** 0.084*** 0.037*** 0.071*** 0.061*** 0.026*** 0.065*** 0.050*** 0.041*** [0.007] [0.007] [0.005] [0.009] [0.006] [0.005] [0.023] [0.017] [0.016] H *** 0.260*** 0.168*** 0.315*** 0.248*** 0.188*** 0.314*** 0.267*** 0.229*** [0.015] [0.015] [0.012] [0.017] [0.013] [0.011] [0.028] [0.020] [0.018] WH *** 0.060*** 0.013*** 0.042*** 0.037*** 0.012** [0.005] [0.005] [0.003] [0.008] [0.007] [0.005] [0.023] [0.016] [0.016] WH *** 0.089*** 0.041*** 0.082*** 0.065*** 0.031*** 0.065*** 0.050*** 0.041*** [0.008] [0.007] [0.005] [0.008] [0.006] [0.005] [0.023] [0.017] [0.016] WH *** 0.263*** 0.171*** 0.328*** 0.255*** 0.194*** 0.314*** 0.267*** 0.229*** [0.015] [0.016] [0.013] [0.018] [0.014] [0.012] [0.028] [0.020] [0.018] I *** 0.021*** *** * * [0.005] [0.004] [0.002] [0.009] [0.006] [0.005] [0.023] [0.017] [0.016] I *** *** 0.022** [0.006] [0.004] [0.003] [0.009] [0.007] [0.006] [0.024] [0.018] [0.016] I *** 0.042*** 0.013*** 0.092*** 0.035*** 0.029*** 0.098*** 0.051*** 0.049*** [0.006] [0.005] [0.003] [0.009] [0.007] [0.006] [0.024] [0.018] [0.017] WI *** 0.014*** *** [0.006] [0.004] [0.003] [0.008] [0.006] [0.005] [0.023] [0.017] [0.016] WI *** ** 0.026*** [0.007] [0.004] [0.003] [0.008] [0.007] [0.006] [0.024] [0.018] [0.016] WI *** 0.043*** 0.013*** 0.095*** 0.037*** 0.030*** 0.098*** 0.051*** 0.049*** [0.006] [0.005] [0.003] [0.008] [0.007] [0.006] [0.024] [0.018] [0.017] Discrete outcome [0.005] [0.005] [0.004] [0.011] [0.010] [0.009] [0.035] [0.030] [0.028] Binary outcome [0.005] [0.005] [0.004] [0.012] [0.011] [0.010] [0.036] [0.031] [0.029] Heterogeneity [0.005] [0.006] [0.004] [0.012] [0.011] [0.010] [0.036] [0.030] [0.028] Heterogeneity [0.005] [0.006] [0.004] [0.012] [0.011] [0.010] [0.037] [0.031] [0.028] 10% treated [0.009] [0.007] [0.007] [0.028] [0.023] [0.021] 90% treated * [0.014] [0.014] [0.012] [0.043] [0.037] [0.033] Population p-score [0.006] [0.004] [0.012] [0.010] [0.032] [0.030] Correct specified model [0.005] [0.006] [0.005] [0.011] [0.011] [0.010] [0.034] [0.032] [0.030] Disc. out. x Het. 1 [0.005] [0.006] [0.004] [0.013] [0.010] [0.009] [0.039] [0.030] [0.027] Disc. out. x Het. 2 [0.005] [0.006] [0.004] [0.013] [0.011] [0.010] [0.041] [0.030] [0.028] Disc. out. x Pop p-score [0.006] [0.004] [0.011] [0.010] [0.032] [0.030] Disc. out. x Corr spec. model [0.004] [0.005] [0.004] [0.011] [0.010] [0.009] [0.035] [0.032] [0.030] Disc. out. x 10% treated [0.009] [0.007] [0.006] [0.027] [0.020] [0.019] Disc. out. x 90% treated [0.016] [0.013] [0.012] [0.050] [0.038] [0.035] Bin. out. x Het [0.006] [0.006] [0.004] [0.014] [0.011] [0.010] [0.042] [0.032] [0.029] Bin. out. x Het [0.006] [0.006] [0.004] [0.014] [0.011] [0.010] [0.043] [0.032] [0.030] Bin. out. x Pop p-score [0.006] [0.004] [0.013] [0.012] [0.035] [0.032] Bin. out. x Corr spec. model [0.004] [0.005] [0.004] [0.012] [0.011] [0.010] [0.038] [0.034] [0.032] Bin. out. x 10% treated [0.009] [0.007] [0.007] [0.028] [0.021] [0.019] Bin. out. x 90% treated [0.017] [0.014] [0.013] [0.054] [0.041] [0.038] < table continues on next page > 9
10 Table D.1: < continued > Manufacturing and Service Workers Het. 1 x Pop p-score [0.006] [0.004] [0.012] [0.010] [0.032] [0.029] Het. 1 x Corr spec. model [0.004] [0.005] [0.004] [0.011] [0.010] [0.009] [0.034] [0.031] [0.029] Het. 1 x 10% treated [0.009] [0.007] [0.007] [0.028] [0.021] [0.020] Het. 1 x 90% treated 0.074*** 0.078*** 0.069*** 0.259*** 0.242*** 0.222*** [0.015] [0.013] [0.012] [0.048] [0.037] [0.034] Het. 2 x Pop p-score [0.006] [0.004] [0.012] [0.011] [0.032] [0.030] Het. 2 x Corr spec. model [0.004] [0.005] [0.004] [0.011] [0.010] [0.009] [0.035] [0.032] [0.030] Het. 2 x 10% treated [0.009] [0.007] [0.007] [0.028] [0.021] [0.020] Het. 2 x 90% treated 0.076*** 0.081*** 0.071*** 0.271*** 0.251*** 0.230*** [0.016] [0.013] [0.012] [0.049] [0.038] [0.035] Pop. p-score x 10% treated [0.007] [0.007] [0.021] [0.019] Pop. p-score x 90% treated [0.015] [0.013] [0.041] [0.038] Corr. spec. model x % treated [0.008] [0.007] [0.007] [0.022] [0.021] [0.019] Corr. spec. model x % treated [0.014] [0.012] [0.011] [0.044] [0.040] [0.037] Constant 0.930*** 0.953*** 0.978*** 0.920*** 0.945*** 0.953*** 0.881*** 0.904*** 0.910*** [0.005] [0.005] [0.004] [0.011] [0.010] [0.009] [0.033] [0.028] [0.026] Obs 792 1,188 1,188 2,376 3,564 3,564 2,376 3,564 3,564 R Note: Results from OLS regressions, the dependent variable is normalized RMSE of the respective estimator. We control for a full set of dummies for the different procedures to handle support problems. The omitted category is to drop no observations (Procedure A). Please find a full description of the different procedures in Table 2 in Section 6.1. Further, we control for all tuning parameters of the different DGPs in a fully interacted way in all regressions (see description in Section 6.1). The results for the tuning parameters of the different DGPs are available from the authors upon request. Robust standard errors are in brackets; ***, **,* indicate significance at 1-, 5-, and 10-percent level, respectively. 10
11 Table D.2: Influence of all procedures to handle support problems on the performance of different estimators in terms of normalized RMSE in specifications without support restrictions for the treatment award of vouchers for technicians (VTEC ). Technicians WA 0.014** *** 0.037*** 0.018* *** 0.018*** ** [0.007] [0.012] [0.009] [0.010] [0.014] [0.007] [0.027] [0.015] [0.016] B *** *** *** 0.285*** 0.151*** 0.234*** 0.836*** 0.632*** 0.699*** [0.008] [0.012] [0.008] [0.045] [0.034] [0.033] [0.142] [0.092] [0.096] B *** *** *** 0.163*** *** 0.576*** 0.374*** 0.461*** [0.008] [0.012] [0.008] [0.047] [0.032] [0.034] [0.146] [0.092] [0.099] WB *** *** *** 0.285*** 0.151*** 0.234*** 0.836*** 0.632*** 0.699*** [0.008] [0.012] [0.008] [0.045] [0.034] [0.033] [0.142] [0.092] [0.096] WB *** *** *** 0.163*** *** 0.576*** 0.374*** 0.461*** [0.008] [0.012] [0.008] [0.047] [0.032] [0.034] [0.146] [0.092] [0.099] C * [0.007] [0.013] [0.006] [0.010] [0.016] [0.007] [0.027] [0.015] [0.016] C *** [0.007] [0.013] [0.005] [0.010] [0.016] [0.007] [0.027] [0.015] [0.016] WC *** 0.024*** 0.018* *** 0.018*** ** [0.007] [0.012] [0.008] [0.010] [0.014] [0.007] [0.027] [0.015] [0.016] WC *** ** *** 0.021*** ** [0.007] [0.012] [0.007] [0.010] [0.014] [0.007] [0.027] [0.015] [0.016] D *** *** *** [0.008] [0.014] [0.007] [0.010] [0.015] [0.006] [0.027] [0.015] [0.016] D [0.007] [0.013] [0.007] [0.010] [0.016] [0.007] [0.027] [0.015] [0.016] WD *** *** *** ** *** *** ** [0.009] [0.012] [0.008] [0.011] [0.015] [0.006] [0.027] [0.015] [0.016] WD *** 0.021*** 0.017* *** 0.018*** ** [0.007] [0.012] [0.008] [0.010] [0.014] [0.007] [0.027] [0.015] [0.016] E *** *** *** *** [0.007] [0.013] [0.006] [0.013] [0.016] [0.008] [0.027] [0.015] [0.017] E *** *** *** *** *** 0.073** ** [0.009] [0.012] [0.008] [0.015] [0.013] [0.009] [0.032] [0.020] [0.018] E *** *** 0.132*** ** 0.489*** 0.312*** 0.363*** [0.023] [0.017] [0.014] [0.036] [0.027] [0.021] [0.089] [0.059] [0.055] WE *** *** *** *** *** *** *** [0.008] [0.012] [0.007] [0.013] [0.015] [0.009] [0.026] [0.016] [0.017] WE *** *** *** *** *** 0.075** ** [0.010] [0.012] [0.008] [0.015] [0.015] [0.009] [0.032] [0.020] [0.018] WE *** *** 0.140*** *** 0.490*** 0.313*** 0.364*** [0.024] [0.017] [0.014] [0.036] [0.027] [0.020] [0.089] [0.059] [0.055] F *** 0.111*** *** 0.030*** 0.080*** ** [0.006] [0.017] [0.006] [0.009] [0.022] [0.006] [0.027] [0.017] [0.016] F *** 0.091*** 0.030*** 0.143*** 0.091*** 0.063*** 0.133*** 0.072*** 0.071*** [0.007] [0.010] [0.005] [0.009] [0.012] [0.006] [0.024] [0.016] [0.016] F *** 0.372*** 0.290*** 0.602*** 0.435*** 0.385*** 0.639*** 0.474*** 0.442*** [0.008] [0.014] [0.008] [0.020] [0.023] [0.013] [0.028] [0.024] [0.019] WF *** 0.063*** *** 0.025* 0.032*** [0.006] [0.011] [0.006] [0.014] [0.014] [0.008] [0.027] [0.015] [0.016] WF *** 0.110*** 0.052*** 0.183*** 0.093*** 0.090*** 0.136*** 0.073*** 0.073*** [0.007] [0.011] [0.007] [0.011] [0.013] [0.007] [0.024] [0.016] [0.016] WF *** 0.391*** 0.309*** 0.617*** 0.448*** 0.399*** 0.638*** 0.472*** 0.442*** [0.009] [0.015] [0.010] [0.018] [0.022] [0.012] [0.028] [0.024] [0.019] G *** 0.055*** *** 0.017* 0.045*** [0.006] [0.014] [0.005] [0.009] [0.017] [0.007] [0.028] [0.015] [0.017] G *** *** 0.077*** *** [0.008] [0.010] [0.007] [0.011] [0.012] [0.007] [0.031] [0.020] [0.019] G *** 0.193*** 0.156*** 0.350*** 0.189*** 0.187*** 0.381*** 0.236*** 0.239*** [0.017] [0.019] [0.014] [0.020] [0.023] [0.013] [0.038] [0.029] [0.024] WG *** *** 0.043*** *** [0.009] [0.010] [0.006] [0.010] [0.013] [0.007] [0.028] [0.015] [0.017] WG *** * 0.100*** *** 0.086*** [0.010] [0.011] [0.008] [0.011] [0.013] [0.007] [0.031] [0.020] [0.019] WG *** 0.212*** 0.172*** 0.364*** 0.199*** 0.198*** 0.381*** 0.235*** 0.239*** [0.018] [0.019] [0.014] [0.019] [0.022] [0.013] [0.038] [0.029] [0.024] < table continues on next page > 11
12 Table D.2: < continued > Technicians H *** 0.098*** *** 0.040*** 0.074*** *** [0.011] [0.017] [0.007] [0.011] [0.021] [0.007] [0.027] [0.016] [0.017] H *** 0.073*** 0.019** 0.144*** 0.071*** 0.055*** 0.176*** 0.082*** 0.092*** [0.016] [0.011] [0.009] [0.012] [0.013] [0.007] [0.031] [0.017] [0.018] H *** 0.274*** 0.202*** 0.500*** 0.324*** 0.298*** 0.732*** 0.535*** 0.515*** [0.024] [0.013] [0.013] [0.026] [0.018] [0.014] [0.067] [0.043] [0.042] WH *** 0.073*** *** *** [0.019] [0.014] [0.012] [0.016] [0.015] [0.009] [0.026] [0.015] [0.016] WH *** 0.095*** 0.043*** 0.184*** 0.075*** 0.082*** 0.180*** 0.084*** 0.094*** [0.022] [0.014] [0.012] [0.015] [0.014] [0.009] [0.031] [0.017] [0.018] WH *** 0.290*** 0.218*** 0.517*** 0.337*** 0.312*** 