Quantiles via moments

We study the conditions under which it is possible to estimate regression quantiles by estimating conditional means. The advantage of this approach is that it allows the use of methods that are only valid in the estimation of conditional means, while still providing information on how the regressors affect the entire conditional distribution. The methods we propose are not meant to replace the well-established quantile regression estimator, but provide an additional tool that can allow the estimation of regression quantiles in settings where otherwise that would be difficult or even impossible. We consider two settings in which our approach can be particularly useful: panel data models with individual effects and models with endogenous explanatory variables. Besides presenting the estimator and establishing the regularity conditions needed for valid inference, we perform a small simulation experiment, present two simple illustrative applications, and discuss possible extensions.