The small-scale open economy dynamic stochastic general equilibrium (DSGE) models are estimated with a second-order approximation. The models differ in monetary policy rules. Optimal policy under commitment is best according to marginal likelihood. The conventional Taylor-type rule performs better in short-term forecasting but loses to other policies in long-term forecasting. Monetary policy rules heavily influence the dynamic and estimated parameters of models. They may produce a "price puzzle" and easily lead to the absence of inflation anchoring. The most interesting results relate to the performance of different rules in economies estimated with other rules. Very hawkish policies in a usual economy lead to a non-unique solution. An explosive trajectory is produced by the usual policy in an economy with a fiscal authority that does not care about debts/assets. Only the optimal policy under commitment can work in each of them. However, it may lead to a worse loss function than that produced by simple rules.