Yuichi Kitamura

An Information-Theoretic Alternative to Generalized Method of Moments Estimation

While optimally weighted generalized method of moments (GAM) estimation has desirable large sample properties, its small sample performance is poor in some applications. The authors propose a computationally simple alternative, for weakly dependent data generating mechanisms, based on minimization of the Kullback-Leibler information criterion. Conditions are derived under which the large sample properties of this estimator are similar to GAM, i.e., the estimator will be consistent and asymptotically normal, with the same asymptotic covariance matrix as GAM. In addition, the authors propose overidentifying and parametric restrictions tests as alternatives to analogous GAM procedures.

NONPARAMETRIC ESTIMATION IN RANDOM COEFFICIENTS BINARY CHOICE MODELS

This paper considers random coefficients binary choice models. The main goal is to estimate the density of the random coefficients nonparametrically. This is an ill-posed inverse problem characterized by an integral transform. A new density estimator for the random coefficients is developed, utilizing Fourier-Laplace series on spheres. This approach offers a clear insight on the identification problem. More importantly, it leads to a closed form estimator formula that yields a simple plug-in procedure requiring no numerical optimization. The new estimator, therefore, is easy to implement in empirical applications, while being flexible about the treatment of unobserved heterogeneity. Extensions including treatments of non-random coefficients and models with endogeneity are discussed.

Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments

This paper develops a general theory of instrumental variables (IV) estimation that allows for both I(1) and I(0) regressors and instruments. The estimation techniques involve an extension of the fully modified (FM) regression procedure that was introduced in earlier work by Phillips-Hansen (1990). FM versions of the generalized instrumental variable estimation (GIVE) method and the generalized method of moments (GMM) estimator are developed. In models with both stationary and nonstationary components, the FM-GIVE and FM-GMM techniques provide efficiency gains over FM-IV in the estimation of the stationary components of a model that has both stationary and nonstationary regressors. The paper exploits a result of Phillips (1991a) that we can apply FM techniques in models with cointegrated regressors and even in stationary regression models without losing the methods good asymptotic properties. The present paper shows how to take advantage jointly of the good asymptotic properties of FM estimators with respect to the nonstationary elements of a model and the good asymptotic properties of the GIVE and GMM estimators with respect to the stationary components. The theory applies even when there is no prior knowledge of the number of unit roots in the system or the dimension or the location of the cointegration space. An FM extension of the Sargan (1958) test for the validity of the instruments is proposed.

Estimation of Cointegrated Systems with I(2) Processes

This paper considers the properties of systems likelihood procedures for cointegrated systems when the I(2) variables are present. Two alternative methods are proposed: one is based on the full system likelihood, whereas another is based on the subsystem likelihood. By eliminating all unit roots in the system by the use of prior information concerning the presence of unit roots, these procedures yield estimates whose asymptotic distributions are mixed normal, free from nuisance parameters, and median-unbiased. Both methods are extensions of a full system maximum likelihood procedure by Phillips (1991a) to I(2) models. Three cases of cointegration with I(2) variables are considered in order to cover a wide variety of cointegration relationships. A triangular ECM representation and the two ML estimates are derived for each case, and the asymptotics are discussed as well. The asymptotic efficiency concerning the two estimates are considered.

Robustness, Infinitesimal Neighborhoods, and Moment Restrictions

This paper is concerned with robust estimation under moment restrictions. A moment restriction model is semiparametric and distribution-free, therefore it imposes mild assumptions. Yet it is reasonable to expect that the probability law of observations may have some deviations from the ideal distribution being modeled, due to various factors such as measurement errors. It is then sensible to seek an estimation procedure that are robust against slight perturbation in the probability measure that generates observations. This paper considers local deviations within shrinking topological neighborhoods to develop its large sample theory, so that both bias and variance matter asymptotically. The main result shows that there exists a computationally convenient estimator that achieves optimal minimax robust properties. It is semiparametrically efficient when the model assumption holds, and at the same time it enjoys desirable robust properties when it does not.

Partial Identification of Finite Mixtures in Econometric Models

We consider partial identification of finite mixture models in the presence of an observable source of variation in the mixture weights that leaves component distributions unchanged, as is the case in large classes of econometric models. We first show that when the number J of component distributions is known a priori, the family of mixture models compatible with the data is a subset of a J(J−1)‐dimensional space. When the outcome variable is continuous, this subset is defined by linear constraints, which we characterize exactly. Our identifying assumption has testable implications, which we spell out for J = 2. We also extend our results to the case when the analyst does not know the true number of component distributions and to models with discrete outcomes.

Identifying Finite Mixtures in Econometric Models

We consider partial identification of finite mixture models in the presence of an observable source of variation in the mixture weights that leaves component distributions unchanged, as is the case in large classes of econometric models. We first show that when the number J of component distributions is known a priori, the family of mixture models compatible with the data is a subset of a J(J-1)-dimensional space. When the outcome variable is continuous, this subset is defined by linear constraints which we characterize exactly. Our identifying assumption has testable implications which we spell out for J = 2. We also extend our results to the case when the analyst does not know the true number of component distributions, and to models with discrete outcomes.

Efficient IV Estimation in Nonstationary Regression

A limit theory for instrumental variables (IV) estimation that allows for possibly nonstationary processes was developed in Kitamura and Phillips (1992, Fully Modified IV, GIVE, and GMM Estimation with Possibly Non-stationary Regressors and Instruments, mimeo, Yale University). This theory covers a case that is important for practitioners, where the nonstationarity of the regressors may not be of full rank, and shows that the fully modified (FM) regression procedure of Phillips and Hansen (1990) is still applicable. FM. versions of the generalized method of moments (GMM) estimator and the generalized instrumental variables estimator (GIVE) were also developed, and these estimators (FM-GMM and FM-GIVE) were designed specifically to take advantage of potential stationarity in the regressors (or unknown linear combinations of them). These estimators were shown to deliver efficiency gains over FM-IV in the estimation of the stationary components of a model.

Nonparametric Likelihood: Efficiency and Robustness

Nonparametric likelihood is a natural generalization of parametric likelihood and it offers effective methods for analysing economic models with nonparametric components. This is of great interest, since econometric theory rarely suggests a parametric form of the probability law of data. Being a nonparametric method, nonparametric likelihood is robust to misspecification. At the same time, it often achieves good properties that are analogous to those of parametric likelihood. This paper explores various applications of nonparametric likelihood, with some emphasis on the analysis of biased samples and data combination problems.

Using Mixtures in Econometric Models: A Brief Review and Some New Results

This paper is concerned with applications of mixture models in econometrics. Focused attention is given to semiparametric and nonparametric models that incorporate mixture distributions, where important issues about model specifications arise. For example, there is a significant difference between a finite mixture and a continuous mixture in terms of model identifiability. Likewise, the dimension of the latent mixing variables is a critical issue, in particular when a continuous mixture is used. We present applications of mixture models to address various problems in econometrics, such as unobserved heterogeneity and multiple equilibria. New nonparametric identification results are developed for finite mixture models with testable exclusion restrictions without relying on an identification‐at‐infinity assumption on covariates. The results apply to mixtures with both continuous and discrete covariates, delivering point identification under weak conditions.