We propose a simple alternative to linear-in-parameters quantile regressions for modeling conditional distributions. Our approach parameterizes the conditional quantile function using a single “location” quantile (typically the median), with other quantiles constructed by adding or subtracting sums of exponentially affine functions—quantile spacings. This generalized location-scale specification preserves the computational tractability of linear quantile regression, avoids quantile crossing, and imposes a scale restriction motivated by a changes-in-changes model (Athey and Imbens, 2006). The method integrates easily with other econometric frameworks, including instrumental variable models, machine learning, quantile factor models, and nonlinear synthetic controls. We illustrate the approach using U.S. employer–employee matched data to study the effects of mass layoffs on the earnings distribution of displaced workers. We find that average effects—consistent with prior literature—mask a substantial thickening of the left tail, especially during downturns. These findings highlight large welfare costs that are not captured by changes in mean earnings alone.
Sample R code which uses our spacing estimator and includes slides with discussion of D-i-D and Census results.
