Online Appendices Practical Procedures to Deal with Common Support Problems in Matching Estimation

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, www.michael-lechner.eu. 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 1155. 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.

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 15,791 7.09 Female dummy 0.48 0.45 4.73-0.369-8,166-1.57-15.66 Age in years 38.29 40.15 15.78-0.036-290 -0.10-0.94 Age 20-24 years 0.15 0.14 1.28-0.452-1,153-0.53-5.74 Age 25-34 years 0.42 0.35 9.27 Age 35-44 years 0.36 0.33 4.05 Age 45-54 years 0.08 0.18 20.85-1.537-1,625-1.17-10.17 Lower secondary school degree 0.37 0.42 6.07 Upper secondary school degree 0.39 0.39 0.61 0.642 1,057 0.61 4.99 University entry school degree 0.23 0.19 6.80 0.805 2,289 0.56 5.02 No vocational degree 0.17 0.15 3.67 0.734-882 -0.38-3.55 Vocational degree 0.83 0.84 3.39 At least one child 0.36 0.33 3.51 0.428 970 0.50 4.66 At least one child < 5 years 0.10 0.09 2.88-0.207-1,445-0.86-7.46 Single 0.34 0.31 3.52 0.370-382 -0.20-2.13 Married 0.45 0.49 5.66-0.128 263 0.12 0.86 Beginning of unemployment 7.11 6.70 9.12 0.153-32 -0.02-0.19 Time to treatment in months 4.35 3.68 14.11 0.185-216 -0.08-0.7 Part-time job 0.13 0.13 0.42-0.045 538 0.17 1.42 Craft, machine operators and related 0.32 0.38 9.58 Service workers and clerks 0.41 0.36 7.35 0.615-539 -0.64-5.35 Technicians, associate professions, 0.27 0.26 2.30 0.912 242-0.27-2.15 professionals, and managers Half-months employed in the last 24 months 44.01 40.29 31.69-0.020 12 0.01 0.08 Number of employment spells in last 24 months 1.21 1.36 20.69-0.311-740 -0.34-2.53 Half-months unemployed in last 24 months 0.81 1.41 17.52 0.056 77 0.02 0.21 Time since last unemployment in last 24 43.86 40.73 22.00 0.009 3 0.00 0.02 months (half-months) No unemployment in last 24 months 0.81 0.67 21.25 0.283-190 -0.16-1.14 Unemployed 24 months before 0.07 0.13 15.66-0.241-192 -0.13-1.39 Number of unemployment spells in last 24 0.27 0.46 19.53 0.027 218 0.14 1.36 months Any program in last 24 months 0.07 0.25 35.39-1.858 324 0.22 1.78 Half-months out of labor force in last 24 1.85 3.74 23.69-0.023 62 0.02 0.22 months Time since last out of labour force in last 24 44.43 40.76 26.25 0.033 78 0.04 0.32 months Amount of unemployment benefit 25.25 22.36 15.55 0.049 97 0.03 0.26 Remaining UI claim 12.59 11.86 9.19 0.001-178 -0.07-0.59 South Germany 0.24 0.21 5.85-0.419 817 0.44 3.62 East Germany 0.26 0.34 12.55-1.115 98 0.76 6.2 North Germany 0.15 0.19 6.07-1.421 1,050 0.61 4.77 West Germany 0.35 0.27 12.06 Employed 4 years before 0.67 0.64 4.15-0.158 723 0.22 1.54 Earnings 4 years before (daily, deflated) 52.78 47.75 9.40-0.012-43 -0.01-0.05 Cumulated duration employed 4 years before 79.49 72.25 22.76 0.009 4 0.03 0.24 (half-months) Cumulated earnings 4 years before (defl., per 1.83 1.57 19.89 0.474 5,542 0.46 3.71 month, in thsd.) Cumulated duration of UI 4 years before 4.12 6.97 20.81-0.016-96 -0.05-0.37 (half-months) Cumulated UI benefits 4 years before (defl., 0.04 0.09 31.18-6.222-532 -0.38-3.54 per month, in thsd.) Female x Age in years 18.69 18.13 1.92 0.017 150 0.03 0.35 Technicians and associate professions x Higher 0.21 0.20 1.48-0.856-111 -0.38-3.92 secondary school degree S i1 Professionals and managers x Higher secondary 0.10 0.10 1.08 0.196 26-0.02-0.59 school degree S i2 Professionals and managers x University or college degree S i3 0.05 0.06 2.47-1.204 3,007 0.19 1.45 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

