Econometrics of Dynamic Index-Threshold Models

9709508白本研究发展了一类非线性动态模型的计量经济学理论，称为动态指数门槛模型。这些模型描述了多种状态，其中状态切换由一个不可观察的指数控制。指数本身是若干指标系数未知的可观察变量的线性组合。本研究解决了以下与动态指数阈值模型有关的问题：1。确定动态指标-阈值模型的概率结构，如平稳性和遍历性；2. 确定估计量的统计性质，如一致性、收敛率和极限分布；3. 动态指数阈值自回归的平稳性检验和4。解决了动态指标-阈值模型的计算问题。尽管动态指数阈值模型在消费者面临由福利计划、税收和大宗定价方案等因素造成的预算组合时对需求分析很有用，但目前还没有针对动态指数阈值模型的通用计量经济学理论。

9709508 Bai This research develops the econometric theory for a class of nonlinear dynamic models, referred to as dynamic index-threshold models. These models describe multiple regimes in which regime switching is governed by an unobservable index. The index itself is a linear combination of a number of observable variables with unknown index coefficients. This research addresses the following issues pertaining to the dynamic-index threshold models: 1. Determining the probability structure of the dynamic index-threshold model, such as its stationarity and ergodicity; 2. Determining the statistical properties of the estimators, such as consistency, rate of convergence, and limiting distributions; 3. Testing the hypothesis of stationarity against dynamic index-threshold autoregression; and 4. Solving the computational problems for the dynamic index-threshold models. No general econometric theory has yet been developed for dynamic index-threshold models despite their usefulness for demand analysis when consumers face a kinked budget set resulting from, say, welfare programs, taxation and block-pricing schemes.