Age and Gender Effects of Workforce Composition on Productivity and Profits: Evidence from a New Type of Data for German Enterprises

This empirical paper documents the relationship between the composition of a firm’s workforce (with a special focus on age and gender) and its performance (productivity and profitability) for a large representative sample of enterprises from manufacturing industries in Germany using newly available, unique data. We find concave age-productivity profiles and a negative correlation of age on firms’ profitability. Moreover, our micro-econometric analysis reveals for the first time that the ceteris paribus lower level of productivity in firms with a higher share of female employees does not go hand in hand with a lower level of profitability in these firms.


Introduction
Economic research has a long tradition of explaining differences in firm performance (e.g., Bartelsman & Doms 2000;Syverson, 2011). Whereas some studies are interested in the effects of work practices (e.g., codetermination, training, incentive schemes) on firm performance, others are more interested in the relationship between the demographic structure of the workforce and firm performance. The latter stream of literature has received increasing attention due to persistent inequalities in the labor market (e.g., wage differentials between men and women, employment problems of older workers), increasing female employ-ment rates, and the demographic change leading to an ageing workforce. To understand such inequality issues and to learn about potential aggregated productivity (welfare) changes in ageing societies with increasing female employment, micro-econometric studies on the effects of the age and gender composition of firms' workforces are important.
In the last two decades, several new databases have been made available to researchers. These databases include establishment and linked employer employee datasets. These new data sources are usually large representative panel datasets obtained by surveys or official statistics and which allow the application of advanced econometric techniques to the analysis of firm performance. In Germany, the most used datasets in this context are the IAB Establishment Panel (Fischer et al., 2009) and the linked employer employee data of the IAB (LIAB) (Alda, Bender, & Gartner, 2005), which combines the survey data of the IAB Establishment Panel with process produced employee data of the social security agencies. A disadvantage of such voluntary survey information is that information about firms' productivity, costs, profits, and other variables are often seen as confidential by firms and might include measurement errors that can distort the empirical link between explanatory variables and outcomes. In this paper, we use a new type of data (KombiFiD project) for German enterprises from the manufacturing sector that combines official statistics of employees covered by social security and information from mandatory enterprise level surveys performed by the German Statistical Offices. Therefore, we have more reliable information than most previous studies. Moreover, we can compute firms' rates of profit, yielding new insights into the firm performance literature, as previous studies have primarily focused on productivity.
A table in the appendix presents a review of recent econometric studies that explicitly address the effects of age and gender on firm performance. All reviewed studies have in common that they use linked employer-employee data to study the productivity effects of age and gender. The used datasets are from different countries (Germany, Netherlands, Denmark, Finland, Belgium, Portugal, Canada, USA, Taiwan).
The main findings of previous research can be summarized as follows. The age-productivity profiles are mostly positive concave or inverse u-shaped. However, the estimates differ among different methods and specifications. The employment share of women has mostly significant negative effects on firm productivity in OLS (Ordinary Least Squares) regressions and non-significant effects in GMM (General Method of Moments) regressions. Especially noteworthy are the last three papers in the appendix table by Cardoso, Guimarares, and Varejao (2011) for Portugal, van Ours and Stoeldraijer (2011) for the Netherlands, and Göbel and Zwick (2012) for Germany, as they are the most comparable to our study with respect to data, variables, specifications, and methods. Although previous research has analyzed firm productivity and the productivity-wage gap, we do not know of any study that has explicitly analyzed the effects of age and gender composition of the workforce on firms' profit-ability. 1 Consequently, we present the first evidence for direct links between workforce composition and firm profits.
In our micro-econometric analysis, we use a bal- The finding for productivity is consistent with standard human capital considerations (amortization periods, depreciation). The finding for profit is consistent with deferred compensation considerations (underpayment of younger and overpayment of older employees). Whereas the concave age-productivity profiles do not support fears of declining productivity due to an ageing workforce and cannot explain the employment problems of older workers, the negative effect of age on firm profits highlights the employment barrier for older workers from a labor demand side. Our analysis furthermore reveals, for the first time, that the ceteris paribus lower level of productivity in firms with a higher share of female employees does not go hand in hand with a lower level of profitability in these firms. If anything, profitability is (slightly) higher in firms with a larger share of female employees. This finding might indicate that a lower productivity of women is (over)compensated by their lower labor costs, which in turn might indicate general labor market discrimination against women or lower reservation wages and less engagement in individual wage bargaining by women.
The rest of the paper is organized as follows. Section 2 describes the data used and the definitions of the variables and presents descriptive statistics. Section 3 presents and discusses the approaches for our micro-econometric investigation. Section 4 contains the results of our micro-econometric analyses. The paper concludes in Section 5 with a summary and discussion of our results as well as comments on the newly available data for enterprises from German manufacturing used for the study.