0.731*** 0.534*** 0.515*** [0.025] [0.014] [0.014] [0.026] [0.018] [0.015] [0.067] [0.043] [0.042] I *** 0.027** *** *** [0.007] [0.014] [0.005] [0.010] [0.017] [0.007] [0.028] [0.015] [0.017] I *** *** *** 0.044*** *** *** 0.067** *** [0.008] [0.010] [0.007] [0.010] [0.012] [0.007] [0.028] [0.019] [0.018] I *** *** *** 0.278*** 0.114*** 0.137*** [0.014] [0.016] [0.011] [0.013] [0.015] [0.010] [0.028] [0.020] [0.018] WI *** *** *** 0.026** *** *** [0.012] [0.011] [0.007] [0.010] [0.013] [0.007] [0.028] [0.015] [0.017] WI *** *** *** 0.061*** *** *** 0.068** *** [0.010] [0.011] [0.007] [0.010] [0.013] [0.007] [0.028] [0.019] [0.018] WI *** *** *** 0.278*** 0.114*** 0.137*** [0.015] [0.016] [0.011] [0.013] [0.015] [0.010] [0.028] [0.020] [0.018] Discrete outcome ** *** *** ** [0.011] [0.010] [0.008] [0.017] [0.015] [0.012] [0.044] [0.033] [0.033] Binary outcome ** *** *** ** [0.011] [0.010] [0.008] [0.017] [0.015] [0.012] [0.044] [0.032] [0.032] Heterogeneity *** 0.049*** 0.050*** 0.205*** 0.157*** 0.156*** [0.013] [0.012] [0.009] [0.020] [0.016] [0.013] [0.052] [0.036] [0.036] Heterogeneity *** 0.044*** 0.045*** 0.189*** 0.142*** 0.142*** [0.013] [0.012] [0.009] [0.019] [0.016] [0.013] [0.051] [0.035] [0.035] 10% treated ** ** * *** * ** [0.015] [0.012] [0.010] [0.039] [0.028] [0.027] 90% treated [0.022] [0.020] [0.016] [0.054] [0.039] [0.039] Population p-score [0.011] [0.009] [0.015] [0.012] [0.033] [0.033] Correct specified model [0.012] [0.012] [0.010] [0.016] [0.016] [0.013] [0.041] [0.034] [0.033] Disc. out. x *** *** *** *** *** *** Het. 1 [0.013] [0.010] [0.008] [0.019] [0.015] [0.013] [0.049] [0.032] [0.033] Disc. out. x *** ** *** *** *** *** Het. 2 [0.013] [0.010] [0.008] [0.018] [0.015] [0.012] [0.049] [0.032] [0.032] Disc. out. x Pop p-score [0.010] [0.007] [0.015] [0.013] [0.034] [0.035] Disc. out. x Corr spec. model [0.010] [0.010] [0.008] [0.016] [0.015] [0.012] [0.043] [0.034] [0.035] Disc. out. x 10% 0.029* *** 0.047* 0.056** treated [0.015] [0.011] [0.009] [0.040] [0.027] [0.025] Disc. out. x 90% * treated [0.022] [0.017] [0.015] [0.060] [0.038] [0.040] Bin. out. x Het *** *** *** *** *** *** [0.012] [0.010] [0.008] [0.019] [0.015] [0.013] [0.049] [0.032] [0.033] Bin. out. x Het *** *** *** *** *** *** [0.012] [0.010] [0.008] [0.018] [0.015] [0.012] [0.048] [0.031] [0.031] Bin. out. x Pop p-score [0.010] [0.007] [0.015] [0.013] [0.033] [0.035] Bin. out. x Corr spec. model [0.009] [0.010] [0.008] [0.016] [0.015] [0.012] [0.042] [0.034] [0.034] Bin. out. x 10% 0.028* *** 0.047* 0.055** treated [0.015] [0.011] [0.009] [0.039] [0.027] [0.025] Bin. out. x 90% * treated [0.021] [0.017] [0.014] [0.060] [0.038] [0.040] < table continues on next page > 12
13 Table D.2: < continued > Technicians Het. 1 x Pop p-score [0.009] [0.007] [0.014] [0.011] [0.029] [0.030] Het. 1 x Corr spec. model [0.009] [0.009] [0.007] [0.014] [0.014] [0.011] [0.036] [0.030] [0.030] Het. 1 x 10% treated [0.013] [0.010] [0.008] [0.035] [0.023] [0.022] Het. 1 x 90% treated 0.076*** 0.069*** 0.073*** 0.225*** 0.178*** 0.197*** [0.019] [0.015] [0.013] [0.051] [0.033] [0.034] Het. 2 x Pop p-score [0.009] [0.007] [0.014] [0.011] [0.029] [0.030] Het. 2 x Corr spec. model [0.009] [0.009] [0.007] [0.013] [0.014] [0.011] [0.036] [0.030] [0.030] Het. 2 x 10% treated [0.013] [0.010] [0.008] [0.034] [0.023] [0.022] Het. 2 x 90% treated 0.075*** 0.070*** 0.073*** 0.230*** 0.184*** 0.204*** [0.019] [0.015] [0.013] [0.050] [0.033] [0.034] Pop. p-score x 10% treated [0.010] [0.008] [0.024] [0.023] Pop. p-score x 90% treated [0.015] [0.013] [0.035] [0.037] Corr. spec. model x % treated [0.011] [0.011] [0.009] [0.029] [0.025] [0.023] Corr. spec. model x % treated [0.016] [0.015] [0.013] [0.044] [0.035] [0.036] Constant 0.903*** 0.984*** 1.004*** 0.906*** 0.979*** 0.953*** 0.958*** 0.970*** 0.941*** [0.011] [0.014] [0.010] [0.017] [0.018] [0.012] [0.044] [0.032] [0.031] Obs 792 1,188 1,188 2,376 3,564 3,564 2,376 3,564 3,564 R Note: See note of Table D.1. 13
14 Table D.3: Influence of all procedures to handle support problems on the performance of different estimators in terms of normalized absolute bias in specifications without support restrictions for the treatment award of vouchers for manufacturing and service workers (VMSW ). Manufacturing and Service Workers WA * [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] B *** 0.479*** 0.440*** 1.159*** 1.160*** 1.077*** [0.005] [0.005] [0.006] [0.077] [0.065] [0.060] [0.194] [0.152] [0.142] B *** 0.343*** 0.314*** 0.827*** 0.801*** 0.756*** [0.005] [0.005] [0.005] [0.079] [0.067] [0.062] [0.199] [0.156] [0.147] WB *** 0.479*** 0.440*** 1.159*** 1.160*** 1.077*** [0.005] [0.005] [0.006] [0.077] [0.065] [0.060] [0.194] [0.152] [0.142] WB *** 0.343*** 0.314*** 0.827*** 0.801*** 0.756*** [0.005] [0.005] [0.005] [0.079] [0.067] [0.062] [0.199] [0.156] [0.147] C ** [0.006] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] C *** 0.040*** * [0.008] [0.007] [0.007] [0.013] [0.011] [0.009] [0.029] [0.023] [0.021] WC * [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WC *** 0.032*** * ** [0.008] [0.007] [0.007] [0.013] [0.010] [0.009] [0.029] [0.023] [0.021] D *** 0.043*** *** [0.007] [0.006] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] D [0.005] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] WD *** 0.035*** *** * [0.006] [0.006] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WD * [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] E * 0.029*** *** [0.006] [0.005] [0.005] [0.010] [0.011] [0.010] [0.028] [0.023] [0.022] E *** 0.011* *** 0.050*** 0.039*** *** 0.107*** 0.093*** [0.007] [0.006] [0.006] [0.011] [0.011] [0.010] [0.026] [0.021] [0.020] E *** 0.101*** 0.035*** 0.205*** 0.203*** 0.162*** 0.448*** 0.458*** 0.416*** [0.020] [0.015] [0.011] [0.023] [0.017] [0.015] [0.051] [0.039] [0.034] WE ** 0.024*** *** 0.021** [0.006] [0.005] [0.005] [0.010] [0.011] [0.009] [0.028] [0.023] [0.022] WE *** 0.011* *** 0.056*** 0.044*** 0.018** 0.114*** 0.107*** 0.093*** [0.007] [0.006] [0.006] [0.011] [0.010] [0.009] [0.026] [0.021] [0.020] WE *** 0.102*** 0.036*** 0.209*** 0.205*** 0.164*** 0.448*** 0.458*** 0.416*** [0.020] [0.016] [0.011] [0.024] [0.017] [0.015] [0.051] [0.039] [0.034] F *** *** [0.006] [0.004] [0.005] [0.013] [0.010] [0.009] [0.029] [0.023] [0.021] F *** [0.007] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] F *** ** *** 