Multicointegration in Stock-Flow Models

Multicointegration, in the sense of Granger and Lee (1990), frequently occurs in models of stock-flow adjustment and implies cointegration amongst I(2) variables and their differences (polynomial cointegration). The purpose of this article is two-fold. First, we demonstrate that based on a multicointegrated vector autoregression (VAR) two equivalent error correction model (ECM) representations can be derived; the first is expressed in terms of adjustments in the flows of the variables (the standard I(2) ECM), and the second is expressed in terms of adjustments in both the stocks and the flows. Secondly, we apply I(2) estimation and testing procedures for multicointegrated time series to analyze data for US housing construction. We find that stocks of housing units started and completed exhibit polynomial cointegration (and hence the flows are multicointegrated) and the associated ECM's are estimated. Lee (1992, 1996) also found multicointegration in this data set but without explicitly exploiting the I(2) property