The hiring of older workers: evidence from Germany

Busch, Fabian; Fenge, Robert; Ochsen, Carsten Article — Published Version The hiring of older workers: evidence from Germany Empirical Economics Provided in Cooperation with: Springer Nature Suggested Citation: Busch, Fabian; Fenge, Robert; Ochsen, Carsten (2024) : The hiring of older workers: evidence from Germany, Empirical Economics, ISSN 1435-8921, Springer, Berlin, Heidelberg, Vol. 68, Iss. 1, pp. 139-163, https://doi.org/10.1007/s00181-024-02637-5 This Version is available at: https://hdl.handle.net/10419/317033 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Empirical Economics (2025) 68:139–163 https://doi.org/10.1007/s00181-024-02637-5 The hiring of older workers: evidence from Germany Fabian Busch1·Robert Fenge1·Carsten Ochsen2 Received: 27 April 2023 / Accepted: 10 June 2024 / Published online: 23 August 2024 © The Author(s) 2024 Abstract This article analyses how hiring older workers adjusts to demographic change in the labour force by using information from more than 500,000 firms in Germany. We find robust evidence that firms faced with an ageing labour market hire relatively more older workers. However, the pace of this adjustment is relatively slow, particularly when ageing happens outside the firm. The tendency to employ older people is more considerable in East Germany, where the demographic change moves forward faster. Furthermore, part-time working models support hiring older workers, but this effect becomes less important in larger firms and East Germany. Finally, while partial retirement regulations enhance flexibility within the firm, they, unfortunately, diminish the employment opportunities for older external job seekers. Keywords Ageing labour force ·Hiring of older workers ·Panel data models JEL Classification J11 ·J23 ·C33 1 Introduction The share of older workers in the German labour force has increased continuously in the last two decades. Compared to younger workers, older workers typically have lower unemployment rates, lower job separation rates and lower job-finding rates (see Ochsen (2023), for example). In addition, on average, older workers have longer job tenure, which means they often grow older within the firm. Therefore, the firms’ share of older workers increases when this group is larger (baby boomers). However, less is known about the behaviour of firms in hiring older workers in ageing societies. BCarsten Ochsen [email protected] 1Department of Economics, University of Rostock, Rostock, Germany 2Department of Labour Economics, University of Applied Labour Studies, Schwerin, Germany 123 140 F. Busch et al. The literature provides empirical evidence that a rising share of older personnel is positively related to the average age at hire or the share of hired older workers.1 Concerning Germany, Heywood et al. (2010) analyse management attitudes towards hiring older workers in general. However, they do not measure the hiring behaviour directly. The literature discussed uses cross-sectional data and comparatively small samples. Hence, they cannot capture developments over time and cannot represent changes in the age structure of the labour force and their relationship to the hiring of older workers. The literature related to the hiring of older unemployed is somewhat different. Axelrad et al. (2018) conclude that the probability of an unemployed individual finding a new job decreases with age. Age discrimination against older unemployed workers in the hiring process is reported by Neumark et al. (2019) for the USA and Oesch (2020) for Switzerland. In the German context, Dietz and Walwei (2011) and Ochsen (2023) calculate the job-finding rates and conclude that these rates decrease steeply with age. Wright (2015) concludes that German establishments are still reluctant to hire older workers, which fosters long-term unemployment.2Consequently, it is a substantial problem for older workers to become re-employed after a job separation, especially if they seek full-time employment (Adams and Heywood 2007 and Daniel and Heywood 2007). None of the above studies analyses the joint implications of the increasing shares of older employed and unemployed in the labour force for the hiring behaviour of firms. For this reason, our research question is how labour market ageing characteristics are related to hiring older workers. In particular, we are interested in the role of the shares of full-time and part-time older employed, the share of partial retirement and the share of older unemployed in the firms’ local area. We use the share of older workers (50–64 years old) hired on all hires as the variable of primary interest. Figure 1reveals the evolution of this variable in Germany from 2000 to 2019. Firms hire increasingly relatively more older workers in the considered period. However, how is this related to the ageing of the labour force? This article contributes to the literature in two ways. Firstly, we analyse panel data using the Establishment History Panel and match this panel with data on unemployment