0.046** [0.007] [0.006] [0.006] [0.013] [0.012] [0.010] [0.028] [0.022] [0.022] WF *** *** [0.006] [0.004] [0.005] [0.014] [0.010] [0.009] [0.029] [0.023] [0.021] WF *** [0.007] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] WF *** ** *** 0.046** [0.007] [0.006] [0.006] [0.013] [0.012] [0.010] [0.028] [0.022] [0.022] G ** 0.057*** ** 0.044*** [0.005] [0.005] [0.005] [0.013] [0.009] [0.009] [0.030] [0.023] [0.021] G *** 0.055*** 0.018** *** 0.021** [0.008] [0.008] [0.007] [0.012] [0.010] [0.009] [0.032] [0.023] [0.021] G *** 0.077*** 0.050*** 0.051*** 0.083*** 0.059*** *** 0.084*** [0.021] [0.016] [0.014] [0.014] [0.012] [0.011] [0.032] [0.025] [0.023] WG *** 0.054*** * 0.042*** [0.005] [0.005] [0.005] [0.012] [0.009] [0.009] [0.030] [0.023] [0.021] WG *** 0.056*** 0.019** *** 0.023*** [0.009] [0.008] [0.008] [0.012] [0.010] [0.009] [0.032] [0.023] [0.021] WG *** 0.077*** 0.051*** 0.052*** 0.084*** 0.060*** *** 0.084*** [0.021] [0.016] [0.014] [0.014] [0.012] [0.011] [0.032] [0.025] [0.023] < table continues on next page > 14
15 Table D.3: < continued > Manufacturing and Service Workers H *** 0.017*** *** [0.010] [0.006] [0.006] [0.013] [0.011] [0.010] [0.031] [0.025] [0.023] H *** 0.032*** *** 0.033*** 0.028** 0.084*** 0.057** 0.050** [0.018] [0.008] [0.012] [0.015] [0.012] [0.011] [0.032] [0.025] [0.022] H *** 0.123*** 0.062** 0.188*** 0.159*** 0.124*** 0.276*** 0.282*** 0.253*** [0.037] [0.023] [0.026] [0.026] [0.020] [0.020] [0.045] [0.035] [0.034] WH *** 0.020*** *** 0.021* [0.012] [0.006] [0.007] [0.014] [0.011] [0.010] [0.031] [0.025] [0.023] WH *** 0.035*** *** 0.038*** 0.032*** 0.084*** 0.057** 0.050** [0.019] [0.009] [0.012] [0.016] [0.012] [0.012] [0.032] [0.025] [0.022] WH *** 0.125*** 0.063** 0.185*** 0.159*** 0.125*** 0.276*** 0.282*** 0.253*** [0.037] [0.023] [0.026] [0.027] [0.020] [0.020] [0.045] [0.035] [0.034] I *** ** [0.006] [0.004] [0.006] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] I *** * [0.007] [0.006] [0.006] [0.013] [0.011] [0.009] [0.030] [0.024] [0.022] I *** 0.025** ** 0.050*** 0.029** 0.075** 0.112*** 0.105*** [0.011] [0.010] [0.009] [0.015] [0.012] [0.011] [0.035] [0.028] [0.026] WI *** * [0.006] [0.005] [0.006] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WI *** [0.008] [0.006] [0.006] [0.013] [0.011] [0.009] [0.030] [0.024] [0.022] WI *** 0.025** ** 0.051*** 0.030*** 0.075** 0.112*** 0.105*** [0.011] [0.010] [0.009] [0.015] [0.012] [0.011] [0.035] [0.028] [0.026] Discrete outcome *** *** ** *** ** ** [0.010] [0.008] [0.008] [0.019] [0.017] [0.016] [0.045] [0.039] [0.037] Binary outcome *** ** *** *** ** [0.011] [0.008] [0.008] [0.019] [0.018] [0.017] [0.046] [0.041] [0.038] Heterogeneity [0.011] [0.008] [0.008] [0.020] [0.018] [0.016] [0.047] [0.040] [0.037] Heterogeneity [0.011] [0.008] [0.008] [0.020] [0.018] [0.017] [0.048] [0.041] [0.038] 10% treated [0.017] [0.014] [0.013] [0.039] [0.032] [0.030] 90% treated [0.023] [0.020] [0.019] [0.054] [0.047] [0.044] Population p-score *** *** * [0.007] [0.007] [0.019] [0.017] [0.042] [0.039] Correct specified 0.025** *** *** model [0.012] [0.010] [0.011] [0.019] [0.018] [0.017] [0.044] [0.042] [0.039] Disc. out. x Het. 1 [0.012] [0.008] [0.009] [0.021] [0.017] [0.016] [0.051] [0.039] [0.037] Disc. out. x * Het. 2 [0.012] [0.008] [0.009] [0.021] [0.017] [0.016] [0.052] [0.040] [0.038] Disc. out. x Pop ** 0.020*** p-score [0.006] [0.007] [0.019] [0.018] [0.042] [0.040] Disc. out. x Corr *** *** ** spec. model [0.009] [0.009] [0.009] [0.018] [0.017] [0.016] [0.045] [0.042] [0.040] Disc. out. x 10% *** * * 0.053** treated [0.015] [0.013] [0.012] [0.036] [0.029] [0.027] Disc. out. x 90% * treated [0.026] [0.021] [0.020] [0.063] [0.049] [0.046] Bin. out. x Het [0.013] [0.008] [0.008] [0.022] [0.018] [0.017] [0.054] [0.042] [0.039] Bin. out. x Het [0.013] [0.008] [0.008] [0.023] [0.019] [0.017] [0.055] [0.042] [0.040] Bin. out. x Pop *** 0.025*** p-score [0.007] [0.006] [0.020] [0.019] [0.045] [0.042] Bin. out. x Corr ** 0.025*** 0.015* *** ** spec. model [0.010] [0.009] [0.009] [0.019] [0.018] [0.017] [0.047] [0.045] [0.042] Bin. out. x 10% ** * ** treated [0.015] [0.013] [0.012] [0.037] [0.030] [0.027] Bin. out. x 90% * treated [0.028] [0.023] [0.021] [0.067] [0.052] [0.049] < table continues on next page > 15
16 Table D.3: < continued > Manufacturing and Service Workers Het. 1 x Pop p-score [0.006] [0.006] [0.019] [0.017] [0.041] [0.039] Het. 1 x Corr spec. model [0.009] [0.008] [0.009] [0.018] [0.017] [0.016] [0.043] [0.041] [0.039] Het. 1 x 10% treated [0.015] [0.013] [0.012] [0.037] [0.029] [0.027] Het. 1 x 90% treated 0.137*** 0.133*** 0.127*** 0.334*** 0.315*** 0.294*** [0.025] [0.021] [0.019] [0.060] [0.047] [0.044] Het. 2 x Pop p-score [0.006] [0.006] [0.019] [0.017] [0.042] [0.040] Het. 2 x Corr spec. model [0.009] [0.008] [0.009] [0.018] [0.017] [0.016] [0.044] [0.042] [0.039] Het. 2 x 10% treated [0.015] [0.013] [0.012] [0.037] [0.029] [0.027] Het. 2 x 90% treated 0.139*** 0.134*** 0.129*** 0.345*** 0.326*** 0.301*** [0.025] [0.021] [0.019] [0.062] [0.048] [0.045] Pop. p-score x 10% treated [0.012] [0.011] [0.028] [0.026] Pop. p-score x 90% treated [0.024] [0.022] [0.052] [0.049] Corr. spec. model x % treated [0.012] [0.012] [0.011] [0.029] [0.029] [0.027] Corr. spec. model x % treated [0.022] [0.021] [0.019] [0.054] [0.052] [0.048] Constant 0.017* 0.056*** 0.056*** [0.010] [0.008] [0.009] [0.018] [0.016] [0.015] [0.042] [0.037] [0.034] Obs 792 1,188 1,188 2,376 3,564 3,564 2,376 3,564 3,564 R Note: Results from OLS regressions, the dependent variable is normalized absolute bias of the respective estimator. We control for a full set of dummies for the different procedures to handle support problems. The omitted category is to drop no observations (Procedure A). Please find a full description of the different procedures in Table 2 in Section 6.1. Further, we control for all tuning parameters of the different DGPs in a fully interacted way in all regressions (see description in Section 6.1). The results for the tuning parameters of the different DGPs are available from the authors upon request. Robust standard errors are in brackets; ***, **,* indicate significance at 1-, 5-, and 10-percent level, respectively. 16
