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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jeconom.2005.01.027 Byline: Jean Boivin (a), Serena Ng (b) Abstract: Factors estimated from large macroeconomic panels are being used in an increasing number of applications. However, little is known about how the size and the composition of the data affect the factor estimates. In this paper, we question whether it is possible to use more series to extract the factors, and yet the resulting factors are less useful for forecasting, and the answer is yes. Such a problem tends to arise when the idiosyncratic errors are cross-correlated. It can also arise if forecasting power is provided by a factor that is dominant in a small dataset but is a dominated factor in a larger dataset. In a real time forecasting exercise, we find that factors extracted from as few as 40 pre-screened series often yield satisfactory or even better results than using all 147 series. Weighting the data by their properties when constructing the factors also lead to improved forecasts. Our simulation analysis is unique in that special attention is paid to cross-correlated idiosyncratic errors, and we also allow the factors to have stronger loadings on some groups of series than others. It thus allows us to better understand the properties of the principal components estimator in empirical applications. Author Affiliation: (a) Graduate School of Business, 821 Uris Hall, Columbia University, New York, USA (b) Department of Economics, University of Michigan, 317 Lorch Hall, Ann Arbor, MI 48109-1022, USA

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jeconom.2005.01.015 Byline: Jushan Bai (a)(b), Serena Ng (c) Abstract: Common factors play an important role in many disciplines of social science. In economics, the factors are the common shocks that underlie the co-movements of the large number of economic time series. The question of interest is whether some observable economic variables are in fact the underlying unobserved factors. We consider statistics to determine if the observed and the latent factors are exactly the same. We also provide simple to construct statistics that indicate the extent to which the two sets of factors differ. The key to the analysis is that the space spanned by the latent factors can be consistently estimated when the sample size is large in both the cross-section and the time series dimensions. The tests are used to assess how well the so-called Fama and French factors as well as several business cycle indicators approximate the factors in portfolio and individual stock returns. Data from a large panel of macroeconomic are also analyzed. Author Affiliation: (a) Department of Economics, 269 Mercer St., New York University, New York, NY 10022, USA (b) Department of Economics, Tsinghua University, School of Economics and Management, Beijing, China (c) Department of Economics, University of Michigan, Ann Arbor, MI 48109, USA Article Note: (footnote) [star] This paper was presented at Yale University, the 2003 IGIER-PIER Conference on Macroeconomics and Finance held at Bocconi University, and the 2003 ISI Meeting in Berlin.

The non-negativity constraint on inventories imposed on the rational expectations theory of speculative storage implies that the conditional mean and variance of commodity prices are non-linear in lagged prices and have a kink at a threshold point. In this paper, the structural parameters of this model are estimated using three simulation-based estimators. In a Monte Carlo experiment, the finite sample properties of the simulated methods of moments estimator of Duffle and Singleton (1993, Econometrica 61 (4), 929-952) the indirect inference estimator of Gourieroux et al. (1993, Journal of Applied Economterics 8, S85-S118) and the efficient method of moments estimator of Gallant and Tauchen (1996, Econometric Theory 12, 657-681) are assessed. Exploiting the invariant distribution implied by the theory allows us to evaluate the error induced by simulations. Our results show that the estimators differ in their sensitivity to the sample size, the number of simulations, choice of auxiliary models, and computation demands. For some estimators, the test for overidentifying restrictions exhibit significant size distortions in small samples. Overall, while the simulation estimators have small bias, they are less efficient than pseudo-maximum likelihood (PMLE). Hence for the small sample sizes considered, the simulation estimators are still inferior to the PMLE estimates in a mean-squared sense.

This paper considers the role of normalization in least-squares estimation of cointegrating vectors. It is shown, using an empirical example and Monte-Carlo simulations of bivariate models, that the least-squares estimates can have very poor finite sample properties when normalized in one direction but are well behaved when normalized in the other. This occurs when one of the I(1) variables is a weak random walk or is nearly stationary. The choice of the regressand also has implications for residual based unit root tests for cointegration. We provide theoretical explanations for why the least-squares estimates from one normalization can be outright inconsistent in well-defined local asymptotic frameworks. Ranking the spectral density at frequency zero of the first differenced series is suggested as a practical guide to determining which variable to use as the regressand. Keywords: Unit root; Cointegration; Normalization; Spectral density function at frequency zero