Labor Demand and Unequal Payments: Does Wage Dispersion Matter? Using German Employer-Employee Data to Analyze the Influence of Intra-Firm Wage Inequality on Labor Demand
-
Arnd Koelling
Abstract
A theoretical analysis examines the relationship between intra-firm wage dispersion and employment at establishments. The analysis relies on the absence of a theoretical consensus regarding the influence of wage dispersion on labor demand. To prove the theoretical considerations, regressions were conducted on German linked employer-employee data from the Institute for Employment Research (LIAB) for 1996 through 2008. More specifically, fractional probit models for the panel data and a fixed effects regression with a log-odds transformation of the dependent variable were used to estimate the share equations of a labor demand model, including different measures of wage dispersion. The results illustrate a negative influence of the residual wage inequality that takes into account the composition of the workforce in the establishment. In addition, an increasing wage dispersion at the lower end of the wage distribution decreases the labor demand of the establishment; however, this leads to the estimates of the overall wage dispersion becoming insignificant.
Acknowledgments
A data appendix with additional results and copies of the computer programs used to generate the results presented in the paper are available from the author. This study used the linked employer-employee panel data from the Institute for Employment Research LIAB waves of 1996 through 2008. Data access was provided via on-site use at the Research Data Centre (FDZ) of the German Federal Employment Agency (BA) at the Institute for Employment Research (IAB) and/or remote data access.
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Appendix
Variable description (establishments with more than 20 employees).
| Variable | Obs. | Mean. | St. Dev. | Min. | Max. |
|---|---|---|---|---|---|
| Share of labor costs | 53900 | 0.272 | 0.219 | 0.000 | 0.999 |
| Log. turnover | 52551 | 16.164 | 1.652 | 8.925 | 23.947 |
| Share of part-time workers | 82218 | 0.173 | 0.224 | 0 | 1 |
| Share of temp. Employed | 82437 | 0.075 | 0.165 | 0 | 1 |
| Share of employed persons subjected to the social insurance scheme | 82959 | 0.911 | 0.153 | 0 | 1 |
| Share of female workers | 82724 | 0.409 | 0.282 | 0 | 1 |
| Share of low skilled workers | 82685 | 0.212 | 0.258 | 0 | 0.999 |
| Est. Covered by a Collective Agreement (dummy, Yes=1) | 82619 | 0.854 | 0.353 | 0 | 1 |
| Share of non-German workers | 80410 | 0.046 | 0.086 | 0 | 1 |
| Dummy for Western Germany | 82960 | 0.617 | 0.486 | 0 | 1 |
Source: LIAB 1996–2008. Note: The model also includes the following dichotomous and auxiliary variables: establishment size (seven dummies), legal form (five), firm profitability (eight), industry (fourty), year (twelve), a dummy for western Germany respective coverage by a collective agreement, the mean of time variant explanatory variables, dummies for the number of observations for an establishment and interaction variables between the means and the dummies. Semi-robust standard errors adjusted for clustering on establishments and years in parentheses. ** and denote significance at the.01 and .05 levels, respectively.
The STATA option „cluster“ is used to calculate the clustered sandwich estimator to obtain a robust variance estimate that adjusts for within-cluster correlation. The STATA code to estimate the fractional panel probit model is provided in Wooldridge (2011).
Columns (a) and (b) use standard error of regression (ser) from censored wage regressions of full time employees (Winter-Ebmer and Zweimüller, 1999), columns (c) and (d) use standard deviation of log. of observed (imputed) wages.
Fractional panel probit estimation of the labor demand model.