17 Table D.4: Influence of all procedures to handle support problems on the performance of different estimators in terms of normalized absolute in specifications without support restrictions for the treatment award of vouchers for technicians (VTEC ). Technicians WA * [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] B *** 0.479*** 0.440*** 1.159*** 1.160*** 1.077*** [0.005] [0.005] [0.006] [0.077] [0.065] [0.060] [0.194] [0.152] [0.142] B *** 0.343*** 0.314*** 0.827*** 0.801*** 0.756*** [0.005] [0.005] [0.005] [0.079] [0.067] [0.062] [0.199] [0.156] [0.147] WB *** 0.479*** 0.440*** 1.159*** 1.160*** 1.077*** [0.005] [0.005] [0.006] [0.077] [0.065] [0.060] [0.194] [0.152] [0.142] WB *** 0.343*** 0.314*** 0.827*** 0.801*** 0.756*** [0.005] [0.005] [0.005] [0.079] [0.067] [0.062] [0.199] [0.156] [0.147] C ** [0.006] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] C *** 0.040*** * [0.008] [0.007] [0.007] [0.013] [0.011] [0.009] [0.029] [0.023] [0.021] WC * [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WC *** 0.032*** * ** [0.008] [0.007] [0.007] [0.013] [0.010] [0.009] [0.029] [0.023] [0.021] D *** 0.043*** *** [0.007] [0.006] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] D [0.005] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] WD *** 0.035*** *** * [0.006] [0.006] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WD * [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] E * 0.029*** *** [0.006] [0.005] [0.005] [0.010] [0.011] [0.010] [0.028] [0.023] [0.022] E *** 0.011* *** 0.050*** 0.039*** *** 0.107*** 0.093*** [0.007] [0.006] [0.006] [0.011] [0.011] [0.010] [0.026] [0.021] [0.020] E *** 0.101*** 0.035*** 0.205*** 0.203*** 0.162*** 0.448*** 0.458*** 0.416*** [0.020] [0.015] [0.011] [0.023] [0.017] [0.015] [0.051] [0.039] [0.034] WE ** 0.024*** *** 0.021** [0.006] [0.005] [0.005] [0.010] [0.011] [0.009] [0.028] [0.023] [0.022] WE *** 0.011* *** 0.056*** 0.044*** 0.018** 0.114*** 0.107*** 0.093*** [0.007] [0.006] [0.006] [0.011] [0.010] [0.009] [0.026] [0.021] [0.020] WE *** 0.102*** 0.036*** 0.209*** 0.205*** 0.164*** 0.448*** 0.458*** 0.416*** [0.020] [0.016] [0.011] [0.024] [0.017] [0.015] [0.051] [0.039] [0.034] F *** *** [0.006] [0.004] [0.005] [0.013] [0.010] [0.009] [0.029] [0.023] [0.021] F *** [0.007] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] F *** ** *** 0.046** [0.007] [0.006] [0.006] [0.013] [0.012] [0.010] [0.028] [0.022] [0.022] WF *** *** [0.006] [0.004] [0.005] [0.014] [0.010] [0.009] [0.029] [0.023] [0.021] WF *** [0.007] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] WF *** ** *** 0.046** [0.007] [0.006] [0.006] [0.013] [0.012] [0.010] [0.028] [0.022] [0.022] G ** 0.057*** ** 0.044*** [0.005] [0.005] [0.005] [0.013] [0.009] [0.009] [0.030] [0.023] [0.021] G *** 0.055*** 0.018** *** 0.021** [0.008] [0.008] [0.007] [0.012] [0.010] [0.009] [0.032] [0.023] [0.021] G *** 0.077*** 0.050*** 0.051*** 0.083*** 0.059*** *** 0.084*** [0.021] [0.016] [0.014] [0.014] [0.012] [0.011] [0.032] [0.025] [0.023] WG *** 0.054*** * 0.042*** [0.005] [0.005] [0.005] [0.012] [0.009] [0.009] [0.030] [0.023] [0.021] WG *** 0.056*** 0.019** *** 0.023*** [0.009] [0.008] [0.008] [0.012] [0.010] [0.009] [0.032] [0.023] [0.021] WG *** 0.077*** 0.051*** 0.052*** 0.084*** 0.060*** *** 0.084*** [0.021] [0.016] [0.014] [0.014] [0.012] [0.011] [0.032] [0.025] [0.023] < table continues on next page > 17
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