Hyungsik Roger Moon

Linear Regression Limit Theory for Nonstationary Panel Data

This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section and time series observations. The limit theory allows for both sequential limits and joins limits, and the relationship between these multidimensional limits is explored. The panel structures considered allow for no time series cointegration, heterogeneous cointegration, homogeneous cointegration, and near-homogeneous cointegration. The paper explores the existence of long-run average relations between integrated panel vectors. In the case of homogeneous and near homogeneous cointegrating panels, a panel fully modified regression estimator is developed and studied.

Nonstationary panel data analysis: an overview of some recent developments

This paper overviews some recent developments in panel data asymptotics, concentrating on the nonstationary panel case and gives a new result for models with individual effects. Underlying recent theory are asymptotics for multi-indexed processes in which both indexes may pass to infinity. We review some of the new limit theory that has been developed, show how it can be applied and give a new interpretation of individual effects in nonstationary panel data. Fundamental to the interpretation of much of the asymptotics is the concept of a panel regression coefficient which measures the long run average relation across a section of the panel. This concept is analogous to the statistical interpretation of the coefficient in a classical regression relation. A variety of nonstationary panel data models are discussed and the paper reviews the asymptotic properties of estimators in these various models. Some recent developments in panel unit root tests and stationary dynamic panel regression models are also reviewed.

Linear Regression for Panel with Unknown Number of Factors as Interactive Fixed Effects

In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed e ffects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data we establish the limiting distribution of the LS estimator for the regression coefficients, as the number of time periods and the number of crosssectional units jointly go to infi nity. The main result of the paper is that under certain assumptions the limiting distribution of the LS estimator is independent of the number of factors used in the estimation, as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients one does not necessarily need to estimate the number of interactive fixed eff ects consistently. Supplementary material for this paper is available here.

Estimation of Autoregressive Roots Near Unity Using Panel Data

E s t i m a t i o n of Autoregressive R o o t s near U n i t y using P a n e l D a t a Hyungsik R. M o o n Department of Economics University of California, Santa Barbara Peter C.B. Phillips* Cowles Foundation for Research i n Economics Yale University This Version, July 1999 First Draft, November 1997 Abstract Time series data are often well modelled by using the device of an autore¬ gressive root that is local to unity. Unfortunately, the localizing parameter (c) is not consistently estimable using existing time series econometric techniques and the lack of a consistent estimator complicates inference. This paper devel¬ ops procedures for the estimation of a common localizing parameter using panel data. Pooling information across individuals in a panel aids the identification and estimation of the localising parameter and leads to consistent estimation in simple panel models. However, in the important case of models with con¬ comitant deterministic trends, it is shown that pooled panel estimators of the localising parameter are asymptotically biased. Some techniques are developed to overcome this difficulty and consistent estimators of c in the region c < 0 are developed for panel models with deterministic and stochastic trends. A limit distribution theory is also established and test statistics are constructed for ex¬ ploring interesting hypotheses, like the equivalence of local to unity parameters across subgroups of the population. The methods are applied to the empirically important problem of the eicient extraction of deterministic trends. They are also shown to deliver consistent estimates of distancing parameters in nonsta- tionary panel models where the initial conditions are in the distant past. In the development of the asymptotic theory this paper makes use of both sequential and joint limit approach. An important limitation in the operation of the joint asymptotics which is sometimes needed in our development is the rate condition *The authors thank the Co-Editor, Bruce Hansen, and four anonymous referees for comments on the earlier version of the paper, and Donald Andrews for helpful discussions. Phillips thanks the NSF for research support under Grant Nos. SBR 94-22922 A SBR 97-30295, and Moon gratefully acknowledges financial support from a C.A. Anderson Prize Fellowship. The paper was typed by the authors in Scientific Word 2.5.

Dynamic linear panel regression models with interactive fixed effects

We analyze linear panel regression models with interactive fixed effects and predetermined regressors, e.g. lagged-dependent variables. The first order asymptotic theory of the least squares (LS) estimator of the regression coefficients is worked out in the limit where both the cross sectional dimension and the number of time periods become large. We find that there are two sources of asymptotic bias of the LS estimator: bias due to correlation or heteroscedasticity of the idiosyncratic error term, and bias due to predetermined (as opposed to strictly exogenous) regressors. We provide an estimator for the bias and a bias corrected LS estimator for the case where idiosyncratic errors are independent across both panel dimensions. Furthermore, we provide bias corrected versions of the three classical test statistics (Wald, LR and LM test) and show that their asymptotic distribution is a chi-square-distribution. Monte Carlo simulations show that the bias correction of the LS estimator and of the test statistics also work well for finite sample sizes. A supplement to this paper can be downloaded here.

Bayesian and Frequentist Inference in Partially Identified Models

A large sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by a finite-dimensional reduced form parameter vector. It is used to analyze the differences between frequentist confidence sets and Bayesian credible sets in partially identified models. A key difference is that frequentist set estimates extend beyond the boundaries of the identified set (conditional on the estimated reduced form parameter), whereas Bayesian credible sets can asymptotically be located in the interior of the identified set. Our asymptotic approximations are illustrated in the context of simple moment inequality models and a numerical illustration for a two-player entry game is provided.

HOW TO ESTIMATE AUTOREGRESSIVE ROOTS NEAR UNITY

A new model of near integration is formulated in which the local to unity parameter is identifiable and consistently estimable with time series data. The properties of the model are investigated, new functional laws for near integrated time series are obtained, and consistent estimators of the localizing parameter are constructed. The model provides a more complete interface between I(0) and I(1) models than the traditional local to unity model and leads to autoregressive coefficient estimates with rates of convergence that vary continuously between the O(/n) rate of stationary autoregression, the O(n) rate of unit root regression and the power rate of explosive autoregression. Models with deterministic trends are also considered, least squares trend regression is shown to be efficient, and consistent estimates of the localising parameter are obtained for this case as well. Conventional unit root tests are shown to be consistent against local alternatives in the new class.

Asymptotic Local Power of Pooled T-Ratio Tests for Unit Roots in Panels with Fixed Effects

. This latter test is equivalent to the well-known pooled t test proposed by Levin et al. (2002, Journal of Econometrics 108, 1--24), and its power depends only on the mean of the local-to-unity parameters. This implies that it has the same power against homogeneous and heterogeneous alternatives with the same mean autoregressive parameter. We then compare these tests to a panel version of the Sargan-Bhargava (1983, Econometrica 51, 153--74) statistic for a unit root and the common point-optimal test of Moon et al. (2007, Journal of Econometrics 141, 416--51). Monte Carlo simulations confirm the usefulness of our local-to-unity framework. Copyright Royal Economic Society 2008

Inference for Vars Identified with Sign Restrictions

There is a fast growing literature that partially identifies structural vector autoregressions (SVARs) by imposing sign restrictions on the responses of a subset of the endogenous variables to a particular structural shock (sign-restricted SVARs). To date, the methods that have been used are only justified from a Bayesian perspective. This paper develops methods of constructing error bands for impulse response functions of sign-restricted SVARs that are valid from a frequentist perspective. The authors also provide a comparison of frequentist and Bayesian error bands in the context of an empirical application - the former can be twice as wide as the latter.

A note on fully-modified estimation of seemingly unrelated regressions models with integrated regressors

Abstract We show how to apply the fully-modified estimation method in the integrated seemingly unrelated regressions model. Three different fully-modified estimators are studied and their asymptotic distributions are found.