Firm-Specific Human Capital as a Shared Investment: Reply

Abstract

As Edwin Leuven and Hessel Oosterbeek (2001) point out, rather than performing the comparative statics analysis on the effect of increasing uncertainty, my original study limited the analysis to degenerate cases and refrained from inferring a possible monotonic relationship between uncertainties and the share ratio (Hashimoto, 1981 pp. 479–80). Leuven and Oosterbeek do not dispute my conclusions for degenerate cases. Donald O. Parsons (1986 p. 826) later asserted such a monotonic relationship without reporting a comparative statics analysis. Leuven and Oosterbeek use a uniform distribution of productivity to dispute Parsons’ assertion. Hashimoto and Jeong-Geon Lee (1994) reached a similar conclusion to theirs. Given the Hashimoto-Lee comparative statics analysis, I view the most significant contribution of Leuven-Oosterbeek to be not so much their comparative statics as their explicit formulation to account for what has become known in the literature as enforceability of contracts. In the 1981 paper I was concerned with the enforceability issues, so I adopted a certaintyequivalent approach to the fixed-wage formulation in the face of double informational asymmetry between the employer and worker. I then focused on the Becker-type share determination of specific human-capital returns (Gary S. Becker, 1962). Leuven and Oosterbeek directly formulate the enforceability of employment contracts in terms of a fixed wage rather than in terms of the sharing ratio. By considering the enforceability (or the incentive compatibility) issues in a fuller perspective, I conclude that the certainty-equivalent formulation I adopted in my 1981 model has an internal infirmity. In my opinion, this infirmity is a point that a serious Comment on Hashimoto (1981) should underscore. I do not think that Leuven and Oosterbeek’s Comment (2001) is sufficiently articulate or structured to highlight this point. Space does not permit a full discussion, so let me remark briefly on an important point that Leuven and Oosterbeek should have highlighted, but did not. The explicit and direct determination of the incentive-compatible fixed wage w leads me to conclude that the joint maximand is not the unconditional expectation Ev (s) 2 Ey(s), as I originally formulated; rather it is the conditional expectation Estay(v (s) 2 y(s)), conditional on both parties not separating. In the latter formulation, the determination of the fixed wage w implies an ex ante determination of the share parameter to be a 5 {Estay(w 2 y(s))}/{Estay(v(s) 2 y(s))}, which is equivalent to Leuven and Oosterbeek’s definition of a. In spite of the difference in formulation between Leuven-Oosterbeek and Hashimoto-Lee, the two studies obtain essentially the same comparative statics results. This is because both formulations rely on incentive-compatibility conditions for separation decisions where the forces at work are basically the same. Thus, Leuven and Oosterbeek confirm the accuracy of the degenerate results reported in Hashimoto (1981). For nondegenerate cases, the comparative statics are generally ambiguous. Using a uniform distribution, Leuven and Oosterbeek do find that the optimal wage decreases with the uncertainty in the market and increases with the uncertainty in the firm (p. 345). These findings are equivalent to what Hashimoto and Lee (1994) found: that the optimal share ratio decreases with the uncertainty in the outside productivity and increases with the uncertainty in the inside productivity. The Leuven-Oosterbeek Comment contributes a technical advance, but it retains the essential economic logic * Department of Economics, 410 Arps Hall, Ohio State University, 1945 North High Street, Columbus, OH 43210. I am grateful to Hajime Miyazaki for extensive discussions that elucidated theoretical issues in modeling information asymmetric employment relations and for improving the exposition, and to Teresa Schoellner for her very competent research assistance. However, I bear full responsibility for any remaining shortcomings. 1 Further analytical details are available upon request.