Modeling Firm-Size Distribution Using Box-Cox Heteroscedastic Regression

Using the Box-Cox regression model with heteroscedasticity, we examine the size distribution of firms. Analyzing the data set of Portuguese manufacturing firms as in Machado and Mata (2000), we show that our approach compares favorably against the Box-Cox quantile regression method. In particular, we are able to answer the key questions addressed by Machado and Mata, with the additional advantage that our empirical quantile functions are monotonic. Furthermore, confidence intervals of the regression quantiles are easy to compute, and the estimation of the Box-Cox heteroscedastic regression model is straightforward.