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Age and gender effects of workforce composition on productivity and profits: Evidence from a new type of data for German enterprises

Data, definition of variables and descriptive statistics
The empirical investigation uses data for manufacturing industry enterprises 2 . These data come from two sources. The first source is the cost structure survey for enterprises in the manufacturing sector. This survey is carried out annually by the statistical offices as a representative random sample survey stratified according to the number of employees and industries (see Fritsch et al., 2004). The sample covered by the cost structure survey represents all enterprises with at least 20 employees from manufacturing industries. Approximately 45 percent of the enterprises with 20 to 499 employees and all enterprises with 500 or more employees are included in the sample. 3 Although firms with 500 or more employees are covered by the cost structure survey in each year, the sample of smaller firms is part of the survey for four years in a row only.
This survey is the source for information on productivity, profitability, firm size and industry affiliation: Productivity is measured as labor productivity, defined as value added per head (in Euro and in current prices). Information on the capital stock of a firm is not available from the cost structure survey, so more elaborate measures of total factor productivity cannot be used in this study. Bartelsman and Doms (2000, p. 575) note that heterogeneity in labor productivity is accompanied by similar heterogeneity in total factor productivity in the reviewed research where both concepts are measured. In a recent comprehensive survey, Chad Syverson (2011) argues that high-productivity producers will tend to appear efficient regardless of the specific way their productivity is measured. 4 Furthermore, Foster, Haltiwanger and Syverson (2008) show that productivity measures that use sales (i.e., quantities multiplied by prices) or quantities only are highly positively correlated. Therefore, we argue that labor productivity is a suitable measure for productivity at the firm level. Labor productivity is computed as: Firm size is measured by the number of people working in a firm. This measure is also included in squares in the empirical models to address non-linearity in the relation between firm size and firm performance.
Industry affiliation of a firm is recorded at the twodigit level.
The second source of data is the Establishment His- Age and gender effects of workforce composition on productivity and profits: Evidence from a new type of data for German enterprises (though not impossible) and is legal only if the firm agrees in writing. The basic idea of the KombiFiD (an acronym that stands for Kombinierte Firmendaten für Deutschland, or combined firm level data for Germany) project, described in detail on the web (see www. kombifid.de), is to ask a large sample of firms from all parts of the German economy to agree to match confidential micro data for these firms. These data are kept separately by three data producers (the Statistical Offices, the Federal Employment Agency, and the German Central Bank) in one dataset. These matched data are made available for scientific research while strictly obeying the data protection law, i.e., without revealing micro level information to researchers outside the data producing agencies. In KombiFiD, 54,960 firms were asked to agree in writing to merge firm level data from various surveys and administrative data for the report- Descriptive statistics for all variables and the pooled data are reported in Table 1. It is evident from these descriptive statistics that the variation of the share of females and of the share of employees in the two qualification groups are small over the four years covered compared with the variation between the firms in the sample. The same holds for the variation in firm size. Therefore, the within firm variation of important dimensions of diversity of the employees over time cannot be used in fixed effects models to sufficiently identify any relationship between changes in firm performance over time and the diversity of employees.
Furthermore, a comparison of the mean and the standard deviation of the variables indicate that some firms may have characteristics that differ by orders of magnitude from the rest of the firms in the sample.
Unfortunately, due to strict data protection rules it is not possible to report the minimum and maximum values of the variables in Table 1 (because these are fig-ures for a single firm that may not be revealed). This is less of a problem for all the variables that are defined as shares because their values are bound between zero and one hundred percent by definition. However, for value added per head, the rate of profit and firm size, we know from (unpublished) results of investigations of the KombiFiD Agreement Sample that there are extremely low or high values of these variables for some firms. These extreme observations, or outliers, may be highly influential in any empirical investigation. This aspect of the data, therefore, should be addressed.

