Yongcheol Shin

Pooled Mean Group Estimation of Dynamic Heterogeneous Panels

Abstract It is now quite common to have panels in which both T, the number of time series observations, and N, the number of groups, are quite large and of the same order of magnitude. The usual practice is either to estimate N separate regressions and calculate the coefficient means, which we call the mean group (MG) estimator, or to pool the data and assume that the slope coefficients and error variances are identical. In this article we propose an intermediate procedure, the pooled mean group (PMG) estimator, which constrains long-run coefficients to be identical but allows short-run coefficients and error variances to differ across groups. We consider both the case where the regressors are stationary and the case where they follow unit root processes, and for both cases derive the asymptotic distribution of the PMG estimators as T tends to infinity. We also provide two empirical applications: Aggregate consumption functions for 24 Organization for Economic Cooperation and Development economies over th...

Structural analysis of vector error correction models with exogenous I(1) variables

This paper presents two generalisations of the existing cointegration analysis literature. Firstly, the problem of efficient estimation of vector error correction models containing I(1) exogenous variables is considered and the asymptotic distributions of the log-likelihood ratio statistics for testing cointegrating rank are derived under different intercept and trend specifications and the respective critical values are tabulated. Tests of the co-trending hypothesis are also developed together with model mis-specification tests. Secondly, the paper considers the problem of efficient estimation of vector error correction models when the lag lengths of the included stationary variables may differ within and between equations. The purchasing power parity and the uncovered interest rate parity hypotheses are re-examined using UK data under the maintained assumption of exogenously given foreign prices.

A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration

This paper proposes a residual-based test of the null of cointegration using a structural single equation model. It is shown that the limiting distribution of the test statistic for cointegration can be made free of nuisance parameters when the cointegrating relation is efficiently estimated. The limiting distributions are given in terms of a mixture of a Brownian bridge and vector Brownian motion. It is also shown that this test is consistent. Critical values are given for standard, demeaned, and detrended cases. Combining results from our test for cointegration with results from the Phillips-Ouliaris test for no cointegration, we find that there is evidence of cointegration between real consumption and real disposable income over the postwar period.

Cointegration and speed of convergence to equilibrium

This paper is concerned with the time profile of the effects of shocks on cointegrating relations in the context of a multivariate VAR(p) model. It considers alternative methods of characterizing and estimating such a time profile, and in particular proposes the application of the ‘persistence profile’ approach introduced in Lee and Pesaran (1993). It is shown that the estimator of the persistence profile of the cointegrating relations is root-T-consistent with a limiting normal distribution. The paper also shows that the persistence profile approach is invariant to the way shocks in the underlying VAR model are orthogonalized, which is not true of the traditional impulse response analysis. The theoretical framework is applied to an exchange rate and interest rate data set, and it is found that the persistence profile of the purchasing power parity (PPP) relation converges to zero very slowly, while the persistence profile of the uncovered interest parity (UIP) relation converges to zero reasonably quickly.

LONG-RUN STRUCTURAL MODELLING

The paper develops a general framework for identification, estimation, and hypothesis testing in cointegrated systems when the cointegrating coefficients are subject to (possibly) non-linear and cross-equation restrictions, obtained from economic theory or other relevant a priori information. It provides a proof of the consistency of the quasi maximum likelihood estimators (QMLE), establishes the relative rates of convergence of the QMLE of the short-run and the long-run parameters, and derives their asymptotic distributions; thus generalizing the results already available in the literature for the linear case. The paper also develops tests of the over-identifying (possibly) non-linear restrictions on the cointegrating vectors. The estimation and hypothesis testing procedures are applied to an Almost Ideal Demand System estimated on U.K. quarterly observations. Unlike many other studies of consumer demand this application does not treat relative prices and real per capita expenditures as exogenously given.

