Abstract This paper demonstrates the extensive scope of an alternative to standard instrumental variables methods, namely covariate-based methods, for identifying and estimating e¤ects of interest in general structural systems. As we show, commonly used econometric methods, speci…cally parametric, semi-parametric, and nonparametric extremum or moment-based methods, can all exploit covariates to estimate well-identi…ed structural e¤ects. The systems we consider are general, in that they need not impose linearity, separability, or monotonicity restrictions on the structural relations. We consider e¤ects of multiple causes; these may be binary, categorical, or continuous. For continuous causes, we examine both marginal and non-marginal e¤ects. We analyze e¤ects on aspects of the response distribution generally, de…ned by explicit or implicit moments or as optimizers (e.g., quantiles). Key for identi…cation is a speci…c conditional exogeneity relation. We examine what happens in its absence and …nd that identi…cation generally fails. Nevertheless, local and near identi…cation results hold in its absence, as we show.

This paper studies nonclassical measurement error in the continuous dependent variable of a semiparametric transformation model. The latter is a popular choice in practice nesting various nonlinear duration and censored regression models. The main complication arises because the (additive) measurement error is allowed to be correlated with a (continuous) component of the regressors as well as with the true, unobserved dependent variable itself. This problem has not yet been studied in the literature, but it is argued that it is relevant for various empirical setups with mismeasured, continuous survey data like earnings or durations. A framework to identify and consistently estimate (up to scale) the parameter vector of the transformation model is developed. The estimator links a two-step control function approach of Imbens and Newey (2009) with a rank estimator similar to Khan (2001) and is shown to have desirable asymptotic properties. Moreover, it is proven that ‘m out of n ’ bootstrap can be used to obtain a consistent approximation of the asymptotic variance. The estimator’s finite sample performance is studied in a Monte Carlo Simulation. To illustrate the empirical usefulness of the procedure, an earnings equation model is estimated using annual data from the Health and Retirement Study (HRS). Some evidence for a bias in the coefficients of years of education and age is found, emphasizing once again the importance to adjust for potential measurement error bias in empirical work. JEL Classification: C14, C34,

The "potential outcome," or Neyman-Rubin (NR) model through which statisticians were first introduced to causal analysis suffers from two fundamental shortcomings: (1) It lacks formal underpinning and (2) it uses conceptually opaque language for expressing causal information. As a results, investigators find it difficult to discern whether a set of formulae represents a faithful picture of one's knowledge, and whether such a set is self-consistent or redundant. These shortcomings can be rectified using counterfactual semantics based on nonparametric structural equations [Pearl, 2000a] which provides both a mathematical foundation for the NR analysis and a conceptually transparent language for expressing causal knowledge. This semantical framework gives rise to a friendly calculus of causation that unifies the graphical, potential outcome and structural equation approaches and resolves longstanding problems in several of the sciences. These include questions of confounding, causal effect estimation, policy analysis, legal responsibility, direct and indirect effects, instrumental variables, surrogate designs, and the integration of data from experimental and observational studies.

Abstract: 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 potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.

This paper introduces empirical researchers to 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, and the conditional nature of causal claims inferred from nonexperimental studies. In particular, the paper advocates a formalism based on nonparametric structural equations [Pearl, 2000a] which provides both a mathematical foundation for the analysis of counterfactuals and a conceptually transparent language for expressing causal knowledge. This framework gives rise to a friendly calculus of causation that uni es the graphical, potential outcome (Neyman-Rubin) and structural equation approaches and resolves long-standing problems in several of the sciences. These include questions of confounding, causal e ect estimation, policy analysis, legal responsibility, direct and indirect e ects, instrumental variables, surrogate designs, and the integration of data from experimental and observational studies.

The intrinsic schism between causal and associational relations presents profound ethical and methodological problems to researchers in the social and behavioral sciences, ranging from the statement of a problem, to the implementation of a study, to the reporting of finding. This paper describes a causal modeling framework that mitigates these problems and offers a simple, yet formal and principled methodology for empirical research. The framework is based on the Structural Causal Model (SCM) described in [Pearl, 2000b] – a nonparametric extension of structural equation models that provides a mathematical foundation and a friendly calculus for the analysis of causes and counterfactuals. In particular, the paper establishes a methodology 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” or “effect decomposition”). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and demonstrates a symbiotic analysis that uses the strong features of both.

We study the interrelations between (conditional) independence and causal relations in settable systems. We provide de…nitions in terms of functional dependence for direct, indirect, and total causality as well as for (indirect) causality via and exclusive of a set of variables. We then provide necessary and su ¢ cient causal and stochastic conditions for (conditional) dependence among random vectors of interest in settable systems. Immediate corollaries ensure the validity of Reichenbach’s principle of common cause and its informative extension, the conditional Reichenbach principle of common cause. We relate our results to notions of d separation and D separation in the arti…cial intelligence literature.

We study the scope of local indirect least squares (LILS) methods for nonparametrically estimating average marginal e¤ects of an endogenous cause X on a response Y in triangular structural systems that need not exhibit linearity, separability, or monotonicity in scalar unobservables. One main …nding is negative: in the fully nonseparable case, LILS methods cannot recover the average marginal e¤ect. LILS methods can nevertheless test the hypothesis of no e¤ect in the general nonseparable case. We provide new nonparametric asymptotic theory, treating both the traditional case of observed exogenous instruments Z and the case where one observes only error-laden proxies for Z.

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 non-parametric structural equation models (SEM)– a natural generalization of those used by econometricians and social scientists in the 1950-60s, 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 non-linear systems. Finally, the paper clarifies the role of propensity score matching in causal analysis, defines the relationships between the structural and potential-outcome frameworks, and develops symbiotic tools that use the strong features of both.

This paper demonstrates the extensive scope of an alternative to standard instrumental variables methods, namely covariate-based methods, for identifying and estimating effects of interest in general structural systems. As we show, commonly used econometric methods, specifically parametric, semi-parametric, and nonparametric extremum or moment-based methods, can all exploit covariates to estimate well-identified structural effects. The systems we consider are general, in that they need not impose linearity, separability, or monotonicity restrictions on the structural relations. We consider e¤ects of multiple causes; these may be binary, categorical, or continuous. For continuous causes, we examine both marginal and non-marginal effects. We analyze effects on aspects of the response distribution generally, defined by explicit or implicit moments or as optimizers (e.g., quantiles). Key for identification is a specific conditional exogeneity relation. We examine what happens in its absence and find that identification generally fails. Nevertheless, local and near identification results hold in its absence, as we show.