Paritosh Shankarrao Junare

Research

Work in Progress

Two Gaussians, Too Many: A bootstrap-based approach to assess identifiability in non-Gaussian structural vector autoregressions

Abstract: We propose a bootstrap-based approach to evaluate the asymptotic validity of Independent Component Analysis (ICA) identification and inference in structural vector autoregressions (SVARs). ICA-based identification requires that out of n mutually independent structural shocks, at most one is Gaussian. The diagnostic evaluates this condition by measuring the divergence between the conditional bootstrap distribution of a maximum likelihood estimator of the structural impact matrix and its asymptotic benchmark under valid identification. We establish that its bootstrap distribution, under the validity of identification conditions, is asymptotically standard normal. This simplifies the diagnostic to a test of normality of the bootstrap replications of the estimator. Crucially, 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). It ensures the test statistic is asymptotically independent of the data. Monte Carlo simulations with Normal-Inverse Gaussian (NIG) structural shocks demonstrate that the diagnostic attains near-exact nominal size under valid identification conditions and exhibits substantial power against identification failure caused by the presence of multiple Gaussian structural shocks. Based on the estimates of a SVAR model in the macroeconomic and financial uncertainty literature, we demonstrate its potential as a practical, robust tool for validating ICA-based identification without any pre-testing bias.

Identification and Inference in Proxy-SVARs with non-Gaussian shocks

Abstract: We develop a hybrid generalized method of moments (HGMM) framework that combines identification through non-Gaussian higher-order moments with external instruments in structural vector autoregressions. By integrating these approaches within a single over-identified system, we achieve point-identification of the target shocks with valid prox ies. We show strict efficiency gains by combining the identification strategies vis-`a-vis proxy identification alone. Under local-to-zero proxy relevance, we prove robust and consistent parameter estimation. For weak instrument robust inference, we also show HGMM estimator provides substantially narrow Anderson-Rubin confidence sets, relative to the inference based only on proxy exogeneity conditions. We establish asymptotic bias bounds due to proxy mis-specification, as strong identification from non-Gaussianity acts as an anchor. We assess the validity of this specification by constructing mutually orthogonal test statistics to separately assess: (i) proxy exogeneity conditional on shock independence, and (ii) shocks’ non-Gaussianity conditional on instrument validity. This provides formal diagnostic tool to assess proxy exogeneity without auxiliary assumptions. The limiting distributions of the test statistics are established, and we use a finite-sample bootstrap procedure with valid criti cal values for heavy-tailed distributions. Monte Carlo simulations demonstrate consistent estimation with appropriate empirical size and power for specification tests across relevant sample sizes. An empirical application to the identification of oil news shocks illustrates the practical relevance of the framework.