Large T and Small N: A Three-Step Approach to the Identification of Cointegrating Relationships in Time Series Models with a Small Cross-Sectional Dimension

Abstract

This paper addresses cointegration in small cross-sectional panel data models. In addition to dealing with cointegrating relationships within the cross-sectional dimension, the paper explicitly addresses the issue of cointegration between cross-sections. The approach is based upon a well-known distributional result for the trace test when some of the cointegrating vectors are a priori known, and advocates a three-step procedure for the identification of the cointegrating space when dealing with two-dimensional data. The first step of this procedure utilizes traditional techniques to identify the long-run relationships within each cross-sectional unit separately. In the second step these first step relationships are then treated as known when searching for potential long run relationships between units in a joint analysis comprising the whole cross-sectional dimension. The third step of the procedure then finally reestimate all free parameters of the identified long-run structure to get rid of a potential simultaneity bias as a result of a non-diagonal covariance matrix. Identification of the long-run structures of Norwegian exports and international interest rate relationships are used as examples. Norwegian mainland exports have here been divided into two cross-sectional units; the traditional goods sector and the service sector. While in the study of international interest rate relationships the two sectors investigated are Germany and the US. The examples are used to address the more general issues of the degree of independence in capital markets and in goods markets of small open economies.