at the administrative district level (Landkreise und kreisfreie Städte). This enables us to analyse the firm’s hiring behaviour over a period of 20 years, which contrasts existing studies that mainly analyse cross-sectional data. Secondly, to consider both the employed and the unemployed part of the labour force, we use variables at different aggregation levels to examine the hiring behaviour of firms. We use the age structure of the employees at the firm level (to control for the effect of an ageing workforce) and the age-specific unemployment shares at the level of the administrative district 1Concerning the average age at hire, see, for example, Adams and Heywood (2007) for Australia and Medeiros Garcia et al. (2017) for Portugal. Related to the share of hired older workers, see, for example, Scottetal.(1995) and Adler and Hilber (2009) for the USA, Heywood et al. (1999) for Hong Kong, Daniel and Heywood (2007) and Kidd et al. (2012) for the UK. 2A closer look at the long-term unemployment statistics reveals that older workers are statistically more prone to be long-term unemployed than all other age groups, which marks a critical indicator of the chances of older people being hired from the labour market. According to data for 2019, 42 per cent of all older (55 to 65 years old) unemployed were long-term unemployed. Moreover, with almost one-third of all long-term unemployed, this age group is the largest among the long-term unemployed. 123 The hiring of older workers: evidence from Germany 141 Fig. 1 Share of hired older workers aged 50–64 where the firm is located (to capture the impact of an ageing pool of unemployed). By considering both types of hired older workers, we can compare the hiring behaviour with respect to older employed and older unemployed persons. We find that the joint effect of an ageing labour force on hiring older workers is positive but inelastic. A higher share of older unemployed increases the firms’ hiring of older workers, but the elasticity varies by around 0.07. The internal age structure at the firm level is more important because the elasticity for full-time workers is 0.33, and the elasticity for part-time workers is 0.54, on average. Hence, firms’ adjustment to the demographic trend is relatively slow, implying firms react hesitantly to the demographic development. In addition, we show that a rising share of employees in partial retirement schemes is negatively related to the share of hired workers aged 50 and older. This result has to be seen in context with particularities of the German law on partial retirement. Although the law intends to alleviate the employment situation of older workers, we show that the regulation impedes hiring older workers. Lastly, we present the results differentiated by firm size, sector, and East and West Germany. This paper is organised as follows. The following section provides some stylised facts. Section 3describes our database and the empirical strategy. Section 4entails the discussion of the results, and a robustness check is provided in Sect. 5. Section 6 concludes. 2 Stylised facts Using data for the US labour market and the period 1983–1995, Hirsch et al. (2000) find that the share of hired older workers (50 years and older) on all hires is about 0.1. In addition, they calculate the percentage of older workers in the workforce and receive an average value of 0.19. Following Hutchens (1986), they finally calculate the openness to older hires (the proportion of hired older workers divided by the proportion of older workers in the workforce) and receive 0.53. A value between 0 and 1 can be 123 142 F. Busch et al. Table 1 Different labour market measures Older workers Rest of the workers (1)Hiring share 50–64 Hold /H0.139 Hiring share 15–49 Hrest/H0.861 (2)Share workers 50–64 Lold /L0.238 Share workers 15–49 Lrest/L0.762 (3)Hiring rate H/L0.263 Hiring rate H/L0.263 (4)Hiring rate 50–64 Hold /Lold 0.153 Hiring rate 15–49 Hrest/Lrest 0.297 (5)Relative hiring ratio (4)/(3)0.583 Relative hiring ratio (4)/(3)1.130 (6)Openness (1)/(2)0.583 Openness (1)/(2)1.130 source: EHP-7520 and own calculations interpreted as information that hiring opportunities are restricted for older workers. Rearranging this measure additionally allows us to interpret it as the relative hiring rate for older workers (the proportion of hired older workers in all older workers divided by the overall hiring rate). From this, it follows that the average hiring rate is about twice as large as the hiring rate of older workers. We consider the Establishment History Panel for Germany to calculate the macroeconomic indicators discussed (Table 1).3Basically, four measures are necessary to examine the general labour market situation for older workers in this context. Measure (1), the share of hires aged 50–64 to all hires (Hold /H), provides information on the general hiring behaviour of firms related to older workers. Measure (2), the share of workers in the workforce who are 50–64 years old (Lold /L), offers the same idea as the first measure, but for the