Linear Regression Limit Theory for Nonstationary Panel Data

Abstract

This paper develops a regression limit theory for nonstationary panel data with large Ž . Ž . numbers of cross section n and time series T observations. The limit theory allows for both sequential limits, wherein T ª ϱ followed by n ª ϱ, and joint limits where T, n ª ϱ simultaneously; 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 when there is no individual time series cointegration and when there is heterogeneous cointegration. These relations are parameterized in terms of the matrix regression coefficient of the long-run average covariance matrix. In the case of homogeneous and near homogeneous cointegrating panels, a panel fully modified regression estimator is developed and studied. The limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population.

Panel cointegration tests of the Fisher effect

“…1. Moreover, by using Theorem 3 of Phillips and Moon (1999), since E i is independent across i, the first term on the right-hand side converges to a standard normal variate. From these results it follows that n 1/2 DH g p nE B i ) N 0, var B i .…”

Private Donations, Government Grants, Commercial Activities, and Fundraising: Cointegration and Causality for NGOs in International Development Cooperation

“…The error-correction term, 1 − it ect , represents the error in, or deviation from, the equilibrium, while the adjustment coefficients a 1 , a 2 , a 3 , and a 4 capture how Donations it , GovGrants it , Com it , and Fundrais it respond to deviations from the equilibrium relationship. From the Granger representation theorem, we know that at least 18 Like the time series FMOLS estimator, the panel FMOLS estimator incorporates a semi-parametric correction to the OLS estimator to eliminate the endogeneity and serial correlation (see, e.g., Phillips and Moon, 1999). one of the adjustment coefficients must be nonzero if a long-run relationship between the variables is to hold.…”

Sieve bootstrap -tests on long-run average parameters

“…Kao (1999) and Phillips and Moon (1999) develop multi-index asymptotic theory to demonstrate that the Least Squares Dummy Variable (LSDV) and Pooled OLS (POLS) estimators are gaussian and p N -consistent for a long run average e¤ect.…”