M. Hashem Pesaran

Estimating long-run relationships from dynamic heterogeneous panels☆

In panel data four procedures are widely used: pooling, aggregating, averaging group estimates, and cross-section regression. In the static case, if the coefficients differ randomly, all four procedures give unbiased estimates of coefficient means. In the dynamic case, when the coefficients differ across groups, pooling and aggregating give inconsistent and potentially highly misleading estimates of the coefficients, though the cross-section can provide consistent estimates of the long-run effects. The theoretical results on the properties of the four procedures are illustrated by UK labour demand functions for 38 industries over 30 years.

A Simple Panel Unit Root Test in the Presence of Cross Section Dependence

A number of panel unit root tests that allow for cross section dependence have been proposed in the literature, notably by Bai and Ng (2002), Moon and Perron (2003) and Phillips and Sul (2002) who use orthogonalization type procedures to asymptotically eliminate the cross dependence of the series. In this paper we propose a simple alternative test where the standard DF (or ADF) regressions are augmented with the cross section averages of lagged levels and first-differences of the individual series. A truncated version of the CADF statistics is also considered. New asymptotic results are obtained both for the individual CADF statistics and their simple averages. It is shown that the CADFi statistics are asymptotically similar and do not depend on the factor loadings under joint asymptotics where N (cross section dimension) and T (time series dimension) ? 8, such that N/T? k, where k is a fixed finite non-zero constant. But they are asymptotically correlated due to their dependence on the common factor. Despite this of the proposed tests are investigated by Monte Carlo experiments for a variety of models. It is shown that the cross sectionally augmented panel unit root tests have satisfactory size and power even for relatively small values of N and T. This is particularly true of cross sectionally augmented and truncated versions of the simple average t-test of Im, Pesaran and Shin, and Choi’s inverse normal combination test.

IMPULSE RESPONSE ANALYSIS IN NONLINEAR MULTIVARIATE MODELS

Abstract This paper presents a unified approach to impulse response analysis which can be used for both linear and nonlinear multivariate models. After discussing the advantages and disadvantages of traditional impulse response functions for nonlinear models, we introduce the concept of a generalized impulse response function which, we argue, is applicable to both linear and nonlinear models. We develop measures of shock persistence and asymmetric effects of shocks derived from the generalized impulse response function. We illustrate the use of these measures for a nonlinear bivariate model of US output and the unemployment rate.

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...

General Diagnostic Tests for Cross Section Dependence in Panels

This paper proposes simple tests of error cross section dependence which are applicable to a variety of panel data models, including stationary and unit root dynamic heterogeneous panels with short T and large N. The proposed tests are based on average of pair-wise correlation coefficients of the OLS residuals from the individual regressions in the panel, and can be used to test for cross section dependence of any fixed order p, as well as the case where no a priori ordering of the cross section units is assumed, referred to as CD(p) and CD tests, respectively. Asymptotic distribution of these tests are derived and their power function analyzed under different alternatives. It is shown that these tests are correctly centred for fixed N and T, and are robust to single or multiple breaks in the slope coefficients and/or error variances. The small sample properties of the tests are investigated and compared to the Lagrange multiplier test of Breusch and Pagan using Monte Carlo experiments. It is shown that the tests have the correct size in very small samples and satisfactory power, and as predicted by the theory, quite robust to the presence of unit roots and structural breaks. The use of the CD test is illustrated by applying it to study the degree of dependence in per capita output innovations across countries within a given region and across countries in different regions. The results show significant evidence of cross dependence in output innovations across many countries and regions in the World.

A Simple Nonparametric Test of Predictive Performance

This paper derives a distribution free procedure for testing the accuracy of forecasts when the focus of the analysis is on the correct prediction of the direction of change in the variable under consideration. The test applies to a general m x n contingency table and it is shown that the standard null hypothesis of independence in a contingency table implies the null hypothesis of the proposed test of predictive failure but not vice versa. As a test of predictive performance the chi-squared test of independence will, in general, be more conservative than the suggested test of predictive failure. The paper also contains two applications: A dichotomous version of the test is applied to the CBIs Industrial Trends Surveys of actual and expected price changes in the manufacturing sector, and a trichotomous version of the test is applied to the demand data from business surveys of French manufacturing industry conducted by INSEE.

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.

Unit Roots and Cointegration in Panels

This paper provides a review of the literature on unit roots and cointegration in panels where the time dimension (T), and the cross section dimension (N) are relatively large. It distinguishes between the first generation tests developed on the assumption of the cross section independence, and the second generation tests that allow, in a variety of forms and degrees, the dependence that might prevail across the different units in the panel. In the analysis of cointegration the hypothesis testing and estimation problems are further complicated by the possibility of cross section cointegration which could arise if the unit roots in the different cross section units are due to common random walk components.

The limits to rational expectations

Methodological issues uncertainty and the process of expectations formation the process of learning and the rational expectations hypothesis heterogeneous information and the rational expectations hypothesis econometric considerations solution of linear rational expectations models identification of linear rational expectations models single equation models simultaneous equation models estimation and hypothesis testing in rational expectations models models with current and lagged expectations models with future expectations use of direct observations on expectations measurement of expectations and direct tests of the R.E.H. models of expectations formation under bounded rationality. Appendices: Conditional expectations and martingales - general properties solution of linear rational expectations models under heterogeneous information solution of rational expectations models with future expectations by the martingale method derivation of present value of prospective yields under the rational expectations hypothesis.

GROWTH AND CONVERGENCE IN A MULTI-COUNTRY EMPIRICAL STOCHASTIC SOLOW MODEL

The paper considers international per capita output and its growth using a panel of data for 102 countries between 1960-1989. It sets out an explicitly stochastic Solow growth model and shows that this has quite different properties from the standard approach where the output equation is obtained by adding an error term to the linearized solution of a deterministic Solow model. It examines the econometric properties of estimates of beta convergence as traditionally defined in the literature and shows that all these estimates are subject to substantial biases. Empirical estimates clearly reflect the nature and the magnitude of these biases as predicted by econometric theory. Steady state growth rates differ significantly across countries and once this heterogeneity is allowed for, the estimates of beta are substantially higher than the consensus in the literature. But they are very imprecisely estimated and difficult to interpret. The paper also discusses the economic implications of these results for sigma convergence.