Temporal causality between house prices and output in the US: A bootstrap rolling-window approach

• Analyze causality between real house price and real GDP per capita in the US.
• Use bootstrap Granger non-causality test based on a fixed-size rolling-window.
• Full-sample test suggests unidirectional causality from real house price to real GDP per capita.
• Parameter constancy test reveals instability in short and long-runs;.
• Rolling causality reveals periods of bi-directional causality.

This paper examines the causal relationships between the real house price index and real GDP per capita in the US, using the bootstrap Granger (temporal) non-causality test and a fixed-size rolling-window estimation approach. We use quarterly time-series data on the real house price index and real GDP per capita, covering the period 1963:Q1 to 2012:Q2. The full-sample bootstrap non-Granger causality test result suggests the existence of a unidirectional causality running from the real house price index to real GDP per capita. A wide variety of tests of parameter constancy used to examine the stability of the estimated vector autoregressive models indicate short- and long-run instability. This suggests that we cannot rely on the full-sample causality tests and, hence, this warrants a time-varying (bootstrap) rolling-window approach to examine the causal relationship between these two variables. Using a rolling window size of 28 quarters, we find that while causality from the real house price to real GDP per capita occurs frequently, significant, but less frequent, evidence of real GDP per capita causing the real house price also occurs. These results imply that while the real house price leads real GDP per capita, in general (both during expansions and recessions), significant feedbacks also exist from real GDP per capita to the real house price.