Download or read book Essays on Identification in Econometric Models written by Tatiana Komarova and published by . This book was released on 2008 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Identification and Inference for Econometric Models written by Donald W. K. Andrews and published by Cambridge University Press. This book was released on 2005-07-04 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 volume contains the papers presented in honor of the lifelong achievements of Thomas J. Rothenberg on the occasion of his retirement. The authors of the chapters include many of the leading econometricians of our day, and the chapters address topics of current research significance in econometric theory. The chapters cover four themes: identification and efficient estimation in econometrics, asymptotic approximations to the distributions of econometric estimators and tests, inference involving potentially nonstationary time series, such as processes that might have a unit autoregressive root, and nonparametric and semiparametric inference. Several of the chapters provide overviews and treatments of basic conceptual issues, while others advance our understanding of the properties of existing econometric procedures and/or propose others. Specific topics include identification in nonlinear models, inference with weak instruments, tests for nonstationary in time series and panel data, generalized empirical likelihood estimation, and the bootstrap.

Download or read book Econometric Essays on Identification and Inference in the Simultaneous Equations Model with Weak Instruments written by Jabonn Kim and published by . This book was released on 2004 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Essays on Partial Identification in Structural Models written by Lixiong Li and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: My studies focus on the partial identification in structural econometric models. This dissertation includes two chapters on partial identification and one chapter on a numerical method of estimating structural discrete choice models. Chapter 1Structural econometric models usually involve parametric distributional assumptions for unobserved heterogeneity. Although these assumptions are typically not informed by economic theory, and undermine the robustness of empirical results, they are generally thought to be necessary to simulate counterfactual predictions. In partially identified and incomplete structural models, counterfactual analysis is also hampered by the multiplicity of admissible structural parameter values and the multiplicity of counterfactual predictions for each structural parameter value. This paper shows how to construct identification conditions for both structural and counterfactual parameters in a large class of structural econometric models, including partially identified and incomplete ones, without imposing parametric distributional assumptions for unobserved variables. The identified set is characterized by moment inequalities, so that existing inferential methods can be applied, including subvector inference when only counterfactual parameters are of interest. The novelty and computational tractability of the methodology is illustrated on a class of discrete choice models and a class of entry models.Chapter 2I investigate a model of one-to-one matching with transferable utilities, where the matching process is subject to time-consuming search frictions. I assume agents have unobserved (to economists) characteristics, which affect the matching surplus along with matching specific random shocks under a separability assumption. I show the matching surplus can be non-parametrically identified with data on matching patterns and distributions on unmatched durations across agents, given any known distribution on unobserved characteristics. In contrast to the existing literature, my identification strategy does not hinge on data on payoffs and panel data with long time series. As in frictionless matching models, I show any interior matching patterns can be rationalized by the model under some parameters. For one type of corner solution, only set identification is attained and a sharp bound has been derived.Chapter 3This paper describes a numerical method to solve for mean product qualities which equates the real market share to the market share predicted by a discrete choice model. The method covers a general class of discrete choice model, including the pure characteristics model in \cite{berry_pure_2007} and the random coefficient logit model in \cite{berry_automobile_1995} (hereafter BLP). The method transforms the original market share inversion problem to an unconstrained convex minimization problem, so that any convex programming algorithm can be used to solve the inversion. Moreover, such results also imply that the computational complexity of inverting a demand model should be no more than that of a convex programming problem. In simulation examples, I show the method outperforms the contraction mapping algorithm in BLP. I also find the method remains robust in pure characteristics models with near-zero market shares.

