This paper investigates the potentials of the bootstrap as a tool for inference on the parameters of macroeconometric models which admit a state space representation. We consider a bootstrap estimator of the parameters of state space models and show that the bootstrap realizations of this estimator, usually employed to approximate asymptotic confidence intervals, p-values, and critical values of tests, can be also constructively used to build a test for forms of misspecifications which invalidate asymptotic normality. The test evaluates how “close or distant” the estimated state space model is from the case where asymptotic inference based on the Gaussian distribution applies. We derive sufficient conditions on the number of bootstrap repetitions, B, relative to the number of sample observations, T, for the test statistic to have a well-defined asymptotic distribution under the null. Throughout the paper, we focus on the state space form of small-scale monetary dynamic stochastic general equilibrium (DSGE) models and investigate the usefulness of our approach through Monte Carlo experiments and empirical illustrations based on US quarterly data. Results show that (i) bootstrapping the state space form provides highly reliable inference and (ii) the suggested test detects weakly identified parameters reasonably well in finite samples.

中文翻译：

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状态空间模型中的引导推理和诊断：应用于动态宏模型

本文研究了 bootstrap 作为推断宏观计量模型参数的工具的潜力，该模型允许状态空间表示。我们考虑了状态空间模型参数的 bootstrap 估计器，并表明该估计器的 bootstrap 实现，通常用于逼近渐近置信区间、p值和测试的临界值，也可以建设性地用于构建使渐近正态性无效的错误规范形式。该测试从应用基于高斯分布的渐近推理的情况评估估计的状态空间模型有多“近或远”。我们推导出自举重复次数B的充分条件，相对于样本观测数T，用于检验统计量在零值下具有明确定义的渐近分布。在整篇论文中，我们关注小规模货币动态随机一般均衡（DSGE）模型的状态空间形式，并通过蒙特卡洛实验和基于美国季度数据的实证说明来研究我们方法的有用性。结果表明（i）自举状态空间形式提供了高度可靠的推理，并且（ii）建议的测试在有限样本中合理地检测到弱识别的参数。