workforce. Measure (3), the ratio of hires to the workforce (the hiring rate), indicates how open firms are to job seekers. Measure (4), a similar proportion, the ratio of hires of older workers to workforce share of older workers (Hold /Lold ), indicates the deviation for older workers from the mean.4 The relative hiring ratio (5) shows that the considered age group is less likely to be hired than the average if the number is below 1. Openness (6) measures the openness to older hires relative to the proportion of older workers in the firm. As mentioned above, both measures provide the same quotient. The results for (1), (2) and (6) are similar to the findings of Hirsch et al. (2000). Hence, on average, in the last two decades, German firms seem not to be more open to older workers than US firms in the 1980s and 1990s. Furthermore, relative labour market opportunities seem not to have improved for older workers, even in ageing times. Concerning measures (5) and (6), we also can conclude that when the share of the older workforce increases only due to ageing within the firm, the relative hiring ratio for older workers must decline when the ratio of hires aged 50–64 to all hires remains unchanged. In contrast, when the ratio of hires aged 50–64 to all hires increases, the relative hiring ratio for older workers must increase when the share of the older workforce remains constant. In the first case, the relative hiring ratio for older workers declines due to the ageing of the workforce, while in the second case, the relative hiring ratio for older workers increases due to a higher share of hired older workers. 3For detailed data description, see Sect. 3. 4For a discussion of the first and second measure, see, for example, Hirsch et al. (2000). 123 The hiring of older workers: evidence from Germany 143 When both causes of ageing happen (what we observe), the relative hiring ratio for older workers may increase, decrease or remain unchanged. On the right-hand side of Table 1, we report the results for the age group 15 to 49 (rest of the workers). The measures (5) and (6) for the rest of the workers are almost twice as large. This is related to an above-average hiring rate of this age group (4) and a hiring share (1) that is larger than the share of workers of this age group (2). We argue in the introduction that we prefer to analyse the share of hired older workers (1) to understand the hiring behaviour of firms. In principle, the hiring rate of older workers (4) seems to be an appropriate alternative. We apply a simple approach to motivate that (1) is more suitable as the dependent variable than (4). Given that we have only two age groups (old and rest), there are different ways to write down the hiring rate: H L=Hrest L+Hold L=Lrest L Hrest Lrest +Lold L Hold Lold Dividing the final expression by H/Lyields the components of the hiring rate that sum up to 1. Lrest L Hrest Lrest L H+Lold L Hold Lold L H=Hrest H+Hold H From this, it follows that the hiring share of older workers (1) equals the weighted relative hiring ratio of older workers. We decided to use (1) as our dependent since it is not directly related to the firm’s workforce ageing. Figure 2provides the development of the variables discussed. The first value of each series is scaled to one to ease comparability. On the one hand, both hiring rates follow a similar trend; consequently, the ratio of both is almost unchanged. Hence, the overall relative labour market opportunities for older workers do not increase during the period considered. On the other hand, the share of hired older workers and the percentage of older in the workforce have a similar positive pattern. This means that firms hire a larger share of older workers, and ageing within the firm increases the share of the older workforce at the same pace. The data analyses below examine the relationship between the share of hired older workers and the share of older employed at the firm level. In addition, we calculate the relative hiring ratio for each considered subset of data. 3 Data and method This study uses the weakly anonymous Establishment History Panel (EHP) for Germany.5The EHP is a 50 per cent sample of all establishments throughout Germany 5Data 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 remote data access (Schmucker et al. 2016). 