Download or read book Essays on Semiparametric Models with Partial Identification written by and published by . This book was released on 2012 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of two self-contained essays on partially identified econometric models, organized in the form of two chapters. The first chapter develops inference methods for conditional moment models in which the unknown parameter is possibly partially identified and may contain infinite-dimensional components. I consider testing the hypothesis that a given restriction on the parameter is satisfied by at least one element of the identification set. I propose using the sieve minimum of a Kolmogorov-Smirnov type statistic as the test statistic, derive its asymptotic distribution, and provide consistent bootstrap critical values. In this way a broad family of restrictions can be consistently tested, making the proposed procedure applicable to various types of inference. In particular, I show how to: (1) test the semiparametric model specification; (2) construct confidence sets for unknown parametric components; and (3) construct confidence sets for unknown functions at a given point. The specification test is consistent against fixed alternatives. The confidence sets have correct asymptotic coverage probability, excluding any value outside the identification set with asymptotic probability one. My methods are robust to partial identification, and allow for the moment functions to be nonsmooth. A Monte Carlo study demonstrates finite sample performance. In the second chapter, I consider estimation in dynamic discrete choice panel data models of short time series, in which neither the cross-sectional heterogeneity nor the initial condition is observed. The major challenges are: (1) point-identification often fails in these models as demonstrated by Honoré and Tamer (2006); and (2) the heterogeneity cannot be differenced out by the standard "within" or first difference transformations due to nonlinearity. I show that the parameter can be equivalently defined by a finite number of conditional moment equalities. And I propose set estimators that are fixed-T consistent with respect to a properly defined Hausdorff distance. Rates of convergence in the Hausdorff distance are derived.

Download or read book Essays on Partial Identification in Econometrics and Finance written by Alfred Galichon and published by . This book was released on 2007 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second essay propose an alternative testing methodology with favorable computational properties, the "Dilation Bootstrap," a testing methodology based on probabilistic coupling representations of the empirical distribution.

Download or read book Essays in Econometrics written by Alexandre Poirier and published by . This book was released on 2013 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of two chapters, both contributing to the field of econometrics. The contributions are mostly in the areas of estimation theory, as both chapters develop new estimators and study their properties. They are also both developed for semi-parametric models: models containing both a finite dimensional parameter of interest, as well as infinite dimensional nuisance parameters. In both chapters, we show the estimators' consistency, asymptotic normality and characterize their asymptotic variance. The second chapter is co-authored with professors Jinyong Hahn, Bryan S. Graham and James L. Powell. In the first chapter, we focus on estimation in a cross-sectional model with independence restrictions, because unconditional or conditional independence restrictions are used in many econometric models to identify their parameters. However, there are few results about efficient estimation procedures for finite-dimensional parameters under these independence restrictions. In this chapter, we compute the efficiency bound for finite-dimensional parameters under independence restrictions, and propose an estimator that is consistent, asymptotically normal and achieves the efficiency bound. The estimator is based on a growing number of zero-covariance conditions that are asymptotically equivalent to the independence restriction. The results are illustrated with four examples: a linear instrumental variables regression model, a semilinear regression model, a semiparametric discrete response model and an instrumental variables regression model with an unknown link function. A Monte-Carlo study is performed to investigate the estimator's small sample properties and give some guidance on when substantial efficiency gains can be made by using the proposed efficient estimator. In the second chapter, we focus on estimation in a panel data model with correlated random effects and focus on the identification and estimation of various functionals of the random coefficient's distributions. In particular, we design estimators for the conditional and unconditional quantiles of the random coefficient's distribution. This model allows for irregularly identified panel data models, as in Graham and Powell (2012), where quantiles of the effect are identified by using two subpopulations of "movers" and "stayers", i.e. those for whom the covariates change by a large amount from one period to another, and those for whom covariates remain (nearly) unchanged. We also consider an alternative asymptotic framework where the fraction of stayers in the population is shrinking with the sample size. The purpose of this framework is to approximate a continuous distribution of covariates where there is an infinitesimal fraction of exact stayers. We also derive the asymptotic variance of the coefficient's distribution in this framework, and we conjecture the form of the asymptotic variance under a continuous distribution of covariates. The main goal of this dissertation is to expand the choice set of estimators available to applied researchers. In chapter one, the proposed estimator attains the efficiency bound and might allow researchers to gain more precision in estimation, by getting smaller standard errors. In the second chapter, the new estimator allows researchers to estimate quantile effects in a just-identified panel data model, a contribution to the literature.

