A Comment on the Economics of Labor Adjustment: Mind the Gap: Reply

In earlier contributions, Ricardo J. Caballero and Eduardo M. R. A. Engel (1993), hereafter CE, and Caballero et al. (1997), hereafter CEH, investigate labor dynamics using a methodology which postulates that employment changes depend on a gap between the actual and target levels of employment. Both studies find evidence of nonlinearities in aggregate timeseries data: employment growth depends on the cross-sectional distribution of employment gaps. This finding is taken as evidence that nonlinear adjustment at the microeconomic level “matters” for aggregate time series. This is important for business cycle and policy analysis as it implies macroeconomics must take the cross-sectional distribution of employment gaps into account. This paper questions the methodology and thus the conclusions of these studies. We argue that these reported aggregate nonlinearities may be the consequence of mismeasurement of the gap rather than nonlinearities in plant-level adjustment. Both CE and CEH rely upon a hypothesis that employment growth ( ẽ) responds to a gap (z) between the desired and actual number of workers at a plant. The advantage to the gap approach is that the choice of employment, an inherently difficult dynamic optimization problem, is characterized through a nonlinear relationship between ( ẽ) and (z). That is, the adjustment rate, ẽ/z, is postulated to be a nonlinear function of z. However, there is no “free lunch”: the desired number of workers, and hence the employment gap, is unobservable. Thus, in order to confront data, this approach needs an auxiliary theory to infer z from observed variables. Both CE and CEH use observed hours variations to infer the employment gap: this inference is one element of our critique of the gap methodology. To assess this methodology, we simulate data from the solution of a dynamic model of labor adjustment assuming quadratic adjustment * Cooper: Department of Economics, University of Texas, Austin, TX 78712 (e-mail: cooper@eco.utexas.edu); Willis: Research Department, Federal Reserve Bank of Kansas City, Kansas City, MO 64198 (e-mail: jonathan. willis@kc.frb.org). We are grateful to seminar participants at Boston University, Emory University, the University of British Columbia, the Federal Reserve Bank of Boston, the University of Haifa, the University of Iowa, the University of Michigan, the University of Pennsylvania, the University of Texas at Austin, the 2002 NBER EF Meeting, and the 2000 CMSG conference at McMaster University for comments and suggestions. Discussions with Eduardo Engel, John Haltiwanger, Daniel Hamermesh, Peter Klenow, and Christopher Ragan were much appreciated. The authors thank the NSF for financial support. We also appreciate comments from the referees. Cooper thanks the Federal Reserve Bank of Minneapolis for its hospitality during revisions of this manuscript. The views expressed herein are solely those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City, the Federal Reserve Bank of Minneapolis, or the Federal Reserve System. 1 Daniel Hamermesh (1989) uses a gap methodology as well but does not adopt the approach of estimating a nonlinear hazard function (explained below) to infer the nature of adjustment costs. Hence we focus on CE and CEH in this discussion of methodology. 2 We do not contest the general view of nonlinear employment adjustment at the plant level. This finding is consistent with other evidence that points to inactivity as well as bursts of employment adjustment at the plant level. For example, Hamermesh (1989) provides a revealing discussion of lumpy labor adjustment at a set of manufacturing plants. Steven Davis and John Haltiwanger (1992) document large employment changes at the plant level. CEH also report evidence of inactivity in plant-level employment adjustment. There seems little doubt that an explanation of plant-level employment dynamics requires a model of adjustment that is richer than the quadratic adjustment cost structure and includes some forms of nondifferentiability and/or nonconvexity. 3 As the gap approach is used in numerous other applications (capital adjustment, durable adjustment, price adjustment) to approximate the solution to dynamic optimization problems, our concerns may be relevant for those exercises as well.