多元协整系统的完全修正最小二乘协整参数估计
Fully Modified Least Squares Cointegrating Parameter Estimation in Multicointegrated Systems
摘要：
多元协整传统上被定义为参数向量自回归模型中变量之间的一种特殊的长期关系，它在这些变量之间以及均衡误差的部分和之间引入了额外的协整联系。本文从参数模型出发，采用半参数公式揭示了长期条件协方差矩阵的奇异性在确定多元协整中所起的明确作用。半参数框架的优点是不需要对短期动态进行建模，并且通过标准技术（例如原始I（1）系统上的完全修改的最小二乘（FM-OLS））进行估计是简单的。本文推导出FM-OLS极限理论中的多重协整设置，显示如何更快的收敛速度实现的奇异性的方向和极限分布取决于分布的条件单侧长期协方差估计FM-OLS估计。Wald回归系数约束检验具有非标准极限理论，一般依赖于干扰参数。通常的测试被证明是保守的，当限制是孤立的奇异性的方向，并在一定条件下，是不变的奇异性，否则。仿真结果表明，在有限的样本中，本文推导的近似工作。实证分析的结果表明，美国政府在战后时期的财政可持续性。
英文摘要：
Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional cointegrating links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals the explicit role that singularity of the long run conditional covariance matrix plays in determining multicointegration. The semiparametric framework has the advantage that short run dynamics do not need to be modeled and estimation by standard techniques such as fully modified least squares (FM-OLS) on the original I(1) system is straightforward. The paper derives FM-OLS limit theory in the multicointegrated setting, showing how faster rates of convergence are achieved in the direction of singularity and that the limit distribution depends on the distribution of the conditional one-sided long run covariance estimator used in FM-OLS estimation. Wald tests of restrictions on the regression coefficients have nonstandard limit theory which depends on nuisance parameters in general. The usual tests are shown to be conservative when the restrictions are isolated to the directions of singularity and, under certain conditions, are invariant to singularity otherwise. Simulations show that approximations derived in the paper work well in finite samples. The findings are illustrated empirically in an analysis of fiscal sustainability of the US government over the post-war period.
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