Two Gaussians, Too Many: A bootstrap-based approach to assess identifiability in non-Gaussian structural Vector Autoregressions
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两个高斯冲击已过多：非高斯结构 VAR 的自助法识别诊断
- 研究问题
- 非高斯结构 VAR 中，如何发现多个高斯冲击导致的识别失败，并避免常规残差正态性预检验扭曲后续推断？
- 方法与思路
- 作者比较极大似然估计量的条件自助分布与有效识别下的极限分布，将诊断化为冲击矩阵自助重复样本的正态性检验。
- 材料陈述的贡献
- 摘要称，诊断在单个高斯冲击的边界情形仍有效，并在适当联合增长下不产生预检验偏差；模拟支持其尺寸与覆盖表现。
- 阅读关注点
- 应核对冲击分布与识别条件、边界处的论证、自助次数和样本量的联合增长率，以及弱识别下覆盖结论的适用范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未列正则条件和增长率，未拒绝诊断也不能证明有限样本识别充分。
原文摘要
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.