  This paper considers the quantile regression approach for partially linear
spatial autoregressive models with possibly varying coefficients. B-spline is
employed for the approximation of varying coefficients. The instrumental
variable quantile regression approach is employed for parameter estimation. The
rank score tests are developed for hypotheses on the coefficients, including
the hypotheses on the non-varying coefficients and the constancy of the varying
coefficients. The asymptotic properties of the proposed estimators and test
statistics are both established. Monte Carlo simulations are conducted to study
the finite sample performance of the proposed method. Analysis of a real data
example is presented for illustration.