123 144 F. Busch et al. Fig. 2 Development of different labour market measures for older Workers with at least one employee subject to social security at the reference date of June 30 for a given year. Hence, the panel structure is yearly firm-level data. Our database consists of 9,595,987 observations for 1,893,345 firms distributed across all 401 administrative districts in Germany from 2000 to 2019.6Our dependent variable is the ratio of hired older workers aged 50–64 to all hires at the firm level. In the baseline specification, we remove all establishments with less than five employees from the panel. Since our dependent variable is a fraction, small firms are more likely to hire fewer people. If a firm hires exactly one person, the share of older workers entering the firm in that respective year is either 0 or 1. Furthermore, we only consider firms in the panel that are included for at least five years. This is due to our general interest in within-firm changes and the relationship between the dependent and independent variables. Hence, for the baseline model, we use 5,879,369 observations for 530,658 firms.7 To capture the age distribution in the workforce, we consider the following variables as controls in our regressions. We include the youth share (15 to 24 years) and the share of older workers (50 to 64 years) and consider the remaining age group (25 to 49 years old) as the reference. We differentiate between full-time and part-time employees to account for flexible working time models. In addition, we include the share of employees working in partial retirement schemes. To proxy the age structure of the labour force further, we consider the youth share and the share of older workers among the unemployed at the administrative district level. The Federal Employment Agency provides these data. Table 2reports summary statistics for the variables of primary interest. For a data description including control variables, see Appendix A. 6We choose the year 2000 as a starting point for reasons of data availability. 7We acknowledge that our restrictions reduce the sample size considerably. For comparison reasons, we also estimate the model on the unrestricted panel. The results are provided in Table 10 in Appendix C. 123 The hiring of older workers: evidence from Germany 145 Table 2 Summary statistics Model Obs Mean Std. err. Min Max Firms Hires 50–64 5,879,369 13.89 23.19 0 100 Full-time 50–64 5,879,369 22.00 23.09 0 100 Full-time 15–24 5,879,369 9.60 16.39 0 100 Part-time 50–64 5,879,369 25.66 25.42 0 100 Part-time 15–24 5,879,369 23.86 27.19 0 100 Partial retirement 5,879,369 0.43 2.14 0 100 Administrative district Share unemployment 50–64 5,879,369 30.23 5.50 17.70 58.33 Share unemployment 15–24 5,879,369 10.47 2.27 2.70 21.09 We analyse the impact of demographic change on the share of hired older workers by using a panel data model with fixed firm-level effects and year effects.8The model is specified as follows: yijt =β0+ k βkFkijt + m λmXmjt +αi+δt+ijt Fis a vector comprising k=1, ..., Kvariables at the firm level, and Xdescribes a vector of m=1, ..., Mvariables at the administrative district level. Index irepresents the firm level, jthe administrative district level and tthe annual time dimension. Finally, depicts the residuals, αfixed effects and δtime effects. Concerning the statistical relevance of our estimates, we provide cluster-robust standard errors at the district level to control for heteroskedasticity, serial correlation and cross-sectional dependence in the residuals.9In addition, we consider the False Positive Risk (FPR) to provide information on the statistical evidence of the estimated coefficients. In contrast to the p-value, the FPR measures the probability of the null hypothesis being true (Colquhoun 2019 and Colquhoun 2017).10 For a discussion of the misinterpretation of p-value, see, for example, Wasserstein and Lazar (2016). For the computation of the FPR, we refer to Appendix B. 4 Results First, we provide the results for our baseline model and Germany overall. In the following subsection, we differentiate by firm size, sector and East and West Germany. 8We used a Hausman test to decide whether a random effects model was more appropriate but found strong evidence for using fixed effects. 9We also test cluster-robust standard errors at the firm level. However, to capture the correlation pattern at the district level, we decide in favour of this level. 10 For example, an FPR of 0.05 corresponds to a p-value of 0.003, and an FPR of 0.01 corresponds to a p-value of 0.0005. 123 146 F. Busch et al. Table 3 Hiring older workers: baseline results Dependent variable: share hires 50–64 Baseline Firm level Full-time 50–64 0.2084‡ (0.0024) Part-time 50–64 0.2945‡ (0.0023) Full-time 15–24 −0.0394‡ (0.0008) Part-time 15–24 −0.0268‡ (0.0006) Partial retirement −0.2454‡ (0.0127) Administrative district level Unemployed 50–64 0.0314‡ (0.0056) Unemployed 15–24 0.0371 (0.0115) Observations 5,879,369 Firms 530,658 R20.1158 Fixed effects regression. For further controls, see the data description. Cluster-robust standard errors at the district level are in parentheses. †: FPR ≤0.05, ‡: FPR ≤0.01 4.1 Baseline model Table 3presents our baseline results. We found a positive correlation between the share of older full-time workers (full-time 50–64) and the share of hired older workers. A 4.8 percentage point increase in the share of older employees corresponds to a one percentage point increase in the share of hired older workers. The corresponding elasticity of about 0.33 suggests a relatively slow adjustment to demographic change. This could be due to firms’ experiences with older employees and adjustments in production processes and services. An increase in the share of older part-time workers (part-time 50 