HRM 3302-22.02.00-5A25-S1, Human Resource Management Unit VII Scholarly Activity Assignment Instructions In this three-part assignment, you will address employee rights and labor relations, total co

eckaus (1963) stated that firms in imperfect labor markets are likely to pay for more training than Becker’s model would predict. for example, firms cannot so easily let workers pay for their training if training \ and regu- lar output are jointly produced and training costs cannot be perfectly iden- tified. More influential is eckaus’s notion that firms would have incentives to pay for training if they could capture rents from it, which would be \ the case for not perfectly mobile workers. katz and Ziderman (1990) and Chang and Wang (1996) emphasized information asymmetries from which imper - fect labor mobility arises. They assumed that current firms have priva\ te information about the productivity of a worker after training. Because o\ ther firms do not have this information, they cannot pay the same wages as the current firm. Consequently, the current firm has at least to some degree the opportunity to pay wages below the trained worker’s marginal product and to capture rents from training. A series of prominent articles by Acemoglu and Pischke (1998, 1999a, 1999b) also analyzed the cost coverage of training in imperfect labor mar - kets. The basic rationale is that firms bear training costs if they ha\ ve monop- sony power and can capture rents from training as a result of wage compression (wages relatively more compressed than productivity, wage increases smaller than productivity increases after training [Acemoglu and Pischke 1999a]). examples are information asymmetries with respect to a worker’s training, ability, and motivation (Acemoglu and Pischke 1998) as well as labor market institutions that affect firms’ wage structure\ s such as employment protection, minimum wages, collective contracts, and codeter - mination (Acemoglu and Pischke 1999b). Dustmann and schönberg (2009) focused in their model on unions that increase wage compression when they bargain minimum wages in collective contracts, which in turn increa\ ses firm-financed training. They presented empirical support for apprent\ ice- ship training in german firms. To sum up, one core element in theoretical models of the new training literature is that firms with more compressed wage structures (lower \ intra- firm wage dispersion) should have larger incentives to pay for traini\ ng because they are better able to capture rents from training. Pischke (2\ 005:

51) concludes: “strictly speaking, labor market institutions are not really necessary for this argument, although the example of a minimum wage highlights the workings of the model nicely. however, what is necessary for firms to invest is simply that the wage structure w(t) is compressed, i.e. that w(t) is flatter than f(t) [wages w and productivity f are functions of the level 437 InTRA-fIRM W Age COMPRessIOn AnD CO veRAge Of TRAInIng COsTs of training t]. If this is the case, then the rents the firm can earn from more skilled workers will be greater than the rents earned from less skilled \ work- ers. hence, it may invest in training.” Consequently, firms with more com- pressed wage structures should also be more likely to cover all training\ costs.

I test this hypothesis below by using linked employer-employee data for large profit-maximizing establishments in germany, which allows me to gen- erate conditional intra-firm wage-dispersion measures. In doing this, \ I partly follow the suggestion by Acemoglu and Pischke (1999b: 567) that “[f\ ]uture empirical work should test the more micro-level implications that follow\ from our analysis and contrast them with those of the standard theory.” Although a large number of empirical studies on firms’ determinants\ of training already exist for germany (e.g., Düll and Bellmann 1998, 1999; ger - lach and Jirjahn 2001; gerlach, hübler, and Meyer 2002; Allaart, Bellman, and Leber 2009; Bellmann, hohendanner, and hujer 2010; goerlitz 2010; stegmaier 2010; goerlitz and stiebale 2011) and other countries (for litera- ture reviews see, for example, Asplund 2005 and Leuven 2005), only a few studies have explicitly examined firms’ determinants of training cost cover - age (Leber 2000; Bellmann and Düll 2001). from several empirical studies, we know, however, that firms bear most of the direct training costs and that much of the training is general (e.g., Loewenstein and spletzer 1998, 1999 and Barron, Berger, and Black 1999 for the United states; Pischke 2001 for germany; Booth and Bryan 2005 for the United kingdom). In my estimation sample, about half of all training establishments cover even all indirec\ t and direct training costs—that is, the training takes place during paid w\ orking time and the establishment pays for all outlays such as course fees and travel costs. such a complete training cost coverage is of course largely inconsistent with Becker’s model, because in that model establishments would not pay at all for general training and only partly for firm-specific training.\ As far as I know, no econometric study has yet explicitly tested whether a positive correlation between intra-firm wage compression and cost cove\ rage of employer-provided further training exists. Two studies by Almeida-santos and Mumford (2005) and ericson (2008), however, looked at the relation- ship between wage compression within occupations and individual worker’\ s training participation. Almeida-santos and Mumford (2005) found with British linked employer-employee data a negative correlation between wage dispersion and training incidence and duration—that is, more compressed wages lead to more training. ericson (2008) found with data from the swed- ish Labour force survey that general training duration is positively corre- lated with wage dispersion, whereas the duration of firm-specific an\ d mixed training is not significantly affected by the wage dispersion measures\ . In both studies, however, the wage compression proxies measured not the intra-firm wage dispersion but the wage dispersion within occupations and across firms. for germany, Beckmann (2002a, 2002b) analyzed indirectly the effect of wage compression on apprenticeship training by using proxi\ es such as collective contract coverage, which positively affects the proba\ bility and intensity of apprenticeship training. 438ILR RevIeW Data and Estimation Strategy Estimation Sample The data I use are the cross-sectional models of the german linked employer- employee data set of the Institute for employment Research (LIAB) (Alda, Bender, and gartner 2005). 1 The LIAB links employer-side information from the IAB establishment Panel with employee information from admin- istrative data. The administrative employee data stem basically from the\ notification procedure for unemployment, pension, and health insurance\ s.

