Abstract: In this paper, we propose a novel spatial-temporal model with individual random effects characterized by a location-scale structure, which allows us to flexibly capture the pure influence of space-specific factors in a quantile regression framework. A hybrid two-stage estimation procedure is introduced for this model. The first stage proposes a Gaussian quasi-maximum likelihood estimator for the spatial-temporal effects, and the second constructs a weighted conditional quantile estimator, which we use to study the conditional quantiles of the random effects related to space-specific attributes. We verify the validity of the two-stage hybrid estimation, and establish the asymptotic properties of our estimators. The results of our simulation study indicate that the proposed estimation procedure performs well in different scenarios with finite-samples. Lastly, we apply the proposed method to data from a real case study on the air quality of China.

Key words and phrases: Dynamic spatial autoregressive models, hybrid estimation, quantile regression, quasi-maximum likelihood estimation, random effects.