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 15,062 6.5618 Female dummy 0.28 0.45 26.26-0.145-8,119-1.57-6.23 Age in years 40.83 40.18 5.53 0.003-298 -0.11-14.90 Age 20-24 years 0.07 0.14 17.17-0.074-1,044-0.44-3.97 Age 25-34 years 0.38 0.35 3.44 Age 35-44 years 0.42 0.33 12.38 Age 45-54 years 0.14 0.18 6.61-0.109-1,453-1.08-9.26 Lower secondary school degree 0.17 0.41 38.82 Upper secondary school degree 0.31 0.39 11.58 0.108 1,087 0.66 9.00 University entry school degree 0.51 0.19 51.22 0.225 2,399 0.61 6.00 No vocational degree 0.02 0.15 33.33-0.166-805 -0.37-4.57 Vocational degree 0.98 0.84 33.50 At least one child 0.35 0.33 2.53 0.053 977 0.52 6.66 At least one child < 5 years 0.10 0.09 2.98-0.045-1,586-0.89-8.02 Single 0.33 0.31 2.83 0.041-263 -0.20-2.30 Married 0.53 0.49 5.58 0.014 441 0.18 2.29 Beginning of unemployment 7.21 6.71 10.85 0.013-27 -0.02-2.10 Time to treatment in months 4.46 3.83 13.68 0.015-241 -0.10-12.01 Part-time job 0.04 0.13 21.81-0.089 574 0.16 1.67 Craft, machine operators and related 0.16 0.38 36.42 Service workers and clerks 0.08 0.36 50.13-0.027-385 -0.57-7.19 Technicians, associate professions, 0.76 0.26 81.57 0.489 498-0.17-1.34 professionals, and managers Half-months employed in the last 24 months 44.91 40.28 41.05 0.008 21 0.01 1.21 Number of employment spells in last 24 months 1.14 1.36 31.94-0.046-872 -0.39-6.57 Half-months unemployed in last 24 months 0.59 1.42 25.39 0.015 110 0.04 1.69 Time since last unemployment in last 24 44.84 40.77 29.91 0.000 6 0.01 1.43 months (half-months) No unemployment in last 24 months 0.84 0.67 27.95-0.022-293 -0.14-1.19 Unemployed 24 months before 0.05 0.13 19.73 0.028-115 -0.12-1.17 Number of unemployment spells in last 24 0.20 0.46 28.11-0.030 212 0.16 2.14 months Any program in last 24 months 0.07 0.25 36.08-0.127 245 0.22 2.54 Half-months out of labor force in last 24 1.60 3.75 27.61 0.006 74 0.03 2.08 months Time since last out of labour force in last 24 45.06 40.77 31.67 0.003 77 0.04 7.75 months Amount of unemployment benefit 32.95 22.34 54.70 0.006 101 0.03 14.30 Remaining UI claim 14.02 11.87 25.43 0.001-181 -0.08-10.49 South Germany 0.28 0.21 11.71 0.105 970 0.51 6.33 East Germany 0.34 0.34 0.46 0.003 309 0.80 10.22 North Germany 0.11 0.19 15.20-0.107 1,093 0.65 7.84 West Germany 0.27 0.27 0.33 Employed 4 years before 0.73 0.64 13.07-0.011 703 0.24 2.61 Earnings 4 years before (daily,deflated) 72.35 47.72 42.19 0.000-45 -0.01-3.66 Cumulated duration employed 4 years before 82.19 72.27 32.00 0.000 7 0.03 10.53 (half-months) Cumulated earnings 4 years before (defl., per 2.45 1.57 62.39 0.000 5,706 0.52 6.16 month, in thsd.) Cumulated duration of UI 4 years before 3.11 6.97 29.38-0.002-98 -0.05-11.72 (half-months) Cumulated UI benefits 4 years before (defl., 0.04 0.09 30.04-0.427-26 -0.04-0.12 per month, in thsd.) Female x Age in years 11.04 18.27 26.00 0.001 152 0.04 5.85 Technicians and associate professions x Higher 0.65 0.20 72.82-0.078-372 -0.56-3.61 secondary school degree S i1 Professionals and managers x Higher secondary 0.36 0.10 44.95-0.126 332 0.01 0.08 school degree S i2 Professionals and managers x University or college degree S i3 0.30 0.06 45.09 0.162 2,603 0.21 1.15 Note: See note of Table A.1. 3

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

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 5.3. 5

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

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

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 0.002-0.012*** 0.003** 0.005-0.017** 0.004 0 0 0 [0.004] [0.005] [0.001] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] B1 0.004-0.013*** -0.005** 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] B2-0.007* -0.015*** -0.007*** 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] WB1 0.004-0.013*** -0.005** 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] WB2-0.007* -0.015*** -0.007*** 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] C1 0.002 0.003 0.001 0 0 0 0 0 0 [0.004] [0.003] [0.002] [0.009] [0.006] [0.005] [0.023] [0.017] [0.016] C2 0.017*** 0.019*** 0.011*** 0.001 0 0.002 0 0 0 [0.004] [0.003] [0.002] [0.008] [0.006] [0.005] [0.023] [0.017] [0.016] WC1 0.004-0.009** 0.004*** 0.005-0.017** 0.004 0 0 0 [0.004] [0.005] [0.001] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] WC2 0.018*** 0.007 0.013*** 0.007-0.017** 0.005 0 0 0 [0.004] [0.005] [0.002] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] D1-0.016*** 0.007*** -0.025*** -0.001 0-0.001 0 0-0.001 [0.004] [0.003] [0.004] [0.009] [0.006] [0.005] [0.023] [0.017] [0.016] D2-0.001 0-0.002 0 0 0 0 0 0 [0.004] [0.003] [0.002] [0.009] [0.006] [0.005] [0.023] [0.017] [0.016] WD1-0.016*** -0.006-0.025*** 0.001-0.017** 0 0 0-0.001 [0.004] [0.004] [0.004] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] WD2 0-0.012*** 0.001 0.005-0.017** 0.003 0 0 0 [0.004] [0.005] [0.002] [0.008] [0.007] [0.005] [0.023] [0.017] [0.016] E1-0.013*** 0.003-0.019*** -0.013 0.001-0.013** -0.003-0.001-0.004 [0.004] [0.003] [0.003] [0.010] [0.006] [0.006] [0.024] [0.017] [0.016] E2-0.010** -0.025*** -0.018*** -0.006-0.021*** -0.004 0.028-0.001 0.019 [0.004] [0.006] [0.004] [0.011] [0.008] [0.007] [0.024] [0.019] [0.017] E3 0.037*** -0.004 0.017*** 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] WE1-0.013*** -0.009** -0.020*** -0.015-0.018** -0.016** -0.003-0.001-0.004 [0.004] [0.004] [0.003] [0.010] [0.007] [0.006] [0.024] [0.017] [0.016] WE2-0.009* -0.025*** -0.018*** -0.008-0.026*** -0.005 0.028-0.001 0.019 [0.004] [0.006] [0.004] [0.011] [0.009] [0.007] [0.024] [0.019] [0.017] WE3 0.038*** -0.004 0.018*** 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] F1 0.028*** 0.052*** 0 0.018** 0.039*** 0.002 0.009 0.013 0.001 [0.003] [0.004] [0.002] [0.008] [0.007] [0.005] [0.024] [0.016] [0.016] F2 0.093*** 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] F3 0.411*** 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] WF1 0.033*** 0.047*** 0.001 0.031*** 0.034*** 0.007 0.009 0.013 0.001 [0.003] [0.003] [0.001] [0.007] [0.007] [0.005] [0.024] [0.016] [0.016] WF2 0.100*** 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] WF3 0.416*** 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] G1 0.009*** 0.019*** -0.013*** 0.003 0.017*** 0.002-0.001 0.002-0.003 [0.003] [0.003] [0.003] [0.009] [0.006] [0.006] [0.024] [0.017] [0.016] G2 0.042*** 0.013*** -0.002 0.032*** 0.014* 0.017*** 0.020 0.004 0.013 [0.003] [0.004] [0.002] [0.009] [0.007] [0.006] [0.024] [0.019] [0.017] G3 0.172*** 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] WG1 0.012*** 0.009*** -0.012*** 0.010 0.005 0.003-0.001 0.002-0.003 [0.003] [0.003] [0.003] [0.008] [0.006] [0.006] [0.024] [0.017] [0.016] WG2 0.046*** 0.015*** -0.001 0.036*** 0.013* 0.019*** 0.020 0.004 0.013 [0.003] [0.003] [0.002] [0.009] [0.007] [0.006] [0.024] [0.019] [0.017] WG3 0.174*** 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

