Identification and Inference in proxy-SVARs with non-Gaussian shocks
Abstract: Two prevalent strategies for identifying structural VARs are external instruments, which carry economic motivation but are often weak, and the non-Gaussianity of the shocks, which provides statistical identification but carries no economic meaning. We combine the two methods in a single generalized method of moments framework that stacks proxy exclusion restrictions with higher-order moment conditions of the structural shocks. This hybrid identification point-identifies the target shocks and identifies the non-target shocks up to sign and ordering. Under certain rank conditions, the higher-order moments anchor the identification uniformly over the proxy strength: under local-to-zero proxy relevance, the estimator remains consistent with standard asymptotic inference, and the Anderson-Rubin confidence sets are substantially narrower than those based on the instrument alone. The hybrid estimator is also more efficient than either source used in isolation: at any fixed proxy relevance, even a weak instrument increases efficiency through its
covariance with the non-Gaussian moment block. Under local proxy endogeneity, we provide asymptotic bias bounds and show that stronger non-Gaussianity of the shocks compresses the bias. Finally, the over-identified structure yields two mutually orthogonal specification tests, for proxy exogeneity and non-Gaussianity of shocks. We derive their limiting distributions and provide a bootstrap procedure for finite-sample critical values. Monte Carlo evidence and two illustrations with identification of oil news-shock and a Euro-area MP shock demonstrate the potential of our framework.
Two Gaussians, Too Many: A bootstrap-based approach to assess identifiability in non-Gaussian structural vector autoregressions
Abstract: Standard pre-tests of normality on reduced-form innovations are insufficient to detect two or more Gaussian shocks and hence, the failure of identification in non-Gaussian SVARs. We instead propose a bootstrap-based approach to evaluate the asymptotic validity of this condition by measuring the divergence between the conditional bootstrap distribution of a maximum likelihood estimator and its limiting distribution under valid identification. We show that, under valid identification and certain regularity conditions, the conditional bootstrap distribution of the impact matrix is asymptotically normal, so the diagnostic reduces to a test of normality of the bootstrap replications. The diagnostic remains valid in the single-Gaussian case, where the shape parameter of the Gaussian shock lies on the boundary, and the full-parameter information is singular; this establishes its validity across the entire null. Under the null of valid identification, the diagnostic induces no pre-testing bias as bootstrap replications and sample size diverge jointly at an appropriate rate. The joint divergence ensures that the test statistic, conditional on the data, is asymptotically pivotal, so conditioning on the diagnostic does not distort subsequent inference. Monte Carlo simulations with Normal-Inverse Gaussian shocks show that the diagnostic attains near-exact nominal size under valid identification and detects the failure due to multiple Gaussian shocks with power increasing in the sample size. Under weak identification with a near-Gaussian shock, conditioning on the bootstrap diagnostic, unlike on residual-based normality pre-tests, preserves the probability coverage of the estimates. Based on estimates of a SVAR model in the macroeconomic and financial uncertainty literature, we demonstrate its potential as a practical, robust tool for validating non-Gaussian identification without pre-testing bias.
arXiv
Assembling time-varying proxies for political attitudes in India
Supervisor: Prof. Alessandro Saia, University of Bologna. (Summer 2022)
ORCiD