employers must notify the social security agencies about all employees wh\ o are covered by social security at the start and at the end of an employm\ ent relationship as well as on the last day of each year. These administrative employee data include socio-demographic characteristics and individual daily gross wages of workers (in euros), which are used to generate va\ riables for the conditional intra-firm wage dispersion as an inverse measure f\ or wage compression. Disadvantages of the data are that no information abou\ t working hours is available and that wages are censored at the upper earn\ - ings limit for social security contributions. 2 Because of the absence of work- ing hours in the data, meaningful aggregate wage variables at the establishment level can be computed only for full-time workers (with th\ e exclusion of apprentices, trainees, etc.). The wage censoring leads to \ a downward bias when proxies for intra-firm wage dispersion are generate\ d because we observe too low wages (wages equal the social security contribu- tion limit) for high-wage workers (wages above the social security con\ tribu- tion limit). This bias should, however, be much smaller for conditional than for unconditional wage-dispersion measures (e.g., standard deviation of\ workers’ wages in an establishment) because the conditional wage disper - sion takes into account differences in worker characteristics (e.g., qu\ alifica- tions) and explicitly right-censored wages by applying censored regress\ ion techniques such as Tobit regressions. As the focus is on establishments’ determinants of complete cost cover - age of further training, the IAB establishment Panel is the main data source for the subsequent analysis. The panel contains data on establishments f\ rom all sixteen german federal states (Bundesländer) and all industries. every year more than 15,000 establishments with at least one employee covered \ by social security are interviewed in an unbalanced panel design survey. The sample is stratified according to 10 establishment sizes and 16 indust\ ries in each federal state, with oversampling of larger establishments. The obse\ rva- tional unit is the establishment—that is, the local unit in which maj\ or activi- ties of an enterprise are carried out. The main goal of the survey is to gain insights into the establishment’s most important parts of operation, deci- sion making, and more specifically employment.   1for more details see http://fdz.iab.de/en/Integrated_establishment_and_Individual_Data/LIAB .aspx (accessed January 4, 2014).

 2Approximately 10% of full-time workers have such right-censored wages. 439 InTRA-fIRM W Age COMPRessIOn AnD CO veRAge Of TRAInIng COsTs for the purpose of this study, I use the waves 2005 and 2007 because they contain information about coverage of direct and indirect training costs\ . 3 Because of the interest in establishments’ profit-maximizing ration\ ales for training cost coverage, the sample is restricted to profit-maximizing \ estab- lishments from the private sector that have trained at least one worker \ in the first half of a survey year. As training is likely to occur not continuously (i.e., most workers are likely to receive their training once in a whil\ e and not the same amount of training in every time period or always in the first half of a survey year), the sample is further restricted to establishments with at least 100 workers to mitigate this problem. The sample restriction to la\ rger establishments is also preferable in order to make the wage-dispersion m\ ea- sures at the establishment level meaningful. Because only full-time work\ ers are considered for the generation of wage variables at the establishment\ level, I impose the additional restriction that there be at least 10 suc\ h work- ers in the establishment from whom the wage information is generated.

finally, I considered only those establishments without missing values in the variables I used. In total, 2,118 establishments for the year 2005 and 2\ ,011 establishments for the year 2007 remain in the sample for the subsequent\ empirical analysis. Of these, 1,136 are represented in both years—tha\ t is, in 2005 as well as 2007 (balanced panel).

Estimation Strategy and Variables To analyze establishments’ determinants of complete training cost cover - age, I generate a binary variable (COSTCOV ), which takes the value 1 if an establishment states that it usually pays for all direct costs (e.g., c\ ourse fees, travel costs) and also bears the indirect costs (i.e., the training ta\ kes place during paid working time). 4 About half of the establishments in the sample completely cover all training costs. Because of the binary dependent vari- able, I estimate binary probit models. The explanatory variable of main interest is the intra-firm wage compression, for which a proxy can be gener - ated from the administrative employee data. The simplest approach would \ be to use the standard deviation of full-time workers’ daily wages in\ a given   3Questions about training cost coverage have been asked by an interviewer in the IAB establishment Panel also in the years 1999 and 2009. I have decided against the use of\ the year 1999 because this wave has a significantly lower sample size and does not contain establishme\ nts from all federal states. since 2000 the IAB establishment Panel is conducted in all german federal states. A minor reason for the restriction is also that major labor market reforms in germany were implemented after 1999. The year 2009 is not included in the analysis in order to exclude the effects fro\ m the economic crisis, during which many establishments in germany used short-time work (kurzarbeit). As one element of short-time work programs is financing training of employed workers, the question about\ training cost coverage by estab- lishments is obviously affected and not comparable with the previous yea\ rs. In fact, the establishments in the IAB establishment Panel have explicitly been asked about training cost coverage by the federal employment Agency under short-term work programs in the year 2009, which \ is an interesting topic but beyond the scope of this article.

