Jean-Yves Pitarakis

Threshold Effects in Cointegrating Relationships

In this paper, we introduce threshold-type nonlinearities within a single-equation cointegrating regression model and propose a testing procedure for testing the null hypothesis of linear cointegration vs. cointegration with threshold effects. Our framework allows the modelling of long-run equilibrium relationships that may change according to the magnitude of a threshold variable assumed to be stationary and ergodic, and thus constitutes an attempt to deal econometrically with the potential presence of multiple equilibria. The framework is flexible enough to accommodate regressor endogeneity and serial correlation.

Specification via model selection in vector error correction models

This paper proposes a model selection approach for the specification of the cointegrating rank in the VECM representation of VAR models. Asymptotic properties of estimates are derived and their features compared with the traditional likelihood ratio based approach.

Lag Length Estimation in Large Dimensional Systems

We study the impact of the system dimension on commonly used model selection criteria (AIC,BIC, HQ) and LR based general to specific testing strategies for lag length estimation in VARs. We show that AICs well known overparameterization feature becomes quickly irrelevant as we move away from univariate models, with the criterion leading to consistent estimates under sufficiently large system dimensions. Unless the sample size is unrealistically small, all model selection criteria will tend to point towards low orders as the system dimension increases, with the AIC remaining by far the best performing criterion. This latter point is also illustrated via the use of an analytical power function for model selection criteria. The comparison between the model selection and general to specific testing strategy is discussed within the context of a new penalty term leading to the same choice of lag length under both approaches.

Regime-Specific Predictability in Predictive Regressions

Predictive regressions are linear specifications linking a noisy variable such as stock returns to past values of a very persistent regressor with the aim of assessing the presence of predictability. Key complications that arise are the potential presence of endogeneity and the poor adequacy of asymptotic approximations. In this article, we develop tests for uncovering the presence of predictability in such models when the strength or direction of predictability may alternate across different economically meaningful episodes. An empirical application reconsiders the dividend yield-based return predictability and documents a strong predictability that is countercyclical, occurring solely during bad economic times. This article has online supplementary materials.

Comment on: Threshold autoregressions with a unit root

In this paper we revisit the results in Caner and Hansen (2001), where the authors obtained novel limiting distributions of Wald type test statistics for testing for the presence of threshold nonlinearities in autoregressive models containing unit roots. Using the same framework, we obtain a new formulation of the limiting distribution of the Wald statistic for testing for threshold effects, correcting an expression that appeared in the main theorem presented by Caner and Hansen. Subsequently, we show that under a particular scenario that excludes stationary regressors such as lagged dependent variables and despite the presence of a unit root, this same limiting random variable takes a familiar form that is free of nuisance parameters and already tabulated in the literature, thus removing the need to use bootstrap based inferences. This is a novel and unusual occurrence in this literature on testing for the presence of nonlinear dynamics.

Total expenditure endogeneity in a system of demand for public consumption expenditures in the UK

Contrary to standard empirical studies of demand for public consumption expenditure a system of demand equations is examined where the total expenditure variable is considered endogenous in the sense that it is correlated with the equation errors. Using a recently available UK dataset we explore alternative specifications of an auxiliary equation for total expenditure, which depend on prices and other instrumental variables, and apply a Hausman-type and a likelihood ratio test of exogeneity. The results reject exogeneity and suggest that when endogeneity of total expenditure is taken into account the constraints of homogeneity and symmetry cannot be rejected.

Model Selection Uncertainty and Detection of Threshold Effects

Inferences about the presence or absence of threshold type nonlinearities in TAR models are conducted within models whose lag length has been estimated in a preliminary stage. Typically the null hypothesis of linearity is then tested against a threshold alternative on which the estimated lag length is imposed on each regime. In this paper we evaluate the properties of test statistics for detecting the presence of threshold effects in autoregressive models when this model uncertainty is taken into account. We show that this approach may lead to important distortions when the underlying model has truly threshold effects by establishing the limiting properties of the estimated lag length in the mispecified linear autoregressive fit and assessing the impact of this model uncertainty on the power of the tests. We subsequently propose a full model selection based approach designed to jointly detect the presence of threshold effects and optimally specify its dynamics and compare its performance with the traditional test based approach.