Table D.1: < continued > Manufacturing and Service Workers H1 0.055*** 0.063*** 0.009*** 0.027*** 0.040*** 0.006-0.009-0.008-0.022 [0.004] [0.006] [0.002] [0.008] [0.007] [0.005] [0.023] [0.016] [0.016] H2 0.114*** 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] H3 0.349*** 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] WH1 0.066*** 0.060*** 0.013*** 0.042*** 0.037*** 0.012** -0.009-0.008-0.022 [0.005] [0.005] [0.003] [0.008] [0.007] [0.005] [0.023] [0.016] [0.016] WH2 0.124*** 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] WH3 0.354*** 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] I1 0.020*** 0.021*** -0.009*** 0.007 0.010* -0.009* -0.009-0.006-0.018 [0.005] [0.004] [0.002] [0.009] [0.006] [0.005] [0.023] [0.017] [0.016] I2 0.037*** 0.005-0.009*** 0.022** -0.003 0.001 0.022-0.003 0.010 [0.006] [0.004] [0.003] [0.009] [0.007] [0.006] [0.024] [0.018] [0.016] I3 0.106*** 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] WI1 0.026*** 0.014*** -0.008*** 0.013-0.001-0.008-0.009-0.006-0.018 [0.006] [0.004] [0.003] [0.008] [0.006] [0.005] [0.023] [0.017] [0.016] WI2 0.042*** 0.007-0.007** 0.026*** -0.004 0.001 0.022-0.003 0.010 [0.007] [0.004] [0.003] [0.008] [0.007] [0.006] [0.024] [0.018] [0.016] WI3 0.107*** 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 -0.002-0.003 0-0.007-0.008-0.004-0.016-0.024-0.018 [0.005] [0.005] [0.004] [0.011] [0.010] [0.009] [0.035] [0.030] [0.028] Binary outcome -0.001-0.003-0.001-0.009-0.012-0.008-0.017-0.029-0.023 [0.005] [0.005] [0.004] [0.012] [0.011] [0.010] [0.036] [0.031] [0.029] Heterogeneity 1-0.001-0.001-0.001 0-0.005-0.003 0.011 0.003 0.002 [0.005] [0.006] [0.004] [0.012] [0.011] [0.010] [0.036] [0.030] [0.028] Heterogeneity 2-0.001-0.001-0.001 0.001-0.004-0.002 0.014 0.006 0.005 [0.005] [0.006] [0.004] [0.012] [0.011] [0.010] [0.037] [0.031] [0.028] 10% treated 0.001-0.004-0.003-0.006-0.010-0.008 [0.009] [0.007] [0.007] [0.028] [0.023] [0.021] 90% treated -0.013-0.024* -0.013-0.017-0.035-0.025 [0.014] [0.014] [0.012] [0.043] [0.037] [0.033] Population p-score 0.002 0.001-0.007-0.004 0.001 0.003 [0.006] [0.004] [0.012] [0.010] [0.032] [0.030] Correct specified 0.003 0.001 0.002 0.009 0.003 0.005 0.027 0.011 0.009 model [0.005] [0.006] [0.005] [0.011] [0.011] [0.010] [0.034] [0.032] [0.030] Disc. out. x 0.002 0.001 0.001 0.003 0.005 0.002 0.005 0.012 0.008 Het. 1 [0.005] [0.006] [0.004] [0.013] [0.010] [0.009] [0.039] [0.030] [0.027] Disc. out. x 0.002 0.001 0.001 0.001 0.003 0.001-0.001 0.007 0.004 Het. 2 [0.005] [0.006] [0.004] [0.013] [0.011] [0.010] [0.041] [0.030] [0.028] Disc. out. x Pop. 0 0 0.001-0.001-0.002-0.004 p-score [0.006] [0.004] [0.011] [0.010] [0.032] [0.030] Disc. out. x Corr. -0.004-0.002-0.001-0.006-0.002-0.004-0.022-0.008-0.007 spec. model [0.004] [0.005] [0.004] [0.011] [0.010] [0.009] [0.035] [0.032] [0.030] Disc. out. x 10% 0.002 0.004 0.002 0.010 0.011 0.009 treated [0.009] [0.007] [0.006] [0.027] [0.020] [0.019] Disc. out. x 90% 0.007 0.013 0.005 0.016 0.034 0.021 treated [0.016] [0.013] [0.012] [0.050] [0.038] [0.035] Bin. out. x Het. 1 0.001 0.001 0.001 0.010 0.012 0.008 0.025 0.031 0.024 [0.006] [0.006] [0.004] [0.014] [0.011] [0.010] [0.042] [0.032] [0.029] Bin. out. x Het. 2 0.002 0.001 0.001 0.008 0.010 0.006 0.020 0.026 0.021 [0.006] [0.006] [0.004] [0.014] [0.011] [0.010] [0.043] [0.032] [0.030] Bin. out. x Pop. 0.001 0.001 0.003 0.001-0.001-0.006 p-score [0.006] [0.004] [0.013] [0.012] [0.035] [0.032] Bin. out. x Corr. -0.003-0.001-0.001-0.006-0.002-0.003-0.023-0.009-0.008 spec. model [0.004] [0.005] [0.004] [0.012] [0.011] [0.010] [0.038] [0.034] [0.032] Bin. out. x 10% 0.001 0.003 0.001 0.009 0.013 0.013 treated [0.009] [0.007] [0.007] [0.028] [0.021] [0.019] Bin. out. x 90% 0.017 0.022 0.013 0.025 0.045 0.033 treated [0.017] [0.014] [0.013] [0.054] [0.041] [0.038] < table continues on next page > 9

