انباشت سرمایه انسانی و انعطاف پذیری جایگزینی نیروی کار : تعصب چقدر بزرگ است؟

I consider two different skill accumulation technologies, learning by doing and Ben-Porath type training. The effect of human capital accumulation in the form of learning by doing is to increase the labor supply elasticity estimate by a factor of 2.1 relative to the estimate that ignores human capital accumulation. The results are similar for the Ben-Porath type training technology, although the estimate of the bias is somewhat higher.

Following Ghez and Becker (1975) a large literature has sought to identify the intertemporal elasticity of substitution for labor from the variation of wages and hours over the life cycle. Notably, MaCurdy (1981) and Altonji (1986) were the first to implement this estimation on individual level panel data. 2 The standard assumption in this literature is that wage changes over the life cycle are exogenous. This approach yields very small elasticities for prime aged males, in the range of 0.3 or less. The result is driven by the fact that hours of work vary little over the life cycle, whereas wages increase rather steeply. The assumption of exogenous wage growth might, however, lead to downward biased estimates of the intertemporal elasticity of substitution parameter. The objective of this paper is to assess the magnitude of the bias on the intertemporal elasticity of substitution of labor supply resulting from the omission of human capital accumulation. To that end, I develop a simple, deterministic life cycle model for an individual agent that I then use to estimate this bias on cohort data for individuals aged 20–62. I consider two alternative skill accumulation technologies, learning by doing and Ben-Porath type training. My results indicate that the estimate of the intertemporal elasticity of substitution increases by a factor of 2.1 after the addition of endogenous human capital accumulation in the form of learning by doing relative to the benchmark with no-human capital. The impact of Ben-Porath type training on the labor supply elasticity is similar, with the estimate increasing by a factor of 2.6 relative to the benchmark. In relating these results to those in the literature, it is worth mentioning that Heckman (1976) was the first to note that the assumption of exogenous wages may negatively bias labor supply elasticity estimates. The first paper to provide a quantitative estimate of this bias was Imai and Keane (2004), who did so in the context of a learning by doing model. They estimate the labor supply elasticity at around 3.8, implying a much larger bias than what my results indicate. The complexity of their framework makes it difficult to know what is driving their results. Moreover, the poor out-of-sample performance of their model is somewhat of a red flag. The objective of this paper is to construct a simpler and more transparent framework to uncover the key economic forces and their interaction. My results show that the magnitude of the bias resulting from the omission of human capital accumulation depends critically on the portion of the life cycle that estimation is based on. The estimates of the bias are largest when estimation is based on data for only the early part of the life cycle. Specifically, when limiting the targeted age range to 20–36, as in Imai and Keane, 3 I get a bias of a factor 5.3 from the omission of human capital accumulation in the form of learning by doing. This, however, is ill advised, as it results in hours worked declining much too steeply relative to the data at older ages. Furthermore, I find that there is some tension in matching the two halves of the life cycle profile for hours worked. In particular, if one matches the later part of the life cycle for hours worked then the early part does not look so good, and if one matches the early part then the later part does not look so good. The nature of the mismatch, however, is most severe when one estimates on early ages and then extrapolates to later ages. An outline of this paper follows. Section 2 presents the models for the two skill accumulation technologies, while Sec- tion 3 outlines the data. Section 4 discusses the method used to select parameter values for the quantitative analysis. Section 5 presents the main results. Section 6 discusses the role the length of the targeted data series plays, while Section 7 provides some sensitivity analysis. Section 8 concludes.

There is a voluminous literature on estimating the intertemporal elasticity of substitution of labor supply. The standard approach of assuming wage changes over the life cycle are exogenous yields very small elasticities for prime aged males. The assumption of exogenous wage growth, however, biases labor supply elasticity estimates downward. Estimating the significanceofthisbiasisthefocusofthispaper. With this focus in mind, I develop a simple, deterministic life cycle model for an individual agent that I then use to estimate the bias in the estimates of the intertemporal elasticity of substitution of labor resulting from the omission of human capital accumulation. In the analysis I target cohort data for individuals aged 20–62. I consider two alternative skill accumulation technologies, learning by doing and Ben-Porath type training. The results are similar for the two technologies. Namely, the effect of human capital accumulation in the form of learning by doing is to increase the labor supply elasticity estimate by a factor of 2.1 relative to the estimate that ignores human capital accumulation, whereas the effect of human capital accumulation in the form of Ben-Porath type training is to increase the estimate by a factor of 2.6. While Heckman (1976) noted that the assumption of exogenous wages may negatively bias labor supply elasticity es- timates, the first paper to provide a quantitative estimate of this bias was Imai and Keane (2004). They estimate a labor supply elasticity of 3.8, implying a much larger bias than my results. I find that the differences in results are accounted for by differences in the length and age range of the targeted data. The magnitude of the bias in labor supply elasticity esti- mates resulting from the omission of skill accumulation depends critically on the portion of the life cycle that estimation is based on. One gets the largest estimates for the bias when one bases estimation on only the beginning of the life cycle. To illustrate, when limiting the targeted age range to 20–36, as in Imai and Keane, I get a bias of a factor 5.3 from the omission of human capital accumulation in the form of learning by doing. This, however, leads to very poor out of sample performance, with hours declining much too steeply at older ages. Traditional estimates of the intertemporal elasticity of substitution of labor are based on life cycle profiles for continu- ously employed people. To isolate the bias on these estimates resulting form the omission of human capital accumulation, I too limit my sample to people with positive hours. If one included everyone, and not just those with positive hours, the hours profile would decline more at older ages. Targeting such a profile would, however, make it impossible to disentangle the effects of human capital accumulation and the extensive margin of labor supply on elasticity estimates. Rogerson and Wallenius (2009) showed that in a model with an endogenous retirement margin the aggregate labor supply elasticity, as defined by the change in total hours in response to a change in the tax rate, is large – irrespective of the value of the intertemporal elasticity of substitution parameter. However, the value of intertemporal elasticity of substitution parameter matters for how the changes in aggregate hours in response to a tax change are broken down between the extensive and intensive margins of labor supply.