两个高斯分布，太多了：一种基于自举法的方法来评估非高斯结构向量自回归中的可识别性
Two Gaussians, Too Many: A bootstrap-based approach to assess identifiability in non-Gaussian structural Vector Autoregressions
AI总结：
研究非高斯结构向量自回归中识别性问题，提出基于自举法评估条件渐近有效性，通过测量分布差异进行诊断，该方法在多种情况下有效且无预检验偏差，模拟显示其能检测识别失败并保持估计概率覆盖，可验证非高斯识别。
AI中文摘要：
对简化形式创新的标准正态性预检验不足以检测两个或更多高斯冲击，从而无法识别非高斯结构向量自回归（SVARs）。我们提出一种基于自举法的方法，通过测量最大似然估计器的条件自举分布与其在有效识别下的极限分布之间的差异，来评估该条件的渐近有效性。在有效识别和特定正则条件下，冲击矩阵的条件自举分布渐近正态，诊断简化为对自举复制的正态性检验。该诊断在单高斯情况下也有效，且在有效识别原假设下无预检验偏差。蒙特卡罗模拟表明，该诊断在有效识别下接近精确名义大小，能检测多高斯冲击导致的识别失败，在弱识别时能保持估计的概率覆盖。基于宏观经济和金融不确定性文献中SVAR模型的估计，证明了其作为无预检验偏差验证非高斯识别的实用、稳健工具的潜力。
英文摘要：
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.
