Trend breaks, long-run restrictions, and contractionary technology improvements

Structural vector autoregressions with long-run restrictions are extraordinarily sensitive to low-frequency correlations. Recent literature finds that the estimated effects of technology shocks are sensitive to how one treats hours per capita. However, after allowing for (statistically and economically significant) trend breaks in productivity, results are much less sensitive: hours fall when technology improves. The issue is that the common high–low–high pattern of productivity growth and hours (i.e., the low-frequency correlation) inevitably leads to a positive estimated response. The trend breaks control for this correlation. This example suggests a practical need for care in using long-run restrictions.