Download or read book Essays on Identification and Weak Identification written by Linchun Chen and published by . This book was released on 2014 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: My doctoral dissertation aims to study several issues on identification and weak identification, with applications in linear instrumental variables (IV) models and transformation models. Chapter 1 is joint with Patrik Guggenberger, Frank Kleibergen and Sophocles Mavroeidis, which considers tests of a simple null hypothesis on a subset of the coefficients of the exogenous and endogenous regressors in a single-equation linear IV model with potentially weak identification. Existing methods of subset inference (i) rely on the assumption that the parameters not under test are strongly identified, or (ii) are based on projection-type arguments. We show that under homoskedasticity the subset Anderson and Rubin (1949) test, which replaces unknown parameters by limited information maximum likelihood (LIML) estimates has correct asymptotic size without imposing additional identification assumptions, but that the corresponding subset Lagrange multiplier (LM) test is size distorted asymptotically. Subsequently, Chapter 2, joint with Qihui Chen and Patrik Guggenberger, derives the asymptotic size of the corresponding subset LM test, and shows it is size distorted. We provide the smallest nonrandom size corrected (SC) critical value that ensures that the resulting "SC subset LM test" has correct asymptotic size. We introduce an easy to implement generalized moment selection plug-in SC subset LM test ("GMS-PSC subset LM test" from now on) that uses a data-dependent critical value that gives correct asymptotic size. Chapter 3 focuses on transformation models. It provides sufficient conditions for transformation models with endogenous regressors H(Y) =X[beta]+U to be identified under conditional moment restrictions, E(U/Z)=0, where Z is the IV for X. Allowing observables (X, Y, Z) and unobservable U to be high-dimensional, we show that the assumption of completeness suffices for identification. Based on the identification results, we propose to apply the penalized sieve minimum distance estimator (ĥ[beta]̂ in Chen and Pouzo (2009) with possible shape constraints to estimate (ĥ[beta]̂. Demand model of differentiated products markets is considered as an application of transformation models, and we provide the identification and PSMD estimation results for its parameters.
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 and Cointegrating Rank Selection written by Xu Cheng and published by . This book was released on 2010 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Identification and Inference for Econometric Models written by Donald W. K. Andrews and published by Cambridge University Press. This book was released on 2005-06-17 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 collection pushed forward the research frontier in four areas of theoretical econometrics.
Download or read book Essays on Weak Identification in High dimensional Models with Applications in Macroeconomics written by Max-Sebastian Dovì and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essays on Identification in Linear IV Models written by Chen Zhang and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation includes two chapters on identifications in linear IV models. Chapter 1: the exogeneity assumption in instrumental variable (IV) regressions is too strong in some empirical applications. A small deviation from the assumption would lead many classical tests to have distorted asymptotic sizes. Thus, the inferences derived from the exogeneity assumption can be subject to critique. For their reason, this paper introduces a new inference method for the structural parameter in linear IV regressions. The method is robust to local deviations of the exogeneity assumption and as powerful as the Wald test when exogeneity holds. To do so, the paper introduces a partial identification approach that only assumes that the covariance between the instruments and the unobservables is in a prespecified set. Based on this assumption, the paper proposes a cone-based (CB) test and shows that (i) the test has correct asymptotic size, and (ii) the test is asymptotically equivalent to the Wald test when the identified set shrinks to a singleton at a rate faster than root n. The paper then examines the linear IV regression model in Conely, Hansen, and Rossi (2012) and shows that the confidence interval constructed by the CB test is asymptotically smaller than the one in that paper. Finally, the paper demonstrates the performance of the CB test through Monte Carlo studies and two empirical applications. Chapter 2: weak IV is often a great concern in empirical research. While there are many weak IV robust inference methods for testing hypothesis about the structural parameters in the linear IV models, there is no clear power ranking among these methods. This chapter introduces a new conditional likelihood ratio (CLR) type test in linear IV regression models. In the chapter, we show that the proposed test has correct asymptotic size in the parameter space allowing for Kronecker Product structure covariance matrices; the test is asymptotically similar and rotationally invariant; the test is nearly uniformly most powerful among a class of invariant similar tests in the parameter space that allows for Kronecker product covariance matrices. In Monte Carlo studies, we show that the test: (i) performs very close to Moreira's CLR test under homoskedasticity; (ii) the test has correct null rejection probability in a larger parameter space that allows for Kronecker product covariance matrix while the original Moreira's CLR test overrejects. (iii) The test performs very close to the heteroskedasticity-- robust AR test under weak IV, but it outperforms the heteroskedasticity-- robust AR test when the model is overidentified and identification is strong.