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Log. of wages | 0.374** | 0.380** | 0.333** | 0.329** |
| 0.041) | (0.042) | (0.045) | (0.046) | |
| Log. wage dispersion | −0.053* | −0.096** | −0.103** | −0.144** |
| 0.027) | (0.033) | (0.024) | (0.029) | |
| Log. of skewness of wage dispersion | −0.004* | −0.006** | ||
| 0.002) | 0.002) | |||
| Log. average 12-month Euribor | 3.641** | 3.643** | 3.596** | 3.604** |
| 0.128) | (0.129) | (0.129) | (0.130) | |
| Log. turnover | −0.164** | −0.165** | −0.165** | −0.165** |
| 0.008) | (0.008) | (0.008) | (0.008) | |
| Share of part-time workers | 0.043 | 0.043 | 0.040 | 0.038 |
| 0.038) | (0.038) | (0.038) | (0.038) | |
| Share of temp. Employed | 0.101* | 0.110* | 0.113* | 0.110* |
| 0.049) | (0.049) | (0.048) | (0.048) | |
| Share of employed persons | 0.059 | 0.031 | 0.027 | 0.026 |
| subjected to the social insurance scheme | (0.070) | (0.069) | (0.070) | (0.071) |
| Share of female workers | 0.005 | 0.011 | 0.008 | 0.015 |
| 0.039) | (0.038) | (0.038) | (0.038) | |
| Share of low skilled workers | 0.039* | 0.041* | 0.040* | 0.041* |
| 0.018) | (0.018) | ](0.018) | (0.018) | |
| Share of non-German workers | 0.314* | 0.293* | 0.293* | 0.295* |
| 0.134) | (0.117) | (0.117) | (0.118) | |
| Constant | −3.260** | −3.151** | −2.998** | −3.001** |
| 0.266) | (0.267) | (0.266) | (0.267) | |
| Log. Pseudolikelihood | −18,785 | −18,747 | −18,750 | −18,744 |
| Wald-Test χ2 (df.) | 9,350** | 9,462** | 9,378** | 9,416** |
| 278) | (292) | (278) | (292) | |
| Obs. | 39,009 | 38,922 | 38,922 | 38,922 |
| (Establ.) | (12,967) | (12,921) | (12,921) | (12,921) |
Source: LIAB 1996–2008. Note: The model also includes the following dichotomous and auxiliary variables: establishment size (seven dummies), legal form (five), firm profitability (eight), industry (fourty), year (twelve) and a dummy for western Germany respective coverage by a collective agreement. Semi-robust standard errors adjusted for clustering on establishments and years in parentheses. ** and denote significance at the .01 and .05 levels, respectively.
Columns (a) and (b) use standard error of regression (ser) from censored wage regressions of full time employees (Winter-Ebmer and Zweimüller, 1999), columns (c) and (d) use standard deviation of log. of observed (imputed) wages.
Fixed effects estimation of the labor demand model /logit transformation of the dependent variable.
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Log. of wages | 0.570** | 0.531** | 0.456** | 0.455** |
| 0.118) | (0.075) | (0.083) | (0.083) | |
| Log. wage dispersion | −0.113* | −0.141** | −0.198** | −0.227** |
| 0.052) | (0.044) | (0.040) | (0.047) | |
| Log. of skewness of wage dispersion | −0.001 | −0.004 | ||
| 0.002) | 0.002) | |||
| Log. turnover | −0.249** | −0.248** | −0.248** | −0.248** |
| 0.008) | (0.008) | (0.008) | (0.008) | |
| Share of part-time workers | 0.079 | 0.073 | 0.075 | 0.076 |
| 0.050) | (0.049) | (0.049) | (0.049) | |
| Share of temp. Employed | 0.291** | 0.307** | 0.304** | 0.304** |
| 0.064) | (0.060) | (0.060) | (0.060) | |
| Share of employed persons subjected to the social insurance scheme | −0.091 | −0.101 | −0.104 | −0.103 |
| 0.101) | (0.093) | (0.093) | (0.093) | |
| Share of female workers | 0.028 | 0.029 | 0.028 | 0.029 |
| 0.052) | (0.050) | (0.050) | (0.050) | |
| Share of low skilled workers | 0.031 | 0.036 | 0.036 | 0.036 |
| 0.024) | (0.023) | (0.023) | (0.023) | |
| Share of non-German workers | 0.686** | 0.157 | 0.151 | 0.151 |
| 0.239) | (0.169) | (0.168) | (0.168) | |
| Adj R-squared | 0.8881 | 0.8980 | 0.8982 | 0.8982 |
| F-test | 216.25** | 238.18** | 245.93** | 245.53** |
| 84; 25,958) | (85; 25,916) | (84; 25,917) | (85; 25,916) | |
| Obs. (Establ.) | 39,009 | 38,922 | 38,922 | 38,922 |
| 12,967) | (12,921) | (12,921) | (12,921) |
Source: LIAB 1996–2008. Note: The model also includes the following dichotomous and auxiliary variables: establishment size (seven dummies), legal form (five), firm profitability (eight), industry (fourty), year (twelve) and a dummy for western Germany respective coverage by a collective agreement. Semi-robust standard errors adjusted for clustering on establishments and years in parentheses. ** and * denote significance at the .01 and .05 levels, respectively.