Download or read book Essays on Identification and Estimation of Structural Economic Models written by Shaomin Wu and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three chapters that study the identification and estimation of structural economic models. Chapter 1, "Identification and Estimation of Nonseparable Triangular Equations with Mismeasured Instruments" studies the nonparametric identification and estimation of the marginal effect of an endogenous variable X on the outcome variable Y , given a potentially mismeasured instrument variable W∗, without assuming linearity or separability of the functions governing the relationship between observables and unobservables. In order to address the challenges arising from the co-existence of measurement error and nonseparability, I first employ the deconvolution technique from the measurement error literature to identify the joint distribution of Y,X,W∗ using two error-laden measurements of W∗. I then recover the structural derivative of the function of interest and the "Local Average Response" (LAR) from the joint distribution via the "unobserved instrument" approach in Matzkin (2016). I also propose nonparametric estimators for these parameters and derive their uniform rates of convergence. Monte Carlo exercises show evidence that the estimators I propose have goodfinite sample performance. Chapter 2, "Two-step Estimation of Network Formation Models with Unobserved Heterogeneities and Strategic Interactions", characterizes the network formation process as a static game of incomplete information, where the latent payoff of forming a link between two individuals depends on the structure of the network, as well as private information on agents' attributes. I allow agents' private unobserved attributes to be correlated with observed attributes through individual fixed effects. Using data from a single large network, I propose a two-step estimator for the model primitives. In the first step, I estimate agents' equilibrium beliefs of other people's choice probabilities. In the second step, I plug in the first-step estimator to the conditional choice probability expression and estimate the model parameters and the unobserved individual fixed effects together using Joint MLE. Assuming that the observed attributes are discrete, I showed that the first step estimator is uniformly consistent with rate N−1/4, where N is the total number of linking proposals. I also show that the second-step estimator converges asymptotically to a normal distribution at the same rate. Chapter 3, "Identification and Estimation in Differentiated Products Markets Where Firms Affect Consumers' Attention" studies the nonparametric identification and estimation of a demand and supply system where firms affect consumers' consideration sets via costly marketing inputs, when market-level data is available. On the demand side, I characterize preferences and considerations nonparametrically, allowing rich heterogeneities and correlations between them. On the supply side, I characterize firms' optimal choices by a set of first-order conditions without specifying the form of the oligopoly model. The demand and supply sides form a simultaneous system of equations in the spirit of Berry and Haile (2014). I then show the identification of the system using the method proposed by Matzkin (2015). Moreover, using the variations of exclusive regressors entering preferences and considerations respectively, I separately identify features of the utility functions and the attention functions. Based on the constructive identification results, I propose nonparametric estimators of the demand, utility, and attention functions and show their asymptotic properties.

Download or read book Essays on Econometric Identification of Network and Choice Models with Limited Consideration written by Matthew Kelly Thirkettle and published by . This book was released on 2020 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is comprised of two papers. In the first paper (Chapter \ref{ch2}), I obtain informative bounds on network statistics in a partially observed network whose formation I explicitly model. Partially observed networks are commonplace due to, for example, partial sampling or incomplete responses in surveys. Network statistics (e.g., centrality measures) are not point identified when the network is partially observed. Worst-case bounds on network statistics can be obtained by letting all missing links take values zero and one. I dramatically improve on the worst-case bounds by specifying a structural model for network formation. An important feature of the model is that I allow for positive externalities in the network-formation process. The network-formation model and network statistics are set identified due to multiplicity of equilibria. I provide a computationally tractable outer approximation of the joint identified region for preferences determining network-formation processes and network statistics. In a simulation study on Katz-Bonacich centrality, I find that worst-case bounds that do not use the network formation model are $44$ times wider than the bounds I obtain from my procedure. The second paper (Chapter \ref{ch3}) is concerned about learning decision makers' (DMs) preferences using data on observed choices from a finite set of risky alternatives with monetary outcomes. This chapter is coauthored with Levon Barseghyan and Francesca Molinari. We propose a discrete choice model with unobserved heterogeneity in consideration sets (the collection of alternatives considered by DMs) and unobserved heterogeneity in standard risk aversion. In this framework, stochastic choice is driven both by different rankings of alternatives induced by unobserved heterogeneity in risk preferences and by different sets of alternatives considered. We obtain sufficient conditions for semi-nonparametric point identification of both the distribution of unobserved heterogeneity in preferences and the distribution of consideration sets. Our method yields an estimator that is easy to compute and that can be used in markets with a large number of alternatives. We apply our method to a dataset on property insurance purchases. We find that although households are on average strongly risk averse, they consider lower coverages more frequently than higher coverages. Finally, we estimate the monetary losses associated with limited consideration in our application.