  4The binary variable COSTCOV is a combination of answers to two questions in the IAB establishment Panel: (1) “Does the training usually take place during paid workin\ g time or during workers’ leisure time?” (COSTCOV = 1 if training during paid working time). (2) “Do workers usuall\ y have to cover all, part, or none of the direct training costs?” (COSTCOV = 1 if workers cover none of the direct costs). 440ILR RevIeW establishment, which would measure the unconditional wage dispersion.

This dispersion has, however, the disadvantage that it does not account for differences in worker characteristics such as qualifications, which affect pro- ductivity and wage classifications. Therefore, a conditional wage-disp\ ersion measure is a much better proxy for wage compression.

I follow the approach of Winter-ebmer and Zweimüller (1999), who ana- lyzed the effect of intra-firm wage dispersion on establishment perfor - mance. 5 exploiting the nature of the linked employer-employee data set, I estimate log-linear Mincer earnings functions for full-time workers sepa- rately for every establishment in a given year. The dependent variable is the log of workers’ individual daily wages. The explanatory variables include the usual productivity-related individual worker characteristics such as age\ , squared age, tenure, squared tenure, highest qualification categories \ (no job qualification as reference group, apprenticeship degree, university degree), and a female dummy. To account for censored wages in the data, I estimate Tobit regressions with different upper earnings limits for east and West germany as well as for the year 2005 and the year 2007. 6 On the basis of the results for an establishment’s earnings function, I then generate the standard error of the Tobit regression as a proxy for the intra-firm wage compression (logWSERT ). The standard error of the regression in an estab- lishment can be interpreted as the standard deviation of workers’ ind\ ividual error terms in an estimated earnings function for this establishment in \ a given year. A larger standard error of the regression indicates a larger condi- tional intra-firm wage dispersion and consequently lower intra-firm \ wage compression. Descriptive statistics for the intra-firm wage compression proxy (log- WSERT ) are displayed in Table 1. Mean standard errors of the regressions are on average approximately 0.22 with a standard deviation of 0.07. 7 When comparing the means and standard deviations of my estimated standard errors of the regressions with the results of Winter-ebmer and Zweimüller (1999), I find only small differences. Winter-ebmer and Zweimüller (1999) used data of workers in 130 firms, which were obtained from Austrian s\ ocial security records for the years 1975 to 1991. Their estimated standard er\ rors of Tobit regressions for the log of monthly income have a mean of 0.205 with a standard deviation of 0.074.   5This approach has been widely used with linked employer-employee data in order to study the effects of wage inequality on firm performance measures such as productivity and profits. for a literature review see Mahy, Rycx, and v olral (2011: Appendix Table A1).

 6The corresponding censoring values for the upper earnings limits for soc\ ial security contributions with respect to daily wages in euros have been set according to the stat\ utory pension fund (accessed at http://doku.iab.de/fdz/Bemessungsgrenzen_de_en.xls [January 4, 2014]): WesT2005=170.96, eAsT2005=144.66, WesT2007=172.60, eAsT2007=149.59.

 7In the robustness check section (see Table 3 and 4), I estimate Iv probit models, in which the first- stage regressions give some insights into the determinants of the intra-\ firm wage compression proxy (logWSERT ). for example, establishments bound to a union-bargained collective contrac\ t have signifi- cantly lower intra-firm wage dispersion, whereas works councils are no\ t significantly correlated with the wage-dispersion variable. Moreover, larger establishments have significantly lower wage dispersion, and establishments with a larger share of women have larger wage dispersion.\ Table 1. variable Definitions and Descriptive statistics for firm Characteristics Year 2005 (n = 2,118) Year 2007 (n = 2,011) Balanced panel (n = 2 x 1,136 = 2,272) Variable DefinitionsMeanStd. dev. MeanStd. dev. MeanStd. dev.

Dependent variable COSTCOV firm covers completely all direct and indirect training costs (dummy) 0.5184 0.48430.5158 Wage variables logWSERT Intra-firm standard error of log daily gross wage regressions for full-time workers obtained from Tobit 0.2187 0.07210.2215 0.0737 0.2205 0.0731 logWMEAN Intra-firm mean of log daily gross wages of full-time workers 4.51560.29334.5119 0.3229 4.5368 0.2933 Control variables Union firm is bound to union-bargained collective contract (dummy) 0.79080.74540.7879 Works council firm has a works council (dummy) 0.84280.80910.8556 number of quits number of quits during first half of survey year 3.838113.3393 5.018916.2395 4.060313.1641 number of layoffs number of layoffs during first half of survey year 3.983516.7185 3.381914.0750 3.693216.6723 number of workers / 1,000 number of workers at June 30 / 1,000 0.64961.87640.5908 1.8959 0.6514 2.0746 firm age < 6 years firm younger than 6 years (dummy, reference) 0.05480.05420.0370 firm age 6–15 years firm age between 6 and 15 years (dummy) 0.24410.16310.1888 firm age > 15 years firm older than 15 years (dummy) 0.70110.78270.7742 Production technology state-of-the-art production technology (0–5; 0: newest, 5:

outdated) 2.0132 0.70951.9866 0.7020 1.9859 0.6920 Profit situation At least good profit situation (subjective perception) in last business year (dummy) 0.4164 0.57630.5040 share women share of female workers 0.34600.24520.3549 0.2532 0.3336 0.2377 share part-time share of part-time workers 0.12940.17700.1405 0.1913 0.1226 0.1695 share qualified share of qualified workers (at least apprenticeship or college degree) 0.7260 0.24790.7460 0.2453 0.7404 0.2370 442ILR RevIeW Because a larger standard error of the wage regression (logWSERT ) might be the result of larger wage levels in an establishment, the probit regr\ essions for COSTCOV also include the mean of log daily wages of full-time workers in an establishment in a given year (logWMEAN ) as a control variable. The pro- bit regressions further control for important differences between establ\ ish- ments that might affect training as well as wage structures. Industrial relations are important in this context because unions and works councils are often associated with more compressed wage structures and more training for workers (e.g., Acemoglu and Pischke 1999b; Dustmann and schönberg 2009). Moreover, the regressions include variables for the number of layoffs and quits, the number of workers, three establishment age categories, st\ ate- of-the-art production technology, profit situation, share of women, share of part-time workers, share of qualified workers, 16 federal state dummie\ s, and 15 industry dummies, which should control for a large set of potential differ - ences between establishments with different degrees of wage compression.\ Table 1 presents complete variable definitions and descriptive statisti\ cs. I estimate the determinants of cost coverage (COSTCOV ) using binary pro- bit models for the separate cross-sections 2005 and 2007 as well as a random- effects probit model for a balanced panel. The random-effects model serves mainly as a robustness check to account for within-establishment variance, because a likelihood-ratio test rejects the hypothesis that the within- establishment variance does not significantly contribute to the total \ variance.

I choose the random-effects model over a fixed-effects model for sever\ al reasons. At first, no consistent fixed-effects estimators exist for \ probit or logit models in short panels because of the incidental parameter problem\ .

fixed-effects linear probability models are also not a feasible estimation strategy because training cost coverage, wage structures, and industrial\ rela- tions are structural establishment characteristics based on strategic de\ ci- sions; thus changes are not common and are unlikely to be in effect rapi\ dly.

Accordingly, within-establishment variance is very low for most variables of interest in my data. nevertheless, in the robustness check section, I estimate an establishment fixed-effects linear probability model and a correlated random-effects probit model, which explicitly take unobserved establish- ment heterogeneity into account. Though not statistically significant \ because of the low within-establishment variance, these estimates suppor\ t the main findings from the cross-section and random-effects probit mod\ els.

In an attempt to further check the sensitivity of the main findings, I\ apply an Iv probit approach in the robustness checks, which again supports the main\ findings that are presented in the next section.

Estimation Results Main Findings Table 2 presents the results of the binary probit regressions for the probabil- ity that an establishment covers completely all direct and indirect trai\ ning 443 InTRA-fIRM W Age COMPRessIOn AnD CO veRAge Of TRAInIng COsTs costs (COSTCOV ). The first column contains the results of the cross-section probit for the year 2005 and the second column the results for the year \ 2007. The third column presents the results of the random-effects probit\ model for the balanced panel. To facilitate the quantitative interpretation, I compute marginal effects at the means of all covariates in each estimati\ on sample. Table 2. Probit Regressions for Complete Training Cost Coverage by firms Variable Year 2005 Cross-section probit Year 2007 Cross-section probit Balanced panel Random-effects probit logWSERT –0.4939***–0.3615** –0.3744* (0.1712)(0.1712) (0.2104) [p = 0.004][p = 0.035] [p = 0.075] logWMEAN 0.1129*0.1026* 0.1555** (0.0586)(0.0561) (0.0764) Union 0.0150–0.0166 0.0181 (0.0309)(0.0295) (0.0386) Works council 0.05380.0856** 0.0390 (0.0363)(0.0356) (0.0487) number of quits –0.0014–0.0002 0.0007 (0.0011)(0.0009) (0.0012) number of layoffs –0.0020**–0.0010 –0.0019* (0.0009)(0.0010) (0.0011) number of workers /1000 –0.00160.0003–0.0008 (0.0071)(0.0067) (0.0075) firm age 6–15 years –0.07110.0246–0.0165 (0.0558)(0.0596) (0.0770) firm age > 15 years –0.1290**–0.0115 –0.0458 (0.0510)(0.0540) (0.0731) Production technology 0.01880.0251 0.0400* (0.0165)(0.0173) (0.0204) Profit situation 0.0150–0.0246 0.0046 (0.0236)(0.0243) (0.0280) share women 0.10530.0243 0.1305 (0.0763)(0.0784) (0.1029) share part-time 0.1795*0.1831** 0.2457** (0.0956)(0.0897) (0.1238) share qualified –0.0833–0.0475 –0.1037 (0.0560)(0.0575) (0.0744) Controls for federal states (16) and industries (15) ye s ye s ye s Pseudo R ² (Mcfadden) 0.06280.0635 number of observations 2,1182,011 2,272 Mean dependent variable 0.51840.4843 0.5158 Notes: Marginal effects at the means of all covariates in each estimation samp\ le on the probability of complete training cost coverage by the firm (COSTCOV); binary probit regressions for 2005 and 2007; random-effects probit regressions for balanced panel. All regressions in\ clude control variables as described in Table 1, 16 federal state and 15 industry dummies. The random-effects probit regression further includes a dummy variable for the year 2007. standard errors (robust for cross-section probits) in parentheses.