Estimation and inference in threshold type regime switching models

Contents: 1. Introduction Nigar Hashimzade and Michael A. Thornton 2. A Review of Econometric Concepts and Methods for Empirical Macroeconomics Kerry Patterson and Michael A. Thornton PART I: PROPERTIES OF MACROECONOMIC DATA 3. Trends, Cycles and Structural Breaks Terence C. Mills 4. Unit Roots, Non-linearities and Structural Breaks Niels Haldrup, Robinson Kruse, Timo Terasvirta and Rasmus T. Varneskov 5. Filtering Macroeconomic Data D.S.G. Pollock PART II: MODELS FOR MACROECONOMIC DATA ANALYSIS 6. Vector Autoregressive Models Helmut Lutkepohl 7. Cointegration and Error Correction James Davidson 8. Estimation and Inference in Threshold Type Regime Switching Models Jesus Gonzalo and Jean-Yves Pitarakis 9. Testing Structural Stability in Macroeconometric Models Otilia Boldea and Alastair R. Hall 10. Dynamic Panel Data Models Badi H. Baltagi 11. Factor Models Jorg Breitung and In Choi 12. Conditional Heteroskedasticity in Macroeconomic Data: UK Inflation, Output Growth and their Uncertainties Menelaos Karanasos and Ning Zeng 13. Temporal Aggregation in Macroeconomics Michael A. Thornton and Marcus J. Chambers PART III: ESTIMATION AND EVALUATION FRAMEWORKS IN MACROECONOMICS 14. Generalized Method of Moments Alastair R. Hall 15. Maximum Likelihood Estimation of Time Series Models: The Kalman Filter and Beyond Tommaso Proietti and Alessandra Luati 16. Bayesian Methods Luc Bauwens and Dimitris Korobilis 17. Forecasting in Macroeconomics Raffaella Giacomini and Barbara Rossi PART IV: APPLICATIONS I: DYNAMIC STOCHASTIC GENERAL EQUILIBRIUM MODELS 18. The Science and Art of DSGE Modelling: I - Construction and Bayesian Estimation Cristiano Cantore, Vasco J. Gabriel, Paul Levine, Joseph Pearlman and Bo Yang 19. The Science and Art of DSGE Modelling: II - Model Comparisons, Model Validation, Policy Analysis and General Discussion Cristiano Cantore, Vasco J. Gabriel, Paul Levine, Joseph Pearlman and Bo Yang 20. Generalized Method of Moments Estimation of DSGE Models Francisco J. Ruge-Murcia 21. Bayesian Estimation of DSGE Models Pablo A. Guerron-Quintana and James M. Nason PART V: APPLICATIONS II: VECTOR AUTOREGRESSIVE MODELS 22. Structural Vector Autoregressions Lutz Kilian 23. Vector Autoregressive Models for Macroeconomic Policy Analysis Soyoung Kim PART VI: APPLICATIONS III: CALIBRATION AND SIMULATIONS 24. Calibration and Simulation of DSGE Models Paul Gomme and Damba Lkhagvasuren 25. Simulation and Estimation of Macroeconomic Models in Dynare Joao Madeira IndexFinancial support from the ESRC is gratefully acknowledged. Address for Correspondence: Jean-Yves Pitarakis, University of Southampton, School of Social Sciences, Economics Division, Southampton, SO17 1BJ, United-Kingdom. Email: j.pitarakis@soton.ac.uk

A joint test for structural stability and a unit root in autoregressions

A test of the joint null hypothesis of parameter stability and a unit root within an ADF style autoregressive specification whose entire parameter structure is potentially subject to a structural break at an unknown time period is developed. The proposed test is a useful diagnostic tool for assessing the interactions of breaks and unit root type of nonstationarities in time series, in addition to offering a powerful device for detecting changes in persistence. As a byproduct the limiting behaviour of a related Wald statistic designed to test solely the null of parameter stability in an environment with a unit root is also obtained. These distributions are free of nuisance parameters and easily tabulated. The finite sample properties of the tests are assessed through a series of simulations, and an application to macroeconomic data illustrates their usefulness.

The allocation of public consumption expenditure in the UK

Using the Almost Ideal Demand System specification we analyse whether UK public consumption expenditure decisions are compatible with traditional utility maximization postulates. Our empirical findings tend to support the validity of the constraints of homogeneity and symmetry.