GROWING APART: THE CHANGING FIRM-SIZE WAGE PREMIUM AND ITS INEQUALITY CONSEQUENCES ONLINE APPENDIX

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1 GROWING APART: THE CHANGING FIRM-SIZE WAGE PREMIUM AND ITS INEQUALITY CONSEQUENCES ONLINE APPENDIX The following document is the online appendix for the paper, Growing Apart: The Changing Firm-Size Wage Premium and Its Inequality Consequences. Contained in this document are some additional descriptive statistics, details on our methodology, and the output for a number of supplementary analyses. Specifically, the document contains the following tables and figures, and are ordered by their reference in the published manuscript: Table A1. Partial Coefficients and Robust Standard Errors Predicting Logged Wage by Percentile using SIPP data Figure A1. Logged Wage Difference from Firms with <25 Employees using SIPP data Description for Creating a Panel using CPS Data Figure A2. Distribution of Workers across Four Firm-Size Categories Figure A3. Proportion of Workers in each Firm-Size Category by Wage Quintile, Table A2. Variable Means by Firm-size for all Variables, CPS Table A3. Correlation Matrix for Selected Variables, CPS Figure A4. Quantile-Specific Treatments and Distributional Consequences (includes some additional explanation for how the RIF approach differs from an OLS approach) Table A4: P-Values for the Differences in Coefficients across Firm-Size and Wage Quantile, Cross- Sectional Analysis Table A5: P-Values for the Differences in Coefficients across Firm-Size and Wage Quantile, Individual- Fixed Effects Analysis Figure A5. Logged Wage Difference from Firms with <100 Employees Over Time 1

2 Table A1. Partial Coefficients and Robust Standard Errors Predicting Logged Wage by Percentile, SIPP th 25th 50th 75th 90th Firm Size (<25 Workers) *** 0.083*** 0.084*** 0.068*** 0.043*** (0.003) (0.002) (0.002) (0.002) (0.002) *** 0.127*** 0.149*** 0.151*** 0.127*** (0.002) (0.002) (0.001) (0.002) (0.002) Human Capital (Less than High School) High School 0.251*** 0.266*** 0.191*** 0.110*** 0.055*** (0.003) (0.002) (0.002) (0.002) (0.002) Some College 0.369*** 0.427*** 0.386*** 0.285*** 0.170*** (0.003) (0.002) (0.002) (0.002) (0.002) College 0.467*** 0.597*** 0.694*** 0.739*** 0.678*** (0.003) (0.003) (0.002) (0.002) (0.003) Advanced Degree 0.479*** 0.635*** 0.816*** 1.041*** 1.237*** (0.004) (0.003) (0.002) (0.003) (0.005) Age 0.016*** 0.025*** 0.042*** 0.057*** 0.057*** (0.001) (0.000) (0.000) (0.000) (0.001) Age Squared *** *** *** *** *** (0.000) (0.000) (0.000) (0.000) (0.000) Tenure 0.027*** 0.031*** 0.028*** 0.019*** 0.012*** (0.000) (0.000) (0.000) (0.000) (0.000) Tenure Squared *** *** *** *** *** (0.000) (0.000) (0.000) (0.000) (0.000) Employment Union 0.077*** 0.121*** 0.161*** 0.091*** *** (0.002) (0.002) (0.002) (0.002) (0.003) Part-Time *** *** *** 0.006*** 0.106*** (0.003) (0.002) (0.002) (0.002) (0.002) N R-Square Note: The models also include year fixed-effects, industry fixed-effects, racial status, the interaction terms between nine Census regions and metropolitan status, and the interaction terms between gender, marital, and parental status. Estimates are available upon request. 2

3 FIGURE A1. LOGGED WAGE DIFFERENCE FROM FIRMS WITH <25 EMPLOYEES, SIPP,

4 DESCRIPTION FOR CREATING A PANEL USING CPS DATA In the Current Population Survey, households are interviewed for four consecutive months, are not in the sample for the next eight months, and then are interviewed for four more consecutive months. We match individuals in the consecutive March files and create a two-year, panel dataset. The panel dataset includes repeated observations for the same individual, which allows us to evaluate whether unobserved skill differences account for the firm size wage premium. We match respondents using the combination of state, household identifier, household number (which changes when a new family moves into the sampled housing unit), individual line number, gender, and racial identification. The matched observations are then verified by the age difference across time. When the change in age is less than -1 or larger than 3, we drop both observations from the panel, following Madrian and Lefgren s recommendation (1999). Because the primary sampling unit in the CPS is the household, we omit respondents who moved away from their original household. We also exclude respondents who changed their gender or racial identification. The matching rates vary from around 43 percent to 70 percent across different years. To address potential selection bias, we estimate a series of year-specific logistic regressions that include race, gender, age, employment, education, marital status, children, and state to predict the likelihood that the respondent would be identified in the subsequent survey. We then divide the sampling weights with the predicted probabilities of entering the panel to moderate potential selection bias. This procedure weights observations that are less likely to be matched to make the matched sample representative of the population. Some consecutive years cannot be matched due to occasional redesigns of the CPS (see Madrian and Lefgren 1999 for a technical discussion; Ziliak, Hardy, and Bollinger 2011 for similar matching results). 4