to 64) is also positively related to hiring older workers. The corresponding elasticity is 0.54, indicating a slightly more elastic relationship. This might highlight the particularities of German law. Usually, part-time employees enjoy the same rights as full-time employees regarding vacation time or dismissal protection. However, paragraph 14, Sect. 3of the Teilzeitund Befristungsgesetz (TzBfG) allows the employer to causelessly limit the employment contract to a maximum of five years if the employee has been unemployed before re-employment for at least four months and is at least 52 years old. This information is important because it grants the employer more flexibility. Employers might specifically target hiring older workers to exploit this option since they do not 123 The hiring of older workers: evidence from Germany 153 Table 7 Elasticities and relative hiring ratio Model Elasticities Full-time 50–64 Part-time 50–64 Partial retirement Unemployed 50–64 Relative hiring ratio Baseline 0.33 0.54 −0.01 0.07 0.58 Firms Small firms 0.28 0.74 −0.003 0.06 0.68 Medium firms 0.33 0.47 −0.01 0.09 0.58 Large firms 0.45 0.29 0.001 0.08 0.51 Sectors Primary sector 0.56 0.40 −0.02 −0.06 0.59 Secondary sector 0.42 0.43 −0.01 0.11 0.62 Tertiary sector 0.28 0.64 −0.01 0.01 0.56 Regions East Germany 0.42 0.40 −0.004 0.13 0.64 West Germany 0.31 0.59 −0.01 0.05 0.57 Cursive values are based upon statistically weak evidence the findings that firms in the East are more open to older workers but less to working time flexibility. In addition, firms in both regions seem more reluctant when ageing happens outside the firm, but the eastern part adjusts more to the advanced ageing process. Finally, we also find the adverse effects of partial retirement for both regions. However, the economic impact is minimal. 5 Robustness In this section, we further analyse how robust our results are. Our specification potentially suffers from a simultaneity bias. Recognising that the share of hired older workers (the flow) and the share of employed older workers (the stock) might influence each other, we provide two approaches to analyse how important this potential problem is to our estimates. In addition, our specification may suffer from a potential omitted variable bias. Therefore, in the next section, we vary the set of control variables to see how our core variables behave. Subsequently, we provide instrumental variable (IV) estimates to detect a potential bias in the parameters for the older worker shares. 5.1 Specification To see how robust the coefficients for the full-time 50–64 and part-time 50–64 variables are, we take the baseline estimates as a reference and exclude different sets of control variables. Table 8provides an overview. Overall, we ran nine regressions. While the five core variables remain in each specification, the rest are excluded in various combinations. This is shown in the lower part of the table. For comparison 123 154 F. Busch et al. Table 8 Hiring older workers: specification tests Dependent variable: share hires 50–64 (1) (2) (3) (4) (5) (6) (7) (8) (9) Firm level Full-time 50–64 0.2083‡0.2083‡0.2077‡0.2077‡0.2068‡0.2085‡0.2064‡0.2084‡0.1833‡ (0.0024) (0.0024) (0.0024) (0.0024) (0.0024) (0.0024) (0.0024) (0.0024) (0.0026) Part-time 50–64 0.2965‡0.2965‡0.2961‡0.2961‡0.2938‡0.2945‡0.2934‡0.2945‡0.2720‡ (0.0022) (0.0022) (0.0022) (0.0022) (0.0022) (0.0023) (0.0022) (0.0023) (0.0019) Full-time 15–24 −0.0432‡−0.0432‡−0.0433‡−0.0433‡−0.0389‡−0.0393‡−0.0390‡−0.0394‡−0.0466‡ (0.0008) (0.0008) (0.0008) (0.0008) (0.0008) (0.0008) (0.0008) (0.0008) (0.0007) Part-time 15–24 −0.0391‡−0.0391‡−0.0389‡−0.0389‡−0.0265‡−0.0268‡−0.0266‡−0.0268‡−0.0398‡ (0.0007) (0.0007) (0.0006) (0.0006) (0.0006) (0.0006) (0.0006) (0.0006) (0.0005) Partial retirement −0.2641‡−0.2641‡−0.2644‡−0.2645‡−0.2489‡−0.2449‡−0.2449‡−0.2454‡−0.3888‡ (0.0130) (0.0130) (0.0129) (0.0129) (0.0128) (0.0127) (0.0127) (0.0127) (0.0140) Additional firm variables  Administrative district variables  Sector dummies  Year dummies  District-year dummies  R20.1145 0.1145 0.1146 0.1146 0.1157 0.1158 0.1157 0.1158 0.1813 Fixed effects regression. Number of observations 5,879,369. Number of Firms 530,658. For further controls, see the data description. Cluster-robust standard errors at the district level are in parentheses. †: FPR ≤0.05, ‡: FPR ≤0.01 123 The hiring of older workers: evidence from Germany 155 reasons, specification (8) is the baseline specification already shown in Table 3. Across regressions (1) to (8), the full-time 50–64 coefficient varies between 0.2085 and 0.2064 and the part-time 50–64 coefficient is between 0.2965 and 0.2934. Both differences are minimal and indicate a robust statistical relation with the dependent variable. In regression (9), we add more than eight thousand dummies at the regional level. Again, the coefficients of interest only change slightly. From this, we conclude that our estimates and calculated elasticities in the former section are statistically reliable. The remaining three variables also vary only a little. 