Testing for rational bubbles in a co-explosive vector autoregression

We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable, are derived both for a model without bubbles and for a model with a rational bubble. In both cases we show how the restrictions can be tested through standard chi-squared inference. The analysis for the no-bubble case is done within the traditional Johansen model for I(1) variables, while the bubble model is analysed using a co-explosive framework. The methodology is illustrated using US stock prices and dividends for the period 1872-2000.Rational bubbles, Explosiveness and co-explosiveness, Cointegration, Vector autoregression, Likelihood ratio tests.

Multicointegration and present value relations

It is well-known that if the forcing variable of a present value (PV) model is an integrated process, then the model will give rise to a particular cointegrating restriction. In this paper we demostrate that if the PV relation is exact, such that no additive error term appears in the specification, then te variables will be multicointegrated such that the cumlation of cointegration errors at one level of cointegration will cointegrate with the forcing variable. Multicointegration thus delivers a statistical property of the data that is necessary, though not sufficient, for this class of models to be valido Estimation and inference of the model are discussed and it is shown that, provided me PV relation is exact, the discount factor of the model can be estimated with arate of convergence that is faster than the usual super-consistent rate characterising estimators in the cointegration literature. Finally, the paper is completed with two empirical analyses of PV models using term structure data and farmland data, respectively

Long-run forecasting in multicointegrated systems

We extend the analysis of Christoffersen and Diebold (1998) on long-run forecasting in cointegrated systems to multicointegrated systems. For the forecast evaluation we consider several loss functions, each of which has a particular interpretation in the context of stock-flow models where multicointegration typically occurs. A loss function based on a standard mean square forecast error (MSFE) criterion focuses on the forecast errors of the flow variables alone. Likewise, a loss function based on the triangular representation of cointegrated systems (suggested by Christoffersen and Diebold) considers forecast errors associated with changes in both stock (modelled through the cointegrating restrictions) and flow variables. We suggest a new loss function which is based on the triangular representation of multicointegrated systems which further penalizes deviations from the long-run relationship between the levels of stock and flow variables as well as changes in the flow variables. Among other things, we show that if one is concerned with all possible long-run relations between stock and flow variables, this new loss function entails high and increasing forecasting gains compared to both the standard MSFE criterion and Christoffersen and Diebold?s criterion. The paper demonstrates the importance of carefully selecting loss functions in forecast evaluation of models involving stock and flow variables

Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the integrated volatility. We show that our approach, which possess an intuitive transparency, can generate rate optimal estimators (with convergence rate n-1/4)

Granger's representation theorem and multicointegration

Digitised version produced by the EUI Library and made available online in 2020

Statistical vs. Economic Significance in Economics and Econometrics: Further comments on McCloskey & Ziliak

I comment on the controversy between McCloskey & Ziliak and Hoover & Siegler on statistical versus economic significance, in the March 2008 issue of the Journal of Economic Methodology. I argue that while McCloskey & Ziliak are right in emphasizing ’real error’, i.e. non-sampling error that cannot be eliminated through specification testing, they fail to acknowledge those areas in economics, e.g. rational expectations macroeconomics and asset pricing, where researchers clearly distinguish between statistical and economic significance and where statistical testing plays a relatively minor role in model evaluation. In these areas models are treated as inherently misspecified and, consequently, are evaluated empirically by other methods than statistical tests. I also criticise McCloskey & Ziliak for their strong focus on the size of parameter estimates while neglecting the important question of how to obtain reliable estimates, and I argue that significance tests are useful tools in those cases where a statistical model serves as input in the quantification of an economic model. Finally, I provide a specific example from economics - asset return predictability - where the distinction between statistical and economic significance is well appreciated, but which also shows how statistical tests have contributed to our substantive economic understanding.Statistical and economic significance, statistical hypothesis testing, model evaluation, misspecified models