The rst chapter co-authored with Tatiana Damjanovic studies optimal mon- etary policy in a New Keynesian model at the zero bound interest rate where households use cash alongside house equity borrowing to conduct transactions. The amount of borrowing is limited by a collateral constraint. When either the loan to value ratio declines or house prices fall, we observe a decrease in the money multiplier. We argue that the central bank should respond to the fall in the money multiplier and therefore to the reduction in house prices or the loan to collateral value ratio. We also nd that optimal monetary policy generates a large and per- sistent fall in the money multiplier in response to the drop in the loan to collateral value ratio. The second chapter is focused on a macroeconomic model with sticky prices, rms borrowing market and the labour market frictions. We study connection be- tween monetary policy and labour market under the negative nancial and the positive productivity shocks. We have found that the interest rate rule with in a- tion and labour market targeting performs better than the rules with the aggregate consumption and debt targeting and is closest to the optimal policy as compared to the other regimes in terms of the welfare measure. We demonstrate too that the sign of the coe¢ cient next to unemployment in the policy rule depends on the value of workers bargaining power. The third chapter co-authored with Tatiana Damjanovic and Keqing Liu uses the classical cobweb model framework to investigate properties of the transition matrix in the bounded memory econometric OLS-type learning. We de ne memory length as the number of past observations used to form a forecast and analytically prove that for any length, the eigenvalues of the transition matrix lie within the unit circle. In addition, we sketch the proof of stationarity of the cobweb model under bounded memory learning. Furthermore, we investigate the relationship between the volatility of forecasts and the length of memory and nd that shorter memory causes higher variance in both forecasts and estimates of the OLS parameters.