Are there long-run effects of the minimum wage?

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Abstract

An empirical consensus suggests that there are small employment effects of minimum wage increases. This paper argues that these are short-run elasticities. Long-run elasticities, which may differ from short-run elasticities, are policy relevant. This paper develops a dynamic industry equilibrium model of labor demand. The model makes two points. First, long-run regressions have been misinterpreted because even if the short- and long-run employment elasticities differ, standard methods would not detect a difference using US variation. Second, the model offers a reconciliation of the small estimated short-run employment effects with the commonly found pass-through of minimum wage increases to product prices.

Section snippets

Adjustment costs on labor

There is a difference between the short- and long-run elasticities if there are adjustment costs for labor. There is a tradition in the minimum wage literature of arguing that high turnover among workers in minimum wage industries means that adjustment costs are likely small.13 High turnover, however, is evidence against adjustment costs for changing the identity of workers rather than for changing the number of jobs.14

The putty-clay model

This section develops a dynamic labor demand model in industry equilibrium (e.g. Hopenhayn, 1992). The model has three features that make it well-suited to study minimum wages. First, it models industry-level variables such as prices. Industry equilibrium means that employment is industry-wide employment as in Dube et al. (2010), rather than employment within a continuing set of firms as in Card and Krueger (1994). Second, it explicitly parameterizes the transition path between the short- and

Interpreting empirical work in light of the model

This section analytically shows how employment and product prices move in response to temporary and permanent minimum wage increases. Surprisingly, product prices move even in response to temporary minimum wage increases.

In this section, a temporary minimum wage increase is an increase that lasts for a single time period. This is a stylized way of capturing what happens if the minimum wage is increased in nominal terms and then eroded by inflation. Section 5 numerically studies environments

Parameter values

Much empirical work in the minimum wage literature, including Dube et al. (2010), has focused on the restaurant industry. Hence, I calibrate the model to the restaurant industry. Table 1 displays the parameter values.

A key parameter is the share of minimum wage workers in firms' expenses, which is set to 0.1. This number is arrived at as follows. Aaronson and French (2007) report that the labor share is 0.3 and the minimum wage worker share in the wage bill is 0.17. They report that about

Quantitative implications of the model with stylized minimum wage variation

To illustrate the quantitative implications of the calibrated version of model, I perform three minimum wage experiments. The first experiment considers a one-time and permanent increase. This experiment corresponds to the ceteris paribus condition implicit in interpreting reduced-form long-run regression coefficients as long-run elasticities. The second experiment considers a one-time increase that is eroded by inflation. This experiment shows how the observed long-run response differs

Quantitative implications of the model with actual minimum wage variation

So far I have studied a dynamic model embodying an important distinction between short- and long-run elasticities. If minimum wage increases are sufficiently temporary, I have shown that there would be little difference in the observed short- and long-run employment responses.

The model emphasizes two channels through which temporariness matters. First, temporariness matters because of how many firms adjust to the realized minimum wage increase: if in realization the minimum wage increase is

Conclusion

If there were differences between short- and long-run employment elasticities would it be possible to tell? This paper has suggested that because of the nature of variation in minimum wages the answer is no. In particular, because minimum wage increases are mostly temporary, the ceteris paribus condition implied in the long-run elasticities—that of a permanent minimum wage increase—is unlikely to obtain. Even without such a ceteris paribus condition, it might be the case that standard

Acknowledgements

Previous drafts of this paper circulated under titles “Why is there (almost) no employment effects of minimum wages?” and “Minimum wages and the dynamics of labor demand.” Thanks to Marco Bassetto (the editor), John Bound, Charles Brown, Jediphi Cabal, Nels Peter Christiansen, Arindrajit Dube, Matthew Fiedler, Eric French, Paul Goldsmith-Pinkham, Francois Gourio, Chris House, Stephen A. O'Connell, Matthew D. Shapiro, Jeff Smith, Henry Swift, Ted To, Justin Wolfers, Mary Wootters, two anonymous

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