Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Sep, 2003, Volume 71, Issue 5

Nonparametric Estimation of Nonadditive Random Functions
p. 1339-1375

Rosa L. Matzkin

We present estimators for nonparametric functions that are nonadditive in unobservable random terms. The distributions of the unobservable random terms are assumed to be unknown. We show that when a nonadditive, nonparametric function is strictly monotone in an unobservable random term, and it satisfies some other properties that may be implied by economic theory, such as homogeneity of degree one or separability, the function and the distribution of the unobservable random term are identified. We also present convenient normalizations, to use when the properties of the function, other than strict monotonicity in the unobservable random term, are unknown. The estimators for the nonparametric function and for the distribution of the unobservable random term are shown to be consistent and asymptotically normal. We extend the results to functions that depend on a multivariate random term. The results of a limited simulation study are presented.

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