In this paper we analyse the effects of informal labour markets on the dynamics of inflation and on the transmission of aggregate demand and supply shocks. In doing so, we incorporate the informal sector in a modified New Keynesian model with labour market frictions as in the Diamond-Mortensen-Pissarides model. Our main results show that the informal economy generates a "buffer" effect that diminishes the pressure of demand shocks on inflation. This finding is consistent with the empirical literature on the effects of informal labour markets in business cycle fluctuations. This result implies that, in economies with large informal labour markets, changes in interest rates are more effective in stimulating real output and there is less impact on inflation. Furthermore, the model produces cyclical flows from informal to formal employment, consistent with the data.