We propose a simple alternative to linear-in-parameters quantile regressions for the modeling of conditional distributions. We parameterize the conditional quantile function in terms of a single "location" quantile (usually the median), to which we add or subtract sums of exponentially affine functions (quantile spacings) to obtain a finite number of other quantiles. Our generalized location-scale specification preserves the computational tractability of standard linear quantile regression, is not subject to the quantile crossing problem, and the separability restriction we impose on scale can be motivated by the non-parametric generalization of differences-in-differences of Athey and Imbens (2006). Thus, under some assumptions, an application of our method extends nonlinear differences-in- differences to allow for many, potentially continuous covariates. We illustrate the utility of the method by considering impacts of mass layoffs on the distribution of displaced workers’ earnings using employer-employee matched data from the US. We find that average effects, which are in line with established literature, are driven by a substantial fattening of the left tail, a phenomenon which is further exacerbated during macroeconomic downturns, suggesting that the welfare costs of cyclical variation in income losses from job displacement are even higher than considering average effects alone.
Sample R code which uses our spacing estimator and includes slides with discussion of D-i-D and new Census results.
Older draft
