10.1.1.480.8620 - Bonus Pay and Wage Inequality Thomas...

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Unformatted text preview: Bonus Pay and Wage Inequality Thomas Lemieux W. Bentley Macleod Daniel Parent UBC USC McGill April 2005 Abstract An increasing fraction of jobs in the U.S. labor market pay workers a bonus in addition to regular wages and salaries. In this paper, we look at the e¤ect of the growing incidence of bonus pay on wage inequality. The basic premise of the paper is that jobs paying bonuses have a more "competitive" pay structure that rewards productivity di¤erences more than other jobs. Consistent with this view, we show that compensation in bonus jobs is more closely tied to both measured (by the econometrician) and unmeasured productive characteristics of workers. We conclude that the growing incidence of bonus jobs accounts for 30 percent of the growth in male wage inequality between the late 1970s and the early 1990s. 1 Introduction In the standard competitive model of the labor market, wages are equal to marginal products and the wage structure is determined by the equilibrium of demand and supply factors. This simple model forms the backbone of most studies on change in wage inequality. For example, Katz and Murphy (1992) argue that the return to schooling increased in the 1980s because the rate of increase in the relative supply of more-educated labor decelerated while relative demand was increasing steadily. Similarly, Juhn et al. (1993) argue that the growth in within-group wage inequality throughout the 1970s and 1980s was driven by an increase in the demand for unobserved skills. More generally, the main strength of the competitive model of the labor market is that it provides a straightforward interpretation of the evolution of the wage structure in terms of the supply and demand for di¤erent types of labor. This being said, it is also well established that the competitive model is at best a good approximation for the way wages are actually determined in the labor market. Unless markets are complete and information is perfect, wages will generally not be equal to marginal products. There indeed a large number of studies that con…rm that wages are not equal to marginal products because of incomplete markets, incomplete (or asymmetric) information, or other considerations. For instance, Beaudry and DiNardo (1991) show compelling evidence that wages depend on labor market conditions at the time a worker started his or her job. This is consistent with a simple risk-sharing implicit contract, but inconsistent with the competitive model that predicts that wages should only depend on current labor market conditions. Farber and Gibbons (1996) and Altonji and Pierret (2001) provide evidence that wages are not equal to marginal products because information is imperfect and it takes time to …rms to learn about the actual productivity of workers. A more “mundane”reason why wages are not equal to marginal products is the presence of labor market institutions. For example, it is well established that labor unions tend to compress the wage structure (Freeman (1980), Card (1996), Lemieux (1998)) and reduce the wage di¤erence between more productive and less-productive workers relative to a nonunion setting. Similarly, a substantial number of workers at the bottom end of the wage distribution are paid a legislated minimum wage instead of their actual marginal product. Because of these contracting, observability, and institutional factors, wages are clearly 1 not equal to marginal products and the full distribution of wages is not simply determined by standard demand and supply factors. This does not mean, however, that changes in the wage distribution are not well explained by changes in demand and supply factors. For example, if contracting, observability, and institutional factors simply introduce an i.i.d. departure between wages and marginal products, changes in the wage structure will not be a¤ected by these factors. Put in these terms, the key question is not whether the competitive model is only an approximation for the way wages are actually set, but whether the quality of the approximation is constant over time. Existing studies already show, however, that the e¤ect of labor market institutions has been changing over time. For instance, DiNardo et al. (1996) attribute to the decline in unionization and in the real value of the minimum wage about a third of the increase in wage inequality in the 1980s. In the context of the above discussion, their …ndings suggest that the competitive model has become an increasingly good approximation for the way wages are actually set in the labor market. Part of the increase in wage inequality thus re‡ects the fact that workers who used to earn a union or a minimum wage are now earning a more competitive wage. These …ndings raise the obvious question of whether departures between wages and marginal products induced by factors other than labor market institutions may