Econometrics of panel structure models and long memory processes

This dissertation has two parts, one dealing with the econometric detection of group structure in panel data, the second dealing with the econometric estimation of long memory in a time series.; The first part consists of Chapters 2 and 3. It proposes and implements a tractable approach to detect group structure in panel data. The mechanism is via a panel structure model, which assumes that individuals form a number of homogeneous groups in a heterogeneous population. Within each group, the (linear) regression coefficients are the same, while they may be different across different groups. The econometrician is not presumed to know the group structure. Instead, a multinomial logistic regression is used to infer which individuals belong to which groups.; Chapter 2 is concerned with developing an asymptotic theory for the panel structure model. This chapter establishes the consistency and asymptotic normality of a global maximum likelihood estimator (MLE) under the assumption that the time dimension is larger than the number of regressors in the linear regression. This is a novel way to overcome the problem of an unbounded likelihood function. Chapter 3 employs the panel structure model and the asymptotic theory developed in Chapter 2 to investigate the convergence club hypothesis.; The second part consists of Chapters 4 and 5, which propose two bias-reduced semiparametric estimators of long-range dependence. Existing semiparametric estimators rely on approximating the short-run component of the spectrum by a constant around the origin. This often results in a considerable finite sample bias. Part II of the dissertation proposes a natural way to reduce this bias that involves replacing the constant in the approximation by a constant plus an even polynomial with either integer or fractional powers. This leads to the local polynomial Whittle (LPW) estimator in Chapter 4 and the nonlinear log-periodogram (NLP) regression estimator in Chapter 5, respectively. The NLP estimator is designed for a fractional component process (also called perturbed fractional process), which is the sum of a fractional process and a weakly dependent process. Under some smoothness assumptions around the origin, Chapters 4 and 5 show that the rates of convergence to zero of the asymptotic MSEs of the LPW and NLP estimators are faster than those of the local Whittle and GPH estimators, respectively.