Columns (a) and (b) use standard error of regression (ser) from censored wage regressions of full time employees (Winter-Ebmer and Zweimüller, 1999), columns (c) and (d) use standard deviation of log. of observed (imputed) wages.
Fractional panel probit estimations with coefficient of variation as measure for wage dispersion.
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Log. of wages | 0.199** | 0.143* | 0.093** | 0.126** |
| 0.067) | (0.072) | (0.013) | (0.018) | |
| Log. wage dispersion | −0.118** | −0.167** | −0.002 | −0.006 |
| 0.027) | (0.033) | (0.005) | (0.007) | |
| Log. of skewness of wage | −0.006** | −0.001 | ||
| dispersion | 0.002) | 0.001) | ||
| Log. average 12-month | 3.436** | 3.383** | 0.061** | 0.080** |
| Euribor | (0.140) | (0.142) | (0.012) | (0.017) |
| Log. turnover | −0.165** | −0.165** | −0.042** | −0.058** |
| 0.008) | (0.008) | (0.002) | (0.003) | |
| Share of part-time workers | 0.040 | 0.039 | 0.019 | 0.026 |
| 0.038) | (0.038) | (0.012) | (0.017) | |
| Share of temp. Employed | 0.112* | 0.109* | 0.020 | 0.028 |
| 0.048) | (0.048) | (0.014) | (0.019) | |
| Share of employed persons | 0.030 | 0.029 | 0.022 | 0.032 |
| subjected to the social insurance scheme | (0.070) | (0.071) | (0.023) | (0.032) |
| Share of female workers | 0.007 | 0.014 | −0.004 | −0.003 |
| 0.038) | (0.038) | (0.012) | (0.017) | |
| Share of low skilled workers | 0.040* | 0.040* | 0.001 | 0.002 |
| 0.018) | (0.018) | (0.006) | (0.008) | |
| Share of non-German | 0.292* | 0.294* | 0.100** | 0.138** |
| workers | (0.117) | (0.118) | (0.037) | (0.051) |
| Dummy for Western | 0.028* | 0.026* | 0.012** | 0.016** |
| Germany | (0.012) | (0.012) | (0.004) | (0.005) |
| Constant | −2.768** | −2.682** | 0.852** | 1.244** |
| 0.276) | (0.279) | (0.140) | (0.194) | |
| Log. Pseudolikelihood | −18,750 | −18,744 | −12,962 | −12,957 |
| Wald-Test χ2 (df.) | 9,365** | 9,407** | 16,544** | 19,801** |
| 278) | (292) | (262) | (275) | |
| Obs. | 38,922 | 38,922 | 26,536 | 26,536 |
| (Establ.) | (12,921) | (12,921) | (8,629) | (8,629) |
Source: LIAB 1996–2008. Note: The model also includes the following dichotomous and auxiliary variables: establishment size (seven dummies), legal form (five), firm profitability (eight), industry (fourty), year (twelve), a dummy for western Germany respective coverage by a collective agreement, the mean of time variant explanatory variables, dummies for the number of observations for an establishment and interaction variables between the means and the dummies. Semi-robust standard errors adjusted for clustering on establishments and years in parentheses. ** and denote significance at the 0.01 and 0.05 levels, respectively.
The STATA option „cluster“ is used to calculate the clustered sandwich estimator to obtain a robust variance estimate that adjusts for within-cluster correlation. The STATA code to estimate the fractional panel probit model is provided in Wooldridge (2011).
