Least squares bias in autoregression and dynamic panel regression is shown to be exacerbated in case of cross section dependence. The bias is substantial and is shown to have serious effects in applications like HAC estimation and dynamic half-life response estimation. To address the bias problem, this paper develops a panel approach to median unbiased estimation that takes into account 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 modiÞed 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 Þnite sample performance of the estimation and test procedures are reported.

Rogoff (1996) describes the “remarkable consensus ” of 3-5 year half-lives of purchasing power parity deviations among studies using long-horizon data. These studies, however, focus on rejections of unit roots in real exchange rates and do not use appropriate techniques to measure persistence. Our half-life estimates explicitly account for serial correlation, sampling uncertainty and, most importantly, small sample bias. Calculating confidence intervals as well as point estimates for long-horizon and post-1973 data, we find that, even though most of the point estimates lie within the 3-5 year range, univariate methods provide virtually no information regarding the size of the half-lives.

The use of asymptotically mean-unbiased estimation is considered as a means of biascorrection, when bootstrap prediction interval is constructed for autoregressive (AR) models with unknown lag order. Its computational efficiency enables application of the endogenous lag order bootstrap algorithm to prediction intervals. Extensive Monte Carlo experiments are conducted using a number of stationary and near unit-root AR models. It is found that bias-correction based on asymptotically mean-unbiased estimation substantially improves small sample properties of bootstrap prediction intervals. In particular, the endogenous lag order bootstrap interval shows highly desirable performances. These features are evident, especially when the sample size is small, the model is near unit-root non-stationary, and the range of order estimation is wide. Keywords. Autoregression, Bias-correction, Endogenous lag order bootstrap algorithm

This paper proposes a standardized version of Swamy’s test of slope homogeneity for panel data models where the cross section dimension (N) could be large relative to the time series dimension (T). The proposed test, denoted by ˜ ∆, exploits the cross section dispersion of individual slopes weighted by their relative precision. In the case of models with strictly exogenous regressors, but with non-normally distributed errors, the test is shown to have a standard normal distribution as (N, T) j → ∞ such that √ N/T 2 → 0. When the errors are normally distributed, a mean-variance bias adjusted version of the test is shown to be normally distributed irrespective of the relative expansion rates of N and T. The test is also applied to stationary dynamic models, and shown to be valid asymptotically so long as N/T → κ, as (N, T) j → ∞, where 0 ≤ κ < ∞. Using Monte Carlo experiments, it is shown that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of N and T. Similar results are also obtained for dynamic panels, but only if the autoregressive coefficient is not too close to unity and so long as T ≥ N.

Univariate studies of the hypothesis of unit roots in real exchange rates have yielded consensus point estimates of the half-life of deviations from purchasing power parity (PPP) of between three to five years (Rogoff, 1996). However, conventional least-squares-based estimates of half-lives are biased downward. Accordingly, as a preferred measure of the persistence of real exchange rate shocks we use median-unbiased estimators of the half-life of deviations from parity, which correct for the downward bias of conventional estimators. We study this issue using real effective exchange rate (REER) data for 20 industrial countries in the post–Bretton Woods period. The serial correlation-robust median-unbiased estimator yields a cross-country average of half-lives of deviations from parity of about eight years, with the REER of several countries displaying permanent deviations from parity. However, using the median-unbiased estimator that is robust to the moving average and heteroskedastic errors present in real exchange rate data reduces the estimated half-life of parity deviations. Using this unbiased estimator, we find that the majority of countries have finite point estimates of half-lives of parity

In this paper we consider time series models belonging to the AR(autoregressive) familiy and deal with the estimation of the residual variance. This is important because estimates of the variance enter, for example, into confidence sets for the parameters of the model, in the estimation of the spectrum , in expressions for the estimated error of prediction and in sample quantities used to make inferences about the order of the model. We consider the asymptotic biases for moment and least squares estimators of the residual variance, and compare them with known results when available and with those for maximum likelihood estimators under normality. For finite samples, simulation results are presented. Key words: AR models, bias, least squares estimator, maximum likelihood estimator, moment estimator, residual variance, time series. 1. Introduction. We consider time series models belonging to the AR(p) family in which the observable stationary process fX t g has EfX t g = ¯ and finite...

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 modiÞed 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 Þnite sample performance of the estimation and test procedures are reported.

comments on earlier drafts. The usual disclaimer applies. The results reported in this paper were generated using GAUSS 3.6. The GAUSS programs used to generate the results reported in this paper are available on request from the authors. Financial Variables and the Predictability of Stock and Bond Returns: An Out-of-Sample Analysis Most studies of the predictability of stock and bond returns rely on in-sample tests. In this paper, we test the ability of ten financial variables that have appeared in the extant literature to predict S&P 500 and CRSP equal-weighted stock returns out-of-sample over horizons of 1-10 years. We also test the ability of two financial variables, the term and default spreads, to predict long-term corporate bond real returns outof-sample. For S&P 500 returns, we identify three variables with out-of-sample predictive ability: the equity share in total new debt and equity issues, term spread, and market value-to-net worth ratio (“Fed q”). For CRSP equal-weighed returns, we find that the dividend yield, price-earnings ratio, Fed q, and equity share all exhibit significant out-of-sample predictive power. In addition, the default spread exhibits significant out-of-sample predictive power for long-term corporate bond returns. As out-ofsample tests of predictive ability raise the bar relative to in-sample tests, our results strengthen the case for stock and bond return predictability.

Beyond point forecasting: evaluation of alternative prediction intervals for tourist arrivals

Abstract. Barndorff-Nielsen and Cox (1994, p.319) modify an estimative prediction limit to obtain an improved prediction limit with better coverage properties. Kabaila and Syuhada (2008) present a simulation-based approximation to this improved prediction limit, which avoids the extensive algebraic manipulations required for this modification. We present a modification of an estimative prediction interval, analogous to the Barndorff-Nielsen and Cox modification, to obtain an improved prediction interval with better coverage properties. We also present an analogue, for the prediction interval context, of this simulation-based approximation. The parameter estimator on which the estimative and improved prediction limits and intervals are based is assumed to have the same asymptotic distribution as the (conditional) maximum likelihood estimator. The improved prediction limit and interval depend on the asymptotic conditional bias of this estimator. This bias can be very sensitive to very small changes in the estimator. It may require considerable effort to find this bias. We show, however, that the improved prediction limit and interval have asymptotic efficiencies that are functionally independent of this bias. Thus, improved prediction limits and intervals obtained using the Barndorff-Nielsen and Cox type of methodology can conveniently be based on the (conditional) maximum likelihood estimator, whose asymptotic conditional bias is given by the formula of Vidoni (2004, p.144). Also, improved prediction limits and intervals obtained using Kabaila and Syuhada type approximations have asymptotic efficiencies that are independent of the estimator on which these intervals are based.