Identification of the Wage Offer Distribution Using Order Statistics

This paper shows the wage offer distribution can be nonparametrically identified from the gaps between any two wage offers received by a worker for those who received two or more offers in a short period of time. While nonparametric estimation is infeasible in practice because it requires an infinite number of moments, we could still estimate the parameters of a certain functional form and test whether it is consistent with data as long as we have more data moments than parameters. Empirically, we find the normal distribution is consistent with the data on (log) wage offers from the Survey of Consumer Expectations. The exponential distribution, whose antilog is the Pareto distribution, is rejected because it has too much density at the bottom end to generate sufficient gains from lower relative to higher order statistics. The standard deviation of log wage offers is estimated to be 0.139. This implies, relative to the first offer after a layoff and holding skills constant, the wage of a worker would increase by about 8 percent after the second offer, and by over 20 percent after the tenth offer