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This paper shows how standard methods can be used to formulate and estimate a dynamic index model for random fields - stochastic processes indexed by time and cross section where the time-series and cross section dimensions are comparable in magnitude. We use these study dynamic co-movements of sectoral employment in the US economy. The dynamics of employment in sixty sectors is well explained using only two unobservable factors; those factors are also strongly correlated with GNP growth.
Quah et al. (Sun,) studied this question.