Empirical estimations suggest heavy-tailed unconditional distributions for inflation, the output gap and the interest rate. However, standard NK models used in policy analysis imply normal distributions for these variables. In this study, we propose a model which replicates the above mentioned empirical features of inflation,the output gap and the interest rate and subsequently investigate the conduct of monetary policy in this model. The novelty of this study is the introduction of random wage indexation as a source of multiplicative shocks. The findings of this study include the following: Firstly, the unconditional distributions of inflation, the output gap and the interest rates exhibit heavy-tailed characteristics. Secondly, under an indexation to lagged inflation scheme, there exists a positive relationship between expected inflation and conditional variance of inflation. Finally, it is better to target current inflation rather than lagged inflation when conducting monetary policy under a Taylor rule.