Chihwa Kao

Spurious regression and residual-based tests for cointegration in panel data

In the first half of the paper we study spurious regressions in panel data when the cross-section and time-series dimensions are comparable. Asymptotic properties of the least-squares dummy variable (LSDV) estimator and other conventional statistics are examined. We show that the LSDV estimatoris consistent for its true value, but the t-statistic diverges so that inferences about the regression coefficient, are wrong with the probability that goes to one. The asymptotics of LSDV are also different from those of the spurious regression in the pure time series. This has an important consequence for residual-based cointegration tests in panel data, because the null distribution of residual-based cointegration tests depends on the asymptotics of LSDV. In the second half of the paper we study residual-based tests for cointegration regression in panel data. We study Dickey-Fuller (DF) tests and an augmented Dickey-Fuller (ADF) test to test the null of no cointegration. Asymptotic distributions of the tests a re derived and Monte Carlo experiments are conducted to evaluate finite sample properties of the proposed tests.

On the Estimation and Inference of a Cointegrated Regression in Panel Data

In this paper, we study the asymptotic distributions for least-squares (OLS), fully modified (FM), and dynamic OLS (DOLS) estimators in cointegrated regression models in panel data. We show that the OLS, FM, and DOLS estimators are all asymptotically normally distributed. However, the asymptotic distribution of the OLS estimator is shown to have a non-zero mean. Monte Carlo results examine the sampling behavior of the proposed estimators and show that (1) the OLS estimator has a non-negligible bias in finite samples, (2) the FM estimator does not improve over the OLS estimator in general, and (3) the DOLS out-performs both the OLS and FM estimators.

Nonstationary Panels, Cointegration in Panels and Dynamic Panels: A Survey

This paper provides an overview of topics in nonstationary panels: panel unit root tests, panel cointegration tests, and estimation of panel cointegration models. In addition it surveys recent developments in dynamic panel data models.

A residual-based test of the null of cointegration in panel data

This paper proposes a residual-based Lagrange Multiplier (LM) test for the null of cointegration in panel data. The test is analogous to the locally best unbiased invariant (LBUI) for a moving average (MA) unit root. The asymptotic distribution of the test is derived under the null. Monte Carlo simulations are performed to study the size and power properties of the proposed test. Overall, the empirical sizes of the LM- FM and LM-DOLS are close to the true size even in small samples. The power is quite good for the panels where T >50, and decent with panels for fewer observations in T. In our fixed sample of N=50 and T=50, the presence of a moving average and correlation between the regressor errors and regressors causes the two tests to perform quite differently, complicating the choice of estimation procedures. In general, the LM- DOLS test seems to be better at correcting these effects, although in some cases the LM-FM test is more powerful. Although much of the non- stationary time series econometrics has been criticized for having more to do with the specific properties of the data set rather than underlying economic models, the recent development of the cointegration literature has allowed for a concrete bridge between economic long run theory and time series methods. Our test now allows for the testing of the null of cointegration in a panel setting and should be of considerable interest to economists in a wide variety of fields.

International R&D Spillovers: An Application of Estimation and Inference in Panel Cointegration

In this paper, we apply the asymptotic theory of panel cointegration developed by Kao and Chiang (1997) to Coe and Helpmans (1995) international R&D spillovers regression. The OLS with bias-correction, the fully-modified (FM) and the dynamic OLS (DOLS) estimations produce different predictions about the impact of foreign R&D on total factor productivity (TFP) although all the estimations support the result that domestic R&D is related to TFP.

Estimation and inference of a cointegrated regression in panel data: a Monte Carlo study

SYNOPTIC ABSTRACTThis paper studies the finite sample properties of the least squares dummy variable (LSDV) estimator and t-statistic in a cointegrated regression in panel data. Through Monte Carlo studies we find that both the LSDV estimator and the t-statistic have a small amount of bias, and the t-statistic diverges as the cross-sectional dimension increases. We also find that the bias-corrected LSDV estimator and the bias-corrected t-statistic do not reduce the magnitude of the bias problem.

A Monte Carlo Comparison of Tests for Cointegration in Panel Data

This paper surveys recent developments and provides Monte Carlo comparison on various tests proposed forcointegration in panel data. In particular, tests for two panel models, varying intercepts and varying slopes, and varying intercepts and common slopes are presented from the literature with a total of seven tests being simulated. In all cases, results on empirical size and size-adjusted power are given.

Asymptotics for Panel Models with Common Shocks

This article develops a novel asymptotic theory for panel models with common shocks. We assume that contemporaneous correlation can be generated by both the presence of common regressors among units and weak spatial dependence among the error terms. Several characteristics of the panel are considered: cross-sectional and time-series dimensions can either be fixed or large; factors can either be observable or unobservable; the factor model can describe either a cointegration relationship or a spurious regression, and we also consider the stationary case. We derive the rate of convergence and the limit distributions for the ordinary least square (OLS) estimates of the model parameters under all the aforementioned cases.

Estimation and identification of change points in panel models with nonstationary or stationary regressors and error term

ABSTRACT This article studies the estimation of change point in panel models. We extend Bai (2010) and Feng et al. (2009) to the case of stationary or nonstationary regressors and error term, and whether the change point is present or not. We prove consistency and derive the asymptotic distributions of the Ordinary Least Squares (OLS) and First Difference (FD) estimators. We find that the FD estimator is robust for all cases considered.

Asymptotic Properties of Estimators for the Linear Panel Regression Model with Random Individual Effects and Serially Correlated Errors: The Case of Stationary and Non-Stationary Regressors and Residuals

This paper studies the asymptotic properties of standard panel data estimators in a simple panel regression model with error component disturbances. Both the regressor and the remainder disturbance term are assumed to be autoregressive and possibly non-stationary. Asymptotic distributions are derived for the standard panel data estimators including ordinary least squares, fixed effects, first-difference, and generalized least squares (GLS) estimators when both T and n are large. We show that all the estimators have asymptotic normal distributions and have different convergence rates dependent on the non-stationarity of the regressors and the remainder disturbances. We show using Monte Carlo experiments that the loss in efficiency of the OLS, FE and FD estimators relative to true GLS can be substantial.