Download or read book Essays on Econometric Models for Games and Censored Data written by Jangsu Yoon and published by . This book was released on 2018 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of two chapters on nonparametric approach to econometric models. The first chapter studies identification and inference in game theoretic models with incomplete information and random coefficients. These models allow for strategic interactions in the presence of incomplete information while incorporating payoff parameter heterogeneity across games. The possibility of multiple Bayesian Nash Equilibria presents challenges to identification, and potential discontinuities in the equilibrium selection rule require attention in estimation and inference. In this work, I establish conditions for point identification of the structural parameters, including the joint distribution function of random coefficients, the equilibrium selection mechanism, and the support of random coefficients. I also suggest the Penalized Sieve Minimum Distance (PSMD) estimator assuming piecewise smooth equilibrium selection, derive asymptotic normality for the distributional parameters of random coefficients, and construct a pointwise confidence interval of the parameter based on Chen and Pouzo (2012, 2015). Empirical applications include an entry game between Walmart and Kmart in the context of Jia (2008), and a labor supply game of husbands and wives motivated by Heckman (1978). Both illustrations show that random coefficients capture heterogeneous entry behavior across markets and the heterogeneous work decisions of married couples with young children. The second chapter provides estimation and inference methods for a nonparametric generalization of Honore (1992)'s classic censored regression model with fixed effects. I consider an unknown nonparametric form of the structural function and first establish identification of this unknown function under the standard assumptions from the previous literature. Next I consider a sieve estimation version of Honore (1992)'s seminal trimmed LAD approach and show the resulting approach yields consistent, asymptotically normal estimates of the structural function. The performance of pointwise confidence intervals for the structural function based on a consistent asymptotic variance estimator and a weighted bootstrap approach are compared in a Monte Carlo simulation. The result verifies a benefit of using the nonparametric estimator when the structural function is nonlinear and the percentage of censored data is modest to moderate. Finally, an empirical application for a simple intertemporal labor supply model examines the potential nonlinear relation of labor supply and hourly wage.

Download or read book Essays on Necessary and Sufficient Conditions for Global and Local Identification in Linear and Nonlinear Models written by Xin Liang and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This Ph.D. thesis consists of three essays on identification theory in econometrics. In view of achieving reliable inference methods when some parameters are not identifiable (or weakly identifiable), we establish necessary and sufficient conditions for identification of linear and nonlinear parameter transformations, when the full parameter vector is not identifiable. The first essay considers a class of generalized linear models (deemed "partially linear models") where parameters of interest determine the distribution of the data through multiplication by a known matrix. This setup not only covers linear regression models with collinearity (such as cases where the number of explanatory variables is potentially very large or the number observations is inferior to the number of variables) and a general error covariance matrix, but a wide spectrum of other models used in econometrics, such as linear median regressions and quantile regressions, generalized linear mixed models, probit and Tobit models, multinomial logit models and other discrete choice models, exponential models, index models, etc. We first provide a general necessary and sufficient condition for the global identification of a general transformation of model parameters (when the full parameter vector is not typically identified) based on a new separability condition. The general result is then applied to partially linear models. Even though none of the original individual parameters of the model may be identified, we describe the class of linear transformations which can be identified. To get usable conditions, different equivalent characterizations are derived. The effect of adding restrictions is also considered, and the corresponding identification conditions are supplied.The second essay reconsiders the problem of characterizing identifiable parameters in linear IV regressions and simultaneous equations models (SEMs), using methods based on the first essay. The recent econometric literature on weak instruments mainly deals with this basic setup, and the appropriate statistical methods depend on whether the parameters of interest are identifiable. We study the general case where some model parameters are not identifiable, without any restriction on the rank of the instrument matrix, and we characterize which linear transformations of the structural parameters are identifiable. An important observation is that identifiable parameters may depend on the instrument matrix (in addition to the parameters of the reduced form), and a number of alternative characterizations are provided. These results are also applicable to partially linear IV-type models where the linear IV structure is embedded in a nonlinear structure, such as a quantile specification or a discrete choice model.The third essay takes up the problem of characterizing the identification of nonlinear functions of parameters in nonlinear models. The setup is fundamentally semiparametric, and the basic assumption is that structural parameters of interest determine a number of identifiable parameters through a nonlinear equation. Again, we consider the general case where not all model parameters are identifiable, with the purpose of characterizing nonlinear parameter transformations which are identifiable. The literature on this problem is thin, and focuses on the identification of the full parameter vector in the equation of interest. In view of the fact global identification is extremely difficult to achieve, this paper looks at the problem from a local identification viewpoint. Both sufficient conditions, as well as necessary and sufficient conditions are derived under assumptions of differentiability of the relevant moment equations and parameter transformations. Some classical results on identification in likelihood models are also derived and extended. Finally, the results are applied to identification problems in DSGE models." --

