Estimating cointegrating relations from a cross section

Abstract

This paper speci…es a regression model describing cointegrating relations between variables at the individual level. The models considered allow for homogeneous cointegration and heterogeneous cointegration.In both cases correlation between the regressors and the regression error can occur through aggregate shocks that are common to all cross-section units so the condition about the regressors being independent of the regression error is not imposed. It is shown that the estimator obtained by a cross-section regression performed at any point in time is a consistent estimator of the cointegrating parameters in the homogeneous case and of the cointegrating parameter means in the heterogeneous case. In both cases the limiting distribution of the cross-section estimator is normal.

Unit root inference in panel data models where the time‐series dimension is fixed: a comparison of different tests

“…mean zero terms as the starting point after having subtracted the cross-section sample means from all variables. A similar result is shown in detail in Madsen (2005) within the framework of a pure cross-section analysis. Assumption 2.3 specifies the initial values and implies that they are such that the time-series processes for y it become mean stationary that is E(y it |α i ) = α i for all t = 0, 1, 2, .…”

Estimación de la función de bienestar social de Amartya Sen para América Latina

“…Los resultados de la regresión se consideran consistentes al existir una relación de largo plazo establecida por las pruebas de cointegración en el panel de datos (Madsen, 2005), e indican que el PIB per cápita y el complemento del coeficiente de Gini son significativos al 1% para explicar el bienestar medido por el IDH. Los impactos de ambas variables sobre el bienestar son positivos.…”

Least Squares Asymptotics in Spurious and Cointegrated Panel Regressions with Common and Idiosyncratic Stochastic Trends*

“…Consider, for example, the least squares cross‐section estimator, whose limit as N →∞ under serial uncorrelatedness is given by which is the same result as for . Madsen (2005) considers a version , in which the observations on x it and y it have been demeaned with respect to a common time effect. Interestingly, this modification has no effect on the asymptotic behaviour of the resulting estimator, as can be seen by noting that as N →∞ where x t and y t are the cross‐sectional averages of x it and y it , respectively.…”