Structural vector-autoregressions with long-run restrictions are extraordinarily sensitive to low-frequency correlations. This paper explores this sensitivity analytically and via simulations, focusing on the contentious issue of whether hours worked rise or fall when technology improves. Recent literature finds that when hours per person enter the VAR in levels, hours rise; when they enter in differences, hours fall. However, once we allow for (statistically and economically plausible) trend breaks in productivity, the treatment of hours is relatively unimportant: Hours fall sharply on impact following a technology improvement. The issue is the common high-low-high pattern of hours per capita and productivity growth since World War II. Such low-frequency correlation almost inevitably implies a positive estimated impulse response. The trend breaks control for this correlation. In addition, the specification with breaks can easily "explain" (or encompass) the positive estimated response when the breaks are omitted; in contrast, the no-breaks specification has more difficulty explaining the negative response when breaks are included. More generally, this example suggests a need for care in applying the long-run-restrictions approach.
G. Fernald, John. 2005. “Trend Breaks, Long-Run Restrictions, and the Contractionary Effects of Technology Improvements,” Federal Reserve Bank of San Francisco Working Paper 2005-21. Available at https://doi.org/10.24148/wp2005-21