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We examine the evolution of economics research using a machine-learning-based classification of publications into fields and styles. The changing field distribution of publications would not seem to favor empirical papers. But economics' empirical shift is a within-field phenomenon; even fields that traditionally emphasize theory have gotten more empirical. Empirical work has also come to be more cited than theoretical work. The citation shift is sharpened when citations are weighted by journal importance. Regression analyses of citations per paper show empirical publications reaching citation parity with theoretical publications around 2000. Within fields and journals, however, empirical work is now cited more.

This paper provides a systematic analysis of identification in linear social interactions models. This is a theoretical and econometric exercise as the analysis is linked to a rigorously delineated model of interdependent decisions. We develop an incomplete information game for individual choice under social influences that nests standard models as special cases. We consider identification of both endogenous and contextual social effects under alternative assumptions regarding an analyst’s a priori knowledge of social structure or access to individual-level or aggregate data. Finally, we discuss potential ramifications for identification of endogenous formation of social structure.

In empirical economics, the size and quality of datasets and computational power has grown substantially, along with the size and complexity of the econometric models and the population parameters of interest. With more and better data, it is natural to expect to be able to answer more subtle questions about population relationships, and to pay more attention to the consequences of misspecification of the model for the empirical conclusions. Much of the recent work in econometrics has emphasized two themes: The first is the fragility of statistical identification. The other, related theme involves the way economists make large-sample approximations to the distributions of estimators and test statistics. I will discuss how these issues of identification and alternative asymptotic approximations have been studied in three research areas: analysis of linear endogenous regressor models with many and/or weak instruments; nonparametric models with endogenous regressors; and estimation of partially identified parameters. These areas offer good examples of the progress that has been made in econometrics.

Improvements in data acquisition and processing techniques have led to an almost continuous flow of information for financial data. High-resolution tick data are available and can be quite conveniently described by a continuous-time process. It is therefore natural to ask for possible extensions of financial time series models to a functional setup. In this paper we propose a functional version of the popular autoregressive conditional heteroskedasticity model. We will establish conditions for the existence of a strictly stationary solution, derive weak dependence and moment conditions, show consistency of the estimators, and perform a small empirical study demonstrating how our model matches with real data.

This article reviews the recent literature on the econometric analysis of games in which multiple solutions are possible. Multiplicity does not necessarily preclude the estimation of a particular model (and, in certain cases, even improves its identification), but ignoring it can lead to misspecifications. The review starts with a general characterization of structural models that highlights how multiplicity affects the classical paradigm. Because the information structure is an important guide to identification and estimation strategies, I discuss games of complete and incomplete information separately. Although many of the techniques discussed here can be transported across different information environments, some are specific to particular models. Models of social interactions are also surveyed. I close with a brief discussion of postestimation issues and research prospects.

Backward induction is a widely accepted principle for predicting behavior in sequential games. In the classic example of the \"centipede game,\" however, players frequently violate this principle. An alternative is a \"dynamic level- k \" model, where players choose a rule from a rule hierarchy. The rule hierarchy is iteratively defined such that the level- k rule is a best response to the level- (k-1) rule, and the level- ∞ rule corresponds to backward induction. Players choose rules based on their best guesses of others' rules and use historical plays to improve their guesses. The model captures two systematic violations of backward induction in centipede games, limited induction and repetition unraveling. Because the dynamic level- k model always converges to backward induction over repetition, the former can be considered to be a tracing procedure for the latter. We also examine the generalizability of the dynamic level- k model by applying it to explain systematic violations of backward induction in sequential bargaining games. We show that the same model is capable of capturing these violations in two separate bargaining experiments. This paper was accepted by Peter Wakker, decision analysis.

The major contributions of twentieth century econometrics to knowledge were the definition of causal parameters within well-defined economic models in which agents are constrained by resources and markets and causes are interrelated, the analysis of what is required to recover causal parameters from data (the identification problem), and clarification of the role of causal parameters in policy evaluation and in forecasting the effects of policies never previously experienced. This paper summarizes the development ofthese ideas by the Cowles Commission, the response to their work by structural econometricians and VAR econometricians, and the response to structural and VAR econometrics by calibrators, advocates of natural and social experiments, and by nonparametric econometricians and statisticians.

The nonparametric estimation of a regression function from conditional moment restrictions involving instrumental variables is considered. The rate of convergence of penalized estimators is studied in the case where the regression function is not identified from the conditional moment restriction. We also study the gain of modifying the penalty in the estimation, considering derivatives in the penalty. We analyze the effect of this modification on the identification of the regression function and the rate of convergence of its estimator.

In this paper we propose a new nonparametric test for conditional heteroskedasticity based on a measure of nonparametric goodness-of-fit (R2) that is obtained from the local polynomial regression of the residuals from a parametric regression on some covariates. We show that after being appropriately standardized, the nonparametric R2 is asymptotically normally distributed under the null hypothesis and a sequence of Pitman local alternatives. We also prove the consistency of the test and propose a bootstrap method to obtain the bootstrap p-values. We conduct a small set of simulations and compare our test with some popular parametric and nonparametric tests in the literature.

The paper develops a new heteroskedasticity and autocorrelation robust test in a time series setting. The test is based on a series long-run variance matrix estimator that involves projecting the time series of interest onto a set of orthonormal bases and using the sample variance of the projection coefficients as the long-run variance estimator. When the number of orthonormal bases K is fixed, a finite-sample-corrected Wald statistic converges to a standard F distribution. When K grows with the sample size, the usual uncorrected Wald statistic converges to a chi-square distribution. We show that critical values from the F distribution are second-order correct under the conventional increasing smoothing asymptotics. Simulations show that the F approximation is more accurate than the chi-square approximation in finite samples.