The solution of a typical new-Keynesian model indicates that inflation and output gap are determined by contemporaneous and historical structural shocks. Thus estimating Taylor rules using OLS has the endogeneity problem. Moreover, if monetary shocks are serially correlated, as argued in the literature, lags of inflation and output gap are also endogenous to monetary shocks, and thus not valid instruments. The conventional estimation of Taylor rules that ignores the endogeneity problem may be biased. This paper investigates the magnitude of the bias. I estimate Taylor rules using two methods that allow for the presence of serial correlation in monetary shocks. The first method uses as instruments a set of strictly exogenous variables. The second method purifies inflation and output gap by removing from them the components attributable to monetary shocks. Both methods show that the endogeneity problem does not cause much bias in the conventional estimation of Taylor rules.