Causal relationships in econometrics are typically based on the concept of predictability and are established in terms of tests for Granger causality. These causal relationships are susceptible to change, especially during times of ﬁnancial turbulence, making the real-time detection of instability an important practical issue. This paper develops a test for detecting changes in causal relationships based on a recursive rolling window, which is analogous to the procedure used in recent work on ﬁnancial bubble detection. The limiting distribution of the test takes a simple form under the null hypothesis and is easy to implement in conditions of homoskedasticity, conditional heteroskedasticity and unconditional heteroskedasticity. Simulation experiments compare the eﬀicacy of the proposed test with two other commonly used tests, the forward recursive and the rolling window tests. The results indicate that both the rolling and the recursive rolling approaches oﬀer good ﬁnite sample performance in situations where there are one or two changes in the causal relationship over the sample period, although the performance of the rolling window algorithm seems to be the best. The testing strategies are illustrated in an empirical application that explores the causal impact of the slope of the yield curve on real economic activity in the United States over the period 1985–2013.
Hurn, Stan; Phillips, Peter C.B.; and Shi, Shu-Ping, "Change Detection and the Causal Impact of the Yield Curve" (2016). Cowles Foundation Discussion Papers. 2520.