Multicointegration in Stock‐Flow Models
证明多重协整的向量自回归可等价表示为两种误差修正模型，并应用于美国住房建设数据，发现开工和完工住房存量存在多项式协整。
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 poly‐ nomial 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.