Estimation and Inference in Quantile Regressions with Multiple Fixed Effects

This paper proposes a method to estimate quantile regression models with multiple fixed effects. We extend the quantile–via–moments estimator of Machado and Santos Silva (2019) and suggest a computationally efficient Frisch–Waugh–Lovell residualization to partial out additive fixed effects in both the location and scale equations. A unified influence-function inference framework is derived, accommodating heteroskedasticity-robust, clustered, and feasible GLS standard errors. Monte Carlo simulations provide strong support for the validity of the proposed procedure in applications with multi-way unobserved heterogeneity and intra-cluster correlated disturbances. An empirical application to Climate Growth-at-Risk illustrates how temperature shocks affect the conditional distribution of macroeconomic outcomes in a panel of 194 countries. Our findings suggest that in low income countries, downside risks to growth are more strongly linked to temperature shocks than the central tendency or upside risks.