INFERENCE CONCERNING THE NUMBER OF FACTORS IN A MULTIVARIATE NONPARAMETRIC RELATIONSHIP

This paper considers the problem of determining the number of nonparam etric factors in a multivariate nonparametric relationship. The defini tion given is broad enough to encompass a number of potential applicat ions in econometrics including inferring the rank of demand, testing w hether for a given set of instruments it is possible to identify a lin ear model, and testing arbitrage pricing theory. The paper gives metho ds for testing hypotheses concerning the number of factors, using seri es and kernel based nonparametric methods and also considers the probl em of estimating the number of factors. The methods are compared in a small simulation study and an application to determining the rank of d emand systems is considered.