Abstract
In productivity research with firm data, the existence of endogenous sample attrition is well known. In addition, endogenous sample selection may occur. In a simple model where heterogenous firms consider entry, exit, worker training and price setting in a monopolistically competitive market, I show that firm heterogeneity leads to self-selecting into the market, which in turn dampens the estimate of the marginal effect of worker training. To address the sample selection issue, I devise a generalized method of simulated moments estimator. Estimations with firm data from China’s shoe manufacturing industry show that an increase of one standard deviation of worker training expenditure intensity results in an around 5.6% decrease in a firm’s labor productivity, larger than the estimate without accounting for endogenous sample selection.
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Notes
For example, to name a few, Heckman (1979, 1990), Newey et al. (1990), Nawata and Nagase (1996), Kyriazidou (1997), Heckman et al. (1998), Vella (1998), Francesconi and Nicoletti (2006), Zimmer and Trivedi (2006), Madden (2008), Lee (2009), Newey (2009), Greene (2010), van Hasselt (2011), Vossmeyer (2016), and Semykina and Wooldridge (2018).
In addition, researchers also survey productivity studies from different dimensions, for example Syverson (2011) on why firms have different productivity levels, Ahmed and Bhatti (2020) on measurement and determinants of multi-factor productivity, and Del Gatto et al. (2011) and Van Beveren (2012) on estimating/measuring productivity/total factor productivity.
For example, firms may need to train their workers for a particular skill which is needed in the production process but not available from the labor market.
Note for individual workers who receive training, their skill sets will expand. However, it can occur that the firm’s average labor productivity decreases.
The expectation is taken over both ζ and λ. Besides, note that in taking expectation with respect to ζ, it is possible that x and τ are endogenous, namely E[ζ|x,τ,λ≥\(\underline \lambda\)] = ∫ζdGζ(ζ|x,τ) is a function of x and τ. For τ, I later also use excluded instruments and report the results in the section “Robustness”. For x, assuming ∫ζdGζ(ζ|x,τ) is a linear function of x, it is then absorbed into the term xβ.
Note in Eq. (6), as I focus on the steady state, by conditioning on \(\lambda \ge \underline \lambda\), one also captures endogenous sample attrition. Future research can account for sample attrition (firm dynamics) more elaborately while addressing the sample selection issue.
Note x and z are the same as in Eq. (6).
A similar algorithm has been used by Sun and Anwar (2022) to estimate product quality.
Here lnλ and ζ can be combined into one term. I use the normal distribution, given its prevalence. One can also use other distributions. A frequently used distribution is the Pareto distribution. However, one disadvantage of using the Pareto distribution is that the sample selection effect cancels out the direct effect of x and τ, namely \(E\left[ {{\rm{ln}}s\left| {x,\tau ,\lambda \ge \underline \lambda } \right.} \right]\) does not depend on x and τ, which suggests that the Pareto distribution assumption is likely to be too strong for empirical estimations.
For example, with a sample of 3703 firms in Taiwanese electronics industry in the years 2000 and 2002–2004, Aw et al. (2011) estimate an ρ of 0.8432 in the domestic market.
Alternatively, one can draw the fixed cost from a given distribution.
Note, as discussed in Footnote 5, estimates of the coefficients of x can pick up the effect of x being endogenous. That is, while factors in x directly affect lnS, they can also indirectly affect lns through ζ.
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Sun, S. Firm heterogeneity, worker training and labor productivity: the role of endogenous self-selection. J Prod Anal 59, 121–133 (2023). https://doi.org/10.1007/s11123-022-00652-1
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DOI: https://doi.org/10.1007/s11123-022-00652-1
Keywords
- Firm heterogeneity
- Worker training
- Labor productivity
- Sample selection
- Method of simulated moments
- Cross-sectional analysis