Frazis, Harley, and Mark A. Loewenstein. 2005. "Reexamining the Returns to Training: Functional Form, Magnitude, and Interpretation." Journal of Human Resources 40(2): 453-476.

We investigate the functional form for formal training in a wage equation and derive estimates of its rate of return. The cube root fits best in our two data sets. We show that if wages are not adjusted continuously, estimating the return to training requires one lag and one lead of training. Using the cube root and a semi-nonparametric estimator, estimated returns are 150-180 percent. Adjusting for heterogeneity in wage growth, promotions, and direct costs reduces the return to 40-50 percent. We find evidence of heterogeneity in returns. Our estimates can thus be regarded as the return to training for the trained, but cannot be extrapolated to the untrained.

Both authors are researchers at the Bureau of Labor Statistics. The authors thank Dan Black, Marilyn Manser, Terra McKinnish, participants in a session of the 1998 Southern Economic Association meetings and at seminars at Virginia Commonwealth University and George Washington University, and an anonymous referee for helpful comments. We thank Alexander Eidelman for assistance in constructing the NLSY data set, Hector Rodriguez for help with figures, and James Spletzer both for help with the NLSY data and for comments. The views expressed here are those of the authors and do not necessarily reflect the views of the U.S. Department of Labor or the Bureau of Labor Statistics. The data used in this article can be obtained beginning October 2005 through September 2008 from Harley Frazis, Bureau of Labor Statistics, 2 Massachusetts Avenue, NE, Room 4945, Washington, D.C. 20212-0001, e-mail Frazis.Harley@bls.gov.