Quantile regression analysis of censored data with selection: an application to non-market valuation data

Recurring statistical issues such as censoring, non-random selection and heteroskedasticity often impact the analysis of observational data from natural and human processes. We investigate the potential advantages of models based on quantile regression (QR) for addressing these issues, with a particular focus on non-market valuation data. First, we provide analytical arguments showing how QR can tackle these issues. Second, we show by means of a Monte Carlo experiment how censored QR (CQR)-based methods perform compared to standard models with selection both accounted for and not accounted for in the modeling. Incidentally, we propose an alternative to the standard estimation procedure for the CQR model with selection, which divides computation time by about 100. Third, we apply these four models to a French contingent valuation survey on flood risk. Our findings suggest that selection-censored models are useful for simultaneously tackling issues often present in observational and human data. In addition, the CQR models give a better picture of the heterogeneity of the coefficients, but the computational complexity of the CQR-selection model does not seem to be offset by better performance.