5 FIGURE A2: DISTRIBUTION OF WORKERS ACROSS THE FOUR FIRM-SIZE CATEGORIES 5

6 FIGURE A3: PROPORTION OF WORKERS IN EACH FIRM-SIZE CATEGORY BY WAGE QUINTILE,

7 TABLE A2: VARIABLE MEANS BY FIRM-SIZE FOR ALL VARIABLES, CPS Firm Size <100 Workers Logged Wage (S.D.) (0.676) (0.644) (0.648) (0.677) (0.682) Human Capital (Less than High School) Total High School Some College College Advanced Degree Age (S.D.) (10.829) (10.684) (10.599) (10.667) (10.733) Employment Union Part-Time Race & Ethnicity (White) Black Hispanic Asian Other Demographic (Men/Married/0Kid) Men/Married/1Kid Men/Married/2Kids Men/Married/3+Kids Men/Single/0Kid Men/Single/1Kid Men/Single/2Kids Men/Single/3+Kids Men/Other/0Kid Men/Other/1Kid Men/Other/2Kids Men/Other/3+Kids Women/Married/0Kid Women/Married/1Kid Women/Married/2Kids Women/Married/3+Kids Women/Single/0Kid Women/Single/1Kid

8 Women/Single/2Kids Women/Single/3+Kids Women/Other/0Kid Women/Other/1Kid Women/Other/2Kids Women/Other/3+Kids Industry (Agriculture) Mining Construction Manufacturing Transportation Utilities Wholesale Retail Finance and Real Estate Business Service Personal Service Entertainment Health Professional Service Location Non-Metropolitan (New England) Middle Atlantic East-North-Central West-North-Central South Atlantic East-South-Central West-South-Central Mountain Pacific Metropolitan New England Middle Atlantic East-North-Central West-North-Central South Atlantic East-South-Central West-South-Central Mountain Pacific

9 TABLE A3. CORRELATION MATRIX FOR SELECTED VARIABLES, CPS Variables Hourly Wage (log) 1 2 Firm size: < Firm size: Firm size: Firm size: Education: < High School Education: High School Education: Some College Education: College Education: Advanced Age Union Part Time Agriculture Mining Construction Manufacturing Transportation Utilities Wholesale Retail FIRE Business Services Personal Services Entertainment Health Professional Services Variables Mining 1 16 Construction Manufacturing Transportation Utilities Wholesale Retail FIRE Business Services Personal Services Entertainment Health Professional Services

10 FIGURE A4. QUANTILE-SPECIFIC TREATMENTS AND DISTRIBUTIONAL CONSEQUENCES Figure A4 presents three hypothetical scenarios to contrast the OLS estimate with the RIF regression approach. β80, β50, and β20, respectively, denote the marginal effects of a certain treatment on the 80th, 50th, and 20th percentiles of the unconditional distribution. In Scenario A, the treatment has a homogeneous effect of 1 across the distribution (β80 = β50 = β20), which increases the mean from 0 to 1 without changing the level of dispersion. In this case, the OLS and the RIF regressions will both yield the identical estimate of 1. In Scenario B, the effect of treatment is larger at the higher end than the lower end of the distribution, which leads to an increase in overall dispersion. In this case, the OLS model is unable to distinguish the difference and would still yield a coefficient of 1. The RIF regression, in contrast, would show a coefficient of 1.6 at the 80th percentile and a coefficient of 0.4 at the 20th percentile. In Scenario C, the effect of treatment is similar to that of a minimum wage increase. It is largest at the bottom but attenuates all the way up. In this case, the OLS regression again would show a coefficient of 1, while the RIF regression would yield an estimate of 0.4 at the 80th and 1.6 at the 20th percentile. 10

11 TABLE A4. P-VALUES FOR THE DIFFERENCES IN COEFFICIENTS ACROSS FIRM-SIZE AND WAGE QUANTILE, CROSS-SECTIONAL ANALYSIS Coefficients Firm size , 10th - 2 Firm size , 25th Firm size , 50th Firm size , 75th Firm size , 90th Firm size , 10th Firm size , 25th Firm size , 50th Firm size , 75th Firm size , 90th Firm size 1,000+, 10th Firm size 1,000+, 25th Firm size 1,000+, 50th Firm size 1,000+, 75th Firm size 1,000+, 90th

12 TABLE A5. P-VALUES FOR THE DIFFERENCES IN COEFFICIENTS ACROSS FIRM-SIZE AND WAGE QUANTILE, INDIVIDUAL-FIXED EFFECTS ANALYSIS Coefficients Firm size , 10th - 2 Firm size , 25th Firm size , 50th Firm size , 75th Firm size , 90th Firm size , 10th Firm size , 25th Firm size , 50th Firm size , 75th Firm size , 90th Firm size 1,000+, 10th Firm size 1,000+, 25th Firm size 1,000+, 50th Firm size 1,000+, 75th Firm size 1,000+, 90th

13 FIGURE A5. LOGGED WAGE DIFFERENCE FROM FIRMS WITH <100 EMPLOYEES OVER TIME 13

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