Three-dimensional panel models are widely used in empirical analysis. Researchers use various combinations of fixed effects for three-dimensional panels while the correct specification is unknown. When one imposes a parsimonious model and the true model is rich in complexity, the fitted model inevitably incurs the consequences of misspecification including potential bias. When a richly specified model is employed and the true model is parsimonious, then the consequences typically include a poor fit with larger standard errors than necessary. It is therefore useful for researchers to have good model selection techniques that assist in determining the “true” model or a satisfactory approximation. In this light, Lu, Miao, and Su (2021, Econometric Reviews 40, 867–898) propose methods of model selection. We advance this literature by proposing a method of post-selection inference for regression parameters. Despite our use of the lasso technique as the means of model selection, our assumptions allow for many and even all fixed effects to be nonzero. This property is important to avoid a degenerate distribution of fixed effects which often reflect economic sizes of countries in gravity analyses of trade. Using an international trade database, we document evidence that our key assumption of approximately sparse fixed effects is plausibly satisfied for gravity analyses of trade. We also establish the uniform size control over alternative data generating processes of fixed effects. Simulation studies demonstrate that the proposed method is less biased than under-fitting fixed effect estimators, is more efficient than over-fitting fixed effect estimators, and robustly allows for inference that is as accurate as the oracle estimator.

Professor Davidson's Econometric Theory offers a clear, well written, graduate level econometrics textbook, which would be highly appropriate as the principal text for the second and/or third semester of a general Ph.D. econometrics sequence or for a specialized course on time series. It provides good reading material for anyone interested in deepening his or her understanding of econometrics and also a valuable reference source for econometricians. Although the book reviews the basics of multivariate regression, it is written at a level that requires either some degree of mathematical sophistication or prior familiarity with econometrics. As a result, it may be too advanced for a first semester Ph.D. course, except where students have strong preparation.

Correcting for heteroskedasticity of unspecified form.

In GARCH-mixed-data sampling models, the volatility is decomposed into the product of two factors which are often interpreted as “short-run” (high-frequency) and “long-run” (low-frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real financial data.

The convergence rates of the sums of α-mixing (or strongly mixing) triangular arrays of heterogeneous random variables are derived. We pay particular attention to the case where central limit theorems may fail to hold, due to relatively strong time-series dependence and/or the nonexistence of higher-order moments. Several previous studies have presented various versions of laws of large numbers for sequences/triangular arrays, but their convergence rates were not fully investigated. This study is the first to investigate the convergence rates of the sums of α-mixing triangular arrays whose mixing coefficients are permitted to decay arbitrarily slowly. We consider two kinds of asymptotic assumptions: one is that the time distance between adjacent observations is fixed for any sample size n; and the other, called the infill assumption, is that it shrinks to zero as n tends to infinity. Our convergence theorems indicate that an explicit trade-off exists between the rate of convergence and the degree of dependence. While the results under the infill assumption can be seen as a direct extension of those under the fixed-distance assumption, they are new and particularly useful for deriving sharper convergence rates of discretization biases in estimating continuous-time processes from discretely sampled observations. We also discuss some examples to which our results and techniques are useful and applicable: a moving-average process with long lasting past shocks, a continuous-time diffusion process with weak mean reversion, and a near-unit-root process.

The purpose of this paper is to provide a systematic treatment of the problem of estimation in systems of linear stochastic equations where some of the disturbances are uncorrelated and where the identifying equations are equivalent to a linear system.

In our paper published in vol. 22, no. 1, of Econometric Theory (2006, pp. 69–97) the proof of (22) in Lemma 3.1 is incorrect as given. The problem in the proof occurs after the first display on p. 93 where we attempted to deduce (22) from the already established relation (21). The argument given there is incorrect, because an existence-quantor was mistaken for an all-quantor. We show how the problem can be repaired. In the course of this, we also note a useful variant of another result in Lemma 3.1.

We describe a (nonparametric) prediction algorithm for spatial data, based on a canonical factorization of the spectral density function. We provide theoretical results showing that the predictor has desirable asymptotic properties. Finite sample performance is assessed in a Monte Carlo study that also compares our algorithm to a rival nonparametric method based on the infinite $AR$ representation of the dynamics of the data. Finally, we apply our methodology to predict house prices in Los Angeles.

This paper is concerned with the general problem of testing one form of covariance structure against another in a normal linear regression. It is shown that all the point-optimal tests recently proposed by King and his associates can be interpreted as special cases of a Cox test for non-nested hypotheses. This provides a synthesis of a whole range of point-optimal tests as well as demonstrating that King and his associates have exposed a class of Cox tests which have an exact distribution.

Trygve Haavelmo and the author were colleagues at the Cowles Commission for Research in Economics during the academic year 1945–46. The econometric analysis of simultaneous equation models and its uses in economic analysis were explored.

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other fixed-effect models for panel data. We use an asymptotic embedding where the noise shrinks with the sample size to calculate the leading bias in the empirical distribution arising from the presence of noise. The leading bias in the empirical quantile function is equally obtained. These calculations are new in the literature, where only results on smooth functionals such as the mean and variance have been derived. We provide both analytical and jackknife corrections that recenter the limit distribution and yield confidence intervals with correct coverage in large samples. Our approach can be connected to corrections for selection bias and shrinkage estimation and is to be contrasted with deconvolution. Simulation results confirm the much-improved sampling behavior of the corrected estimators. An empirical illustration on heterogeneity in deviations from the law of one price is equally provided.

In this article, we introduce and analyze a new methodology to estimate the volatility functions of jump diffusion models. Our methodology relies on the standard kernel estimation technique using truncated bipower increments. The relevant asymptotics are fully developed, allowing for the time span to increase as well as the sampling interval to decrease, and accommodate both stationary and nonstationary recurrent processes. We evaluate the performance of our estimators by simulation and provide some illustrative empirical analyses.

This paper considers the estimation of dynamic causal effects using a proxy structural vector-autoregressive model with possibly nonstationary regressors. We provide general conditions under which the asymptotic normal approximation remains valid. In this case, the asymptotic variance depends on the persistence property of each series. We further provide a consistent asymptotic covariance matrix estimator that requires neither knowledge of the presistence properties of the variables nor pretests for nonstationarity. The proposed consistent covariance matrix estimator is robust and is easy to implement in practice. When all regressors are indeed stationary, the method becomes the same as the standard procedure.