Table D.1: < continued > Manufacturing and Service Workers Het. 1 x Pop. 0.001 0 0.012 0.008 0.007 0.006 p-score [0.006] [0.004] [0.012] [0.010] [0.032] [0.029] Het. 1 x Corr. 0.001 0.002 0.001-0.001 0-0.001 0 0 0.001 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 0.002 0.005 0.004 0.021 0.024 0.021 [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. 0.001 0 0.011 0.008 0.005 0.004 p-score [0.006] [0.004] [0.012] [0.011] [0.032] [0.030] Het. 2 x Corr. 0.001 0.001 0.001-0.001 0-0.001-0.001 0 0 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 0.003 0.005 0.004 0.023 0.026 0.022 [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% 0.003 0.002-0.001 0.004 treated [0.007] [0.007] [0.021] [0.019] Pop. p-score x 90% 0.021 0.014 0.007 0.009 treated [0.015] [0.013] [0.041] [0.038] Corr. spec. model x -0.003-0.002 0-0.002-0.001-0.002 10% treated [0.008] [0.007] [0.007] [0.022] [0.021] [0.019] Corr. spec. model x -0.003-0.002-0.002-0.004-0.002 0.001 90% 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 2 0.966 0.894 0.886 0.521 0.453 0.432 0.353 0.352 0.354 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

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** -0.097*** 0.037*** 0.018* -0.092*** 0.018*** 0.001-0.037** 0.003 [0.007] [0.012] [0.009] [0.010] [0.014] [0.007] [0.027] [0.015] [0.016] B1-0.023*** -0.110*** -0.065*** 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] B2-0.038*** -0.112*** -0.069*** 0.163*** 0.036 0.118*** 0.576*** 0.374*** 0.461*** [0.008] [0.012] [0.008] [0.047] [0.032] [0.034] [0.146] [0.092] [0.099] WB1-0.023*** -0.110*** -0.065*** 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] WB2-0.038*** -0.112*** -0.069*** 0.163*** 0.036 0.118*** 0.576*** 0.374*** 0.461*** [0.008] [0.012] [0.008] [0.047] [0.032] [0.034] [0.146] [0.092] [0.099] C1-0.004 0.003-0.011* 0 0 0 0 0 0 [0.007] [0.013] [0.006] [0.010] [0.016] [0.007] [0.027] [0.015] [0.016] C2-0.007 0.014-0.036*** 0.002 0 0.003 0 0 0 [0.007] [0.013] [0.005] [0.010] [0.016] [0.007] [0.027] [0.015] [0.016] WC1 0.010-0.096*** 0.024*** 0.018* -0.092*** 0.018*** 0.001-0.037** 0.003 [0.007] [0.012] [0.008] [0.010] [0.014] [0.007] [0.027] [0.015] [0.016] WC2 0.006-0.089*** -0.006 0.020** -0.091*** 0.021*** 0.001-0.037** 0.003 [0.007] [0.012] [0.007] [0.010] [0.014] [0.007] [0.027] [0.015] [0.016] D1-0.047*** 0.017-0.113*** -0.011 0.001-0.020*** -0.001 0-0.004 [0.008] [0.014] [0.007] [0.010] [0.015] [0.006] [0.027] [0.015] [0.016] D2-0.002 0-0.004-0.001 0 0 0 0 0 [0.007] [0.013] [0.007] [0.010] [0.016] [0.007] [0.027] [0.015] [0.016] WD1-0.045*** -0.095*** -0.112*** -0.023** -0.102*** -0.029*** 0-0.037** -0.001 [0.009] [0.012] [0.008] [0.011] [0.015] [0.006] [0.027] [0.015] [0.016] WD2 0.006-0.099*** 0.021*** 0.017* -0.092*** 0.018*** 0.001-0.037** 0.003 [0.007] [0.012] [0.008] [0.010] [0.014] [0.007] [0.027] [0.015] [0.016] E1-0.039*** 0.004-0.082*** -0.039*** 0-0.048*** -0.016-0.003-0.023 [0.007] [0.013] [0.006] [0.013] [0.016] [0.008] [0.027] [0.015] [0.017] E2-0.039*** -0.123*** -0.098*** -0.019-0.097*** -0.049*** 0.073** -0.040** 0.020 [0.009] [0.012] [0.008] [0.015] [0.013] [0.009] [0.032] [0.020] [0.018] E3 0.032-0.106*** -0.059*** 0.132*** -0.013 0.053** 0.489*** 0.312*** 0.363*** [0.023] [0.017] [0.014] [0.036] [0.027] [0.021] [0.089] [0.059] [0.055] WE1-0.046*** -0.101*** -0.096*** -0.039*** -0.106*** -0.054*** -0.018-0.043*** -0.026 [0.008] [0.012] [0.007] [0.013] [0.015] [0.009] [0.026] [0.016] [0.017] WE2-0.037*** -0.132*** -0.098*** -0.014-0.121*** -0.050*** 0.075** -0.040** 0.021 [0.010] [0.012] [0.008] [0.015] [0.015] [0.009] [0.032] [0.020] [0.018] WE3 0.040-0.101*** -0.054*** 0.140*** -0.007 0.059*** 0.490*** 0.313*** 0.364*** [0.024] [0.017] [0.014] [0.036] [0.027] [0.020] [0.089] [0.059] [0.055] F1 0.053*** 0.111*** -0.023*** 0.030*** 0.080*** 0 0.002 0.033** -0.007 [0.006] [0.017] [0.006] [0.009] [0.022] [0.006] [0.027] [0.017] [0.016] F2 0.160*** 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] F3 0.540*** 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] WF1 0.113*** 0.063*** -0.002 0.079*** 0.025* 0.032*** 0.005 0.003-0.006 [0.006] [0.011] [0.006] [0.014] [0.014] [0.008] [0.027] [0.015] [0.016] WF2 0.209*** 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] WF3 0.571*** 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] G1 0.029*** 0.055*** -0.043*** 0.017* 0.045*** -0.011-0.002 0.013-0.017 [0.006] [0.014] [0.005] [0.009] [0.017] [0.007] [0.028] [0.015] [0.017] G2 0.091*** -0.010-0.026*** 0.077*** -0.012 0.008 0.085*** -0.012 0.022 [0.008] [0.010] [0.007] [0.011] [0.012] [0.007] [0.031] [0.020] [0.019] G3 0.364*** 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] WG1 0.077*** -0.005-0.035*** 0.043*** -0.033*** 0.001-0.002-0.023-0.017 [0.009] [0.010] [0.006] [0.010] [0.013] [0.007] [0.028] [0.015] [0.017] WG2 0.125*** 0.002-0.013* 0.100*** -0.019 0.021*** 0.086*** -0.012 0.023 [0.010] [0.011] [0.008] [0.011] [0.013] [0.007] [0.031] [0.020] [0.019] WG3 0.393*** 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