5.2 IV estimation A more formal way to handle a potential simultaneity bias is to apply IV estimates. We instrument the share of older full-time and part-time employees to control for a possible simultaneity bias using the following two instruments: First, the one-year lagged labour force shares of older (50–64 years) people in the administrative district (county).13 This variable covers the complete regional labour supply of the old in the former year. This instrument is independent of the firm’s hiring decisions in the current year, not only because of the time lag but also because this is aggregated information unknown to the individual firm. As a second instrument, we use the average employment share of older workers in other firms in the same county. While the first instrument covers the complete regional labour force, this second instrument covers the average share of older workers in neighbourhood firms. This variable is taken from the same sample data as the potential endogenous variable. This instrument is independent of the firm’s hiring decisions because this information is unknown to the individual firm. Both instruments are correlated with the share of older workers in a specific firm but are not causally related to the dependent variable. However, potentially, our instrumental variables could be correlated with other not-considered county-level variables that, in turn, might influence the hiring behaviour of firms. Consequently, the instruments would not be exogenous, and the results would be biased. In addition, we must keep in mind that the share of older unemployed is larger than that of older workers or older workers hired. Hence, there is no evidence of higher market tightness in this age group compared to others. We provide three IV regressions (Table 9). In the first, we instrument the variable full-time 50–64; in the second, we instrument the variable part-time 50–64. In the third regression, we instrument both variables. In the table, we report the coefficients of the instruments from the first stage regression and below the second stage coefficient of the instrumented variable. Taking all three results together, we do not see essential differences to the baseline reference in Table 3. The additional test statistics in the lower part of the table give us further information on the regression quality. The Kleibergen– Paap LM test gives information on underidentification, while the Wald test is employed because of potentially weak instruments. The null hypothesis of underidentification is rejected, and there is also no evidence for weak instruments. The Hansen statistic tests 13 We obtain this instrument from data from the Federal Institute for Research on Building, Urban Affairs and Spatial Development. 123 156 F. Busch et al. Table 9 Hiring older workers: baseline IV estimates Dependent variable: share hires 50–64 (1) (2) (3) First stage Instrumented variable Full-time 50–64 Part-time 50–64 Full-time 50–64 Part-time 50–64 Share of the old in the district labour force t−10.2619‡0.3163‡0.2655‡0.5389‡ (0.0257) (0.0300) (0.0256) (0.0395) Share of the old in the neighbour firms 0.3060‡0.2277‡0.3049‡0.1620‡ (0.0233) (0.0211) (0.0233) (0.0298) Second stage Full-time 50–64 0.2710‡0.2424‡ (0.0276) (0.0340) Part-time 50–64 0.3517‡0.3312‡ (0.0278) (0.0362) Kleibergen–Paap LM 91.1‡59.3‡73.0‡ Kleibergen–Paap Wald 261.4‡125.0‡63.7‡ Hansen J-statistic χ21.0 1.3 – Test of endogeneity χ25.1 4.5 6.2 Observations 5,879,369 5,879,369 5,879,369 Firms 530,658 530,658 530,658 R20.1137 0.1135 0.1142 IV = Instrumental variable regression. For further controls, see the data description. Cluster-robust standard errors at the district level are in parentheses. †: FPR ≤0.05, ‡: FPR ≤0.01 123 The hiring of older workers: evidence from Germany 157 the overidentification of all instruments and states that the instruments are coherent with each other in both cases. Finally, the endogeneity test provides no evidence that the potential endogenous regressors are, in fact, endogenous. Overall, we conclude that a simultaneity bias is small or nonexistent. The results in this section support the robustness of the results provided in Sect. 4. 6 Conclusions This article analyses how the labour force’s internal and external age structure is related to hiring older workers. Unlike previous studies, we combine panel data from the Establishment History Panel and regional unemployment data. Encouragingly, we find a positive relationship between hiring older workers and ageing among both the employed and unemployed. This suggests a gradual adjustment to demographic shifts. However, the pace of this adjustment is disappointingly slow. Our measure of the relative hiring ratio for older workers further substantiates our findings. We find adverse labour market opportunities for different firm sizes, sectors, and East and West Germany. Consequently, our measure shows that the labour market is less open for older workers. The calculated elasticities further support these findings. Moreover, we find that the speed of