Causal change detection in possibly integrated systems: revisiting the money–income relationship

This paper re-examines changes in the causal link between money and income in the United States over the past half century (1959–2014). Three methods for the data-driven discovery of change points in causal relationships are proposed, all of which can be implemented without prior detrending of the data. These methods are a forward recursive algorithm, a rolling window algorithm, and a recursive evolving algorithm all of which utilize subsample tests of Granger causality within a lag-augmented vector autoregressive framework. The limit distributions for these subsample Wald tests are provided. Bootstrap methods are developed to control family-wise size in the implementation of the recursive testing algorithms. The results from a suite of simulation experiments suggest that the recursive evolving window algorithm provides the most reliable results, followed by the rolling window method. The forward expanding window procedure is shown to have the worst performance. Both the rolling window and recursive evolving approaches find evidence of Granger causality running from money to income during the Volcker period in the 1980s. The forward algorithm does not find any evidence of causality over the entire sample period.