Table D.2: < continued > Technicians H1 0.074*** 0.098*** -0.019*** 0.040*** 0.074*** 0.004 0.023 0.042*** 0.001 [0.011] [0.017] [0.007] [0.011] [0.021] [0.007] [0.027] [0.016] [0.017] H2 0.160*** 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] H3 0.446*** 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] WH1 0.159*** 0.073*** 0.014 0.091*** 0.023 0.037*** 0.029 0.012 0.004 [0.019] [0.014] [0.012] [0.016] [0.015] [0.009] [0.026] [0.015] [0.016] WH2 0.215*** 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] WH3 0.473*** 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] I1 0.022*** 0.027** -0.060*** 0.007 0.022-0.028*** 0.005 0.016-0.018 [0.007] [0.014] [0.005] [0.010] [0.017] [0.007] [0.028] [0.015] [0.017] I2 0.048*** -0.059*** -0.066*** 0.044*** -0.055*** -0.027*** 0.067** -0.052*** -0.009 [0.008] [0.010] [0.007] [0.010] [0.012] [0.007] [0.028] [0.019] [0.018] I3 0.172*** 0.012-0.006 0.170*** 0.010 0.035*** 0.278*** 0.114*** 0.137*** [0.014] [0.016] [0.011] [0.013] [0.015] [0.010] [0.028] [0.020] [0.018] WI1 0.055*** -0.035*** -0.056*** 0.026** -0.059*** -0.021*** 0.006-0.020-0.019 [0.012] [0.011] [0.007] [0.010] [0.013] [0.007] [0.028] [0.015] [0.017] WI2 0.067*** -0.057*** -0.061*** 0.061*** -0.065*** -0.019*** 0.068** -0.051*** -0.008 [0.010] [0.011] [0.007] [0.010] [0.013] [0.007] [0.028] [0.019] [0.018] WI3 0.185*** 0.020 0.001 0.181*** 0.019 0.044*** 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 -0.014-0.012-0.008-0.034** -0.022-0.012-0.142*** -0.086*** -0.067** [0.011] [0.010] [0.008] [0.017] [0.015] [0.012] [0.044] [0.033] [0.033] Binary outcome -0.016-0.014-0.010-0.037** -0.021-0.013-0.150*** -0.085*** -0.067** [0.011] [0.010] [0.008] [0.017] [0.015] [0.012] [0.044] [0.032] [0.032] Heterogeneity 1 0.020 0.010 0.012 0.069*** 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 2 0.019 0.009 0.011 0.064*** 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 -0.034** -0.024** -0.019* -0.111*** -0.051* -0.057** [0.015] [0.012] [0.010] [0.039] [0.028] [0.027] 90% treated -0.011-0.027 0.006-0.058-0.057 0.001 [0.022] [0.020] [0.016] [0.054] [0.039] [0.039] Population p-score 0.001-0.004-0.006-0.008-0.021-0.013 [0.011] [0.009] [0.015] [0.012] [0.033] [0.033] Correct specified 0 0.003 0.002-0.005 0.004 0-0.030-0.008-0.005 model [0.012] [0.012] [0.010] [0.016] [0.016] [0.013] [0.041] [0.034] [0.033] Disc. out. x -0.017-0.008-0.010-0.061*** -0.044*** -0.050*** -0.175*** -0.125*** -0.136*** Het. 1 [0.013] [0.010] [0.008] [0.019] [0.015] [0.013] [0.049] [0.032] [0.033] Disc. out. x -0.013-0.005-0.008-0.050*** -0.034** -0.040*** -0.140*** -0.095*** -0.107*** Het. 2 [0.013] [0.010] [0.008] [0.018] [0.015] [0.012] [0.049] [0.032] [0.032] Disc. out. x Pop. 0 0.004-0.002 0.003 0.018 0.011 p-score [0.010] [0.007] [0.015] [0.013] [0.034] [0.035] Disc. out. x Corr. -0.001-0.005-0.002 0.007-0.005 0.002 0.029 0.008 0.006 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* 0.014 0.012 0.124*** 0.047* 0.056** treated [0.015] [0.011] [0.009] [0.040] [0.027] [0.025] Disc. out. x 90% -0.010 0.005-0.025* 0.019 0.041-0.026 treated [0.022] [0.017] [0.015] [0.060] [0.038] [0.040] Bin. out. x Het. 1-0.019-0.009-0.012-0.062*** -0.045*** -0.050*** -0.172*** -0.123*** -0.134*** [0.012] [0.010] [0.008] [0.019] [0.015] [0.013] [0.049] [0.032] [0.033] Bin. out. x Het. 2-0.017-0.008-0.010-0.056*** -0.041*** -0.045*** -0.157*** -0.111*** -0.123*** [0.012] [0.010] [0.008] [0.018] [0.015] [0.012] [0.048] [0.031] [0.031] Bin. out. x Pop. 0.001 0.006-0.002 0.003 0.017 0.011 p-score [0.010] [0.007] [0.015] [0.013] [0.033] [0.035] Bin. out. x Corr. -0.002-0.004-0.002 0.006-0.005 0.002 0.028 0.007 0.006 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* 0.013 0.012 0.122*** 0.047* 0.055** treated [0.015] [0.011] [0.009] [0.039] [0.027] [0.025] Bin. out. x 90% -0.010 0.002-0.027* 0.015 0.034-0.033 treated [0.021] [0.017] [0.014] [0.060] [0.038] [0.040] < table continues on next page > 12