Approaches for the microeconometric investigation
The investigation of the link between the diversity of employees (especially the composition of the workforce by age and gender) and two dimensions of firm performance (productivity measured as value added per head in Euros and profitability measured as the rate of profit in percent) 12 uses empirical models that regress the performance variable on the shares of employees from different age groups, the share of female employees 13 , the shares of highly and medium quali- tions are simply a vehicle to test for and estimate the size of the relation between firm performance and one dimension of workforce diversity controlling for other firm characteristics. Furthermore, note that productivity differences at the firm level are notoriously difficult to explain empirically. "At the micro level, productivity remains very much a measure of our ignorance" (Bartelsman & Doms 2000, p. 586). Syverson (2011) surveys the recent literature on determinants of productivity at the firm level. Inter alia, he mentions effects of competition, organizational structures within firms, payment systems, other human resources practices, managerial talent, human capital, higher-quality capital inputs, information technology (IT) and R&D. All these determinants of productivity are important for profitability as well, and they cannot be examined here with the data at hand. These limitations should be kept in mind when putting the results in perspective.
In a first step, the empirical models were estimated for the pooled data from 2003 to 2006 by Ordinary Least Squares (OLS). The descriptive statistics presented above revealed that the variation of the share of females and of employees in the two large qualification groups are small over the four years covered compared with the variation between the firms in the sample. The same holds for the variation of firm size. Therefore, the within firm variation of important dimensions of diversity of the employees over time cannot be used to identify any relationship between changes in firm performance over time and the diversity of employees by adding fixed firm effects. To address the dependence of the error term between observations from one firm over the four years, the standard errors of the estimated regression coefficients are clustered at the firm level. 16 In a second step, we address the problem that some In contrast to the least squares estimator, the quantile regression estimates place less weight on outliers and are found to be robust to departures from normality. " Quantile regression at the median is identical to least absolute deviation (LAD) regression, which minimizes the sum of the absolute values of the residuals rather than the sum of their squares (as in OLS). This estimator is also known as the L 1 , or median regression,

Results of the micro-econometric investigation
Our main empirical results for the links between dimensions of workforce composition and firm productivity (value added per head in Euro) are reported in Table 2  To check for potentially influential outliers, we reestimated Model 1 with the robust MM regression technique, which supports our main findings from OLS. The estimated coefficients are slightly smaller and the estimated standard errors are substantially smaller for most variables in the robust MM regression, which leads to higher significance levels. Although the coefficient for the oldest age group is now significant and positive, we still find an inverse u-shaped relationship between age and productivity. The estimated negative coefficient of the employment share of women is 189 Euros in the robust MM regression compared with 219 Euros in OLS. A noteworthy difference arises for firm size that is likely driven by influential outliers.
Whereas OLS indicates a positive concave relationship, because the maximum is reached at more than 70,000 employees, the robust MM regression suggests an inverse u-shape with a maximum at approximately 4,000 to 5,000 employees.
Because we are especially interested in age-productivity profiles, Model 2, with less aggregated age groups, is also estimated with OLS and robust MM regressions. The results in Table 2 show no noteworthy changes in the estimated parameters for the other variables, so we focus on age. To facilitate interpretation, we plotted the estimated coefficients and corresponding 95% confidence intervals for OLS in Figure 1 and for robust MM in Figure 2. Note that the share of employees aged below 20 years serves as a reference group and that we neglect the oldest age group with workers aged 65 years and older because they may no longer be normal workers. Both plotted age-productivity profiles show in principal the same pattern. Productivity increases for younger workers until approximately age 30 and does not significantly change afterward. Thus, we find a more positive concave than inverse u-shaped age-productivity profile that does not support potential negative productivity effects due to an ageing workforce.
Our results from pooled OLS and robust MM regressions, which address influential outliers in the data, are in principal only correlations and need not be causal due to potential endogeneity issues stemming from omitted variables and reverse causality. Therefore, we perform GMM first difference regressions for   Age and gender effects of workforce composition on productivity and profits: Evidence from a new type of data for German enterprises Model 2 as robustness checks, whose results for productivity are presented in the last column of in the case of negative productivity shocks. Figure 3 plots the age-productivity profile, which is again positive concave and supports our previous findings from the pooled OLS and robust MM regressions.  Table 3. Estimates for profitability Note: The dependent variable is rate of profit (%). All models include dummy variables for years and 2-digit-level industries. Standard errors clustered at the firm level are in parentheses for OLS and MM regressions. Two-step GMM first difference regressions for model 2; first differences are instrumented with second and third lags of their own levels. Robust standard errors are in parentheses for GMM regressions. Coefficients are significant at * p<0.10, ** p<0.05, and *** p<0.01.

