Stochastic trends and cointegrating relationships in a substate area

In traditional regional econometric models, many economic relationships are expressed in terms of deterministic trends. These models assume that regional and national time series are stationary. If the variables under investigation are nonstationary, it is easy to produce a spurious model and the usual distributional results and tests of parameter significance are no longer valid. This study examines the stochastic characteristics of substrate area, urban area, and U.S. economic variables. The empirical results show that most of the variables have stochastic trends (unit roots), implying that these variables will deviate from their average or trend by some unpredictable random amount after a shock. Statistical inferences based on undifferenced data are misleading and probably characterize most work in regional econometric modeling. This study also investigates cointegrating relationships between a substrate area and U.S., the substrate area and a nearby urban area, and among the substrate area, urban area, and U.S. The results show that the strength of these relationships varies across industrial sectors but is very weak in the majority of sectors. Following the cointegration tests for the substrate area and U.S. variables, a multiequation modeling system for the substrate area is developed. The modeling strategy is top-down in that U.S. variables are used to determine the associated substrate area variables. According to the stochastic characteristics of each individual equation in the modeling system, three different types of models are selected: (1) error correction models, (2) differences models, (3) levels models. The ex-post projection results show that the overall performance of the error correction model is better than the other two types of models