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40
Instrumental variable treatment of nonclassical measurement error models.
 Econometrica,
, 2008
"... Abstract While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors ..."
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Cited by 64 (18 self)
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Abstract While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errorsinvariables models with continuously distributed variables. Our main identifying assumption is that, conditional on the value of the true regressors, some "measure of location" of the distribution of the measurement error (e.g. its mean, mode or median) is equal to zero. The proposed approach relies on the eigenvalueeigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to "index" the eigenfunctions so that the decomposition is unique. We propose a convenient sievebased estimator, derive its asymptotic properties and investigate its finitesample behavior through Monte Carlo simulations.
Causal inference in statistics: An Overview
, 2009
"... This review presents empirical researcherswith recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all ca ..."
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Cited by 61 (12 self)
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This review presents empirical researcherswith recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects ” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret, ” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper defines the formal and conceptual relationships between the structural and potentialoutcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.
The Mediation Formula: A guide to the assessment of causal pathways in nonlinear models
 STATISTICAL CAUSALITY. FORTHCOMING.
, 2011
"... ..."
Trygve Haavelmo and the Emergence of Causal Calculus
, 2012
"... Haavelmo was the first to recognize the capacity of economic models to guide policies. This paper describes some of the barriers that Haavelmo’s ideas have had (and still have) to overcome, and lays out a logical framework for capturing the relationships between theory, data and policy questions. Th ..."
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Cited by 15 (5 self)
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Haavelmo was the first to recognize the capacity of economic models to guide policies. This paper describes some of the barriers that Haavelmo’s ideas have had (and still have) to overcome, and lays out a logical framework for capturing the relationships between theory, data and policy questions. The mathematical tools that emerge from this framework now enable investigators to answer complex policy and counterfactual questions using embarrassingly simple routines, some by mere inspection of the model’s structure. Several such problems are illustrated by examples, including misspecification tests, identification, mediation and introspection. Finally, we observe that modern economists are largely unaware of the benefits that Haavelmo’s ideas bestow upon them and, as a result, econometric research has not fully utilized modern advances in causal analysis. 1
Settable Systems: An Extension of Pearl’s Causal Model with Optimization, Equilibrium, and Learning
, 2008
"... Judea Pearl’s Causal Model is a rich framework that provides deep insight into the nature of causal relations. As yet, however, the Pearl Causal Model (PCM) has not had much impact on economics or econometrics. This may be due in part to the fact that the PCM is not as well suited to analyzing econo ..."
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Cited by 14 (6 self)
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Judea Pearl’s Causal Model is a rich framework that provides deep insight into the nature of causal relations. As yet, however, the Pearl Causal Model (PCM) has not had much impact on economics or econometrics. This may be due in part to the fact that the PCM is not as well suited to analyzing economic structures as might be desired. We o¤er the settable systems framework as an extension of the PCM that embodies features of central interest to economists and econometricians: optimization, equilibrium, and learning. Because these are common features of physical, natural, or social systems, our framework may prove generally useful. In particular, settable systems o¤er a number of advantages relative to the PCM for machine learning. Important distinguishing features of the settable systems framework are its countable dimensionality, its treatment of attributes, the absence of a …xedpoint requirement, and the use of partitioning and partitionspeci…c response functions to accommodate the behavior of optimizing and interacting agents. A series of closely related machine learning examples and examples from game theory and machine learning with feedback demonstrates limitations of the PCM and motivates the distinguishing features of settable systems.
The Foundations of Causal Inference
 SUBMITTED TO SOCIOLOGICAL METHODOLOGY.
, 2010
"... This paper reviews recent advances in the foundations of causal inference and introduces a systematic methodology for defining, estimating and testing causal claims in experimental and observational studies. It is based on nonparametric structural equation models (SEM) – a natural generalization of ..."