have also changed over time. There are indeed a number reasons to believe that this may be the case. For example, improvements in the functioning of …nancial markets may reduce the need for …rms to provide insurance to workers through implicit contracts. This means that …rms are paying a wage that is increasingly close to the actual marginal product of workers. Perhaps even more important, the advances in information and communication technologies have dramatically reduced to cost of gathering and processing information. One important implication of these changes is that it may now be cheaper for …rms to collect and process detailed information about the individual performance and productivity of workers. In about any model where wages are not set to marginal products because information is costly, a reduction in the cost of information will lead to wages being closer to marginal products. If the amount of information used by …rms in setting wages was available in standard data sets, it would be relatively straightforward to check whether the increased availability of information about individual productivity has made wages closer to marginal products 2 and may have, by doing so, contributed to recent changes in wage inequality. The “e¤ect” of information on the wage structure could be estimated in the same way that the e¤ect of union status on the wage structure is estimated in standard data sets. These estimates could then be used to assess the contribution of changes in information quality on wage inequality. But even though the quality of information about individual productivity is not observed in existing data sets, we argue that some existing variables about the form of compensation used are useful proxies for the quality of information available to …rms. In particular, the basic assumption of the paper is that bonus pay is a useful proxy for the quality of information about workers’ productivity available to …rms. The idea is simply that …rms need better information about worker’s productivity to decide on bonuses to be paid that when wages are simply set using administrative procedures based on job rank, seniority, etc. The better the quality of the information is, the more bonus pay we should observe. The contribution of this paper is threefold. We …rst show, using data from the PSID, that the incidence of bonus pay has increased substantially since the late 1970s. This increase is consistent with the view that the cost of collecting and processing information has declined over time with the advances in information and communication technologies. Second, we show that wages tend to be less equally distributed in bonus jobs than in other jobs. In particular, the college-high school wage gap is larger (and increasingly so) in bonus jobs. Combining these two sets of …ndings together, we then show that the growth in bonus jobs has contributed substantially to the rise in wage inequality in the United States during the 1980s. The paper is an interesting complement to studies that have looked at the role of technology and labor market institutions in the growth in wage inequality. Indeed, we suggest a new channel through which technological change could a¤ect the wage distribution. While existing studies have emphasized the e¤ect of skill-biased technological change on the relative demand for skilled labor, we point out that technological change can also change the structure of compensation used by …rms. Wages may be growing more unequal simply because technological advances enable …rms to better di¤erentiate between more and less productive workers, and adjust their compensation accordingly. Our focus on workers paid bonuses also complements studies on labor market institutions that tend to focus on a very di¤erent segment of the workforce. We show that workers paid 3 bonus are relatively unlikely to belong to unions or to be paid around the minimum wage. Just like the decline of unionization and in the real value of the minimum wage may have made wages in the middle and low end of the wage distribution closer to marginal products, the growing incidence of bonus pay appears to be producing a similar outcome for workers higher up in the wage distribution. The plan of the paper is as follows. In section 2 we present a simple model illustrating 1) why …rms are more likely to pay bonuses when better information about workers productivities is available, 2) why the resulting wage is closer to marginal product, and 3) why this tends to increase wage inequality and returns to skill. In Section 3 we present the PSID data used for the empirical analysis, illustrate the growth in the incidence of bonus pay over time. Section 4 present estimates of the e¤ect of bonus pay on the wage structure. We argue that this evidence is consistent with the view that wages on bonus jobs are closer to marginal products than wages on other jobs. We then show in Section 5 how the growth in bonus jobs has contributed to the growth in wage inequality. We conclude in Section 6. 