ABSTRACT This article constructs a Bayesian estimated three different types of representative agents. New Keynesian (THRANK) model includes housing rental market to explain the transmission of monetary policy to inequality, as well as explore the role that rents play in. The concept of rent rigidity following the Calvo stickiness setting is introduced in model. In addition, based on the significance of rental inflation on interest rates in the OLS regression, rental inflation is added to Taylor rule in the model. It is found that: (1) Tight monetary policy widens income inequality and asset inequality. Among the main triggers that magnify income inequality are the interest income generated by higher interest rates and the profit income generated by firms under the markup surge. (2) Rent stickiness of the households is greater than the firms. (3) Sticky rents stabilize fluctuations in rental inflation and total social inflation, when the monetary authority employs the Taylor rule which includes the rental inflation for setting interest rates, will deepen this response.