Sensitivity of Impulse Responses to Small Low Frequency Co-movements: Reconciling the Evidence on the Effects of Technology Shocks.

Nikolay Gospodinov, Alex Maynard and Elena Pesavento

This paper clarifies the empirical source of the debate on the effect of technology shocks on hours worked. Providing theoretical support for previous contentions made in the literature, we find that the contrasting conclusions from levels and differenced VAR specifications can be explained by a small low frequency co-movement between hours worked and labour productivity growth, which is allowed for in the levels specification but is implicitly set to zero in the differenced VAR. This is due to a discontinuity in the solution for the structural coefficients identified by long-run restrictions that exists only when this correlation is present. Consequently, even when the root of hours is very close to one and the low frequency co-movement is quite small, removing it can give rise to biases large enough to account for the empirical difference between the two specifications. While this low frequency correlation has recently been interpreted as evidence against the levels specification, we find that if it is a true property of the correctly identified model, then it can actually lead to substantial biases in the differenced rather than the levels specification. Similar biases may result from HP pre-filtering or trend-break removal.

Keywords Technology shocks, impulse response functions, structural VAR, long-run identification, low frequency co-movement.