New Panel Unit Root Tests under Cross Section Dependence for Practitioners

This paper studies the principle of common recursive mean adjustment and proposes a new detrending method in dynamic panel models. By utilizing recursive mean adjustment, this paper provides three unit root tests: a recursive mean adjusted (RMA) unit root test, a covariate RMA and a pooled RMA-feasible generalized least squares tests. The first two tests are designed for testing the cross sectional average of panel time series data to examine if the common factors in a panel are stationary or not. The third test is designed to test if the idiosyncratic errors are stationary or not. The proposed panel unit root test under cross section dependence is precise and powerful especially when T is larger than Nrecursive detrending, panel unit root tests, cross section dependence

Dynamic Panel Estimation and Homogeneity Testing Under Cross Section Dependence

This paper deals with cross section dependence, homogeneity restrictions and small sample bias issues in dynamic panel regressions. To address the bias problem we develop a panel approach to median unbiased estimation that takes account of cross section dependence. The new estimators given here considerably reduce the effects of bias and gain precision from estimating cross section error correlation. The paper also develops an asymptotic theory for tests of coefficient homogeneity under cross section dependence, and proposes a modified Hausman test to test for the presence of homogeneous unit roots. An orthogonalization procedure is developed to remove cross section dependence and permit the use of conventional and meta unit root tests with panel data. Some simulations investigating the finite sample performance of the estimation and test procedures are reported.Autoregression, Bias, Cross section dependence, Dynamic factors, Dynamic panel estimation, GLS estimation, Homogeneity tests, Median unbiased estimation, Modified Hausman tests, Median unbiased SUR estimation, Orthogonalization procedure, Panel unit root test

The Use of Predictive Regressions at Alternative Horizons in Finance and Economics

When a k period future return is regressed on a current variable such as the log dividend yield, the marginal significance level of the t-test that the return is unpredictable typically increases over some range of future return horizons, k. Local asymptotic power analysis shows that the power of the long-horizon predictive regression test dominates that of the short-horizon test over a nontrivial region of the admissible parameter space. In practice, small sample OLS bias, which differs under the null and the alternative, can distort the size and reduce the power gains of long-horizon tests. To overcome these problems, we suggest a moving block recursive Jackknife estimator of the predictive regression slope coefficient and test statistics that is appropriate under both the null and the alternative. The methods are applied to testing whether future stock returns are predictable. Consistent evidence in favor of return predictability shows up at the 5 year horizon.

Transition Modeling and Econometric Convergence Tests

A new panel data model is proposed to represent the behavior of economies in transition allowing for a wide range of possible time paths and individual heterogeneity. The model has both common and individual specific components and is formulated as a nonlinear time varying factor model. When applied to a micro panel, the decomposition provides flexibility in idiosyncratic behavior over time and across section, while retaining some commonality across the panel by means of an unknown common growth component. This commonality means that when the heterogeneous time varying idiosyncratic components converge over time to a constant, a form of panel convergence holds, analogous to the concept of conditional sigma convergence. The paper provides a framework of asymptotic representations for the factor components which enables the development of econometric procedures of estimation and testing. In particular, a simple regression based convergence test is developed, whose asymptotic properties are analyzed under both null and local alternatives, and a new method of clustering panels into club convergence groups is constructed. These econometric methods are applied to analyze convergence in cost of living indices among 19 US. metropolitan cities.Club convergence, Relative convergence, Common factor, Convergence, log t regression test, Panel data, Transition

Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence

Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N approaching infinity. The results extend earlier work by Nickell (1981) and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic trends, predetermined and exogenous regressors, and errors that may be cross sectionally dependent. The asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coe.cient. Another finding of interest is that, when there is cross section error dependence, the probability limit of the dynamic panel regression estimator is a random variable rather than a constant, which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where N is very large. Some proposals for bias correction are suggested and finite sample performance is analyzed in simulations.Autoregression, Bias, Cross section dependence, Dynamic factors, Dynamic panel estimation, Incidental trends, Panel unit root

