Developments in the Study of Cointegrated Economic Variables

At the least sophisticated level of economic theory lies the belief that certain pairs of economic variables should not diverge from each other by too great an extent, at least in the long-run. Thus, such variables may drift apart in the short-run or according to seasonal factors, but if they continue to be too far apart in the long-run, then economic forces, such as a market mechanism or government intervention, will begin to bring them together again. Examples of such variables are interest rates on assets of different maturities, prices of a commodity in different parts ofthe country, income and expenditure by local government and the value of sales and production costs of an industry. Other possible examples would be prices and wages, imports and exports, market prices of substitute commodities, money supply and prices and spot and future prices of a commodity. In some cases an economic theory involving equilibrium concepts might suggest close relations in the long-run, possibly with the addition of yet further variables. However, in each case the correctness of the beliefs about long-term relatedness is an empirical question. The idea underlying cointegration allows specification of models that capture part of such beliefs, at least for a particular type of variable that is frequently found to occur in macroeconomics. Since a concept such as the long-run is a dynamic one, the natural area for these ideas is that of time-series theory and analysis. It is thus necessary to start by introducing some relevant time series models. Consider a single series Xf, measured at equal intervals of time. Time series theory starts by considering the generating mechanism for the series. This mechanism should be able to generate att of the statistical properties of the series, or at very least the conditional mean, variance and temporal autocorrelations, that is the 'linear properties' of the series, conditional on past data. Some series appear to be 'stationary', which essentially implies that the linear properties exist and are timeinvariant. Here we are concerned with the weaker but more technical