We derive a closed-form expression for the asymptotic distribution of the LIML estimator for the coefficients of both endogenous and exogenous variables in a partially identified linear structural equation. We extend previous results of Phillips (1989) and Choi and Phillips (1992), where the focus was on IV estimators. We show that partial failure of identification affects the LIML in that its moments do not exist even asymptotically.

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.

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.

This study considers the estimation of spatial autoregressive models with censored dependent variables, where the spatial autocorrelation exists within the uncensored latent dependent variables. The estimator proposed in this paper is semiparametric, in the sense that the error distribution is not parametrically specified and can be heteroskedastic. Under a median restriction, we show that the proposed estimator is consistent and asymptotically normally distributed. As an empirical illustration, we investigate the determinants of the risk of assault and other violent crimes including injury in the Tokyo metropolitan area.

Correcting for heteroskedasticity of unspecified form.

This paper presents results on the issue of weak convergence of a TVP-GQARCH-M(1,1) process. These suggest that the weak limit of this endogenous volatility model is an exogenous (stochastic) volatility continuous time process. Under the appropriate assumptions, we derive the invariant distributions at which the process converges in various cases. They reveal an approximate distributional relation between the GARCH or the asymmetric GQARCH variance processes and the continuous time Ornstein–Uhlenbeck models with respect to appropriate nonnegative Levy processes.I am grateful to Ritsa Panagiotou, Phyllis Alexander, Antonis Demos, Bruce Hansen, Nicholas Magginas, Nour Meddahi, Enrique Sentana, Paolo Zaffaroni, two anonymous referees, and the seminar participants at the Department of International and European Economic Studies for their valuable comments.

George C. Tiao is a well-known figure among statisticians and econometricians. He has made substantial contributions to the fields of Bayesian statistics, environmetrics, time series modeling, intervention analysis, and outlier detection that have had profound and lasting influence. It is fair to say that much of the current research in time series econometrics began with his work or is influenced by his ideas.

A semiparametric model is proposed in which a parametric filtering of a nonstationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Tests with standard asymptotics for I(1) and other hypotheses are thereby justified. Estimation of the trend function is also considered. We include a Monte Carlo study of finite-sample performance.

In many stated choice experiments researchers observe the random variables Vt, Xt, and Yt = 1{U + δ⊤Xt + εt < Vt}, t ≤ T, where δ is an unknown parameter and U and εt are unobservable random variables. We show that under weak assumptions the distributions of U and εt and also the unknown parameter δ can be consistently estimated using a sieved maximum likelihood estimation procedure.

This paper shows that if the errors in a multiple regression model are heavy-tailed, the ordinary least squares (OLS) estimators for the regression coefficients are tail-dependent. The tail dependence arises, because the OLS estimators are stochastic linear combinations of heavy-tailed random variables. Moreover, tail dependence also exists between the fitted sum of squares (FSS) and the residual sum of squares (RSS), because they are stochastic quadratic combinations of heavy-tailed random variables.

The 12th meeting of the New Zealand Econometrics Study Group (NZESG) was held in Wellington at the Reserve Bank of New Zealand on Friday afternoon, 17 October 2003, and at Old Government Buildings, Victoria University, on Saturday, 18 October 2003. It was well attended by approximately 50 participants (7 from overseas) with a full program of 20 speakers, including an opening address by Dr Alan Bollard, Governor, Reserve Bank of New Zealand. Full details of the program, including abstracts and photographs of the event, are available at the conference web site http://www.vuw.ac.nz/nzesg/ and at the NZESG home web site http://yoda.eco.auckland.ac.nz/nzesg/.

Despite an abundance of semiparametric estimators of the transformation model, no procedure has been proposed yet to test the hypothesis that the transformation function belongs to a finite-dimensional parametric family against a nonparametric alternative. In this article, we introduce a bootstrap test based on integrated squared distance between a nonparametric estimator and a parametric null. As a special case, our procedure can be used to test the parametric specification of the integrated baseline hazard in a semiparametric mixed proportional hazard model. We investigate the finite sample performance of our test in a Monte Carlo study. Finally, we apply the proposed test to Kennan’s strike durations data.

We estimate and test for multiple structural breaks in distribution via an empirical characteristic function approach. By minimizing the sum of squared generalized residuals, we can consistently estimate the break fractions. We propose a sup-F type test for structural breaks in distribution as well as an information criterion and a sequential testing procedure to determine the number of breaks. We further construct a class of derivative tests to gauge possible sources of structural breaks, which is asymptotically more powerful than the smoothed nonparametric tests for structural breaks. Simulation studies show that our method performs well in determining the appropriate number of breaks and estimating the unknown breaks. Furthermore, the proposed tests have reasonable size and excellent power in finite samples. In an application to exchange rate returns, our tests are able to detect structural breaks in distribution and locate the break dates. Our tests also indicate that the documented breaks appear to occur in variance and higher-order moments, but not so often in mean.

This paper considers parametric estimation problems with independent, identically nonregularly distributed data. It focuses on rate efficiency, in the sense of maximal possible convergence rates of stochastically bounded estimators, as an optimality criterion, largely unexplored in parametric estimation. Under mild conditions, the Hellinger metric, defined on the space of parametric probability measures, is shown to be an essentially universally applicable tool to determine maximal possible convergence rates. These rates are shown to be attainable in general classes of parametric estimation problems.

This paper considers estimating a panel data simultaneous equations model under both coefficient and covariance matrix restrictions in a scenario where one or the other set of identifying restrictions may be invalid or may hold only weakly. We study the limiting properties of various estimators in an asymptotic framework, which takes both the cross-sectional dimension N and the time dimension T to infinity. In this setting as in the pure cross-sectional setup, the performance of the 2SLS estimator depends on the strength of the identifying conditions imposed on the coefficients of the model, and it fails to be consistent once these conditions break down sufficiently resulting in instruments that are too weakly correlated with the endogenous regressors. On the other hand, the between-group (BG) estimator is consistent and asymptotically normal even when coefficient restrictions fail, but it has the shortcoming that its precision depends only on variations in the cross-sectional dimension; and, hence, it is less efficient and has slower rate of convergence than alternatives, which make better use of the large time dimension. A GMM estimator, which combines the moment conditions of the BG estimator with that of the within-group IV estimator, is more robust to instrument weakness than 2SLS and is more efficient than the BG estimator, but it has a second-order bias even under strong instruments if the assumed covariance restrictions do not hold. To remedy the deficiency of the aforementioned estimators, we propose in this paper two new model averaging estimators, which are weighted averages of the GMM estimator and a bias-corrected GMM estimator. The two proposed estimators have weighting functions that depend on alternative transformations of the Bayesian Information Criterion (BIC), which is employed here to assess the validity of the covariance restrictions. We show that these new estimators have some nice robustness properties against possible failure of either the coefficient restrictions or the covariance restrictions.