2 Model The basic idea of the model is very simple. Take an extreme case where …rms have no information about the individual productivities of workers. In a simple competitive model, all workers will be paid the same wage since there is no way for …rms to discriminate between more- and less-productive workers. We refer to this basic case as the "pooled case". In a more general setting, however, even if …rms have no information about workers’ productivity they may still pay di¤erent workers di¤erent wages for a variety of di¤erent reasons. For instance, …rms may introduce some administrative pay structures based on factors like seniority (that may not be related to productivity) to achieve other objectives such as reduced turnover. Similarly, …rms with more productive workers (on average) may pay higher wages (to all of their workers) than …rms with less productive workforces. It would thus be too extreme to assume that everybody will be paid exactly the same wage in the pooling case. A more realistic assumption is simply that there should not be a systematic relationship between wages and individual productivities. At the other extreme, when …rms have perfect information about the productivity of a 4 worker, the wage will simply be equal to individual productivity. For administrative or other reasons, however, …rms are then assumed to pay total compensation as the sum of a base or administrative wage plus a performance-based bonus that may or may not be paid in a given year. Let’s call this case the "separating" case where employers are able to discriminate among workers on the basis of productivities. In this simple setting, we get two distinct empirical models of wage setting under the pooling and separating assumptions. In both cases, the underlying productivity of worker i working for …rm j at time t is given by: yijt = xit t + dt i + uit where xit represents standard measurable (by the econometrician) characteristics like potential experience and education, i represents a worker-speci…c productivity term, and uit is an idiosyncratic productivity term. The parameters t and dt are the returns (in terms of productivity) to measured and unmeasured characteristics. In the separating model where …rms also pay bonuses, the wage is equal to productivity: wits = yijt = xit t + dt i + uit By contrast, in the pooling case we assume that there are no systematic relationship between wages and productivity. We nonetheless let the wage depend on following type of …rm-speci…c wages policies witp = j + eijt where j is a "…rm-speci…c" wage term and eijt is an idiosyncratic pay component. The …rm-speci…c component could be linked, for instance, the average level of productivity of workers employed by the …rm. Even if …rms do not observe individual productivities, …rms that turn out to have more productive workers will be able to pay higher (pooled) wages to all workers. By contrast, when individual productivities are controlled for, there is no reason to observe a …rm-speci…c pay component above and beyond the pay related to individual characteristics xit and i . Our measure of bonus pay discussed in the next section is admittedly an imperfect measure of whether a …rms pays a pooled or a separating wage. As a consequence, some jobs we classify as bonus jobs will pay a pooling wage, while some jobs we classify as non-bonus job will pay a separating wage. To capture this formally, let sb and sn be the probability that workers classi…ed as bonus and non-bonus workers, respectively, are actually paid a separat5 ing wage. For bonuses to be informative measures it must be that sb > sn . Conditional on bonus status, the expected wage of worker i at time t becomes: witb = xit bt + dbt i + bj + "bijt ; for bonus jobs and witn = xit nt + dnt i + nj + "nijt ; for non-bonus jobs where n b n b n n b b t ; dt = s dt ; dt = s dt ; t = s t; t = s and var( bj ) = (1 sb )var( bj ); var( nj ) = (1 sn )var( j ); var("bijt ) = (sb )var(uit ) + (1 sb )var(eijt ); var("nijt ) = (sn )var(uit ) + (1 sn )var(eijt ) A number of interesting predictions can be drawn from the model: 1. The return to measurable characteristics xit is larger in bonus jobs than non-bonus b jobs ( t > nt ) 2. The return to unmeasurable person-speci…c characteristics i is larger in bonus jobs than non-bonus jobs (dbt > dnt ). One related implication is that, for a given distribution of i , the variance of the person-speci…c component will be larger in bonus than non-bonus jobs. When comparing workers on bonus and non-bonus jobs, the variance could also be di¤erent because of di¤erences in the variance of i among these two groups of workers. We will adjust for this empirically by comparing the variance of the person-speci…c component in bonus and non-bonus jobs for a subsample of "switchers" who are observed both on bonus and non-bonus jobs. 3. The variance of the …rm-speci…c component is smaller in bonus jobs than nonbonus jobs (var( bj ) < var( nj )) 4. The variance of the idiosyncratic term in bonus jobs, var("bijt ), may either be larger (if var(uit ) > var(eijt ) ) or smaller (if var(uit ) < var(eijt )) than the variance of the idiosyncratic term in non-bonus jobs, var("nijt ). The predictions will be tested in Section 4. 