Table D.2: < continued > Technicians Het. 1 x Pop. 0.001 0.001 0.007 0.006-0.003-0.001 p-score [0.009] [0.007] [0.014] [0.011] [0.029] [0.030] Het. 1 x Corr. 0.003 0.004 0.003-0.001 0.002 0.001-0.008-0.004-0.003 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 -0.008-0.002-0.003-0.013-0.002-0.006 [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. 0 0 0.007 0.006-0.003-0.001 p-score [0.009] [0.007] [0.014] [0.011] [0.029] [0.030] Het. 2 x Corr. 0.002 0.004 0.003-0.001 0.002 0.001-0.005-0.001-0.002 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 -0.009-0.001-0.002-0.015-0.001-0.005 [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% 0.010 0.007 0.013 0.014 treated [0.010] [0.008] [0.024] [0.023] Pop. p-score x 90% 0.022 0.009 0.009 0.001 treated [0.015] [0.013] [0.035] [0.037] Corr. spec. model x 0.003 0.002 0.002 0.010 0.003 0.004 10% treated [0.011] [0.011] [0.009] [0.029] [0.025] [0.023] Corr. spec. model x -0.003 0.001-0.004-0.003-0.002-0.006 90% 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 2 0.925 0.873 0.878 0.620 0.515 0.534 0.395 0.368 0.380 Note: See note of Table D.1. 13

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 -0.000-0.006 0.000-0.001 0.018* 0.001 0.000-0.000-0.000 [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] B1 0.003 0.002 0.001 0.438*** 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] B2 0.004-0.003-0.005 0.331*** 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] WB1 0.003 0.002 0.001 0.438*** 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] WB2 0.004-0.003-0.005 0.331*** 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] C1 0.007 0.010** -0.004-0.000 0.000 0.000 0.000-0.000-0.000 [0.006] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] C2 0.033*** 0.040*** -0.012* -0.003 0.002 0.001 0.000-0.000-0.000 [0.008] [0.007] [0.007] [0.013] [0.011] [0.009] [0.029] [0.023] [0.021] WC1 0.007 0.002-0.004-0.001 0.018* 0.001 0.000-0.000-0.000 [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WC2 0.033*** 0.032*** -0.012* -0.003 0.020** 0.003 0.000-0.000-0.000 [0.008] [0.007] [0.007] [0.013] [0.010] [0.009] [0.029] [0.023] [0.021] D1 0.021*** 0.043*** -0.021*** 0.003 0.005-0.001 0.003 0.002 0.000 [0.007] [0.006] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] D2 0.000 0.001-0.001 0.000 0.000 0.000 0.000-0.000-0.000 [0.005] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] WD1 0.022*** 0.035*** -0.021*** 0.004 0.020* -0.001 0.003 0.002 0.000 [0.006] [0.006] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WD2 0.000-0.006-0.001-0.001 0.018* 0.001 0.000-0.000-0.000 [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] E1 0.010* 0.029*** -0.016*** 0.015 0.016-0.008 0.009-0.000-0.003 [0.006] [0.005] [0.005] [0.010] [0.011] [0.010] [0.028] [0.023] [0.022] E2 0.031*** 0.011* -0.026*** 0.050*** 0.039*** 0.014 0.114*** 0.107*** 0.093*** [0.007] [0.006] [0.006] [0.011] [0.011] [0.010] [0.026] [0.021] [0.020] E3 0.118*** 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] WE1 0.012** 0.024*** -0.018*** 0.021** 0.014-0.005 0.009-0.000-0.003 [0.006] [0.005] [0.005] [0.010] [0.011] [0.009] [0.028] [0.023] [0.022] WE2 0.033*** 0.011* -0.026*** 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] WE3 0.119*** 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] F1-0.002 0.046*** -0.003 0.009 0.036*** 0.000 0.006 0.003-0.000 [0.006] [0.004] [0.005] [0.013] [0.010] [0.009] [0.029] [0.023] [0.021] F2-0.001 0.031*** -0.004-0.011 0.017-0.000-0.013 0.007 0.015 [0.007] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] F3 0.007 0.016*** -0.006-0.008 0.027** 0.004 0.002 0.057*** 0.046** [0.007] [0.006] [0.006] [0.013] [0.012] [0.010] [0.028] [0.022] [0.022] WF1-0.002 0.044*** -0.003 0.005 0.032*** 0.001 0.006 0.003-0.000 [0.006] [0.004] [0.005] [0.014] [0.010] [0.009] [0.029] [0.023] [0.021] WF2-0.002 0.031*** -0.003-0.015 0.016 0.000-0.013 0.007 0.015 [0.007] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] WF3 0.007 0.016*** -0.005-0.008 0.029** 0.006 0.002 0.057*** 0.046** [0.007] [0.006] [0.006] [0.013] [0.012] [0.010] [0.028] [0.022] [0.022] G1 0.010** 0.057*** 0.006-0.025** 0.044*** 0.008-0.008 0.002 0.001 [0.005] [0.005] [0.005] [0.013] [0.009] [0.009] [0.030] [0.023] [0.021] G2 0.035*** 0.055*** 0.018** -0.011 0.044*** 0.021** -0.044 0.007 0.020 [0.008] [0.008] [0.007] [0.012] [0.010] [0.009] [0.032] [0.023] [0.021] G3 0.087*** 0.077*** 0.050*** 0.051*** 0.083*** 0.059*** 0.018 0.079*** 0.084*** [0.021] [0.016] [0.014] [0.014] [0.012] [0.011] [0.032] [0.025] [0.023] WG1 0.013*** 0.054*** 0.006-0.021* 0.042*** 0.010-0.008 0.002 0.001 [0.005] [0.005] [0.005] [0.012] [0.009] [0.009] [0.030] [0.023] [0.021] WG2 0.038*** 0.056*** 0.019** -0.007 0.046*** 0.023*** -0.044 0.007 0.020 [0.009] [0.008] [0.008] [0.012] [0.010] [0.009] [0.032] [0.023] [0.021] WG3 0.088*** 0.077*** 0.051*** 0.052*** 0.084*** 0.060*** 0.018 0.079*** 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

