This chapter explains the logic of structural econometric models and compares them to other types of econometric models. We provide a framework researchers can use to develop and evaluate structural econometric models. This framework pays particular attention to describing different sources of unobservables in structural models. We use our framework to evaluate several literatures in industrial organization economics, including the literatures dealing with market power, product differentiation, auctions, regulation and entry.

Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator (GMC). The latter interpretation provides a clear connection between EL, GMM, GEL and other related estimators. Second, EL is shown to have various advantages over other methods. The theory of large deviations demonstrates that EL emerges naturally in achieving asymptotic optimality both for estimation and testing. Interestingly, higher order asymptotic analysis also suggests that EL is generally a preferred method. Third, extensions of EL are discussed in various settings, including estimation of conditional moment restriction models, nonparametric specification testing and time series models. Finally, practical issues in applying EL to real data, such as computational algorithms for EL, are discussed. Numerical examples to illustrate the efficacy of the method are presented.

This essay reviews progress in empirical economics since Leamer’s (1983) critique. Leamer highlighted the benefits of sensitivity analysis, a procedure in which researchers show how their results change with changes in specification or functional form. Sensitivity analysis has had a salutary but not a revolutionary effect on econometric practice. As we see it, the credibility revolution in empirical work can be traced to the rise of a design-based approach that emphasizes the identification of causal effects. Design-based studies typically feature either real or natural experiments and are distinguished by their prima facie credibility and by the attention investigators devote to making the case for a causal interpretation of the findings their designs generate. Design-based studies are most often found in the microeconomic fields of Development, Education, Environment, Labor, Health, and Public Finance, but are still rare in Industrial Organization and Macroeconomics. We explain why IO and Macro would do well to embrace a design-based approach. Finally, we respond to the charge that the design-based revolution has overreached.

We review key aspects of forecasting using nonlinear models. Because economic models are typically misspecified, the resulting forecasts provide only an approximation to the best possible forecast. Although it is in principle possible to obtain superior approximations to the optimal forecast using nonlinear methods, there are some potentially serious practical challenges. Primary among these are computational difficulties, the dangers of overfit, and potential difficulties of interpretation. In this chapter we discuss these issues in detail. Then we propose and illustrate the use of a new family of methods (QuickNet) that achieves the benefits of using a forecasting model that is nonlinear in the predictors while avoiding or mitigating the other challenges to the use of nonlinear forecasting methods. 1.

Choice models with nonlinear budget sets are important in econometrics. In this paper we propose a nonparametric approach to estimation of choice models with nonlinear budget sets. The basic idea is to think of the choice, in our case hours of labor supply, as being a function of the entire budget set. Then we can account nonparametrically for a nonlinear budget set by estimating a nonparametric regression where the variable in the regression is the budget set. We reduce the dimensionality of this problem by exploiting additive structure implied by utility maximization with convex budget sets. This structure leads to a polynomial convergence rate for the estimator. We give asymptotic normality results also. The usefulness of the estimator is demonstrated in Monte Carlo and empirical work, where we find it can have a large impact on estimated e#ects of tax changes. JEL Classification: C14, C24 Keywords: Nonlinear budget sets, nonparametric estimation, additive models. # Financial support from the Bank of Sweden Tercentenary Foundation is gratefully acknowledged. We are grateful to Matias Eklof for competent research assistance. We thank participants at the Harvard-MIT econometrics workshop and the NBER for helpful comments. 1.

In this article, we provide for the first time general regularity conditions and a rigorous proof of the asymptotic normality of Cox’s statistic for testing separate families of hypotheses. The Cox test for choosing between competing linear regression models is discussed as an example. 1.

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This paper unifies three complementary approaches to defining, identifying, and estimating causal effects: the classical structural equations approach of the Cowles Commision; the treatment effects framework of Rubin (1974) and Rosenbaum and Rubin (1983); and the Directed Acyclic Graph (DAG) approach of Pearl. The settable system framework nests these prior approaches, while affording significant improvements to each. For example, the settable system approach permits identification of causal effects without requiring exogenous instruments; instead, a weaker conditional exogeneity condition suffices. It removes the stable unit treatment value assumption of the treatment effect approach and provides significant insight into the selection of covariates. It generalizes the DAG ap-proach by accommodating mutual causality and attributes. We provide a variety of results ensuring structural identification of general covariate-conditioned average causal effects, laying the founda-tion for parametric and nonparametric estimation of effects of interest and new tests for structural identification.

Abstract: This paper explores the relevance of unknown nonlinearities for growth empirics. Recent theoretical contributions and case-study evidence suggest that nonlinearities are pervasive in the growth process. I show that the postwar data provide strong evidence in favor of generalized non-linearities. I provide two alternative mechanisms for making inference about the effects of production-function shifters on growth that do not make a priori assumptions about functional form: monotonicity tests and average derivative estimation. The results of these tests point towards a greater role for structural variables and a smaller role for policy variables than the linear model.

This paper shows that estimators that have high breakdown points in cross section regression still can provide good protection against contamination in time series regression, as long as the maximum number of lags is not too large. Breakdown properties are of course not the only important aspect of an estimator. The distributional aspects of estimators are also of concern. For this reason, each paper that proposes a high breakdown point estimator also studies large sample properties of the proposed estimator. In particular, Rousseeuw and Yohai (1984) investigate the large sample properties of S-estimators of linear regression models in the i.i.d. setup. We extend their results to cover nonlinear regression for the cases of heterogeneous cross section data and time series data, cases which have not been analyzed previously. We clearly distinguish the data generating process given by the "nature" and the regression model specified by a researcher. This distinction naturally allows for possibilities of misspecification. S-estimators are extremum estimators with the special feature that their estimation objective functions are only defined as implicit functions of the data and the regression parameters. This feature makes our asymptotic analysis a little more complicated than the analysis for many familiar QML estimators. Nevertheless, it turns out that we can still apply standard results in the extremum estimation literature in our analysis. Consistency is established by showing that the S-estimation objective function is convergent to its population counterpart uniformly in the regression parameters and that the population objective function is identifiable. We find that the generalized score in S-estimation is continuously differentiable under suitable conditions, and we...