Columns (a) and (b) use actual values, columns (c) and (d) contain lagged values of the coefficient of variation.
Fixed effects estimations with coefficient of variation as measure for wage dispersion /logit transformation of the dependent variable.
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Log. of wages | 0.456** | 0.455** | 0.599** | 0.599** |
| 0.083) | (0.083) | (0.119) | (0.121) | |
| Log. wage dispersion | −0.198** | −0.227** | 0.036 | 0.035 |
| 0.040) | (0.047) | (0.025) | (0.030) | |
| Log. of skewness of wage dispersion | −0.004 | 0.000 | ||
| 0.002) | 0.003) | |||
| Log. turnover | −0.248** | −0.248** | −0.230** | −0.230** |
| 0.008) | (0.008) | (0.009) | (0.009) | |
| Share of part-time workers | 0.075 | 0.076 | 0.100 | 0.100 |
| 0.049) | (0.049) | (0.056) | (0.056) | |
| Share of temp. | 0.304** | 0.304** | 0.312** | 0.312** |
| Employed | (0.060) | (0.060) | (0.072) | (0.072) |
| Share of employed persons subjected to the social insurance scheme | −0.104 | −0.103 | −0.228* | −0.228* |
| 0.093) | (0.093) | (0.114) | (0.114) | |
| Share of female workers | 0.028 | 0.029 | −0.013 | −0.013 |
| 0.050) | (0.050) | (0.062) | (0.062) | |
| Share of low skilled workers | 0.036 | 0.036 | 0.004 | 0.004 |
| 0.023) | (0.023) | (0.028) | (0.028) | |
| Share of non-German workers | 0.151 | 0.151 | 0.682* | 0.681* |
| 0.168) | (0.168) | (0.301) | (0.301) | |
| Adj R-squared | 0.8982 | 0.8982 | 0.9022 | 0.9022 |
| F-test | 245.93** | 245.53** | 238.21** | 234.94** |
| 84; 25,917) | (85; 25,916) | (82; 17,825) | (83; 17,824) | |
| Obs. | 38,922 | 38,922 | 26,536 | 26,536 |
| (Establ.) | (12,921) | (12,921) | (8,629) | (8,629) |
Source: LIAB 1996–2008. Note: The model also includes the following dichotomous and auxiliary variables: establishment size (seven dummies), legal form (five), firm profitability (eight), industry (fourty), year (twelve) and a dummy for western Germany respective coverage by a collective agreement. Semi-robust standard errors adjusted for clustering on establishments and years in parentheses. ** and denote significance at the .01 and .05 levels, respectively.
Columns (a) and (b) use actual values, columns (c) and (d) contain lagged values of the coefficient of variation.
Fractional panel probit estimations with intra firm wage relations as measure for wage dispersion.
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Log. of wages | 0.375** | 0.372** | 0.104** | 0.097** |
| 0.039) | (0.039) | (0.011) | (0.010) | |
| Intra firm wage Relation (90th to | −0.024** | −0.013 | 0.000 | 0.014 |
| 10th percentile) | (0.008) | (0.029) | (0.002) | (0.008) |
| Intra firm wage Relation (50th to 10th percentile) | −0.015 | −0.016 | ||
| 0.030) | 0.009) | |||
| Log. average 12-month Euribor | 3.648** | 3.636** | 0.067** | 0.062** |
| 0.127) | (0.127) | (0.011) | (0.011) | |
| Log. turnover | −0.166** | −0.166** | −0.046** | −0.043** |
| 0.008) | (0.008) | (0.002) | (0.002) | |
| Share of part-time workers | 0.042 | 0.040 | 0.018 | 0.017 |
| 0.038) | (0.038) | (0.012) | (0.011) | |
| Share of temp. Employed | 0.104* | 0.104* | 0.020 | 0.020 |
| 0.049) | (0.049) | (0.014) | (0.013) | |
| Share of employed persons subjected to the social insurance scheme | 0.065 | 0.067 | 0.019 | 0.019 |
| 0.073) | (0.073) | (0.022) | (0.020) | |
| Share of female workers | 0.006 | 0.008 | −0.007 | −0.007 |
| 0.039) | (0.039) | (0.012) | (0.011) | |
| Share of low skilled workers | 0.038* | 0.039* | 0.008 | 0.007 |
