In this paper we study the effect of monetary policy shocks on housing rents. Our main finding is that, in contrast to house prices, housing rents increase in response to contractionary monetary policy shocks. We also find that, after a contractionary monetary policy shock, rental vacancies and the homeownership rate decline. This combination of results suggests that monetary policy may affect housing tenure decisions (own versus rent). In addition, we show that, with the exception of the shelter component, all other main components of the consumer price index (CPI) either decline in response to a contractionary monetary policy shock or are not responsive. These findings motivated us to study the statistical properties of alternative measures of inflation that exclude the shelter component. We find that measures of inflation that exclude shelter have most of the statistical properties of the widely used measures of inflation, such as the CPI and the price index for personal consumption expenditures, but have higher standard deviations and react more to monetary policy shocks. Finally, we show that the response of housing rents accounts for a large proportion of the “price puzzle” found in the literature.