Download or read book Essays on the Identification and Estimation of Network Models written by Yiran Xie and published by . This book was released on 2022 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three main chapters that study social interactions in networks. In Chapter 1, I study a market with many-to-many contracts when the number of market participants increases. Many-to-many contracts allow a seller to trade with multiple buyers and a buyer to trade with multiple sellers. I focus on investigating the identification of payoff parameters through data observed from equilibrium matches in a large many-to-many matching market. In many-to-many matching markets, several issues have to be addressed: bias would arise since the outcomes are only observed when links are formed between two agents, and the maximum number of relationships an agent can enter into would possibly affect the set of stable outcomes. I show that under certain conditions, the number of firms (workers) that are willing to be matched to a specific worker (firm) grows at a rate regardless of the capacity of both sides. Furthermore, I show a correspondence between the stable matching outcomes in a many-to-many matching framework and that in a one-to-one matching framework. In Chapter 2, I conduct a structural econometric analysis of the diffusion process with players who observe their neighbors and make decisions based on their neighbors' decisions. I study the identification and estimation of diffusion processes in social and economic networks. Compared to the classic econometric diffusion literature that assumes a continuous population with a stochastic network structure, I provide a new econometric framework to analyze diffusion processes in fixed networks where Bayesian players observe their close neighbors. I demonstrate the existence of the equilibrium of the model and characterize the unique symmetric equilibrium. Based on these theoretical findings, I propose a consistent and tractable two-step estimator for payoff parameters using feasible data from a single large network. I evaluate the finite sample performance using Monte Carlo simulations. Chapter 3 applies the network diffusion model to data on the participation of a microfinance program in Indian villages to describe the impact of neighbors on individual decisions. Our model allows us to study the various network effect across different types of agents who care about their neighbors' opinions. It depends on unknown equilibrium beliefs, which specify agents' expectations about their neighbors' decisions. Using participation data from 43 villages, each including about 200 villagers, I estimate these equilibrium beliefs and the network effects.

Download or read book Essays on Econometrics written by and published by . This book was released on 2015 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three chapters on semiparametric/nonparametric econometric models with endogeneity. The first chapter considers conditional moment models where the parameters of interest include both finite-dimensional parameters and unknown functions. First, we provide new methods of pointwise and uniform inference for the estimates of both finite- and infinite-dimensional components of the parameters and functionals of the parameters. Second, under partial identification, we show how to construct pointwise confidence regions by inverting a quasi-likelihood ratio (QLR) statistic. We provide a consistent bootstrap procedure for obtaining critical values corresponding to the QLR. Furthermore, we generalize the uniform confidence bands from point identified case to uniform confidence sets over the domain of the unknown functions by inverting a sup-QLR statistic. The new methods are applied to construct pointwise confidence intervals and uniform confidence bands for shape-invariant Engel curves. The second chapter considers the problem of choosing the regularization parameter and the smoothing parameter in nonparametric instrumental variables estimation. We propose a Mallows' C p -type criterion to select these two parameters simultaneously. We show that the proposed selection criterion is optimal in the sense that the selected estimate asymptotically achieves the lowest possible mean squared error among all candidates. To account for model uncertainty, we introduce a new model averaging estimator for nonparametric instrumental variables regressions. We propose a Mallows criterion for the weight selection and demonstrate its asymptotic optimality. The third chapter develops empirical likelihood ratio tests for conditional moment models in which the unknown parameter can contain infinite-dimensional components. We obtain (1) the limiting distribution of the sieve conditional empirical likelihood ratio (SCELR) test statistic for functionals of parameters under the null hypothesis and local alternatives, and (2) the limiting distribution of the SCELR test statistics for conditional moment restrictions (a consistent specification test) under null hypothesis and local alternatives.