6 3 Data 3.1 The Panel Study of Income Dynamics (1976-1999) The sample consists of male heads of households aged 18 to 65 with average hourly earnings between $1.00 and $100.00 (in $79) for the period spanning the years 1976-1998.1 Individuals in the public sector or who are self-employed are excluded from the analysis. This leaves us with a total sample of 22,093 observations for 3,101 workers. Summary statistics are reported in Appendix Table 1. 3.1.1 Measurement Issues Determining whether a bonus is received For interview years 1976-1992 we are only able to determine whether a worker received a bonus over the previous calendar year through the use of multiple questions. First, workers are asked the amount of money they received from either working overtime, from commissions, or from bonuses paid by the employer.2 Secondly, we know whether workers worked overtime and whether they received commissions.3 So we simply delete from the analysis all workers reporting working overtime and/or receiving commissions. One obvious drawback is that it is likely the bonus measure we back out from this sample selection procedure will be noisy, both in terms of magnitude conditional on being positive and in terms of having false positives and false negatives. Starting with interview year 1993, there are separate questions on the separate amounts earned in bonuses, commissions, tips, and overtime work over the previous calendar year. Thus there is no need to back out an estimate of bonuses from an aggregate amount since the question is asked directly. For the sake of comparability across years, we nevertheless delete all overtime and commission workers from that subsample as well. Finally, note that starting with interview year 1994, both the old aggregate question as 1 In the PSID, data on hours worked during year t, as well as on total labor earnings, bonuses/commissions/overtime income, and overtime hours, are asked interview year t+1. Thus we actually use data covering interview years 1976-1999. 2 Note that the question refers speci…cally to any amounts earned from bonuses, overtime, or commissions in addition to wages and salaries earned. 3 In some years overtime hours are reported while in other years we only know whether they worked overtime or not. 7 well as the new direct one were asked, which allows us to check the reliability of the measure used for all the interview years prior to 1993. As it turns out, the raw correlation between the “arti…cial”bonus measure and the actual one reported for the years 1994-1999 is 92%. De…ning bonus pay jobs4 One of the main goals of this paper is to see whether employment relationships in which bonuses are paid are systematically di¤erent from those in which no such bonuses are ever received. Thus we de…ne bonus pay jobs as jobs in which a bonus is received at least once. In some sense, we are not so much interested in what happen within an employment relationship at the time a bonus is received as to what happen when workers move from one type of job to another.5 Two related measurement issues arise. The …rst one is a simple measurement error issue. On the one hand, we are likely to misclassify bonus pay jobs as non bonus pay jobs if some employment relationships are terminated before a bonus is received. This would be particularly problematic if the receipt of the …rst bonus, which identi…es the job as a bonus pay job, tends to occur later instead of sooner in the course of the employment relationship. On the other hand, some of the jobs are wrongly classi…ed as bonus pay jobs. While it is a priori di¢ cult to assess which of the false positive or false negative problems are more important, their consequence is the same: assuming there is a genuine di¤erence between the two types of jobs, misclassi…cation will tend to attenuate such di¤erences. The second related issue is the “end points”problem: given our de…nition of bonus pay jobs, we may mechanically understate the fraction of workers in such jobs at the start of our sample period because most employment relationships started before 1976. At the same time, jobs which started toward the end of the sample period may be bonus pay jobs but are classi…ed otherwise because they have not lasted long enough. If bonuses are reported sooner (later) instead of later (sooner) over the course of an employment relationship, the underestimation problem would be more severe in 1976 (1998) than in 1998 (1976). Data checks strongly 4 To avoid confusion, note that we use ”jobs”, “employment relationship”, and “job match”interchangeably. Although in most of the survey years spanning the sample period, the PSID does have information on tenure in the posit...
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