Some considerations concerning the functional form of earnings

The problem of choosing the correct functional form of earnings has plagued studies of social inequality and labor market segmentation. Although this choice has often been made on superficial grounds, the results presented in the current paper demonstrate that this choice has very significant implications for the empirical findings that emerge from the study of earnings determination. Four functional forms of earnings are compared: dollar earnings, earnings rank based on social perceptions as calibrated by P. Coleman and L. Rainwater (1978, Social Standing in America, Basic Books, New York) the natural logarithm of earnings, and the best-fitting power function transformation of earnings as estimated by the Box-Cox technique. Evaluation of a generalized earnings determination model on a sample of private sector employees produces very similar results across these four functional forms of earnings. More divergent results are obtained when the models are compared across subsamples based on class, economic sector, and gender. Significant contrasts between earnings coefficients across groups are much more likely when utilizing log earnings or the Box-Cox power transformation than when using either dollar earnings or perceived earnings. In addition, the contrasts observed for log earnings and Box-Cox earnings are frequently in the opposite direction of those observed for dollar earnings or perceived earnings. The paper concludes with a discussion of the implications of these findings for theoretical developments in the study of social inequality and labor market segmentation.