Latent local-to-unity models
研究了一类状态方程是局部单位根过程的潜在状态空间模型，分析了最小二乘和工具变量估计量在测量误差和长记忆扰动下的渐近性质，发现工具变量估计能有效减小偏差。
The article studies a class of state-space models where the state equation is a local-to-unity process. The parameter of interest is the persistence parameter of the latent process. The large sample theory for the least squares (LS) estimator and an instrumental variable (IV) estimator of the persistent parameter in the autoregressive (AR) representation of the model is developed under two sets of conditions. In the first set of conditions, the measurement error is independent and identically distributed, and the error term in the state equation is stationary and fractionally integrated with memory parameter d∈(−0.5,0.5). For both estimators, the convergence rate and the asymptotic distribution crucially depend on d. The LS estimator has a severe downward bias, which is aggravated even more by the measurement error when d≤0. The IV estimator eliminates the effects of the measurement error and reduces the bias. In the second set of conditions, the measurement error is independent but not necessarily identically distributed, and the error term in the state equation is strongly mixing. In this case, the IV estimator still leads to a smaller bias than the LS estimator. Special cases of our models and results in relation to those in the literature are discussed.