Download or read book Essays in Weak Identification written by Isaiah Smith Andrews and published by . This book was released on 2014 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic researchers and policymakers need reliable tools both to estimate economic relationships and to measure the uncertainty surrounding their estimates. Unfortunately, economic data sometimes contains limited information useful for estimating relationships of interest. In such cases, the statistical techniques commonly used in applied economics can break down and fail to accurately reflect the level of uncertainty present in the data. If they rely on such tools, researchers and policymakers may come away with serious misconceptions about the precision and reliability of their estimates. Econometricians refer to models where the lack of information in the data causes common statistical techniques to break down as weakly identified. In this thesis, I examine several questions relating to weak identification. In the first chapter, I introduce the class of conditional linear combination tests. These tests control size under weak identification and have a number of optimality properties in a conditional problem. I suggest using minimax regret conditional linear combination tests and propose a computationally tractable class of tests that plug in an estimator for a nuisance parameter. In the second chapter, I consider the problem of detecting weak identification. When weak identification is a concern researchers frequently calculate confidence sets in two steps, first assessing the strength of identification and then deciding whether to use an identification-robust confidence set. Two-step procedures of this sort may generate highly misleading confidence sets, and I demonstrate that two-step confidence sets based on the first stage F-statistic can have extremely poor coverage in linear instrumental variables models with heteroskedastic errors. I introduce a simple approach to detecting weak identification and constructing two-step confidence sets which controls coverage distortions. In the third chapter, joint with Anna Mikusheva, we consider minimum distance statistics and show that in a broad class of models the problem of testing under weak identification is closely related to the problem of testing a "curved null" in a finite-sample Gaussian model. Using the curvature of the model, we develop new finite-sample bounds on the distribution of minimum-distance statistics, which we show can be used to detect weak identification and to construct tests robust to weak identification.

Download or read book Essays on Weak Identification Model Selection and Hypothesis Testing in Econometrics written by Purevdorj Tuvaandorj and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This thesis makes contributions to weak identification, modelselection and hypothesis testing in econometrics. It consists of thefollowing essays.In Chapter 1, we study likelihood-basedinference in models with possible identification failure. The results relyheavily on the properties of the mapping from structural parameters togeneralized reduced-form parameters (which are identified by construction).We establish an asymptotic chi-square bound on the likelihood ratio (LR)statistic for testing restrictions on the possibly unidentified structuralparameters with degrees of freedom equal to the dimension of the reducedform parameter vector through which the tested parameters enter thelikelihood function. We also propose pivotal C(alpha)-type statisticsthat are robust to potential identification failure and are flexible inincorporating a wide class of estimators of the (strongly identified)nuisance parameters. Furthermore, we develop a generalized version of theclassical Anderson-Rubin (AR)-type statistic in linear simultaneousequations and an identification-robust pretest-based inference procedure.In Chapter 2, we study the invariance properties of various test criteria which have been proposed for hypothesis testing in the context of incompletely specified models, such asmodels which are formulated in terms of estimating functions (Godambe, 1960, Ann. Math. Stat.) or moment conditions and are estimated bygeneralized method of moments (GMM) procedures (Hansen, 1982, Econometrica), and models estimated by pseudo-likelihood (Gourieroux,Monfort and Trognon, 1984, Econometrica) and M-estimation methods.The invariance properties considered include invariance to (possiblynonlinear) hypothesis reformulations and reparameterizations. The teststatistics examined include Wald-type, LR-type, LM-type, score-type, and C(alpha)-type criteria. In Chapter 3, we propose generalized C(alpha) tests for testing linear and nonlinear parameterrestrictions in models specified by estimating functions. The asymptotic distribution of theproposed statistic is established under weak regularity conditions. We show that earlierC(alpha)-type statistics are included as special cases. The problem of testing hypotheses fixinga subvector of the complete parameter vector of the model is discussed in detail. In Chapter 4, we consider conditional distribution and conditional density functionalsin the space of generalized functions. We obtain the limit of the kernel estimators for weakly dependent data, evenunder non-differentiability of the distribution function; the limit Gaussian process is characterizedas a stochastic random functional (random generalized function) on the suitablefunction space. An alternative simple to compute estimator based on the empirical distribution function is proposed for the generalized random functional. For test statistics based on this estimator, limit properties are established.Chapter 5, considers the issue of selecting the number of regressors and the numberof structural breaks in multivariate regression models in the possible presence of multiplestructural changes. We develop a modified Akaike's information criterion (AIC), amodified Mallows' Cp criterion and a modified Bayesian information criterion (BIC). Thepenalty terms in these criteria are shown to be different from the usual terms." --