significant at *p < 0.10; **p < 0.05; ***p < 0.01. 444ILR RevIeW The main finding can be seen from the first row of marginal effects \ in Table 2. A larger standard error of an establishment’s workforce wage regres- sion (logWSERT) is significantly negatively correlated with the probability that an establishment pays all direct and indirect training costs throug\ hout all three regressions—that is, establishments with lower intra-firm\ condi- tional wage dispersion (more compressed wage structures) are on average more likely to cover all training costs. A 0.1 log point higher standard\ error of the wage regression decreases the cost coverage probability in the ye\ ar 2005 on average by 4.9 percentage points (p = 0.004) and in the year 2007 by 3.6 percentage points (p = 0.035). 8 The random-effects probit regression yields a comparable marginal effect of minus 3.7 percentage points (p = 0.075) per 0.1 log point higher standard error of the regression. The fi\ nd- ings are consistent with the theoretical consideration that establishments can capture rents from training because of intra-firm wage compression\ , which provides incentives for establishments to pay for further training\ . Moreover, the results in Table 2 indicate that unions have no significant effects throughout all regressions, whereas works councils are positivel\ y cor - related with the probability that an establishment completely covers tra\ in- ing costs. hence, it seems as if establishment-level codetermination is more influential in this context than union bargaining. Only a few control \ vari- ables significantly affect the cost coverage probability in a consiste\ nt pattern across the regressions. establishments with more layoffs have a lower prob- ability of completely covering all training costs, which might be explai\ ned by amortization aspects and a loss in employment flexibility if adjust\ ment costs increase after the establishment has paid for training. furthermore, the share of part-time workers indicates a positive correlation with the train- ing cost coverage probability. This finding might be surprising at first glance if amortization aspects are taken into account. Because part-time worker\ s are often associated with the flexible part of an establishment’s workforce (periphery), one would expect establishments to invest less in their human capital. There may be several explanations for these findings. first, since I use aggregate establishment-level data, the share of part-time workers, as part of the peripheral workforce, might be an indicator for the existenc\ e of dual internal labor markets, in which establishments rely on stable empl\ oy- ment relationships with, and provide training for, their core workforce. sec- ond, workers of the peripheral workforce are by definition more often \ newly employed by an establishment and might need work instructions that are paid for by the establishment. Third, part-time workers have on average \ lower income, which might lead to credit constraints so that the establi\ sh- ment might have to pay for the training. These interpretations are, howe\ ver, only speculations that cannot be tested with the data I use.   8for the interpretation of the economic significance of the effect size \ recall that logWSERT has a mean of 0.22 with a standard deviation of 0.07 (see descriptive statist\ ics in Table 1). Thus, an increase by one standard deviation of logWSERT decreases the cost coverage probability by approximately three percentage points. 445 InTRA-fIRM W Age COMPRessIOn AnD CO veRAge Of TRAInIng COsTs Robustness Checks I have performed several robustness checks on the sensitivity of the main find - ings, summarized below. 9 I have used alternative proxies for the intra-firm wage compression (dispersion) variable. first, I have used the standard deviation of full-time workers’ daily wages in an establishment (unc\ ondi- tional wage dispersion). second, I have used simple linear regressions instead of Tobit regressions to generate the standard errors of the wage regressions for each establishment. Both alternative variables are negat\ ively correlated with the probability that an establishment pays all training \ costs at even higher significance levels than the standard errors of Tobit regres- sions (logWSERT ).

The next robustness checks deal explicitly with unobserved establishment heterogeneity. I have applied two panel estimation techniques that are both problematic for my data because of very low within-establishment variance for most variables of interest. nevertheless, they should be mentioned. first, I have estimated an establishment fixed-effects linear probability model.