Download or read book Essays on Identification written by Roy Henry Allen and published by . This book was released on 2017 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first two chapters of this dissertation study identification of a new class of demand models termed \textit{perturbed utility models}. The first chapter provides sufficient conditions under which structural functions in these models can be uniquely determined from knowledge of conditional means. The second chapter proposes a definition of complementarity/substitutability for these models and shows how to recover this measure from data. The third chapter of this dissertation studies inference in a class of partially identified models. Specifically, this chapter provides a finite-sample power comparison between two existing tests of moment inequalities.
Download or read book The Art of Identification written by Rex Ferguson and published by Penn State University Press. This book was released on 2021-09-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the mid-nineteenth century, there has been a notable acceleration in the development of the techniques used to confirm identity. From fingerprints to photographs to DNA, we have been rapidly amassing novel means of identification, even as personal, individual identity remains a complex chimera. The Art of Identification examines how such processes are entangled within a wider sphere of cultural identity formation. Against the backdrop of an unstable modernity and the rapid rise and expansion of identificatory techniques, this volume makes the case that identity and identification are mutually imbricated and that our best understanding of both concepts and technologies comes through the interdisciplinary analysis of science, bureaucratic infrastructures, and cultural artifacts. With contributions from literary critics, cultural historians, scholars of film and new media, a forensic anthropologist, and a human bioarcheologist, this book reflects upon the relationship between the bureaucratic, scientific, and technologically determined techniques of identification and the cultural contexts of art, literature, and screen media. In doing so, it opens the interpretive possibilities surrounding identification and pushes us to think about it as existing within a range of cultural influences that complicate the precise formulation, meaning, and reception of the concept. In addition to the editors, the contributors to this volume include Dorothy Butchard, Patricia E. Chu, Jonathan Finn, Rebecca Gowland, Liv Hausken, Matt Houlbrook, Rob Lederer, Andrew Mangham, Victoria Stewart, and Tim Thompson.
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 in Econometrics written by Laura Chioda and published by . This book was released on 2005 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essays in the Limits of Experiments Approach to Econometrics written by Richard Kingsley Crump and published by . This book was released on 2009 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essays on Forecast Evaluation Under General Loss Functions written by Carlos Capistran Carmona and published by . This book was released on 2005 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 PRICE DISCOVERY AND MODEL SELECTION IN PRESENCE OF WEAK INSTRUMENTS written by MICHAEL NELSON AGUESSY and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis organized in three chapters, essentially covers two main fields: finance and econometric theory with an application to macroeconomics. The first chapter proposes a methodology to uniquely measure price discovery, the mechanism by which the price of a security or an asset cross-listed on multiple markets is determined. The second chapter develops an information criterion that remains robust in presence of weaker instruments. Finally, the third chapter illustrates the benefits of optimal instruments' selection in assessing the impact of an example of monetary policy. Being a process that allows market participants to uncover the real worth of an asset in a timely manner, the price discovery may lead to arbitrage opportunities. As such, the Information Share (IS) commonly used to measure it, needs to be as accurate as possible to help mitigate related market inefficiencies. In the first chapter of this thesis, we investigate the identification issues encountered by the IS due to its sensitivity to price ordering. This translates to price innovations vectors leading to a serious lack of robustness of the IS metric. Exploiting some statistical features of price innovations, we propose to use Independent Component Analysis (ICA) in order to decompose the residuals into independent signals. Compared to leading measures in the literature, our approach is shown to perform well in the standard two-market data framework. We also obtain consistent results while extending our simulations to larger number of markets framework, notably the three-market set-up. We finally confirm our findings by studying the mechanism of price discovery in two analogous empirical applications. The first analyzes futures and spot prices in the European Union Allowances (EUAs) market for CO2 emissions, and the second concentrates on three Exchange Traded Funds (ETFs) tracking the performance of the Russell 2000 index. Our evidence suggests that futures prices and the IWM (ETF issued by iShares), respectively dominate their companions in contribution to price discovery. The second chapter is motivated by the fact that the usual exogeneity assumption is essential to the least squares estimator as it guarantees its consistency. However, when this condition fails, the explanatory variable is said to be endogenous and Instrumental Variable (IV) regressions is one of the methods available to the researcher to obtain consistent estimates. In response to the importance of the instruments selection step in the construction of a good IV estimator, we propose the alternative Relevant Moment Selection Criterion (aRMSC). This information criterion improves model selection when