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Cited by 11 (4 self)
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This paper reviews recent advances in the foundations of causal inference and introduces a systematic methodology for defining, estimating and testing causal claims in experimental and observational studies. It is based on nonparametric structural equation models (SEM) – a natural generalization of those used by econometricians and social scientists in the 195060s, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring the effects of potential interventions (also called “causal effects” or “policy evaluation”), as well as direct and indirect effects (also known as “mediation”), in both linear and nonlinear systems. Finally, the paper clarifies the role of propensity score matching in causal analysis, defines the relationships between the structural and
Granger Causality and Dynamic Structural Systems
, 2008
"... We analyze the relations between Granger (G) noncausality and a notion of structural causality arising naturally from a general nonseparable recursive dynamic structural system. Building on classical notions of G noncausality, we introduce interesting and natural extensions, namely weak G noncaus ..."
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Cited by 10 (2 self)
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We analyze the relations between Granger (G) noncausality and a notion of structural causality arising naturally from a general nonseparable recursive dynamic structural system. Building on classical notions of G noncausality, we introduce interesting and natural extensions, namely weak G noncausality and retrospective weak G noncausality. We show that structural noncausality and certain (retrospective) conditional exogeneity conditions imply (retrospective) (weak) G noncausality. We strengthen structural causality to notions of (retrospective) strong causality and show that (retrospective) strong causality implies (retrospective) weak G causality. We provide practical conditions and straightforward new methods for testing (retrospective) weak G noncausality, (retrospective) conditional exogeneity, and structural noncausality. Finally, we apply our methods to explore structural causality in industrial pricing, macroeconomics, and …nance.
Robustness checks and robustness tests in applied economics. working paper
, 2010
"... A common exercise in empirical studies is a "robustness check, " where the researcher examines how certain "core " regression coe ¢ cient estimates behave when the regression speci cation is modi
ed by adding or removing regressors. If the coe ¢ cients are plausible and robust, t ..."
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Cited by 9 (0 self)
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A common exercise in empirical studies is a "robustness check, " where the researcher examines how certain "core " regression coe ¢ cient estimates behave when the regression speci cation is modi
ed by adding or removing regressors. If the coe ¢ cients are plausible and robust, this is commonly interpreted as evidence of structural validity. Here, we study when and how one can infer structural validity from coe ¢ cient robustness and plausibility. As we show, there are numerous pitfalls, as commonly implemented robustness checks give neither necessary nor su ¢ cient evidence for structural validity. Indeed, if not conducted properly, robustness checks can be completely uninformative or entirely misleading. We discuss how critical and noncritical core variables can be properly speci
ed and how noncore variables for the comparison regression can be chosen to ensure that robustness checks are indeed structurally informative. We provide a straightforward new Hausman (1978)type test of robustness for the critical core coe ¢ cients, additional diagnostics that can help explain why robustness test rejection occurs, and a new estimator, the Feasible Optimally combined GLS (FOGLeSs) estimator, that makes relatively e ¢ cient use of the robustness check regressions. A new procedure for Matlab, testrob, embodies these methods. 1
Instrumental Variables Methods for Recovering Continuous Linear Functionals
 Journal of Econometrics
, 2011
"... This paper develops methods for estimating continuous linear functionals in a nonparametric instrumental variables (IV) setting. Examples of such functionals include consumer surplus and applications to tests for shape restrictions like monotonicity, concavity and additive separability. The estimati ..."
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Cited by 7 (2 self)
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This paper develops methods for estimating continuous linear functionals in a nonparametric instrumental variables (IV) setting. Examples of such functionals include consumer surplus and applications to tests for shape restrictions like monotonicity, concavity and additive separability. The estimation procedure is robust to a setting where the underlying model is not identified but the linear functional of interest is. In order to attain such robustness, it is necessary to use a nuisance parameter that is not identified. A procedure is proposed that circumvents this challenge and delivers a √ n asymptotically normal estimator for the linear functional of interest. A Monte Carlo study examines the finite sample performance of the procedure.