Robust Inference in Structural VAR Models identified by Non-Gaussianity
Abstract: All parameters in structural vector autoregressive (SVAR) models are locally identified when the structural shocks are independent and follow non-Gaussian distributions. Unfortunately, standard inference methods that exploit such features of the data for identification fail to yield correct coverage for structural functions of the model parameters when deviations from Gaussianity are small. To this extent, we propose a robust semi-parametric approach to conduct hypothesis tests and construct confidence sets for structural functions in SVAR models. The methodology fully exploits non-Gaussianity when it is present, but yields correct size / coverage regardless of the distance to the Gaussian distribution. Empirically we revisit two macroeconomic SVAR studies where we document mixed results. For the oil price model of Kilian and Murphy (2012) we find that non-Gaussianity can robustly identify reasonable confidence sets, whereas for the labour supply-demand model of Baumeister and Hamilton (2015) this is not the case. Moreover, these exercises highlight the importance of using weak identification robust methods to assess estimation uncertainty when using non-Gaussianity for identification.
Specification Tests Robust to Multiple Instabilities
Abstract: I develop a hypothesis test for model evaluation which is robust to time-variation in parameters. The proposed method can be applied in-sample and out-of-sample to any economic model based on moment conditions. In-sample, the test selects between two nested model specifications in the presence of parameter instabilities. Out-of-sample, the test can be used to evaluate the performance of model or judgmental forecasts robust to time-variation. The key feature of the proposed test is that it is particularly powerful in the presence of multiple shifts in parameters without imposing a specific form of time-variation. Further, the test statistic provides narrative evidence on which parts of the sample drive the rejection of the null hypothesis. Simulations show that the test is accurately sized in finite samples and is more powerful than tests assuming constant coefficients or a single break if the data-generating process exhibits multiple shifts in parameters. Using the proposed test, I document the presence of short-horizon predictability in the U.S. equity premium during the postwar period. I find evidence of predictability for a large set of variables once time-variation is taken into account. The test further provides evidence of heterogeneity in the location of predictability episodes across variables. The findings explain why traditional tests often fail to uncover predictability in the full sample and why studies that split the sample at different dates often arrive at conflicting results regarding the predictive ability of a wide class of variables.