Ryo Okui

Constructing Optimal Instruments by First‐Stage Prediction Averaging

This paper considers model averaging as a way to construct optimal instruments for the two-stage least squares (2SLS), limited information maximum likelihood (LIML), and Fuller estimators in the presence of many instruments. We propose averaging across least squares predictions of the endogenous variables obtained from many different choices of instruments and then use the average predicted value of the endogenous variables in the estimation stage. The weights for averaging are chosen to minimize the asymptotic mean squared error of the model averaging version of the 2SLS, LIML, or Fuller estimator. This can be done by solving a standard quadratic programming problem. Copyright 2010 The Econometric Society.

Heteroskedasticity-Robust Cp Model Averaging

This paper proposed a model averaging method, which is called Generalized Mallows’ Cp model averaging (GC). It works well for heteroskedastic models. Under some regularity conditions, we show that our GC has asymptotic optimality as a model averaging method, and also has asymptotic optimality as a model selection method as well for heteroskedastic model. Some Monte-Carlo studies are performed to investigate the small sample properties of GC. The simulation results show that our method works well, gives better performance than other alternative methods.This paper proposes a new model-averaging method, called the Heteroskedasticity-Robust Cp (HRCp) method, for linear regression models with heteroskedastic errors. We provide a feasible form of the Mallows’ Cp-like criterion for choosing the weighting vector for averaging. Under some regularity conditions, we show that the HRCp method has asymptotic optimality. The simulation results show that our method works well and performs better than alternative methods in finite samples when the number of candidate models is large and/or the population coefficient of determination is not small.

Heteroscedasticity‐Robust C Model Averaging

This paper proposes a new model-averaging method, called the Heteroskedasticity-Robust Cp (HRCp) method, for linear regression models with heteroskedastic errors. We provide a feasible form of the Mallows’ Cp-like criterion for choosing the weighting vector for averaging. Under some regularity conditions, we show that the HRCp method has asymptotic optimality. The simulation results show that our method works well and performs better than alternative methods in finite samples when the number of candidate models is large and/or the population coefficient of determination is not small.

ASYMPTOTICALLY UNBIASED ESTIMATION OF AUTOCOVARIANCES AND AUTOCORRELATIONS WITH LONG PANEL DATA

An important reason for analyzing panel data is to observe the dynamic nature of an economic variable separately from its time-invariant unobserved heterogeneity. This paper examines how to estimate the autocovariances of a variable separately from its time-invariant unobserved heterogeneity. When both cross-sectional and time series sample sizes tend to infinity, we show that the within-group autocovariances are consistent, although they are severely biased when the time series length is short. The biases have the leading term that converges to the long-run variance of the individual dynamics. This paper develops methods to estimate the long-run variance in panel data settings and to alleviate the biases of the within-group autocovariances based on the proposed long-run variance estimators. Monte Carlo simulations reveal that the procedures developed in this paper effectively reduce the biases of the estimators for small samples.

A Specification Test for Instrumental Variables Regression with Many Instruments

This paper considers specification testing for instrumental variables estimation in the presence of many instruments. The test proposed is a modified version of the Sargan (1958, Econometrica 26(3): 393-415) test of overidentifying restrictions. The test statistic asymptotically follows the standard normal distribution under the null hypothesis of correct specification when the number of instruments increases with the sample size. We find that the new test statistic is numerically equivalent up to a sign to the test statistic proposed by Hahn and Hausman (2002, Econometrica 70(1): 163-189). We also assess the size and power properties of the test.

Asymptotically Unbiased Estimation of Autocovariances and Autocorrelations with Panel Data in the Presence of Individual and Time Effects

This article proposes asymptotically unbiased estimators of autocovariances and autocorrelations for panel data with both individual and time effects. We show that the conventional autocovariance estimators suffer from the bias caused by the elimination of individual and time effects. The bias related to individual effects is proportional to the long-run variance, and it related to time effects is proportional to the value of the estimated autocovariance. For the conventional autocorrelation estimators, the elimination of time effects does not cause a bias while the elimination of individual effects does. We develop methods to estimate the long-run variance and propose bias-corrected estimators based on the proposed long-run variance estimator. We also consider the half-panel jackknife estimation for bias correction. The theoretical results are given by employing double asymptotics under which both the number of observations and the length of the time series tend to infinity. Monte Carlo simulations show that the asymptotic theory provides a good approximation to the actual bias and that the proposed bias-correction methods work well.

Asymptotic Inference for Dynamic Panel Estimators of Infinite Order Autoregressive Processes

In this paper we consider the estimation of a dynamic panel autoregressive (AR) process of possibly infinite order in the presence of individual effects. We employ double asymptotics under which both the cross-sectional sample size and the length of time series tend to infinity and utilize the sieve AR approximation with its lag order increasing with the sample size. We establish the consistency and asymptotic normality of the fixed effects estimator and propose a bias-corrected fixed effects estimator based on a theoretical asymptotic bias term. Monte Carlo simulations demonstrate the usefulness of bias correction. As an illustration, the proposed methods are applied to dynamic panel estimation of the law of one price deviations among US cities.

Network-Motivated Lending Decisions

We demonstrate theoretically and empirically that monopolistic or collusive banks will keep lending to a loss-making firm at an interest rate lower than the prime rate if the firm is located in an influential position in an inter-firm supply network. An influential firm generates a positive externality, and its exit damages sales in the supply network. To internalize this externality, the banks may forbear on debt collection and/or bail out such influential firms when the cost to support the loss-making influential company can be recouped by imposing high interest rates on less influential companies. The analytical model shows that such forbearance can improve welfare. Our empirical study, performed using a unique dataset containing information about inter-firm transactions, provides evidence for such network-motivated lending decisions. In particular, this effect is observed more clearly at less credit-worthy firms whose main bank is a regional bank. Notably, we observe that such banks are often dominant lenders in the local loan market, and most of their clientele do not have direct access to the stock and bond markets.

Asymptotic Efficiency in Factor Models and Dynamic Panel Data Models

This paper studies the asymptotic efficiency in factor models with serially correlated errors and dynamic panel data models with interactive effects. We derive the efficiency bound for the estimation of factors, factor loadings and common parameters that describe the dynamic structure. We use double asymptotics under which both the cross-sectional sample size and the length of the time series tend to in nity. The results show that the efficiency bound for factors is not affected by the presence of unknown factor loadings and common parameters, and analogous results hold for the bounds for factor loadings and common parameters. The efficiency bound is derived by using an in nite-dimensional con- volution theorem. Perturbation to the in nite-dimensional parameters, which consists in an important step of the derivation of the efficiency bound, is nontrivial and is discussed in detail.

Heterogeneous structural breaks in panel data models

This paper develops a new model and a new estimation procedure for panel data that allow us to identify heterogeneous structural breaks. In many applications, there are good reasons to suspect that structural breaks occur at different time points across individual units and the sizes of the breaks differ too. We model individual heterogeneity using a grouped pattern such that individuals within a given group share the same regression coefficients. For each group, we allow common structural breaks in the coefficients, while the number of breaks, the break points, and the size of breaks can differ across groups. To estimate the model, we develop a hybrid procedure of the grouped fixed effects approach and adaptive group fused Lasso (least absolute shrinkage and selection operator). We show that our method can consistently identify the latent group structure, detect structural breaks, and estimate the regression parameters. Monte Carlo results demonstrate a good performance of the proposed method in finite samples. We apply our method to two cross-country empirical studies and illustrate the importance of taking heterogeneous structural breaks into account.