Kaddour Hadri

Testing for stationarity in heterogeneous panel data

This paper proposes a residual-based Lagrange multiplier (LM) test for a null that the individual observed series are stationary around a deterministic level or around a deterministic trend against the alternative of a unit root in panel data. The tests which are asymptotically similar under the null, belong to the locally best invariant (LBI) test statistics. The asymptotic distributions of the statistics are derived under the null and are shown to be normally distributed. Finite sample sizes and powers are considered in a Monte Carlo experiment. The empirical sizes of the tests are close to the true size even in small samples. The testing procedure is easy to apply, including, to panel data models with fixed effects, individual deterministic trends and heterogeneous errors across cross-sections. It is also shown how to apply the tests to the more general case of serially correlated disturbance terms.

The Influence of VAR Dimensions on Estimator Biases

Vector AutoRegressions (VARs) have now become the most popular tool of Time Series analysis amongst econometricians. Unfortunately, little is known about the analytic finite-sample properties of parameter estimators for such systems. The asymptotic analysis of VARs published to date does not address questions regarding the influence of the number and nature of the systems variates on parameter estimates. Clearly, both questions will have repercussions on the way VARs are used, and we intend to address them here.We consider the implications of varying the dimensions of VARs on the biases of Maximum Likelihood and Least Squares Estimators (MLE and LSE, respectively). In the purely nonstationary case (k-dimensional random walk), estimator biases are approximately equal to the dimension of the system (k) times the univariate bias, even when the variates are generated independently of each other. We show that the variance too increases with the dimension of the system, hence also raising the Mean Squared Error (MSE) of the estimator. When some stable linear combinations exist, the biases are generally smaller and are asymptotically proportional to the sum of the characteristic roots of the VAR. One source of such combinations is meaningful economic relations that are represented by the cointegration of some of the components of the VAR. Adding economically-irrelevant variables to a VAR is thus shown to have more serious negative consequences in integrated time series than in classical ergodic or cross section analyses. The findings strengthen the case for parsimonious modelling and for the reduction step of the general-to-specific marginalization method. They also support the use of seasonally unadjusted data whenever possible.

Estimating Option Implied Risk-Neutral Densities Using Spline and Hypergeometric Functions

We examine the ability of two recent methods -- the smoothed implied volatility smile method (SML) and the density functionals based on confluent hypergeometric functions (DFCH) -- for estimating implied risk-neutral densities (RNDs) from European-style options. Two complementary Monte Carlo experiments are conducted and the performance of the two RND estimators is evaluated by the root mean integrated squared error (RMISE) criterion. Results from both experiments show that the DFCH method outperforms the SML method for the overall quality of the estimated RNDs concerning both accuracy and stability. An application of the two methods to the OTC currency options market is also presented. Copyright Royal Economic Society 2007

Panel unit root tests in the presence of cross-sectional dependence: finite sample performance and an application

This paper examines the finite sample properties of three testing regimes for the null hypothesis of a panel unit root against stationary alternatives in the presence of cross-sectional correlation. The regimes of Bai and Ng (2004), Moon and Perron (2004) and Pesaran (2007) are assessed in the presence of multiple factors and also other non-standard situations. The behaviour of some information criteria used to determine the number of factors in a panel is examined and new information criteria with improved properties in small-N panels proposed. An application to the efficient markets hypothesis is also provided. The null hypothesis of a panel random walk is not rejected by any of the tests, supporting the efficient markets hypothesis in the financial services sector of the Australian Stock Exchange. Copyright

Maximum likelihood estimation of higher-order integer-valued autoregressive processes

In this paper, we extend earlier work of Freeland and McCabe (2004) and develop a general framework for maximum likelihood (ML) estimation of higher-order integer-valued autoregressive (INAR(p)) processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is Binomial. A recursive representation of the transition probability for the INAR(p) model is proposed. Based on this representation, we derive expressions for the score function and the Fisher information matrix of the INAR(p) model, which form the basis for maximum likelihood estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. These new expressions enhance the interpretation of these quantities and lead naturally to new de?nitions for residuals for the INAR(p) model. Using the INAR(2) speci?cation with Poisson innovations, we examine the asymptotic effciency gain of implementing the ML technique over the widely used conditional least squares (CLS) method. We conclude that, if the Poisson assumption can be justified, there are substantial gains to be had from using ML especially when the thinning parameters are large.

Political Business Cycles and Central Bank Independence

This paper develops a dynamic model of Rational Partisan Business Cycles in which wage contracts overlap elections and wage setters have to make a prediction about the election result. Empirical analysis of 20 OECD countries supports the theoretical implication that left wing incumbents increase output, but increased expectation of a left wing regime reduces it. The model is extended to incorporate the effects of alternative measures of Central Bank Independence (CBI). The measure of objective independence outperforms the other measures and it is found that CBI reduces politically induced business cycles. Copyright Royal Economic Society 2003

Is More Information a Good Thing? Bias Nonmonotonicity in Stochastic Difference Equations

It is shown that the bias of estimated parameters in autoregressive models can increase as the sample size grows. This bias is also a nonmonotonic function of the largest autoregressive root, contrary to what asymptotic approximations had indicated so far in the literature. These unusual results are due to the effect of the initial sample observations that are typically neglected in theoretical asymptotic analysis, in spite of their empirical relevance. Implications for practical economic modelling are considered, including a comparison of the likely inaccuracies of parameter estimates in alternative models based on competing macroeconomic theories.

The Accuracy of the Higher Order Bias Approximation for the 2SLS Estimator

Mikhail (1972a) found that estimated 2SLS biases, obtained through simulation using antithetic variables and control variate methods, were closer to each other than to Nagars bias approximation to order T-1. As remarked by Kiviet and Phillips (1996), this result represents one of a very small number of higher order approximations in the econometric literature yet there is no published evidence of its accuracy. In this paper the accuracy of the approximation is explored in the context of a framework similar to that chosen by Mikhail (1972a) and it is found that the higher order approximation is clearly superior. In cases where the bias is severe, the results support the belief that, when the first order approximation is poor but not terrible, the higher order approximation mops up most of the error.

Does Central Bank Independence Smooth the Political Business Cycle in Inflation? Some OECD Evidence

In this paper, electoral and partisan effects in inflation are identified for eighteen OECD countries via regression analysis, building on the work of A. Alesina, G. Cohen, and N. Roubini. The correlation of the size of these effects across countries with the level of central bank independence is investigated; the results suggest a negative correlation. Copyright 1998 by Blackwell Publishers Ltd and The Victoria University of Manchester

Testing For Stationarity With a Break in Panels Where the Time Dimension is Finite

In this paper, we consider the case of finite time dimension in the panel stationarity tests with structural breaks. By fixing T; the finite sample properties of the tests for both micro (T small and N large) and macro (both T and N large) panel data are generally greatly improved. More importantly, the derivation of the tests for finite T and N -> infinity, as opposed to joint asymptotic where N and T -> infinity simultaneously, avoids the imposition of the rate condition N/T -> 0; making the test valid for any (T;N) blend. Four models corresponding to the usual combination of breaks are considered. The asymptotic distributions of the test are derived under the null and are shown to be normally distributed. Their moments for T fixed are derived analytically employing two approaches. The first method is based on the Laplace Transform and the second derivation is based on Ghazal’s (1994) corollary. The case with unknown breaks is also considered. The proposed tests have generally empirical sizes that are very close to the nominal size. The Monte-Carlo simulations show that the power of the test statistics increases substantially with N and T.