Econometrics and Economic Theory in the 20th Century: An Autoregressive Distributed-Lag Modelling Approach to Cointegration Analysis

Introduction Econometric analysis of long-run relations has been the focus of much theoretical and empirical research in economics. In cases in which the variables in the long-run relation of interest are trend-stationary, the general practice has been to de-trend the series and to model the de-trended series as stationary autoregressive distributed-lag (ARDL) models. Estimation and inference concerning the long-run properties of the model have then been carried out using standard asymptotic normal theory. For a comprehensive review of this literature, see Hendry, Pagan, and Sargan (1984) and Wickens and Breusch (1988). The analysis becomes more complicated when the variables are difference-stationary, or integrated of order 1 [ I (1) for short]. The recent literature on cointegration has been concerned with analysis of the long-run relations between I (1) variables, and its basic premise has been, at least implicitly, that in the presence of I (1) variables the traditional ARDL approach is no longer applicable. Consequently, large numbers of alternative estimation and hypothesis-testing procedures have been specifically developed for the analysis of I (1) variables. See the pioneering work of Engle and Granger (1987), Johansen (1991), Phillips (1991), Phillips and Hansen (1990), and Phillips and Loretan (1991).

A Long run structural macroeconometric model of the UK

A new modelling strategy is introduced which provides a practical approach to incorporating long-run structural relationships, suggested by economic theory, in an otherwise unrestricted VAR model. The strategy is applied in the construction of a small quarterly macroeconometric model of the UK, estimated over the period 1965-1995 in eight core variables: domestic and foreign outputs, domestic and foreign prices (both measured relative to oil prices), the nominal effective exchange rate, nominal domestic and foreign interest rates and real money balances. The aim is to develop a core model with a transparent and theoretically coherent foundation. Tests of restrictions on the long-run relations of the model are presented and the dynamic properties of the model are discussed.

TESTING FOR COINTEGRATION IN NONLINEAR SMOOTH TRANSITION ERROR CORRECTION MODELS

This paper proposes a new testing procedure to detect the presence of a cointegrating relationship that follows a globally stationary smooth transition process. In the context of nonlinear smooth transition error correction models (ECMs) we provide two simple operational versions of the tests. First, we obtain the associated nonlinear ECM-based tests. Second, we derive the nonlinear analogue of the residual-based test for cointegration in linear models. We derive the asymptotic distributions of the proposed tests. Monte Carlo simulation exercises confirm that our proposed tests have much better power than the linear counterparts against the alternative of a globally stationary nonlinear cointegrating process. In an application to the price-dividend relationship, our test is able to find cointegration, whereas the linear-based tests fail to do so.We are grateful to an associate editor, two anonymous referees, Richard Baillie, In Choi, Atanas Christev, Hira Koul, Richard Harris, Cheng Hsiao, Changjin Kim, Joon Park, Peter Schmidt, Yoonjae Whang, Jeff Wooldridge, and seminar participants at University of Edinburgh, Heriot-Watt University, Korea University, University of Leeds, Michigan State University, University of Newcastle, and Sungkunkwan University for their helpful comments. Partial financial support from the ESRC (grant R000223399) is gratefully acknowledged. The usual disclaimer applies.

Unit Root Tests in Three-Regime Setar Models

This paper proposes a simple direct testing procedure to distinguish a linear unit root process from a globally stationary three-regime self-exciting threshold autoregressive process. We derive the asymptotic null distribution of the Wald statistic, and show that it does not depend on unknown fixed threshold values. Monte Carlo evidence clearly indicates that the exponential average of the Wald statistic is more powerful than the Dickey-Fuller test that ignores the threshold nature under the alternative.

Forecast Uncertainties in Macroeconomic Modeling: An Application to the U.K. Economy

Weargue that probability forecasts convey information on the uncertainties that surround macroeconomic forecasts in a straightforward manner that is preferable to other alternatives, including the use of confidence intervals. Probability forecasts obtained using a small benchmark macroeconometric model and a number of other alternatives are presented and evaluated using recursive forecasts generated over the period 1999q1–2001q1. Out-of-sample probability forecasts of inflation and output growth are also provided over the period 2001q2–2003q1, and their implications are discussed in relation to the Bank of Englands inflation target and the need to avoid recessions, both as separate events and jointly. The robustness of the results to parameter and model uncertainties is also investigated using Bayesian model-averaging techniques.