This thesis examines the transmission of monetary policy and the effects of persistent cost-push shocks in the presence of high household indebtedness (DTI) and frictions in fixed-rate mortgage (FRM) interest rates. A dynamic stochastic general equilibrium (DSGE) model incorporating housing, household debt, and long-term FRMs is estimated to accomplish this. The key findings can be summarized as follows: (i) A higher DTI leads to a stronger transmission of monetary policy, although this effect is dampened by the degree of interest rate fixation periods. (ii) Cost-push shocks propagates more strongly to inflation when the interest rate fixation periods is longer, resulting in delayed and slightly muted effects on output and consumption compared to adjustable-rate mortgages (ARM). (iii) While stronger responses to inflation help mitigate the cost-push shock, this comes at the expense of a larger output gap but with a slightly faster stabilization of the economy with a somewhat steeper recovery.