Economic Transition and Growth

Some extensions of neoclassical growth models are discussed that allow for cross section heterogeneity among economies and evolution in rates of technological progress over time. The models offer a spectrum of transitional behavior among economies that includes convergence to a common steady state path as well as various forms of transitional divergence and convergence. Mechanisms for modeling such transitions and measuring them econometrically are developed in the paper. A new regression test of convergence is proposed, its asymptotic properties are derived and some simulations of its finite sample properties are reported. Transition curves for individual economies and subgroups of economies are estimated in a series of empirical applications of the methods to regional US data, OECD data and Penn World Table data.Economic growth, Growth convergence, Heterogeneity, Neoclassical growth, Relative transition, Transition curve, Transitional divergence

The Elusive Empirical Shadow of Growth Convergence

Two groups of applied econometricians have figured prominently in empirical studies of growth convergence. In terms of a popular caricature, one group believes it has found a black hat of convergence (evidence for growth convergence) in the dark room of economic growth, even though the hat may not exist (the task may be futile). A second group believes it has found a black coat of divergence (evidence against growth convergence) even though this object also may not exist (empirical reality, including the nature of growth divergence, is ever more complex than the models used to characterize it). The present paper seeks to light a candle to see whether there is a hat, a coat or another object of identifiable clothing in the room of regional and multi-country economic growth. After our examination, we find that the candle power of applied econometrics is too low to clearly distinguish a black hat in the huge dark room of economic growth. However, in our theory model, we find an important new role for heterogeneity over time and across economies in the transitional dynamics of economic growth; and, in our empirical work, these transitional dynamics reveal an elusive shadow of the conditional convergence hat in both US regional and inter-country OECD growth patterns.Convergence Parameter, Conditional Convergence, Economic Growth, Growth Convergence, Heterogeneity, Neoclassical Economics, Transition measures

Cointegration Vector Estimation by Panel DOLS and Long-Run Money Demand

We study the panel DOLS estimator of a homogeneous cointegration vector for a balanced panel of N individuals observed over T time periods. Allowable heterogeneity across individuals include individual-specific time trends, individual-specific fixed effects and time-specific effects. The estimator is fully parametric, computationally convenient, and more precise than the single equation estimator. For fixed N as T approaches infinity, the estimator converges to a function of Brownian motions and the Wald statistic for testing a set of linear constraints has a limiting chi-square distribution. The estimator also has a Gaussian sequential limit distribution that is obtained first by letting T go to infinity then letting N go to infinity. In a series of Monte Carlo experiments, we find that the asymptotic distribution theory provides a reasonably close approximation to the exact finite sample distribution. We use panel dynamic OLS to estimate coefficients of the long-run money demand function from a panel of 19 countries with annual observations that span from 1957 to 1996. The estimated income elasticity is 1.08 (asymptotic s.e.=0.26) and the estimated interest rate semi-elasticity is -0.02 (asymptotic s.e.=0.01).

The Use of Predictive Regressions at Alternative Horizons in Finance and Economics

When a k period future return is regressed on a current variable such as the log dividend yield, the marginal significance level of the t-test that the return is un- predictable typically increases over some range of future return horizons, k. Local asymptotic power analysis shows that the power of the long-horizon predictive regression test dominates that of the short-horizon test over a nontrivial region of the admissible parameter space. In practice, small sample OLS bias, which differs under the null and the alternative, can distort the size and reduce the power gains of long-horizon tests. To overcome these problems, we suggest a moving block recursive Jackknife estimator of the predictive regression slope coefficient and test statistics that is appropriate under both the null and the alternative. The methods are applied to testing whether future stock returns are predictable. Consistent evidence in favor of return predictability shows up at the 5 year horizon.Predictive regression, Long horizons, Stock returns, Small sample bias, Local asymptotic power

Uniform Asymptotic Normality in Stationary and Unit Root Autoregression

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution which holds uniformly in the autoregressive coefficient rho including stationary and unit root cases. The rate of convergence is root of n when |rho|Aggregating information, Asymptotic normality, Bias Reduction, Differencing, Efficiency, Full aggregation, Maximum likelihood estimation