Table D.3: < continued > Manufacturing and Service Workers H1 0.047*** 0.017*** -0.002 0.041*** 0.017 0.007 0.031 0.019 0.021 [0.010] [0.006] [0.006] [0.013] [0.011] [0.010] [0.031] [0.025] [0.023] H2 0.089*** 0.032*** 0.006 0.068*** 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] H3 0.189*** 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] WH1 0.054*** 0.020*** 0.001 0.049*** 0.021* 0.012 0.031 0.019 0.021 [0.012] [0.006] [0.007] [0.014] [0.011] [0.010] [0.031] [0.025] [0.023] WH2 0.093*** 0.035*** 0.008 0.073*** 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] WH3 0.192*** 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] I1 0.004 0.042*** -0.003-0.005 0.025** 0.001-0.009 0.001 0.004 [0.006] [0.004] [0.006] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] I2 0.009 0.023*** -0.004 0.004 0.017* 0.006 0.026 0.022 0.026 [0.007] [0.006] [0.006] [0.013] [0.011] [0.009] [0.030] [0.024] [0.022] I3 0.038*** 0.025** -0.000 0.033** 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] WI1 0.005 0.039*** -0.003-0.006 0.019* 0.002-0.009 0.001 0.004 [0.006] [0.005] [0.006] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WI2 0.010 0.022*** -0.005 0.005 0.017 0.006 0.026 0.022 0.026 [0.008] [0.006] [0.006] [0.013] [0.011] [0.009] [0.030] [0.024] [0.022] WI3 0.039*** 0.025** -0.000 0.034** 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 -0.030*** -0.053*** 0.010-0.041** -0.062*** -0.011-0.035-0.090** -0.081** [0.010] [0.008] [0.008] [0.019] [0.017] [0.016] [0.045] [0.039] [0.037] Binary outcome -0.013-0.059*** -0.003-0.040** -0.068*** -0.021-0.012-0.106*** -0.093** [0.011] [0.008] [0.008] [0.019] [0.018] [0.017] [0.046] [0.041] [0.038] Heterogeneity 1 0.001-0.007-0.002 0.018 0.004 0.012 0.050 0.041 0.042 [0.011] [0.008] [0.008] [0.020] [0.018] [0.016] [0.047] [0.040] [0.037] Heterogeneity 2 0.000-0.008-0.003 0.018 0.005 0.014 0.053 0.043 0.046 [0.011] [0.008] [0.008] [0.020] [0.018] [0.017] [0.048] [0.041] [0.038] 10% treated 0.021-0.016-0.007-0.003-0.022-0.014 [0.017] [0.014] [0.013] [0.039] [0.032] [0.030] 90% treated -0.003-0.025-0.013 0.016-0.064-0.034 [0.023] [0.020] [0.019] [0.054] [0.047] [0.044] Population p-score -0.032*** -0.019*** -0.031* -0.010-0.033-0.017 [0.007] [0.007] [0.019] [0.017] [0.042] [0.039] Correct specified 0.025** -0.012-0.003 0.064*** -0.002 0.015 0.120*** -0.011 0.006 model [0.012] [0.010] [0.011] [0.019] [0.018] [0.017] [0.044] [0.042] [0.039] Disc. out. x 0.012 0.012 0.004 0.003 0.011-0.001-0.004 0.008 0.004 Het. 1 [0.012] [0.008] [0.009] [0.021] [0.017] [0.016] [0.051] [0.039] [0.037] Disc. out. x 0.015 0.014* 0.006 0.006 0.010-0.000-0.013 0.002 0.000 Het. 2 [0.012] [0.008] [0.009] [0.021] [0.017] [0.016] [0.052] [0.040] [0.038] Disc. out. x Pop. 0.016** 0.020*** 0.003-0.003 0.018 0.007 p-score [0.006] [0.007] [0.019] [0.018] [0.042] [0.040] Disc. out. x Corr. -0.025*** 0.013 0.008-0.055*** -0.009-0.020-0.097** -0.000-0.016 spec. model [0.009] [0.009] [0.009] [0.018] [0.017] [0.016] [0.045] [0.042] [0.040] Disc. out. x 10% 0.016 0.035*** -0.020* 0.042 0.047* 0.053** treated [0.015] [0.013] [0.012] [0.036] [0.029] [0.027] Disc. out. x 90% 0.003 0.037* 0.018 0.004 0.056 0.043 treated [0.026] [0.021] [0.020] [0.063] [0.049] [0.046] Bin. out. x Het. 1-0.000 0.009 0.003 0.011 0.021 0.008 0.019 0.030 0.024 [0.013] [0.008] [0.008] [0.022] [0.018] [0.017] [0.054] [0.042] [0.039] Bin. out. x Het. 2 0.001 0.011 0.005 0.009 0.019 0.008 0.018 0.029 0.023 [0.013] [0.008] [0.008] [0.023] [0.019] [0.017] [0.055] [0.042] [0.040] Bin. out. x Pop. 0.025*** 0.025*** 0.011 0.008 0.022 0.006 p-score [0.007] [0.006] [0.020] [0.019] [0.045] [0.042] Bin. out. x Corr. -0.021** 0.025*** 0.015* -0.053*** 0.000-0.008-0.105** -0.001-0.010 spec. model [0.010] [0.009] [0.009] [0.019] [0.018] [0.017] [0.047] [0.045] [0.042] Bin. out. x 10% 0.017 0.030** -0.023* 0.008 0.042 0.058** treated [0.015] [0.013] [0.012] [0.037] [0.030] [0.027] Bin. out. x 90% 0.030 0.041* 0.015-0.010 0.071 0.054 treated [0.028] [0.023] [0.021] [0.067] [0.052] [0.049] < table continues on next page > 15

