Nonparametric Estimation of Nonadditive Random Functions

By Rosa L. Matzkin. 2003

429 citations recorded by the source corpus.

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. Copyright The Econometric Society 2003.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ae7500033fec5cc3cd63089f91b3f9174f56928a

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Citations in the corpus

Control functions in nonseparable simultaneous equations models (2014, background): “Given the distribution of η or of (ηη y 2 ) (Matzkin (2003), Imbens and Newey (2009)), one can obtain the probability that Y 1 = 1 when Y 2 = y 2 and ε 1 is distributed with its marginal distribution as F ε 1 g(y 2 ) = Pr(Y 1 = 1|Y 2 = y 2 η = t)f η (t) dt The derivative with respect to y 2 of the…”
Instrumental variable estimation of nonseparable models (2007, positive): “The model can also be thought of as extending conditional quantile identification and estimation as considered by Hendricks and Koenker (2002), Matzkin (2003), and others, to allow for endogeneity.”
Unobserved heterogeneity and endogeneity in nonparametric frontier estimation (2016, background): “The model defined in (2.15) is nonseparable in V and has been studied in several papers in econometrics (see for example, Matzkin, 2003).”
Nonparametric identification (2020, methodology): “Nonparametric models of this type were studied in Roehrig (1988), Olley and Pakes (1996), Brown and Matzkin (1998), Matzkin (1999, 2003), Altonji and Ichimura (2000), Altonji and Matzkin (2001), and Imbens and Newey (2003), among others.”
Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors (2005, methodology): “Assumptions 5.1-5.3 were used in Matzkin (1999) to identify m and the distribution of e when e is independent of x. Assumption 5.4 imposes a shape restriction on the conditional distribution of the unobservable variable, which, as we show below, allows us to differentiate the change in y which is…”
Identification in Nonparametric Simultaneous Equations Models (2008, methodology): “We first consider the single equation model, with G = 1, considered in Matzkin (1999, 2003): y = m (x, u) We show below that, in this model, with m strictly increasing in u, application of our theorems implies the well known result that for all u, ∂m (x, u) ∂x , the partial derivative of m with…”
Vector Quantile Regression (2014, background): “It is also noteworthy that in the classical case of Y and U being scalars we recover the classical conditional quantile function as well as the strong representation formula based on this function ([28], [17]).”
Identification and estimation of local average derivatives in non-separable models without monotonicity (2009, neutral): “1 See Matzkin (2003) for further examples, mainly from the duration literature.”
Unconditional Quantile Regressions (2007, result): “Under the hypothesis that X and ε are independent and h is strictly monotonic in ε, we may invoke the results of Matzkin (2003) that guarantee that both the distribution of ε, Fε, and the link function h are nonparametrically identified under an additional normalization assumption.”
Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation (2007, methodology): “Matzkin (1993) considers identification of polychotomous discrete choice models under the conditions of Theorem 1 below.”