In this paper, we study estimation  of a partially
specified spatial autoregressive model with heteroskedasticity
error term. Under the assumption of exogenous regressors and
exogenous spatial weighting matrix, we propose an instrumental
variable estimation. Under some sufficient conditions, we show
that the proposed estimator for the finite dimensional parameter
is root-$n$ consistent and asymptotically normally distributed and
the proposed estimator for the unknown function is consistent and
also asymptotically distributed though at a rate slower than
root-$n$.
Monte Carlo simulations verify our theory and the results suggest that the proposed method has some practical value.