The estimated marginal effects for the intra-firm wage-dispersion vari\ able have the negative sign known from the previous probit models. Because of\ the low within-establishment variance, however, the effects are not statisti- cally significant. still, the results indicate a negative rather than a positive correlation between intra-firm wage dispersion and training cost cover\ age if time-invariant unobserved establishment heterogeneity is taken into account in a fixed-effects linear probability model. Moreover, I have reesti- mated the random-effects probit model with additional variables that con\ - tain the means of each observed establishment characteristic over time, which is known as Mundlak’s approach (Mundlak 1978). The inclusion of group means in random-effects models controls intuitively for unobserved heterogeneity and allows dependence between the random effects and the regressors. This approach is a widespread method in econometrics and can\ also be applied for probit models (Chamberlain 1980), which are some- times called correlated random-effects probit models (for a detailed te\ xt- book discussion see, for example, Wooldridge 2010: 610–19). The results of the correlated random-effects models indicate again a negative rather th\ an a positive correlation between intra-firm wage dispersion and training\ cost coverage, even though the effects are not statistically significant be\ cause of the low within-establishment variance. Another source of endogeneity might be reverse causality—that is, the\ causal link might not go from wage compression to training cost coverage\ but the other way around. If establishments pay for training, workers mi\ ght receive lower returns to training, which decreases wage differentials be\ tween trained and untrained workers and consequently increases wage compres- sion. To deal with this endogeneity problem, I have estimated instrumental variable (Iv) probit regressions (for detailed discussions see Rivers and  9The complete results of the robustness checks can be requested from the author. 446ILR RevIeW vuong 1988 and Wooldridge 2010: 585–94). note that Iv estimation strate- gies are also suitable to deal with potential omitted variable biases. As instruments, which affect the intra-firm wage compression, I use th\ e lowest observed wage of a worker in an establishment and the mean of the intra-firm standard errors of log daily wage regressions within indust\ ry and federal state cells. Previous studies about training have often emphasiz\ ed institutional minimum wages, which are, however, not that common in ger - many and not observed in the data. Whereas institutional minimum wages can be seen as exogenous to establishments, the lowest observed wage in an establishment is a rather technical instrument that has the advantage of\ exploiting large between-establishment variance. The rationales for usin\ g the mean of the intra-firm standard errors of log daily wage regressio\ ns within industry and federal state cells as a second instrument are norms and spillover effects in regional labor markets (e.g., an establishment’\ s wage structure is affected by institutional developments in the past and by w\ age structures of other establishments in the same industry and region). from a theoretical point of view, both instruments should be significantly corre- lated with the intra-firm wage compression in the first-stage regres\ sion. But to be valid instruments, they should have no further direct impact on th\ e probability of training cost coverage in the second-stage regression. Th\ e lowest observed wage in an establishment might fulfill this critical condition because it seems unlikely that larger establishments adjust their genera\ l employment policies such as training cost coverage explicitly to the low\ est- paid worker. for the mean of the intra-firm wage dispersion within industry and federal state cells, it is, however, not so easy to justify this condition because norms and spillover effects in regional labor markets that affec\ t establishments’ wage structures might also affect their decisions abo\ ut train- ing cost coverage. Besides these potential problems, I start with Iv probit estimates that use both instruments before using the lowest observed log daily wage in an establishment as a single instrument. I estimate the first stage in the Iv probit framework with linear regres- sions that use the lowest observed log daily wage in an establishment (logW- MINIMUM) and the mean of the intra-firm standard errors of log daily wage regressions within 15 industry and 16 federal state cells (logWSERTis) as instruments for an establishment’s intra-firm standard error of log daily wage regressions (logWSERT ). Table 3 shows that logWMINIMUM is indeed negatively correlated and logWSERTis is positively correlated with logWSERT at high statistical significance levels in the first-stage regressio\ ns. I then esti- mate the second stage with binary probit regressions that include the stan- dardized predicted error terms for every establishment from the first-stage regressions ( j first first / ).

The coefficients for the standardized predicted error terms are not si\ g- nificantly different from zero in either 2005 or 2007, and the Wald test of exogeneity cannot be rejected. Therefore, endogeneity seems not to be an\ important issue in my application. Marginal effects on the probability o\ f complete training cost coverage by the establishment (COSTCOV) ˆ ˆ Table 3. Iv Probit Regressions for Complete Training Cost Coverage by firms Year 2005: IV probit Year 2007: IV probit Variable 1st stage2nd stage mfx1st stage 2nd stage mfx logWMINIMUM –0.0467***–0.0471*** (0.0018)(0.0020) logWSERTis 0.6601***0.6543*** (0.0592)(0.0611) logWSERT –1.1486*–0.4577* –1.0598–0.4225 (0.6508)(0.2593) (0.6641)(0.2647) [p = 0.078][p = 0.111] logWMEAN 0.0152*0.2864*0.1141*0.0093 0.2514*0.1002* (0.0083)(0.1483)(0.0591)(0.0062) (0.1420)(0.0566) Union –0.0206***0.03990.0159–0.0202*** –0.0449–0.0179 (0.0030)(0.0784)(0.0313)(0.0030) (0.0750)(0.0299) Works council –0.00230.13400.0534–0.0039 0.2170**0.0865** (0.0038)(0.0914)(0.0364)(0.0039) (0.0911)(0.0363) number of quits 0.0002**–0.0035 –0.0014–0.00001 –0.0005–0.0002 (0.0001)(0.0027)(0.0011)(0.0001) (0.0021)(0.0008) number of layoffs 0.0002***–0.0050** –0.0020**–0.0001 –0.0025–0.0010 (0.00005)(0.0022)(0.0009)(0.0001) (0.0024)(0.0010) number of workers /1000 –0.0055***–0.0039–0.0016–0.0049*** 0.00080.0003 (0.0012)(0.0178)(0.0071)(0.0008) (0.0168)(0.0067) firm age 6–15 years 0.0008–0.1779 –0.07090.0004 0.06210.0247 (0.0052)(0.1403)(0.0559)(0.0059) (0.1494)(0.0596) firm age >15 years –0.0012–0.3264**–0.1301**0.0080 –0.0269–0.0107 (0.0049)(0.1314)(0.0524)(0.0052) (0.1357)(0.0541) Production technology –0.00130.04780.01900.0010 0.06240.0249 (0.0015)(0.0415)(0.0165)(0.0018) (0.0433)(0.0173) Profit situation –0.00050.03700.0148–0.0034 –0.0621–0.0247 (0.0023)(0.0591)(0.0236)(0.0025) (0.0610)(0.0243) (continued) Year 2005: IV probit Year 2007: IV probit Variable 1st stage2nd stage mfx1st stage 2nd stage mfx share women 0.0360***0.25960.10340.0414*** 0.06930.0276 (0.0089)(0.1931)(0.0769)(0.0081) (0.1989)(0.0793) share part-time 0.01920.4499*0.1793*0.0165 0.4586**0.1828** (0.0122)(0.2399)(0.0956)(0.0115) (0.2251)(0.0897) share qualified 0.0083–0.2107 –0.08400.0012 –0.1167–0.0465 (0.0058)(0.1409)(0.0561)(0.0063) (0.1444)(0.0576) Controls for federal states (16) and industries (15) ye sye sye sye s ye sye s Constant 0.1519***–0.0842 0.1725***–0.3225 (0.0386)(0.7765) (0.0306)(0.7675) jfirst first / –0.00800.0137 (0.0419)(0.0442) number of observations 2,1182,1182,1182,011 2,0112,011 Notes: (Iv : logWMINIMUM and logWSERTis). The first stage is estimated with linear regressions that use the \ lowest observed daily wage in a firm (logWMINIMUM) and the mean of logWSERT within industry and federal state cells (logWSERTis) as instruments for firms’ intra-firm standard error of log dai\ ly wage regressions (logWSERT). The second stage is estimated with binary probit regressions that include the standardized predicted error terms\ for every firm from the first-stage regressions ( j first first / ). Marginal effects at the means of all covariates in each estimation sample on the probability of complete training cost coverage by the firm (COSTCOV ) are presented in the third column for every year. All regressions include control variables as described in Table 1, 16 federal state and 15 industry dummies. Robust standard errors in parentheses.