Table D.3: < continued > Manufacturing and Service Workers Het. 1 x Pop. 0.003-0.001 0.023 0.014 0.013 0.009 p-score [0.006] [0.006] [0.019] [0.017] [0.041] [0.039] Het. 1 x Corr. 0.012 0.013 0.014-0.000 0.007 0.004-0.002 0.005 0.006 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 0.010 0.017 0.017 0.036 0.040 0.033 [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. 0.004 0.002 0.022 0.013 0.008 0.004 p-score [0.006] [0.006] [0.019] [0.017] [0.042] [0.040] Het. 2 x Corr. 0.010 0.012 0.013-0.002 0.006 0.002-0.007 0.000 0.002 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 0.011 0.016 0.015 0.033 0.039 0.030 [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% 0.016 0.016-0.008 0.043 treated [0.012] [0.011] [0.028] [0.026] Pop. p-score x 90% 0.025 0.022 0.020 0.034 treated [0.024] [0.022] [0.052] [0.049] Corr. spec. model x -0.017 0.003 0.017-0.001 0.016-0.014 10% treated [0.012] [0.012] [0.011] [0.029] [0.029] [0.027] Corr. spec. model x -0.010 0.010 0.007-0.016 0.019 0.020 90% treated [0.022] [0.021] [0.019] [0.054] [0.052] [0.048] Constant 0.017* 0.056*** 0.056*** 0.006 0.017 0.006-0.022-0.001-0.026 [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 2 0.514 0.466 0.264 0.344 0.330 0.341 0.347 0.348 0.349 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

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 0-0.006 0-0.001 0.018* 0.001 0 0 0 [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] B1 0.003 0.002 0.001 0.438*** 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] B2 0.004-0.003-0.005 0.331*** 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] WB1 0.003 0.002 0.001 0.438*** 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] WB2 0.004-0.003-0.005 0.331*** 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] C1 0.007 0.010** -0.004 0 0 0 0 0 0 [0.006] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] C2 0.033*** 0.040*** -0.012* -0.003 0.002 0.001 0 0 0 [0.008] [0.007] [0.007] [0.013] [0.011] [0.009] [0.029] [0.023] [0.021] WC1 0.007 0.002-0.004-0.001 0.018* 0.001 0 0 0 [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WC2 0.033*** 0.032*** -0.012* -0.003 0.020** 0.003 0 0 0 [0.008] [0.007] [0.007] [0.013] [0.010] [0.009] [0.029] [0.023] [0.021] D1 0.021*** 0.043*** -0.021*** 0.003 0.005-0.001 0.003 0.002 0 [0.007] [0.006] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] D2 0 0.001-0.001 0 0 0 0 0 0 [0.005] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] WD1 0.022*** 0.035*** -0.021*** 0.004 0.020* -0.001 0.003 0.002 0 [0.006] [0.006] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] WD2 0-0.006-0.001-0.001 0.018* 0.001 0 0 0 [0.005] [0.005] [0.005] [0.012] [0.010] [0.009] [0.029] [0.023] [0.021] E1 0.010* 0.029*** -0.016*** 0.015 0.016-0.008 0.009 0-0.003 [0.006] [0.005] [0.005] [0.010] [0.011] [0.010] [0.028] [0.023] [0.022] E2 0.031*** 0.011* -0.026*** 0.050*** 0.039*** 0.014 0.114*** 0.107*** 0.093*** [0.007] [0.006] [0.006] [0.011] [0.011] [0.010] [0.026] [0.021] [0.020] E3 0.118*** 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] WE1 0.012** 0.024*** -0.018*** 0.021** 0.014-0.005 0.009 0-0.003 [0.006] [0.005] [0.005] [0.010] [0.011] [0.009] [0.028] [0.023] [0.022] WE2 0.033*** 0.011* -0.026*** 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] WE3 0.119*** 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] F1-0.002 0.046*** -0.003 0.009 0.036*** 0 0.006 0.003 0 [0.006] [0.004] [0.005] [0.013] [0.010] [0.009] [0.029] [0.023] [0.021] F2-0.001 0.031*** -0.004-0.011 0.017 0-0.013 0.007 0.015 [0.007] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] F3 0.007 0.016*** -0.006-0.008 0.027** 0.004 0.002 0.057*** 0.046** [0.007] [0.006] [0.006] [0.013] [0.012] [0.010] [0.028] [0.022] [0.022] WF1-0.002 0.044*** -0.003 0.005 0.032*** 0.001 0.006 0.003 0 [0.006] [0.004] [0.005] [0.014] [0.010] [0.009] [0.029] [0.023] [0.021] WF2-0.002 0.031*** -0.003-0.015 0.016 0-0.013 0.007 0.015 [0.007] [0.004] [0.005] [0.012] [0.011] [0.009] [0.029] [0.023] [0.021] WF3 0.007 0.016*** -0.005-0.008 0.029** 0.006 0.002 0.057*** 0.046** [0.007] [0.006] [0.006] [0.013] [0.012] [0.010] [0.028] [0.022] [0.022] G1 0.010** 0.057*** 0.006-0.025** 0.044*** 0.008-0.008 0.002 0.001 [0.005] [0.005] [0.005] [0.013] [0.009] [0.009] [0.030] [0.023] [0.021] G2 0.035*** 0.055*** 0.018** -0.011 0.044*** 0.021** -0.044 0.007 0.020 [0.008] [0.008] [0.007] [0.012] [0.010] [0.009] [0.032] [0.023] [0.021] G3 0.087*** 0.077*** 0.050*** 0.051*** 0.083*** 0.059*** 0.018 0.079*** 0.084*** [0.021] [0.016] [0.014] [0.014] [0.012] [0.011] [0.032] [0.025] [0.023] WG1 0.013*** 0.054*** 0.006-0.021* 0.042*** 0.010-0.008 0.002 0.001 [0.005] [0.005] [0.005] [0.012] [0.009] [0.009] [0.030] [0.023] [0.021] WG2 0.038*** 0.056*** 0.019** -0.007 0.046*** 0.023*** -0.044 0.007 0.020 [0.009] [0.008] [0.008] [0.012] [0.010] [0.009] [0.032] [0.023] [0.021] WG3 0.088*** 0.077*** 0.051*** 0.052*** 0.084*** 0.060*** 0.018 0.079*** 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