Serial correlation in dynamic panel data models with weakly exogenous regressor and fixed effects

Our paper wants to present and compare two estimation methodologies for dynamic panel data models in the presence of serially correlated errors and weakly exogenous regressors. The ¯rst is the ¯rst di®erence GMM estimator as proposed by Arellano and Bond (1991) and the second is the transformed Maximum Likelihood Estimator as proposed by Hsiao, Pesaran, and Tahmiscioglu (2002). Thereby, we consider the ¯xed e®ects case and weakly exogenous regressors. The ¯nite sample properties of both estimation methodologies are analysed within a simulation experiment. Furthermore, we will present an empirical example to consider the performance of both estimators with real data. JEL Classification: C23, J6

Bootstrap tests for unit root AR(1) models

In this paper, we propose bootstrap tests for unit roots in first-order autoregressive models. We provide the bootstrap functional limit theory needed to prove the asymptotic validity of these tests both for independent and autoregressive errors; in this case, the usual corrections due to innovations dependence can be avoided. We also present a power empirical study comparing these tests with existing alternative methods

Explaining Cointegration Analysis: Part II

We describe the concept of cointegration, its implications in modelling and forecasting, and discuss inference procedures appropriate in integrated-cointegrated vector autoregressive processes (VARs). Particular attention is paid to the properties of VARs, to the modelling of deterministic terms, and to the determination of the number of cointegration vectors. The analysis is illustrated by empirical examples.VAR; Deterministic Components; Rank Determination; Gasoline Prices

Inflation as a Function of Labor Force Change Rate: Cointegration Test for the USA

Previously, a linear and lagged relationship between inflation and labor force change rate, π(t)= A1dLF(t-t1)/LF(t-t1)+A2 (where A1 and A2 are empirical country-specific coefficients), was found for developed economies. The relationship obtained for the USA is characterized by A1=4.0, A2=-0.03075, and t1=2 years. It provides a root mean square forecasting error (RMFSE) of 0.8% at a two-year horizon for the period between 1965 and 2002 (the best among other inflation forecasting models) and has a perfect parsimony - only one predictor. The relationship is tested for cointegration. Both variables are integrated of order one according to the presence of a unit root in the series and its absence in their first differences. Two methods of cointegration testing are applied - the Engle-Granger one based on the unit root test of the residuals including a variety of specification tests and the Johansen cointegration rank test based on the VAR representation. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds. According to the Granger causality test, the labor force change is proved to be a weakly exogenous variable - a natural result considering the time lead and the existence of a cointegrating relation. VAR and VECM representations do not provide any significant improvement in RMSFE. There are numerous applications of the equation: from purely theoretical - a robust fundamental relation between macroeconomic and population variables, to a practical one - an accurate out-of-sample inflation forecasting at a two-year horizon and a long-term prediction based on labor force projections. The predictive power of the relationship is inversely proportional to the uncertainty of labor force estimates. Therefore, future inflation research programs should start from a significant improvement in the accuracy of labor force estimations

Telling cause from effect in deterministic linear dynamical systems

Inferring a cause from its effect using observed time series data is a major challenge in natural and social sciences. Assuming the effect is generated by the cause trough a linear system, we propose a new approach based on the hypothesis that nature chooses the "cause" and the "mechanism that generates the effect from the cause" independent of each other. We therefore postulate that the power spectrum of the time series being the cause is uncorrelated with the square of the transfer function of the linear filter generating the effect. While most causal discovery methods for time series mainly rely on the noise, our method relies on asymmetries of the power spectral density properties that can be exploited even in the context of deterministic systems. We describe mathematical assumptions in a deterministic model under which the causal direction is identifiable with this approach. We also discuss the method's performance under the additive noise model and its relationship to Granger causality. Experiments show encouraging results on synthetic as well as real-world data. Overall, this suggests that the postulate of Independence of Cause and Mechanism is a promising principle for causal inference on empirical time series.Comment: This article is under review for a peer-reviewed conferenc

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method. Dans cet article, nous proposons des procédures d'inférence valides à distance finie pour des modèles autorégressifs (AR) stationnaires et non-stationnaires. La méthode suggérée est fondée sur des propriétés particulières des processus markoviens combinées à une technique de subdivision d'échantillon. Les résultats sur les processus de Markov (indépendance intercalaire, troncature) ne requièrent que l'existence de densités conditionnelles. Nous démontrons les propriétés requises pour des processus markoviens multivariés possiblement non-stationnaires et non-gaussiens. Pour le cas des modèles de régression linéaires avec erreurs autorégressives d'ordre un, nous montrons comment utiliser ces résultats afin de simplifier les propriétés distributionnelles du modèle en considérant la distribution conditionnelle d'une partie des observations étant donné le reste. Cette transformation conduit à un nouveau modèle qui a la forme d'une autorégression bilatérale à laquelle on peut appliquer les techniques usuelles d'analyse des modèles de régression linéaires. Nous montrons comment obtenir des tests et régions de confiance pour la moyenne et les paramètres autorégressifs du modèle. Nous proposons aussi un test pour l'ordre d'une autorégression. Nous montrons qu'une technique de combinaison de tests obtenus à partir de plusieurs sous-échantillons peut améliorer la performance de la procédure. Enfin la méthode est appliquée à un modèle de l'investissement aux États-Unis.Time series, Markov process, autoregressive process, autocorrelation, dynamic model, distributed-lag model, two-sided autoregression, intercalary independence, exact test, finite-sample test, Ogawara-Hannan, investment, Séries chronologiques, processus de Markov, processus autorégressif, autocorrélation, modèle dynamique, modèle à retards échelonnés, autorégression bilatérale, indépendance intercalaire, test exact, Ogawara-Hannan, investissement