adjustment is even slower when ageing occurs outside the firm. This coincides with low job-finding rates for older workers in Germany. Surprisingly, a rising share of employees in partial retirement schemes is negatively related to the share of hired older workers. Thus, while this policy enhances flexibility for internal employees, it unfortunately diminishes the employment opportunities for older external job seekers. Our results should be viewed in the context of the ongoing debate in Germany about the retirement age, particularly considering the policy reform 2008, which gradually increased the mandatory retirement age from 65 to 67 years, starting in 2012. Firms do respond to demographically induced changes in the labour force composition by hiring more older workers. However, the proportion of older people among the unemployed outweighs their share among the hired or within the firm, and the hiring elasticity of older unemployed is very small. These findings have important implications for policymakers and professionals in the labour market, highlighting the need for strategies to improve the employment prospects of older workers in Germany. A promising agenda for future research might be the consideration of gender-related questions. Specifically, the hiring behaviour towards women in general, particularly older women, might yield interesting results since female labour is seen as a potential resource of labour supply. 123 158 F. Busch et al. Appendix Appendix A: Data description Firm level variables The dependent variable is the ratio of hires aged 50–64 to all hires at the firm level. Concerning the explanatory variables at the firm level, we control for the existing age structure of full-time and part-time employees. For both groups of employees, We include the youth share (15 to 24 years) and the share of older workers (50–64 years) and consider the age group 25 to 49 years old as the reference group. We also include the firm size, measured by the number of employees. Furthermore, we consider the share of part-time workers in each firm. In addition to the age structure, we consider the share of employees with an academic background as a control. We also add the share of low-skilled employees and take the share of medium-skilled employees as a reference. Furthermore, we consider the share of employees undergoing vocational training. We also include the share of marginal part-time workers whose monthly earnings are at most 450 EUR. In addition, we include the ratio of older workers who left the firm to all separations and the share of job-to-job movers. The latter variable is the share of hired workers with an employment relationship with another firm in the previous year. Finally, we control for industry-specific differences in the hiring behaviour of firms by including 13 sector-specific dummy variables.14 Administrative district level variables To proxy the size and age structure of the labour force, we consider the share of the youth and older workers among the unemployed and the total number of unemployed at the administrative district level. The reference is the share of unemployed aged 25 to 49 years. Also, we control for the degree of urbanisation at the administrative district level. We obtained the data from BBSR (see fn. 5) and followed their classification, which defines four basic categories. The first entails cities with at least 100,000 inhabitants. Category 2 comprises all districts where at least 50 per cent of all inhabitants live in major or medium-sized cities, and the population density is at least 150 inhabitants per km2. Category 3 encloses all districts sharing the attributes from Category 2 but reports a population density between 100 and 150 inhabitants per km2. Finally, Category 4 comprises all districts where under 50 per cent of the population lives in major or medium-sized cities, and the population density is at most 100 inhabitants per km2. Appendix B: Computation of the false positive risk The false positive risk (FPR) was introduced by Colquhoun (2019,2017) and measures the probability that the result occurred by chance P(H0|data). The approach is 14 For a detailed depiction, see the FDZ data report of the Sample of Integrated Labour Market Biographies Regional File (SIAB-R) 1975–2021, Table A9 on page 74. 