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This paper considers quantile regression for dynamic fixed effects panel data
models with Hausman–Taylor instrumental variables (HTIV). The fixed effects estimators
of panel data are typically biased when there existing lagged dependent variables
and endogenous covariates as regressors, so we suggest the use of the Hausman–Taylor
instrumental variables to reduce the dynamic bias. HTIV can be used even if independent
variables do not vary with time when the unobserved heterogeneity is related to
the independent variables. Besides, there is no need for HTIV to adapt instrumental
variables beyond the model. In this paper, we consider Hausman–Taylor instrumental
variables and propose two quantile regression estimators. We study the asymptotic
properties of the proposed estimators. Monte Carlo simulation studies are conducted
to examine the performance of the two proposed estimators. In addition, we illustrate
the new approaches with an application to analyze the factors affecting price of commercialized
residential buildings of 35 big and moderate cities in China, finding out
that pre-price has a marked effect on current price.