Download or read book Three Essays on Spatial Econometric Models with Missing Data written by Wei Wang and published by . This book was released on 2010 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This dissertation is composed of three essays on spatial econometric models with missing data. Spatial models that have a long history in regional science and geography have received substantial attention in various areas of economics recently. Applications of spatial econometric models prevail in urban, developmental and labor economics among others. In practice, an issue that researchers often face is the missing data problem. Although many solutions such as list-wise deletion and EM algorithm can be found in literature, most of them are either not suited for spatial models or hard to apply due to technical difficulties. My research focuses on the estimation of the spatial econometric models in the presence of missing data problems. The first chapter develops a GMM method based on linear moments for the estimation of mixed regressive, spatial autoregressive (MRSAR) models with missing observations in the dependent variables. The estimation method uses the expectation of the missing data, as a function of the observed independent variables and the parameters to be estimated, to replace the missing data themselves in the estimation. The proposed GMM estimators are shown to be consistent and asymptotically normal. Feasible optimal weighting matrix for the GMM estimation is given. We extend our estimation method to MRSAR models with heteroskedastic disturbances, high order MRSAR models and unbalanced spatial panel data models with random effects as well. From these extensions, we see that the proposed GMM method has more compatibility, compared with the conventional EM algorithm. The second chapter considers a group interaction model first proposed by Lee (2006); this model is a special case of the spatial autoregressive (SAR) models. It is a first attempt to estimate the model in a more general random sample setting, i.e. a framework in which only a random sample rather than the whole population in a group is available. We incorporate group heteroskedasticity along with the endogenous, exogenous and group fixed effects in the model. We prove that, under some basic assumptions and certain identification conditions, the quasi maximum likelihood (QML) estimators are consistent and asymptotically normal when the functional form of the group heteroskedasticity is known. Two types of misspecifications are considered, and, under each, the estimators are inconsistent. We also propose IV estimation in the case that the group heteroskedasticity is unknown. A LM test of group heteroskedasticity is given at the end. The third chapter considers the same group interaction model as that in the second chapter, but focuses on the large group interaction case and uses a random effects setting for the group specific characters. A GMM estimation framework using moment conditions from both within and between equations is applied to the model. We prove that under some basic assumptions and certain identification conditions, the GMM estimators are consistent and asymptotically normal, and the convergence rates of the estimators are higher than those of the estimators derived from the within equations only. Feasible optimal GMM estimators are proposed.

Download or read book Essays on Theories and Applications of Spatial Econometric Models written by Xu Lin and published by . This book was released on 2006 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: As an effective method in analyzing interdependence among the observations, the spatial autoregressive (SAR) models have witnessed ever-increasing applications. This dissertation intends to enrich both the spatial econometrics theory and the social interaction estimations. In the first essay, a SAR model with group unobservables is applied to analyze peer effects in student academic achievement. Unlike the linear-in-means model in Manski (1993), the SAR model can identify both endogenous and contextual social effects due to variations in the peer measurements, thus resolving the "reflection problem". The group fixed effects term captures the confounding effects of the common variables faced by the same group members. I use datasets from the National Longitudinal Study of Adolescent Health (Add Health) survey and specify peer groups as friendship networks. I find evidence for both endogenous and contextual effects, even after controlling for school-grade fixed effects. The result indicates that students benefit from the presence of high quality peers, and that associating with peers living with both parents helps improve a student's GPA, while associating with peers whose mothers receive welfare has a negative effect. The second essay considers the GMM estimation of SAR models with unknown heteroskedasticity. We show that MLE is inconsistent whereas GMM estimators obtained from certain moment conditions are robust. Asymptotically valid inferences can be drawn from the consistent covariance matrix estimator. And efficiency can be improved by constructing the optimal weighted GMM estimation. We also propose some general tests for heteroskedasticity. In the Monte Carlo study, 2SLS estimators have large variances and biases in finite samples for cases where regressors do not have strong effects. The robust GMM estimator has desirable properties while the biases associated with MLE and non-robust GMM estimator may remain in large sample, especially, for the spatial effect coefficient and the intercept term. However, the magnitudes of biases are only moderate and those biases may be statistically insignificant with moderate large sample sizes. The various approaches are applied to the study of county teenage pregnancy rates. The results suggest a strong spatial convergence among county teenage pregnancy rates with a significant spatial effect.