| 0.018) | (0.018) | (0.006) | (0.005) | |
| Share of non-German workers | 0.272* | 0.273* | 0.112** | 0.104** |
| 0.136) | (0.136) | (0.038) | (0.035) | |
| Constant | −3.301** | −3.281** | 0.804** | 0.747** |
| 0.270) | (0.269) | (0.132) | (0.123) | |
| Log. Pseudolikelihood | −18,747 | −18,744 | −14,278 | −14,276 |
| Wald-Test χ2 (df.) | 9,188** | 9,370** | 19,963** | 18,560** |
| 278) | (292) | (262) | (275) | |
| Obs. | 38,932 | 38,932 | 29,223 | 29,223 |
| (Establ.) | (12,953) | (12,953) | (9300) | (9300) |
Source: LIAB 1996–2008. Note: The model also includes the following dichotomous and auxiliary variables: establishment size (seven dummies), legal form (five), firm profitability (eight), industry (fourty), year (twelve), a dummy for western Germany respective coverage by a collective agreement, the mean of time variant explanatory variables, dummies for the number of observations for an establishment and interaction variables between the means and the dummies. Semi-robust standard errors adjusted for clustering on establishments and years in parentheses. ** and * denote significance at the .01 and .05 levels, respectively.
The STATA option “cluster” is used to calculate the clustered sandwich estimator to obtain a robust variance estimate that adjusts for within-cluster correlation. The STATA code to estimate the fractional panel probit model is provided in Wooldridge (2011).
Fixed effects estimation with intra firm wage relations as measure for wage dispersion /logit transformation of the dependent variable.
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Log. of wages | 0.617** | 0.623** | 0.630** | 0.629** |
| 0.107) | (0.107) | (0.115) | (0.115) | |
| Intra firm wage Relation | −0.008 | 0.085 | −0.005 | 0.045 |
| (90th to 10th percentile) | (0.013) | (0.064) | (0.012) | (0.060) |
| Intra firm wage Relation | −0.100 | −0.056 | ||
| (50th to 10th percentile) | 0.063) | 0.064) | ||
| Log. turnover | −0.248** | −0.248** | −0.239** | −0.239** |
| 0.008) | (0.008) | (0.009) | (0.009) | |
| Share of part-time workers | 0.086 | 0.084 | 0.117* | 0.117* |
| 0.050) | (0.050) | (0.054) | (0.054) | |
| Share of temp. Employed | 0.297** | 0.300** | 0.305** | 0.306** |
| 0.064) | (0.064) | (0.077) | (0.077) | |
| Share of employed persons | −0.085 | −0.084 | −0.158 | −0.155 |
| subjected to the social insurance scheme | (0.100) | (0.100) | (0.109) | (0.109) |
| Share of female workers | 0.032 | 0.030 | −0.024 | −0.025 |
| 0.052) | (0.052) | (0.061) | (0.061) | |
| Share of low skilled workers | 0.031 | 0.032 | 0.034 | 0.034 |
| 0.024) | (0.024) | (0.029) | (0.029) | |
| Share of non-German | 0.723** | 0.717** | 0.650* | 0.650* |
| workers | (0.239) | (0.237) | (0.273) | (0.272) |
| Adj R-squared | 0.8886 | 0.8886 | 0.8957 | 0.8957 |
| F-test | 212.93** | 207.45** | 162.08** | 160.23** |
| 84, 25895) | (85, 25,894) | (82, 19,841) | (83, 19,840) | |
| Obs. | 38,932 | 38,932 | 29223 | 29223 |
| (Establ.) | (12,953) | (12,953) | (9,300) | (9,300) |
Source: LIAB 1996–2008. Note: The model also includes the following dichotomous and auxiliary variables: establishment size (seven dummies), legal form (five), firm profitability (eight), industry (fourty), year (twelve) and a dummy for western Germany respective coverage by a collective agreement. Semi-robust standard errors adjusted for clustering on establishments and years in parentheses. ** and denote significance at the .01 and .05 levels, respectively.
