This paper considers the properties of estimators based on numerical solutions to a class of economic models. In particular, the numerical methods discussed are those applied in the solution of linear integral equations, specifically Fredholm equations of the second kind. These integral equations arise out of economic models in which endogenous variables appear linearly in the Euler equations, but for which easily characterized solutions do not exist. Tauchen and Hussey [24] have proposed the use of these methods in the solution of the consumption-based asset pricing model. In this paper, these methods are used to construct method of moments estimators where the population moments implied by a model are approximated by the population moments of numerical solutions. These estimators are shown to be consistent if the accuracy of the approximation is increased with the sample size. This result depends on the solution method having the property that the moments of the approximate solutions converge uniformly in the model parameters to the moments of the true solutions.

Solution to Normal's deconvolution and the independence of sample mean and variance problem.

This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T. We derive an error bound on the estimator that holds uniformly in the quantile level. The order of the bound implies uniform consistency of the estimator and is nearly optimal for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of interactive fixed effects at any quantile level. We demonstrate the performance of the estimator via Monte Carlo simulations.

We propose a new approach to the semiparametric analysis of panel data binary choice models with fixed effects and dynamics (lagged dependent variables). The model under consideration has the same random utility framework as in Honoré and Kyriazidou (2000, Econometrica 68, 839–874). We demonstrate that, with additional serial dependence conditions on the process of deterministic utility and tail restrictions on the error distribution, the (point) identification of the model can proceed in two steps, and requires matching only the value of an index function of explanatory variables over time, rather than the value of each explanatory variable. Our identification method motivates an easily implementable, two-step maximum score (2SMS) procedure – producing estimators whose rates of convergence, in contrast to Honoré and Kyriazidou’s (2000, Econometrica 68, 839–874) methods, are independent of the model dimension. We then analyze the asymptotic properties of the 2SMS procedure and propose bootstrap-based distributional approximations for inference. Evidence from Monte Carlo simulations indicates that our procedure performs satisfactorily in finite samples.

Diffusion over a network refers to the phenomenon of a change of state of a cross-sectional unit in one period leading to a change of state of its neighbors in the network in the next period. One may estimate or test for diffusion by estimating a cross-sectionally aggregated correlation between neighbors over time from data. However, the estimated diffusion can be misleading if the diffusion is confounded by omitted covariates. This paper focuses on the measure of diffusion proposed by He and Song (2022, Preprint, arXiv:1812.04195v4 [stat.ME]), provides a method of decomposition analysis to measure the role of the covariates on the estimated diffusion, and develops an asymptotic inference procedure for the decomposition analysis in such a situation. This paper also presents results from a Monte Carlo study on the small sample performance of the inference procedure.

This note gives a proof of the equivalence between two expressions of the moving-average impact matrix; one is given by Johansen (1995, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models) and Paruolo (1997, Econometric Theory 13, 79–118), and the other appears in Phillips (1998, Journal of Econometrics 83, 21–56) as the limit of the impulse response function. Because these expressions are shown to be parametrically equivalent, we can make the same statistical inference about the impact matrix based on either Johansen (1995) and Paruolo (1997) or Phillips (1998).

Joseph B. Kadane, usually known as Jay among his friends and colleagues, is a well-known figure among statisticians and econometricians. He has made substantial contributions to the fields of Bayesian statistics, econometrics, and many applied areas. He is well known for his work in applying statistics to how people make decisions and draw conclusions from data.

This note discusses the (dis-)similarities between automated inference and computer-aided decisions, at the interface of econometrics and economics. It is argued that computer-aided decisions are best suited for scientific communication. For the future, the topic of learning is singled out as one of the most promising areas of integration of econometric techniques and economics.I thank Peter Phillips and an anonymous referee for useful remarks on a previous version of this comment. The usual disclaimer applies.

Functional linear regression has gained popularity as a statistical tool for studying the relationship between function-valued variables. However, in practice, it is hard to expect that the explanatory variables of interest are strictly exogenous, due to, for example, the presence of omitted variables and measurement error. This issue of endogeneity remains insufficiently explored, in spite of its empirical importance. To fill this gap, this article proposes new consistent FPCA-based instrumental variable estimators and develops their asymptotic properties in detail. Simulation experiments under a wide range of settings show that the proposed estimators perform considerably well. We apply our methodology to estimate the impact of immigration on native labor market outcomes in the US.

This issue of Econometric Theory marks 20 full years of publication of the journal ET and the beginning of our third decade. To celebrate the occasion, I invited a group of econometricians, including all the present and past co-editors of ET, to reflect on the future of econometrics. To focus discussion, I selected a theme that relates to a recent trend in the practical use of econometric methodology, one that seems destined to play an increasing role in the future of the subject—automated modeling and inference. Accordingly, this issue contains contributions on various aspects of the theme of automation, introducing the notion of automated discovery, analyzing the validity of selection procedures, and discussing the practical utility of these automated methods in econometric modeling exercises.