Inference in Nearly Nonstationary SVAR Models With Long-Run Identifying Restrictions

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

“…The estimator from the levels specification exhibits a modest bias that arises from the biased estimation of the largest root of hours and a very large sample uncertainty (Gospodinov, 2006). The estimator from the specification with HP filtered labour productivity growth performs similarly to the differenced estimator although it is slightly biased and more dispersed.…”

“…While the levels VAR appears to provide a more reliable framework for analysis in this setup, it may also produce biased and highly variable IRF estimates especially if hours worked are a near-integrated process. Imposing additional restrictions on the model (see, for example, Gospodinov, 2006) can lead to improved inference for the structural parameters and impulse responses.…”

“…As shown in the figure, the VAR in levels (top-left panel) estimates an IRF that is close to the true IRF, except for a small bias (see Gospodinov, 2006, for an explanation). On the other hand, the VAR with hours in first differences (top-right panel) incorrectly estimates a negative initial impact of the technology shock even though the true impact is positive.…”

“…The levels approach will explicitly take into account and estimate a possible non-zero upper off-diagonal element in Φ but it suffers from some statistical problems when hours worked are highly persistent (Gospodinov, 2006). On the other hand, the differenced approach will produce valid and asymptotically well behaved IRF estimates in the exact unit root case but it ignores any possible information in levels when hours worked is stationary and gives rise to highly misleading IRFs even for very small deviations from the unit root assumption on hours.…”

“…Gospodinov (2006) shows that the large sampling uncertainty associated with the IRFs in the levels specification arises from a weak instrument problem when the largest root of hours worked is near the nonstationary boundary. Similarly, Pesavento and Rossi (2006) demonstrate that the impulse response functions from both the levels and difference VAR specifications may be unreliable when the root in hours worked is close to one.…”