Empirical studies have documented the presence of asymmetric effects of monetary policy. For example, some studies show that the magnitude of the response of output to different types of shocks depends on whether the economy is in recession or expansion or whether the shock is negative or positive (Garcia and Schaller, 1999). In this paper I use a theoretical model capable of capturing asymmetric effects of monetary policy found in real data. I use a standard New Keynesian model and impose the Zero Lower Bound (ZLB) constraint on the nominal interest rate. The presence of the ZLB constraint leads to a kink in the solution of the model. As a re- sult the standard approximation technique in the literature (the projection method with the Chebyshev polynomials) is not reliable. To deal with the kink problem in the policy function of the nominal interest rate I employ the projection method with the spline polynomials. To preserve nonlinear- ities of the model and reveal possible asymmetries I obtain fully nonlinear solution. As a preliminary step there is an overview of the related litera- ture as well as empirical analysis of the U.S. data using a Markov-switching model.