Wage Dynamics and Unobserved Heterogeneity Time Preference or Learning Ability.docx

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1、 IZA DP No. 1436 Wage Dynamics and Unobserved Heterogeneity: Time Preference or Learning Ability? Lalith Munasinghe Nachum Sicherman December 2004 Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor D I SCUSSI O N PAPERS E R I ES Wage Dynamics and Unobserved Heterogeneity: Tim

2、e Preference or Learning Ability? Lalith Munasinghe Barnard College, Columbia University Nachum Sicherman Columbia Graduate School of Business and IZA Bonn Discussion Paper No. 1436 December 2004 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 Email: izaiza.org This

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7、vailable directly from the author. IZA Discussion Paper No. 1436 December 2004 ABSTRACT Wage Dynamics and Unobserved Heterogeneity: Time Preference or Learning Ability?A large fraction of the variation in wage levels and wage growth rates among individuals remains unexplained. Economists argue that

8、“unobserved” heterogeneity is among the more likely reasons for this unexplained variation in wages. The source of individual heterogeneity is typically attributed to data limitations and the unobservability of certain productivity related factors. In this paper we present a theory of career choice

9、and derive a discriminating test between two inherently unobservable sources of heterogeneity learning ability and workers inter-temporal preferences (discounting) both of which can clearly account for the variation in wage levels and wage growth rates. We apply this test to the large observed diffe

10、rences in wages and wage growth rates between smokers and non-smokers. The empirical evidence suggests that smoking is a proxy for individual discount rates. JEL Classification: J22, J24, J31 Keywords: wage dynamics, unobserved heterogeneity, discount rates, learning ability Corresponding author: La

11、lith Munasinghe Department of Economics Barnard College Columbia University 3009 Broadway New York, NY 10027 USA Email: lm25columbia.edu We thank Pierre-Andr Chiappori, Maria Guadalupe, Michael Grossman, Enrico Moretti, Brendan OFlaherty, Randall Reback, and Paolo Siconolfi for many helpful comments

12、. 1 1 Introduction Despite several decades of research in labor economics and dramatic improvements in data collection, a substantial fraction of individual distributions of wage levels and wage growth rates still remains unexplained. As a consequence, the study of unobserved sources of indi- vidual

13、 heterogeneity is important not only for the well-known purpose of correctly estimating wage eects of key observed factors such as schooling, but also for our understanding and assessment of some of these less tractable determinants of wages. The obvious and most commonly cited source of heterogenei

14、ty appeals to dierences in individual productivity. Although information on productivity related characteristics is widespread from intelligence test scores to detailed schooling information various other dimensions of productivity and learning ability, including drive, motivation, discipline, fo- c

15、us, charisma and communication skills among others, are inherently unobservable to the econometrician. A second source of heterogeneity is related to preferences. For example, dif- ferences in the relative valuation of earnings with other on-the-job and o-the-job amenities are likely to aect occupat

16、ional and job choices, and thus give rise to earnings dieren- tials. While this type of heterogeneity has been extensively discussed in the literature (e.g. Rosen 1972), another important source of preference related heterogeneity i.e., dierences in individual time preference has received much less

17、attention. The crux of the issue is that unobserved variations in either learning ability or time preference can account for the unexplained variation in wage levels and wage growth rates. So the question is whether the source of the unexplained variation in wage dynamics is due to unobserved learni

18、ng ability or time preference. The objective of this paper is to present a simple theory of wage dynamics and derive a discrimating test to empirical assess the relative importance of these two potential sources of unobserved heterogeneity in wage determination over the life cycle. The discriminatin

19、g test we propose consists of a two-part strategy. The first part is to 2 find a variable that is highly correlated with wage levels and especially with wage growth rates (net of other observable eects), but where this observed correlation is not causal. Such a correlation raises the possibility tha

20、t this candidate variable is a likely proxy for some unobserved factor such as learning ability or time preference that is directly related to wage dynamics. The second part of the strategy is to design a discriminating test to address whether this candidate variable is indeed a proxy for learning a

21、bility or time preference. Our candidate variable is whether people smoke or not. Smoking is highly (negatively) correlated with wages and wage growth. Smokers earn less than non-smokers and have substantially lower wage growth rates. While it is possible that some of the dierences between smokers a

22、nd non-smokers are due to direct eects (e.g., health), it is more likely that these dierences are due to other variables that are jointly correlated with smoking and wage growth. Indeed, the estimated dierence in wage growth rates across smokers and non- smokers is reduced substantially after includ

23、ing a rich set of variables such as schooling and test scores. However, the net dierences in wage growth rates still remain large and highly significant.1 We contend that time preference and learning ability are two likely sources of unobserved heterogeneity that could account for the net gap in wag

24、e growth rates across smokers and non-smokers. The first explanation is that individuals dier in their rates of time preference, and those who discount the future more heavily will clearly weigh their current wages (first wage) relative to their future wages (wage growth) more heavily than those who

25、 discount the future less.2 Since discount rates are likely to aect all forms of investments, individuals 1 Smokers in the U.S. earn substantially less than non-smokers. For example, Levine et. al. (1997), using the National Longitudinal Surveys of Youth (NLSY), find that smokers earn 11% and 17% le

26、ss than non- smokers in 1984 and 1991, respectively. After controlling for a host of individual and family characteristics, this wage gap reduces to 4.2% and 6.9%. Using the same NLSY data, we find that the major source of this wage gap is the dramatic dierences in wage growth rates between smokers

