Note on the Stock-Wise Utility Function Used in Their Option-Value Analysis

The option value of postponing retirement is the difference between the utility when retiring at the age that maximizes utility minus the utility when retiring now. This note shows that a utility function which depends only weakly on the value of leisure such as the utility function proposed by Stock and Wise (1990) and used in many applications (see Gruber and Wise, various issues) makes this difference flat relative to a more leisure-sensitive utility function. This explains the poor results observed in many European countries which have participated in the Gruber-Wise exercise where the option value was based on the Stock-Wise utility function and in which leisure (here: early retirement) is much more highly valued than in the United States.