instruments are only weakly correlated with the endogenous variable. Through Monte Carlo simulations, we first illustrate that existing information criteria are not robust to these types of issues; naively selecting the larger models. We benefit from recent development on the importance of the strength of identification in achieving efficient estimation, and leverage it to evaluate how this may affect instruments selection when the candidate instruments available to the researcher are equally weakened or a pool of instruments with various strengths. Our evidence suggests that despite their weakness some instruments still contribute to improving the estimator's efficiency, in such a way that the selection of the most parsimonious model is possible. In the final chapter of this thesis, we first illustrate the performance of our proposed information criterion in a macroeconomic application. Moreover, we study empirically the relationship between news from forward guidance and monetary policy. We account for interactions both between various macroeconomic variables while considering their own lagged values using a structural vector autoregressive (VAR) model including interest rates, consumer price index, industrial production and excess bond premium. Our analysis relies on Gertler and Karadi's (2015) high frequency identification (HFI) approach for monetary policy shocks to extend monetary policy indicators to the 2 year government bond rate even though authors initially considered it as facing weak instruments issues. The aRMSC allows us to identify relevant instruments in the VAR model with the 2 year government bond rate and compare our results to those predicted with the 1 year rate, a stronger instrument. We also consider the limited information maximum likelihood estimator (LIML) to improve the instruments' selection. All together, our results highlight that the model based on the optimal set of instruments in comparison to the model with the naive inclusion of all instruments from the candidate set, produces more accurate impulse responses for economic and financial variables regardless of the estimator used to obtain the alternative information criterion.
Download or read book Essays on Descartes written by Paul Hoffman and published by Oxford University Press. This book was released on 2009-04-17 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of Paul Hoffman's wide-ranging essays on Descartes composed over the past twenty-five years. The essays in Part I include his celebrated "The Unity of Descartes' Man," in which he argues that Descartes accepts the Aristotelian view that soul and body are related as form to matter and that the human being is a substance; a series of subsequent essays elaborating on this interpretation and defending it against objections; and an essay on Descartes' theory of distinction. In the essays in Part II he argues that Descartes retains the Aristotelian theory of causation according to which an agent's action is the same as the passion it brings about, and explains the significance of this doctrine for understanding Descartes' dualism and physics. In the essays in Part III he argues that Descartes accepts the Aristotelian theory of cognition according to which perception is possible because things that exist in the world are also capable of a different way of existing in the soul, and he shows how this theory figures in Descartes' account of misrepresentation and in the controversy over whether Descartes is a direct realist or a representationalist. The essays in Part IV examine Descartes' theory of the passions of the soul: their definition; their effect on our happiness, virtue, and freedom; and methods of controlling them.
Download or read book Essays on Causal Inference and Econometrics written by Haitian Xie and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is a collection of three essays on the econometric analysis of causal inference methods. Chapter 1 examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. We show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff under shape restrictions, including monotonicity and smoothness conditions. Based on the nonparametric identification equation, we propose a three-step semiparametric estimation procedure and establish the asymptotic normality of the estimator. The semiparametric estimator achieves the same convergence rate as in the case of a binary treatment variable. As an application of the method, we estimate the causal effect of sleep time on health status by using the discontinuity in natural light timing at time zone boundaries. Chapter 2 examines the local linear regression (LLR) estimate of the conditional distribution function F(y|x). We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform asymptotic linear representation. The uniformity in the above results is with respect to both x and y and therefore has not previously been addressed in the literature on local polynomial regression. Such uniform convergence results are especially useful when the conditional distribution estimator is the first stage of a semiparametric estimator. Chapter 3 studies the estimation of causal parameters in the generalized local average treatment effect model, a generalization of the classical LATE model encompassing multi-valued treatment and instrument. We derive the efficient influence function (EIF) and the semiparametric efficiency bound for two types of parameters: local average structural function (LASF) and local average structural function for the treated (LASF-T). The moment condition generated by the EIF satisfies two robustness properties: double robustness and Neyman orthogonality. Based on the robust moment condition, we propose the double/debiased machine learning (DML) estimators for LASF and LASF-T. We also propose null-restricted inference methods that are robust against weak identification issues. As an empirical application, we study the effects across different sources of health insurance by applying the developed methods to the Oregon Health Insurance Experiment.