27、and non-smokers. In another study (Munasinghe and Sicherman, 2003) we report that over a period of about ten years non- smokers experience, on average, wage growth rates that are about 60% greater than those of non-smokers. Controlling for an extraordinary rich set of controls, the dierences are red

28、uced substantially, to around 20%, but remain large and significant. 2 Since individual discount rates are defined in terms of current versus future consumption and not in 3 with high discount rates will be less likely to make other investments, including investing in their health. Hence the discoun

29、ting hypothesis is that individuals with high discount rates will be more likely to smoke and more likely to have flatter wage profiles.3 The second explanation is that individuals dier in their learning ability, and that more ecient (able) learners are likely to invest more in schooling as well as

30、in other forms of human capital, including job training. As a consequence, ecient learners will have a higher first wage and a steeper wage profile. If ecient learners are also less likely to smoke because their higher learning ability leads them to better understand the negative eects of smoking th

31、en it is possible that this unobserved dimension of learning ability could be the culprit behind the observed negative correlation between smoking and wage growth rates. In sum, both hypotheses lead to the same prediction, namely, a negative correlation between smoking and wage growth rates. The dis

32、criminating test we propose in this paper is based on theoretical implications of time preference versus learning ability on the trade-o between the first wage and subse- quent wage increases, two key parameters that describe individual careers. In particular, we show that the correlation between th

33、e first period wage and wage growth rate across smokers and non-smokers dier markedly under the two alternative hypotheses. To pre- view our modeling results: First, holding learning ability constant, the first period wage and wage growth rate are negatively correlated because individual discount ra

34、tes are unob- served. More importantly, however, if smoking is correlated with individual discount rates terms of current versus future incomes, we implicitly assume that workers face borrowing constraints against returns on investments in human capital. It should be noted, however, that even if the

35、 capital market is perfect, the returns on an investment in schooling, for example, depend on hours of work if schooling raises market productivity by a larger percentage than it raises non-market productivity. Individuals who are more future-oriented desire relatively more leisure at older ages. Th

36、erefore, they work more at younger ages and have a higher discounted marginal benefit on a given investment than persons who are more present oriented. 3 The idea that smoking is a proxy for discount rates is extensively documented in the economics literature (Fuchs, 1982). Empirical studies find co

37、rrelations between smoking and various other behaviors related to future outcomes, including health status, educational attainment, earnings levels, use of seat belts, physical exercise, and brushing and flossing teeth (Hersch and Viscusi 1990; Hersch 1996; Levine et. al. 1997; Hersch 2000; Viscusi

38、and Hersch 2001). 4 then this negative trade-o between the first period wage and wage growth rate is larger among smokers than among non-smokers. Second, if non-smokers are simply more ecient learners and the distribution of discount rates is similar across smokers and non-smokers, then the observed

39、 negative trade-o will typically be smaller among smokers than among non-smokers. As a consequence, the discounting and learning hypotheses predict a dierent sign on the interaction term between smoking and the first wage in a wage growth equation. In our model of career choice individuals face a tr

40、ade-o between the first wage and wage growth rate as depicted in Figure 1. The technology of on-the-job human capital production is based on the following considerations. Increase in training time and eort (and the corresponding reductions in first period wages) increases future productivity and thu

41、s future wages. However, the fixity of the human body and initial level of human capital would clearly imply that this increase occurs at a diminishing rate. Hence, all else constant, the production possibility frontier, or more specifically, the constraint function between the first period wage and

42、 wage growth rate will be concave to the origin. Thus the negative slope of this constraint will decrease in absolute value i.e. a decreasing marginal rate of transformation as more and more resources are diverted from current wages to training that enhances future wages (and thus the wage growth ra

43、te). We use this relatively simple two-period model of career choice to study the ramifications of the discounting and learning hypotheses. Under the discounting hypothesis, the key assumption of the model that generates the negative interaction eect between smoking and first-period wages is diminis

44、hing returns to training or learning i.e. the fact, as mentioned above, that the constraint function between the first period wage and wage growth rate is concave to the origin. Note that for a given production constraint, the optimal choice point on this constraint will be determined by an individu

45、als time preference. Put dierently, heterogeneity of time preference will simply trace this non-linear production constraint. The first model implication is of course that holding initial human capital constant, the first period wage will be negatively correlated 5 with the wage growth rate. Moreove

46、r, low discount workers will locate in the flatter region of the constraint where the ratio of second period wage increase to first period wages are relatively high, and high discount workers will locate in the steeper region of the constraint where the ratio of second period wage growth to first pe

47、riod wages is relatively lower. If smokers have relatively higher discount rates than non-smokers then the observed negative correlation between first period wages and second period wage increases will be larger among smokers than among non-smokers (holding initial level of human capital constant).

48、These details are graphically depicted in Figure 2.4 On the other hand, if the source of unobserved heterogeneity is dierences in learning abil- ity then workers with dierent learning abilities will locate on dierent production possibility frontiers. Since we assume that all workers start their care

49、ers with the same level of human capital, the production frontier of the more able workers will be higher the same first period wage intercept but a higher second period wage increase intercept and thus steeper than the production frontier of their less able counterparts. Therefore, if non-smokers are more able learners than their smoker counterparts then the observed negative correlation between first period wages and second