Columns (c) and (d) use lagged values for the wage relation.
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Log. of wages | −0.735 | −0.734 | −0.767 | −0.770 |
| Log. wage dispersion | −0.038 | −0.067 | −0.072 | −0.101 |
| Log. of skewness of wage dispersion | −0.003 | −0.004 | ||
| Log. average 12-month Euribor | 2.579 | 2.546 | 2.513 | 2.518 |
| Log. turnover | 0.884 | 0.885 | 0.885 | 0.885 |
Columns (a) and (b) use standard error of regression (ser), columns (c) and (d) use standard deviation of log. of observed wages.
Average elasticities from the fixed effects estimations in Table A.3 (eqs (9a)–(12a)).
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Mean (s.d.) | Mean (s.d.) | Mean (s.d.) | Mean (s.d.) | |
| Log. of wages | −0.553 | −0.583 | −0.642 | −0.643 |
| (0.096) | (0.090) | (0.077) | (0.077) | |
| Log. wage dispersion | −0.089 | −0.110 | −0.155 | −0.178 |
| (0.019) | (0.024) | (0.033) | (0.038) | |
| Log. of skewness of wage dispersion | −0.001 | −0.003 | ||
| (0.000) | (0.001) | |||
| Log. turnover | 0.805 | 0.805 | 0.805 | 0.805 |
| (0.042) | (0.042) | (0.042) | (0.042) |
Columns (a) and (b) use standard error of regression (ser), columns (c) and (d) use standard deviation of log. of observed wages. Because of the within transformation it is not possible to estimate elasticities for only time variant variables like the Euribor. Standard deviation of the estimated elasticities in parenthesis.
Average elasticities from the fractional panel probit estimations in Table 2 (eqs (9b)–(12b)).
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Log. of wages | −0.923 | −0.934 | −0.931 | −0.961 |
| Log. wage dispersion | −0.001 | −0.006 | −0.002 | −0.003 |
| Log. of skewness of wage dispersion | −0.000 | −0.000 | ||
| Log. average 12-month Euribor | 0.048 | 0.039 | 0.045 | 0.025 |
| Log. turnover | 0.969 | 0.972 | 0.970 | 0.983 |
Columns (a) and (b) use standard error of regression (ser), columns (c) and (d) use standard deviation of log. of observed wages.
Average elasticities from the fixed effects estimations in Table 3 (eqs (9a)–(12a)).
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Mean (s.d.) | Mean (s.d.) | Mean (s.d.) | Mean (s.d.) | |
| Log. of wages | −0.500 | −0.544 | −0.543 | −0.543 |
| (0.108) | (0.098) | (0.098) | (0.098) | |
| Log. wage dispersion | 0.002 | −0.020 | 0.009 | −0.003 |
| (0.000) | (0.004) | (0.002) | (0.001) | |
| Log. of skewness of wage dispersion | −0.002 | −0.002 | ||
| (0.000) | (0.000) | |||
| Log. turnover | 0.819 | 0.819 | 0.819 | 0.819 |
| (0.039) | (0.039) | (0.039) | (0.039) |
Columns (a) and (b) use standard error of regression (ser), columns (c) and (d) use standard deviation of log. of observed wages. Because of the within transformation it is not possible to estimate elasticities for only time variant variables like the Euribor. Standard deviation of the estimated elasticities in parenthesis.
Average elasticities from the fractional panel probit estimations in Table 4 (eqs (9b)–(12b)).
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Log. of wages | −0.962 | −0.935 | −0.943 | −0.932 |
| Log. wage dispersion | −0.084 | 0.044 | −0.066 | 0.011 |
| Log. of skewness of wage dispersion | 0.021 | 0.021 | ||
| Log. average 12-month Euribor | 0.027 | 0.042 | 0.043 | 0.049 |
| Log. turnover | 0.982 | 0.971 | 0.971 | 0.967 |
Columns (a) and (b) use standard error of regression (ser), columns (c) and (d) use standard deviation of log. of observed wages.