significant at *p < 0.10; **p < 0.05; ***p < 0.01. Table 3. Continued ˆˆ ˆ ˆ 449 InTRA-fIRM W Age COMPRessIOn AnD CO veRAge Of TRAInIng COsTs are presented in the third column for every year. As I have used the same estimation samples and compute comparable marginal effects at the means \ of all covariates in each estimation sample, the Iv probit results can be com- pared in size with the probit results in Table 2. The results in Table 3 reveal marginal effects of minus 4.6 percentage points in the year 2005 and min\ us 4.2 percentage points in the year 2007 per 0.1 log point higher standard\ error of the wage regression. These marginal effects are comparable in s\ ize to the results in Table 2. The statistical significance levels, however, are lower in the Iv probit regressions because of larger standard errors (p = 0.078 in the year 2005, p = 0.111 in the year 2007).

Table 4 presents Iv probit results for the use of the lowest observed log daily wage in an establishment (logWMINIMUM ) as a single instrument in order to check the sensitivity of the above Iv probit regressions with two instruments. The results do not change notably. Again, the coefficients for the standardized predicted error terms are not significantly different\ from zero in either 2005 or 2007, and the Wald test of exogeneity cannot be rejected. A 0.1 log point increase of the standard error of the wage reg\ res- sion decreases the probability of complete cost coverage by 4.6 percenta\ ge points (p = 0.099) in the year 2005 and by 3.8 percentage points (p = 0.164) in the year 2007, which is comparable in size with the previous results.\ The last robustness check is concerned with the establishment sample, which is very conservative with respect to establishment size because only establishments with at least 100 workers have been included. The prefer - ence for this conservative sample restriction was driven by potential sample selectivity and measurement errors with respect to training and the intr\ a- firm wage-dispersion variables in smaller establishments. Despite thes\ e potential problems, I have relaxed the sample restriction and reestimate\ d all regressions for a sample of establishments with at least 10 workers.\ The overall results do not change notably. The estimated marginal effects for the wage compression (dispersion) variable are statistically significant at even higher levels than in the sample of larger establishments, which can be \ at least partly attributed to the larger sample size, which has increased t\ o more than 4,000 establishments in each year and to more than 2,000 establish- ments in the balanced panel.