123 The hiring of older workers: evidence from Germany 159 based on the Bayes theorem that we express in odds: posterior odds on H1=Bayes factor prior odds This is equal to P(H1|data)/P(H0|data)=P(data|H1)/P(data|H0)P(H1)/P(H0) Following Colquhoun, the Bayes factor becomes a likelihood ratio (LR), and the prior odds can be expressed using the probability that there is a real effect, P(H1):P(H1)/(1−P(H1)). Among others, Sellke et al. (2001) provide an approach to calculate the LR based on the p-value: LR =1/(−eplog(p)). However, this measure can be considered only as long as p<1/e, with eas Euler’s number. Taking things together and considering P(H0|data)=1−P(H1|data)gives us the FPR: FPR =(1/(1+(1/(−eplog(p))(P(H1))/(1−P(H1))))) Applying the FPR approach requires to specify P(H1)first. However, specifying the prior probability in regression analysis is (even in replication studies) difficult, and we should always be careful when defining this unknown number (you have to convince the reader). We use P(H1)/(1−P(H1)) =0.5/(1−0.5)=1 which means that both probabilities have the same weight. This is equal to a 50:50 chance for a real effect specified before the data are analysed. This seems reasonable when we do not know what to choose or are open to the results. Hence, the prior probability of a real effect, P(H1),isfixedto0.5. In this case, the FPR is much larger than the corresponding p-value, and for example, p=0.05 is equal to a FPR of 0.2893. Appendix C 123 160 F. Busch et al. Table 10 Hiring older workers: unrestricted panel Dependent variable: share hires 50–64 Baseline firm level Full-time 50–64 0.2702‡ (0.0030) Part-time 50–64 0.4333‡ (0.0023) Full-time 15–24 −0.0446‡ (0.0006) Part-time 15–24 −0.0252‡ (0.0004) Partial retirement −0.3988‡ (0.0128) Administrative district level Unemployed 50–64 0.0139 (0.0055) Unemployed 15–24 0.0098 (0.0116) Observations 9,595,987 Firms 1,893,345 R20.2003 Fixed effects regression. For further controls, see the data description. Cluster-robust standard errors at the district level are in parentheses. †: FPR ≤0.05, ‡: FPR ≤0.01 123 The hiring of older workers: evidence from Germany 161 Table 11 Summary statistics for subsections Obs Mean Std. err Obs Mean Std. err Obs Mean Std. err Small firms Medium firms Large firms Hires 50–64 2,839,260 13.78 29.44 2,905,010 14.04 22.50 750,970 14.29 14.68 Full-time 50–64 2,839,260 14.17 26.71 2,905,010 23.26 22.07 750,970 28.24 16.08 Full-time 15–24 2,839,260 10.97 23.65 2,905,010 9.29 14.34 750,970 7.29 8.05 Part-time 50–64 2,839,260 21.30 29.60 2,905,010 26.23 24.92 750,970 28.99 20.62 Part-time 15–24 2,839,260 21.48 31.10 2,905,010 24.45 26.93 750,970 25.75 24.63 Partial retirement 2,839,260 0.09 1.41 2,905,010 0.38 2.07 750,970 1.07 2.83 Share unemployment 50–64 2,839,260 30.03 5.46 2,905,010 30.33 5.52 750,970 30.14 5.48 Share unemployment 15–24 2,839,260 10.52 2.27 2,905,010 10.48 2.28 750,970 10.38 2.27 Primary sector Secondary sector Tertiary sector Hires 50–64 141,683 16.47 25.01 2,058,404 14.55 23.37 3,663,985 13.41 22.98 Full-time 50–64 141,683 26.47 21.29 2,058,404 22.98 21.67 3,663,985 21.26 23.87 Full-time 15–24 141,683 8.60 14.26 2,058,404 8.86 14.15 3,663,985 10.07 17.59 Part-time 50–64 141,683 30.48 30.28 2,058,404 24.38 26.54 3,663,985 26.19 24.49 Part-time 15–24 141,683 23.01 28.66 2,058,404 28.80 29.93 3,663,985 21.14 25.04 Partial retirement 141,683 0.90 3.22 2,058,404 0.22 1.30 3,663,985 0.53 2.44 Share unemployment 50–64 141,683 31.40 5.95 2,058,404 30.52 5.63 3,663,985 30.01 5.39 Share unemployment 15–24 141,683 10.70 2.28 2,058,404 10.65 2.28 3,663,985 10.37 2.26 123 162 F. Busch et al. Table 12 Summary statistics for subsections Obs Mean Std. err Obs Mean Std. err East Germany West Germany Hires 50–64 1,023,460 17,09 25.69 4,855,909 13.22 22.57 Full-time 50–64 1,023,460 25,99 23.56 4,855,909 21.15 22.90 Full-time 15–24 1,023,460 6,98 13.01 4,855,909 10.15 16.97 Part-time 50–64 1,023,460 26,53 29.04 4,855,909 25.48 24.59 Part-time 15–24 1,023,460 23,53 30.80 4,855,909 23.93 26.36 Partial retirement 1,023,460 0,63 2.99 4,855,909 0.39 1.92 Share unemployment 50–64 1,023,460 31,87 6.94 4,855,909 29.88 5.07 Share unemployment 15–24 1,023,460 9,80 2.26 4,855,909 10.62 2.25 Acknowledgements We would like to thank Axel Börsch-Supan, Bernhard Boockmann, Ulrich Walwei, and two anonymous referees for helpful comments. Funding Open Access funding enabled and organized by Projekt DEAL. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. References Adams SJ, Heywood JS (2007) The age of hiring and deferred compensation: evidence from Australia. Econ Rec 83(261):174–190 Adler G, Hilber D (2009) Industry hiring patterns of older workers. Res Aging 31(1):69–88 Axelrad H, Malul M, Luski I (2018) Unemployment among younger and older individuals: does conventional data about unemployment tell us the whole story?. J Labour Mark Res 52(3) Cai L, Law V, Bathgate M (2014) Is part-time employment a stepping stone to full-time employment? Econ Rec 90(291):462–485 Colquhoun D (2017) The reproducibility of research and the misinterpretation of Pvalues. R Soc Open Sci 4:171085 Colquhoun D (2019) The false positive risk: a proposal concerning what to do about p-values. Am Stat 73:192–201 Daniel K, Heywood JS (2007) The determinants of hiring older workers: UK evidence. Labour Econ 14:35–51 Dietz M, Walwei U (2011) Germany - no country for old workers? J Labour Mark Res 44(4):363–376 Heywood JS, Jirjahn U, Tsertsvardze G (2010) Hiring older workers and employing older workers: Germans evidence. J Popul Econ 23(2):595–615 Heywood JS, Ho L-S, Wei X (1999) The Determinants of Hiring Older Workers: Evidence from Hong-Kong. ILR Rev 52(3):444–459 Hirsch BT, Macpherson DA, Hardy MA (2000) Occupational age structure and access for older workers. ILR Rev 53(3):401–418 123