In this dissertation, I consider linear, binary response correlated random coefficient (CRC) panel data models and a truncated CRC panel data model which are frequently used in economic analysis. I focus on the nonparametric identification and estimation of panel data models under unobserved heterogeneity which is captured by random coefficients and when these random coefficients are correlated with regressors. For the analysis of linear CRC models, I give the identification conditions for the average slopes of a linear CRC model with a general nonparametric correlation between regressors and random coefficients. I construct a sqrt(n) consistent estimator for the average slopes via varying coefficient regression. The identification of binary response panel data models with unobserved heterogeneity is difficult. I base identification conditions and estimation on the framework of the model with a special regressor, which is a major approach proposed by Lewbel (1998, 2000) to solve the heterogeneity and endogeneity problem in the binary response models. With the help of the additional information on the special regressor, I can transfer a binary response CRC model to a linear moment relation. I also construct a semiparametric estimator for the average slopes and derive the sqrt(n)-normality result. For the truncated CRC panel data model, I obtain the identification and estimation results based on the special regressor method which is used in Khan and Lewbel (2007). I construct a sqrt(n) consistent estimator for the population mean of the random coefficient. I also derive the asymptotic distribution of my estimator. Simulations are given to show the finite sample advantage of my estimators. Further, I use a linear CRC panel data model to reexamine the return from job training. The results show that my estimation method really makes a difference, and the estimated return of training by my method is 7 times as much as the one estimated without considering the correlation between the covariates and random coefficients. It shows that on average the rate of return of job training is 3.16% per 60 hours training.

This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

The focus of the paper is the nonparametric estimation of an instrumental regression function f defined by conditional moment restrictions stemming from a structural econometric model: E [Y - f (Z) | W] = 0, and involving endogenous variables Y and Z and instruments W. The function f is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyses identification and overidentification of this model and presents asymptotic properties of the estimated nonparametric instrumental regression function.

This dissertation examines the assumptions presumed throughout the literature to establish valid estimation procedures for non-linear models. The following three chapters addresses issues of identification, consistent and efficient estimation, and incorporating heteroskedasticity and serial correlation for binary response models in cross-sectional and panel data settings. Chapter 1: Parametric Identification of Multiplicative Exponential Heteroskedasticity Multiplicative exponential heteroskedasticity is commonly seen in latent variable models such as Probit or Logit where correctly modelling the heteroskedasticity is imperative for consistent parameter estimates. However, it appears the literature lacks a formal proof of point identification for the parametric model. This chapter presents several examples that show the conditions presumed throughout the literature are not sufficient for identification and as a contribution provides proofs of point identification in common specifications. Chapter 2: Relaxing Conditional Independence in an Endogenous Binary Response Model For binary response models, control function estimators are a popular approach to address endogeneity. But these estimators utilize a Control Function assumption that imposes Conditional Independence (CF-CI) to obtain identification. CF-CI places restrictions on the relationship between the latent error and the instruments that are unlikely to hold in an empirical context. In particular, the literature has noted that CF-CI imposes homoskedasticity with respect to the instruments. This chapter identifies the consequences of CF-CI, provides examples to motivate relaxing CF-CI, and proposes a new consistent estimator under weaker assumptions than CF-CI. The proposed method is illustrated in an application, estimating the effect of non-wife income on married women's labor supply. Chapter 3: Behavior of Pooled and Joint Estimators in Probit Model with Random Coefficients and Serial Correlation This chapter compares a pooled maximum likelihood estimator (PMLE) to a joint (full) maximum likelihood estimator (JMLE), the dominant estimation method for mixture models, for dealing with potential individual-specific heterogeneity and serial correlation in a binary response Probit Mixture model. The JMLE is more statistically efficient but computationally demanding and the implementation becomes more difficult if one tries to model the serial correlation over time. On the other hand, the PMLE is computationally simple and robust to arbitrary forms of serial correlation. Focusing on the Average Partial Effects, this chapter finds it imperative for the model to allow the individual-specific heterogeneity to be potentially correlated with the covariates (not a standard specification in Mixture models). Moreover, the JMLE can produce quite satisfactory estimates that seem robust to serial correlation even under misspecification of the likelihood function. Results are illustrated in an application, estimating the effects of different interventions on high risk men's behavior, complementing the original study of Blattman, Jamison, and Sheridan (2017).

It is increasingly common for analysts to seek out the opinions of individuals and organizations using attitudinal scales such as degree of satisfaction or importance attached to an issue. Examples include levels of obesity, seriousness of a health condition, attitudes towards service levels, opinions on products, voting intentions, and the degree of clarity of contracts. Ordered choice models provide a relevant methodology for capturing the sources of influence that explain the choice made amongst a set of ordered alternatives. The methods have evolved to a level of sophistication that can allow for heterogeneity in the threshold parameters, in the explanatory variables (through random parameters), and in the decomposition of the residual variance. This book brings together contributions in ordered choice modeling from a number of disciplines, synthesizing developments over the last fifty years, and suggests useful extensions to account for the wide range of sources of influence on choice.