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This paper uses a factor-augmented vector autoregressive model to examine the impact of monetary policy shocks on housing prices. To simultaneously estimate the model parameters and unobserved factors we rely on Bayesian estimation and inference. Policy shocks are identified using high-frequency surprises around policy announcements as an external instrument. Impulse response functions reveal differences in regional housing price responses, which in some cases are substantial. The heterogeneity in policy responses is found to be significantly related to local regulatory environments and housing supply elasticities. Moreover, housing prices responses tend to be similar within states and adjacent regions in neighboring states