Average elasticities from the fixed effects estimations in Table 5 (eqs (9a)–(12a)).
| (a) | (b) | (c) | (d) | |
|---|---|---|---|---|
| Mean (s.d.) | Mean (s.d.) | Mean (s.d.) | Mean (s.d.) | |
| Log. of wages | −0.515 | −0.540 | −0.563 | −0.549 |
| (0.104) | (0.099) | (0.094) | (0.097) | |
| Log. wage dispersion | −0.792 | −0.673 | −0.592 | −0.499 |
| (0.170) | (0.145) | (0.127) | (0.107) | |
| Log. of skewness of wage dispersion | 0.018 | 0.022 | ||
| (0.004) | (0.005) | |||
| Log. turnover | 0.811 | 0.808 | 0.810 | 0.808 |
| (0.041) | (0.041) | (0.041) | (0.041) |
Columns (a) and (b) use standard error of regression (ser), columns (c) and (d) use standard deviation of log. of observed wages. Because of the within transformation it is not possible to estimate elasticities for only time variant variables like the Euribor. Standard deviation of the estimated elasticities in parenthesis.
Technical appendix (Fractional Panel Probit Model)
The Fractional Panel Probit model bases on the work of Papke and Wooldridge (1996). The formulation that is used in the work at hand is presented in Papke and Wooldridge (2008). They used a normal distribution (e.g., a probit model) that led to simple estimators in the presence of unobserved heterogeneity. In particular, they assumed the following model:
where yit is the response variable, 0 ≤ yit ≤ 1; t = 1, …, T, ci are the firm specific heterogeneities and Φ is the standard normal cumulative distribution function (cdf). The partial effects not only depend on the estimated β’s, but also on the density function ϕ:
As the cdf is a monotonic function, the value of β identifies the direction of the partial effect. Unfortunately, because of the unobserved nature of ci, it is not possible to calculate the partial effects from eq. (A.2). One possibility that can be applied to calculate the partial effects in this model is to average the individual partial effects and model the distribution of ci, given strictly exogenous covariates xi, so that the selection becomes ignorable (Papke and Wooldrigde, 2008, 123, 2010). The average partial effects (APE) are given by:
These APE depend on β and x, but not on c (Papke and Wooldridge, 2008, 123). In addition, Wooldridge (2010) assumes that the distribution of the unobserved heterogeneity changes with the number of observations for an establishment within the unbalanced panel. As such, Wooldridge proposed a linear function of time averages for E(ci|ki), where ki is a vector of all known selection indicators due to the unbalanced characteristics of the panel (Wooldridge, 2010):
where r is the number of observations of an establishment in the panel,
where τ is the variance of the base group and ωr indicates the deviation of each subgroup from τ. Placing eqs (A.4) and (A.5) into eq. (A.1) yields:
A convenient reparameterization leads to (Wooldridge, 2010):
Variables do not vary across I (i.e., the time dummies were omitted from the
The APE’s are then given by the derivative of eq. (A.8) with respect to xi:
In the current paper, the focus is not on the calculation of the APE’s, but on the determination of the factor and output elasticities. Therefore, the average elasticities are derived from the APE’s by using the ASF in eq. (A.9) as the expected means of the cdf. According to eqs (9)–(12), the average elasticities for the estimated parameters of lnw, lny and ln(Euribor) are now given as follows:
© 2017 Oldenbourg Wissenschaftsverlag GmbH, Published by De Gruyter Oldenbourg, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Labor Demand and Unequal Payments: Does Wage Dispersion Matter? Using German Employer-Employee Data to Analyze the Influence of Intra-Firm Wage Inequality on Labor Demand
- The Role of the Number of Banks on Debt Dynamics: Evidence from Eurozone Countries
- Infrastructure Development Versus Direct Cash Transfer: A General Equilibrium Comparison
Articles in the same Issue
- Frontmatter
- Labor Demand and Unequal Payments: Does Wage Dispersion Matter? Using German Employer-Employee Data to Analyze the Influence of Intra-Firm Wage Inequality on Labor Demand
- The Role of the Number of Banks on Debt Dynamics: Evidence from Eurozone Countries
- Infrastructure Development Versus Direct Cash Transfer: A General Equilibrium Comparison