Conclusion In this empirical article, I have used german linked employer-employee data, which contain information about establishments’ cost coverage of training and allow me to generate the conditional intra-firm wage disp\ er - sion as proxy for an establishment’s wage compression. The main finding of my econometric analysis is that establishments with more compressed wage\ structures are more likely to cover all direct and indirect training cos\ ts. This finding is inconsistent with Becker’s model of on-the-job training in perfect labor markets, but it is consistent with theoretical considerations of the new training literature that firms can capture rents from training because\ of Table 4. Iv Probit Regressions for Complete Training Cost Coverage by firms Year 2005: IV probit Year 2007: IV probit Variable 1st stage2nd stage mfx1st stage 2nd stage mfx logWMINIMUM –0.0500***–0.0494*** (0.0019)(0.0020) logWSERT –1.1420*–0.4551* –0.9608–0.3830 (0.6928)(0.2761) (0.6910)(0.2754) [p = 0.099][p = 0.164] logWMEAN 0.0180**0.2867*0.1143*0.00960.2553* 0.1018* (0.0088)(0.1485)(0.0592)(0.0064)(0.1422) (0.0567) Union –0.0237***0.04010.0160–0.0221*** –0.0429 –0.0171 (0.0032)(0.0787)(0.0314)(0.0031)(0.0750) (0.0299) Works council –0.00320.13390.0534–0.0035 0.2165** 0.0863** (0.0041)(0.0915)(0.0364)(0.0041)(0.0911) (0.0363) number of quits 0.0002**–0.0035 –0.0014–0.00001–0.0005 –0.0002 (0.0001)(0.0027)(0.0011)(0.0001)(0.0021) (0.0009) number of layoffs 0.0002***–0.0050** –0.0020**–0.00004–0.0025 –0.0010 (0.0001)(0.0022)(0.0009)(0.0001)(0.0024) (0.0010) number of workers /1000 –0.0058***–0.0039–0.0016–0.0052*** 0.0007 0.0003 (0.0013)(0.0178)(0.0071)(0.0009)(0.0168) (0.0067) firm age 6–15 years –0.0010–0.1779–0.0709–0.0014 0.0619 0.0247 (0.0057)(0.1403)(0.0559)(0.0062)(0.1494) (0.0595) firm age > 15 years –0.0018–0.3264**–0.1300** 0.0064–0.0281 –0.0112 (0.0055)(0.1314)(0.0524)(0.0055)(0.1357) (0.0541) Production technology –0.00160.04780.01910.00120.0628 0.0250 (0.0016)(0.0416)(0.0166)(0.0019)(0.0433) (0.0173) (continued) Year 2005: IV probit Year 2007: IV probit Variable 1st stage2nd stage mfx1st stage 2nd stage mfx Profit situation –0.00130.03700.0147–0.0037 –0.0619 –0.0247 (0.0024)(0.0591)(0.0236)(0.0026)(0.0610) (0.0243) share women 0.0408***0.25920.10330.0429***0.0639 0.0255 (0.0094)(0.1934)(0.0771)(0.0084)(0.1990) (0.0793) share part-time 0.01760.4500*0.1793*0.01730.4590** 0.1830** (0.0132)(0.2399)(0.0956)(0.0121)(0.2251) (0.0897) share qualified 0.0081–0.2109 –0.0840 0.0039–0.1183 –0.0471 (0.0063)(0.1409)(0.0561)(0.0065)(0.1445) (0.0576) Controls for federal states (16) and industries (15) ye sye sye sye sye s ye s Constant 0.3068***–0.0868 0.3071***–0.3569 (0.0376)(0.7819) (0.0301)(0.7725) jfirst first / –0.00820.0047 (0.0446)(0.0461) number of observations 2,1182,1182,1182,0112,0112,011 Notes: (Iv : logWMINIMUM). The first stage is estimated with linear regressions that use the \ lowest observed daily wage in a firm (logWMINIMUM) as an instrument for the intra- firm standard error of log daily wage regressions (logWSERT). The second stage is estimated with binary probit regressions that include the standardized predicted error terms for every firm from the first-stage regressions ( j first first / ). Marginal effects at the means of all covariates in each estimation s\ ample on the probability of complete training cost coverage by the firm (COSTCOV ) are presented in the third column for every year. All regressions include control variables as described in Table 1, 16 federal state and 15 industry dummies. Robust standard errors in parentheses.

significant at *p < 0.10; **p < 0.05; ***p < 0.01. Table 4. Continued ˆˆ ˆ ˆ 452ILR RevIeW wage compression in imperfect labor markets, which provides incentives for them to pay for training. Moreover, it seems as if union-bargained collective contracts have no significant direct effects on training cost coverage\ that go beyond the effects of unions on general wage compression, whereas the existence of a works council is rather positively correlated with comple\ te cost coverage, even after controlling for differences in establishments’ wage structures. Thus, codetermination at the establishment level seems to be\ more important than union bargaining when it comes to strategic training\ decisions in establishments, which accords with the explicit role of wor\ ks councils in establishments’ training practices stated in the german Works Constitution Act (Betriebsverfassungsgesetz).

Three caveats are in order with respect to my empirical analysis, which leave room for future research. first, the presented results might still suffer from omitted-variable bias and reverse-causality issues. To deal with those endogeneity problems and to establish a causal effect, it would be helpf\ ul to have longer panel data sets and better instrumental variables. The appli\ ed Iv approach in this article did not indicate problems of endogeneity, however.

second, although I use a linked employer-employee data set to compute vari- ables for the intra-firm wage compression, the data comprise training \ infor - mation only at the aggregated establishment level and not for individual\ workers. Therefore, my analysis could not account for worker heterogenei\ ty with respect to differences in training cost coverage. Third, the focus \ of my analysis is on testing one core element of the new training literature, \ namely, the positive effect of wage compression on training cost coverage by fi\ rms.

To provide concrete policy recommendations for stimulating human capital investments, “in future work, the link between these stories and trai\ ning can be more carefully derived, yielding empirical predictions to determine w\ hich sources of wage compression, if any, are important in encouraging firm- sponsored training” (Acemoglu and Pischke 1999b: 567). My finding\ that establishments with union-bargained collective contracts have signific\ antly lower wage dispersion (see first-stage regressions in Table 3 and Table 4) shows that unions influence establishments’ wage structures. This fi\ nding and those of Beckmann (2002a, 2002b) and Dustmann and schönberg (2009) suggest that unions are likely to be one important factor in th\ e con- text of stimulating human capital investments, even if their effect migh\ t run through the indirect channel of compressed wage structures.

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Wooldridge, Jeffrey M. 2010. Econometric Analysis of Cross Section and Panel Data. 2nd ed. Cam- bridge, MA: MIT Press. Copyright ofIndustrial &Labor Relations Reviewisthe property ofCornell University and its content maynotbecopied oremailed tomultiple sitesorposted toalistserv without the copyright holder'sexpresswrittenpermission. However,usersmayprint, download, oremail articles forindividual use.