Important dynamic indices in spatial models

The purpose of this paper is twofold. First, in the context of a spatial model we generalize two indices. One is a dynamic generalization of the emanating effect that was introduced by Kelejian and colleagues. This index describes how events in one unit spill over time to other units due to spatial interactions. As an analogy, it corresponds to the effect that the smoking habits of a given teenager might have on the smoking habits of each of his/her friends. In a sense, our second index, termed the vulnerability index, is the reverse of the first one in that it describes the response of a given unit over time to events in neighbouring units. The analogy here would be how the smoking habits of a given teenager is affected by the smoking habits of all of his/her friends. Second, we empirically implement our indices in the context of a model explaining GDP per capita growth in various countries. In this context the vulnerability index describes the sensitivity of GDP growth in one country with respect to events in other countries; the emanating effect describes how events in one country effect the GDP growth in other countries.