Capital markets integration and cointegration: Testing for the correct specification of stock market indices

In this paper we develop a comprehensive Vector Autoregression Model consisting of five variables; the stock market and price indices of pairs of countries, as well as their bilateral nominal exchange rate. Then, we show that under certain long-run restrictions, our approach encompasses a large number of specifications encountered in the voluminous literature on testing for capital integration with cointegration techniques. This approach minimizes the risk of accepting the null of no cointegration between the equity price indices because of the introduction of additional stochastic trends through the transformation of those indices on a “real or nominal US dollar” basis. Furthermore, other interesting long run specifications emerge either with I(1) only stochastic shocks or with the presence of some I(2) disturbances characterizing the system. We apply the testing methodology on monthly data for the US, UK, Germany, and Japan for the period January 1980-May 2019. The main findings provide partial support in favor of cointegration, and therefore for capital markets integration, among stock market indices when proper attention is given to issues like the identification and temporal stability of the cointegration vectors as well as the choice of units that the stock indices are expressed in.