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Age and gender effects of workforce composition on productivity and profits: Evidence from a new type of data for German enterprises  The OLS results for Model 1 in Table 3 Figure 5 for the robust MM regressions. It can be seen that profitability increases until age 30, as was the case for productivity, and decreases afterward compared with the rather flat productivity profiles.
The results of the GMM regression for profitability are presented in the last column of Table 3. As was the case for productivity, the estimated coefficients and standard errors are larger than in the pooled OLS and robust MM regressions. The estimates reveal positive coefficients for some age groups and for the female employment share, although it is not significant. The ageprofit profile in Figure 6 shows an increase until age 30 and a slight decline afterward, although the differences between age groups are not statistically significant.
Despite low statistical significance, the overall GMM results support our previous findings from the pooled OLS and robust MM regressions.

Discussion and concluding remarks
We start our discussion with a short summary of our basic findings about age and gender effects on firm performance. In line with previous research, we find

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Age and gender effects of workforce composition on productivity and profits: Evidence from a new type of data for German enterprises concave age-productivity profiles that increase until age 30 and are flat afterward. The age-profit profiles indicate an increase until age 30 and a decline afterward.
The employment shares of women and productivity are significantly negatively correlated in our pooled OLS and robust MM regressions but are significantly positively correlated in the GMM regressions. Profitability seems to be positively correlated with the share of female employees in all our regressions, although not significantly in the GMM regressions. Overall, most of our findings on firm productivity are in line with findings from previous research, which has been summarized in the appendix table, and we have provided new findings on firm profitability.
Our finding for age and productivity is consistent with standard human capital considerations. Human capital theory (Mincer, 1974) implies that incentives to invest in human capital decrease with age as the amortization period decreases. Moreover, human capital is usually subject to depreciation. Both arguments lead to concave or even inverse u-shaped age-productivity profiles. Our finding for age and profit is consistent with deferred compensation considerations (Lazear, 1979). In deferred compensation models with longterm employment contracts, younger workers are paid below their marginal product and older workers are paid above their marginal product to provide work incentives. Consequently, firms' short term profits are positively affected by younger workers with short tenure, who pay loans to the firm, and negatively by older workers with long tenure, who receive the repayments of their loans. Although we cannot explicitly analyze tenure effects due to missing information in the data, age can be interpreted in this context because the German manufacturing sector is characterized by stable employment, making age and tenure quite collinear. Moreover, seniority arrangements with respect to age are usually part of collective contracts, which are binding to most firms in the German manufacturing sector. Whereas the concave age-productivity profiles cannot explain the employment problems of older workers, the negative effect of older workers on profits highlights the employment barrier for older workers from a labor demand side that might be explained by deferred compensation schemes (Heywood, Jirjahn, & Tsertsvardze, 2010;Hutchens, 1986). A similar conclusion can be drawn from previous studies that analyze the productivity-wage gap (e.g., Cardoso et al., 2011;Cataldi, Kampelmann, & Rycx, 2011;van Ours & Stoeldraijer, 2011). Moreover, our findings are important in that they do not support the fear of declining productivities in ageing societies.
Although our findings for gender and productivity are unclear from a causal perspective, we were able to document that firms with higher shares of female employees do not have lower levels of profitability. If anything, profitability is ( However, if firms' profits are only larger due to an underpayment of women caused by lower reservation wages and fewer wage bargaining activities, equal pay legislation might not have adverse effects on female employment but will negatively impact firms' profits.
Overall, a combination of female quotas and equal pay legislation might be necessary to effectively improve the employment situation of women and to reduce gender wage gaps. Whether such a policy would be ef-

Workforce composition measures
Main findings Haltiwanger, Lane, and Spletzer (1999) USA , 1985, -1997, , linked employer employee data OLS: pooled levels 1990, & 1994, , pooled differences 1986, -1990, & 1990, -1994 (Spengler 2008, p. 502) 8 Note that this information on the diversity of the employees is not available in greater detail; for example, the number of female employees aged 10 The sample is limited to firms from West Germany.
There are large differences between enterprises from West Germany and the former communist East Germany, even many years after the unification in 1990.
Therefore, an empirical study should be performed separately for both parts of Germany. The KombiFiD Age and gender effects of workforce composition on productivity and profits: Evidence from a new type of data for German enterprises 14 The reference category in our regression models is the share of employees who are either known not to be medium or highly qualified employees or whose qualification level is not reported in the data and which is, therefore, unknown.