Econometric Theory

Marco Lippi was born in Rome in 1943. An indefatigable and inspiring pedagogue, he has been teaching mathematics, economics, the history of economic thought, and econometrics to generations of students at the Universities of Perugia, Rome (La Sapienza, Tor Vergata, and LUISS), Modena, the Scuola Superiore Sant’Anna in Pisa, and the European Center for Advanced Research in Economics and Statistics…

This article develops a new test to detect changes in generalized autoregressive conditionally heteroscedastic (GARCH(1,1)) processes without imposing a stationary assumption. Specifically, the procedure tests the null hypothesis of a GARCH process with constant parameters, either in (strictly) stationary or explosive regimes, against the alternative hypothesis of parameter changes. We derive the…

We investigate the properties of the linear two-way fixed effects (FE) estimator for panel data when the underlying data generating process (DGP) does not have a linear parametric structure. The FE estimator is consistent for some pseudo-true value and we characterize the corresponding asymptotic distribution. We show that the rate of convergence is determined by the degree of model misspecificat…

This article proposes a novel method for estimating quantile regression models that account for sample selection. Unlike the approach by Arellano and Bonhomme (2017, Econometrica 85(1), 1–28; hereafter referred to as AB17), which employs a parametric selection equation, our method utilizes a standard binary quantile regression model to handle the selection issue, thereby accommodating general het…

This article considers a three-dimensional latent factor model in the presence of one set of global factors and two sets of local factors. We show that the numbers of global and local factors can be estimated uniformly and consistently. Given the number of global and local factors, we propose a two-step estimation procedure based on principal component analysis (PCA) and establish the asymptotic …

For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing, and uncertainty quantification admit a representation as functionals of the empirical process and therefore inherit its slow convergence. As a result, inference based on the asymptotic distribution of those q…

Detecting structural changes in economic relationships has been a longstanding challenge in econometrics. Most of the literature on structural breaks has considered abrupt structural breaks. Existing tests for detecting smooth structural change typically rely on kernel estimation. In this article, we introduce a novel tuning-parameter-free test that minimizes a criterion function over all possibl…

This article studies the identification of complete economic models with testable assumptions. We start with a local average treatment effect ( ) model where the “No Defiers,” the independent IV assumption, and the exclusion restrictions can be jointly refuted by some data distributions. We propose two relaxed assumptions that are not refutable, with one assumption focusing on relaxing the “No De…

We propose a family of weighted statistics based on the CUSUM process of the WLS residuals for the online detection of changepoints in a Random Coefficient Autoregressive model, using both the standard CUSUM and the Page-CUSUM process. We derive the asymptotics under the null of no changepoint for all possible weighing schemes, including the case of the standardized CUSUM, for which we derive a D…

This study proposes two novel time-varying model-averaging methods for time-varying parameter regression models. When the number of predictors is small, we propose a novel time-varying complete subset-averaging (TVCSA) procedure, where the optimal time-varying subset size is obtained by minimizing the local leave- h -out cross-validation criterion. The TVCSA method is asymptotically optimal for a…

This article studies estimation and inference in the autoregressive (AR) models with unspecified and heavy-tailed heteroskedastic noises. A piece-wise locally stationary structure of the noise is constructed to capture various forms of heterogeneity, without imposing any restrictions on the tail index. The new nonstationary AR model allows for not only time-varying conditional features but also u…

This article considers a general class of varying coefficient models defined by a set of moment equalities and/or inequalities, where unknown functional parameters are not necessarily point-identified. We propose an inferential procedure for a subvector of the varying parameters and establish the asymptotic validity of the resulting confidence sets uniformly over a broad family of data-generating…

We study the uniform convergence rates of nonparametric estimators for a probability density function and its derivatives when the density has a known pole. Such situations arise in some structural microeconometric models, for example, in auction, labor, and consumer search, where uniform convergence rates of density functions are important for nonparametric and semiparametric estimation. Existin…

We study minimax regret treatment rules under matched treatment assignment in a setup where a policymaker, informed by a sample of size N , needs to decide between T different treatments for a . Randomized rules are allowed for. We show that the generalization of the minimax regret rule derived in Schlag (2006, ELEVEN—Tests needed for a recommendation , EUI working paper) and Stoye (2009, Journal…

This article extends the validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003, Econometrica 71(4), 1027-–1048) to instrumental variable regression models with unknown homoskedastic error variance and many weak instruments. We argue that the conventional CLR test with estimated error variance loses exact similarity and is asymptotically invalid in this setting. We pro…

We consider the problem of identifying the parameters of a time-homogeneous bivariate Markov chain when only one of the two variables is observable. We show that, subject to conditions that we spell out, the transition kernel and the distribution of the initial condition are uniquely recoverable (up to an arbitrary relabelling of the state space of the latent variable) from the joint distribution…

We consider bootstrap inference in predictive (or Granger-causality) regressions when the parameter of interest may lie on the boundary of the parameter space, here defined by means of a smooth inequality constraint. For instance, this situation occurs when the definition of the parameter space allows for the cases of either no predictability or sign-restricted predictability. We show that in thi…

This study proposes a test for coefficient randomness in autoregressive models where the autoregressive coefficient is local to unity, which is empirically relevant given earlier work. Under this specification, we analyze the effect of the correlation between the random coefficient and disturbance on the properties of tests, a matter that remains largely unexplored in the literature. Our analysis…

Relatively, recent work by Jeganathan (2008, Cowles Foundation Discussion Paper 1649) and Wang (2014, Econometric Theory , 30(3), 509–535) on generalized martingale central limit theorems (MCLTs) implicitly introduces a new class of instrument arrays that yield (mixed) Gaussian limit theory irrespective of the persistence level in the data. Motivated by these developments, we propose a new semipa…