# Econometrics and Statistics Seminar SoSe 2017

Dienstag, 16-17h in der Fakultätslounge, Juridicum, Adenauerallee 24-42, 53113 Bonn

Seminar-Agenda Sommersemester 2017

**Mai 09, 2017**

**Enno Mammen **(Uni Heidelberg)

**Titel:** “Statistical inference in sparse high-dimensional nonparametric models” (with Karl Gregory, Martin Wahl)

**Abstract:** In this talk we discuss the estimation of a nonparametric component f_1 of a nonparametric additive model Y = f_1(X_1) +...+ f_q(X_q) + e. We allow the number q of additive components to grow to infinity and we make sparsity assumptions about the number of nonzero additive components. We compare this estimation problem with that of estimating f_1 in the oracle model Z = f_1(X_1) + e, for which the additive components f_2,...,f_q are known. We construct a two-step presmoothing-and-resmoothing estimator of f_1 in the additive model and state finitesample bounds for the difference between our estimator and some smoothing estimators in the oracle model which satisfy mild conditions. In an asymptotic setting these bounds can be used to show asymptotic equivalence of our estimator and the oracle estimators; the paper thus shows that, asymptotically, under strong enough sparsity conditions, knowledge of f_2,...,f_q has no effect on estimation efficiency. Our first step is to estimate all of the components in the additive model with undersmoothing using a group-Lasso estimator. We then construct pseudo responses hat(Y) by evaluating a desparsified modification of our undersmoothed estimator of f_1 at the design points. In the second step the smoothing method of the oracle estimator of f_1 is applied to a nonparametric regression problem with "responses" hat(Y) and covariates X_1. Our mathematical exposition centers primarily on establishing properties of the presmoothing estimator. We also present simulation results demonstrating close-tooracle performance of our estimator in practical applications. The main results of the paper are also important for understanding the behavior of the presmoothing estimator when the resmoothing step is omitted.

**Mai 16, 2017**

t.b.a

**Mai 23, 2017**

**Yuichi Kitamura** (Yale & Cowles)

**Titel:** "Nonparametric Analysis of Finite Mixtures" (with Louise Laage)

**Abstract:** Finite mixture models are useful in applied econometrics. They can be used to model unobserved heterogeneity, which plays major roles in labor economics, industrial organization and other fields. Mixtures are also convenient in dealing with contaminated sampling models and models with multiple equilibria. This paper shows that finite mixture models are nonparametrically identified under weak assumptions that are plausible in economic applications. The key is to utilize the identification power implied by information in covariates variation. It then shows that fully nonparametric estimation of the entire mixture model is possible, by forming a sample analogue of one of the new identification strategies. The estimator is shown to possess a desirable polynomial rate of convergence. Lastly, an application to auction models with unobserved heterogeneity is discussed. This may be attractive for practitioners as it offers new ways to account for unobserved heterogeneity in auctions while allowing for arbitrary affiliation patterns and imposing only mild separability restrictions.

**Mai 30, 2017**

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**June 13, 2017**

**Aureo de Paula** (UCL)

**Titel:** “Identifying and Estimating Social Connections from Outcome Data”

**Abstract:** Knowledge of the relevant linkages between individuals is usually necessary for the estimation of social interaction models. We obtain results that allow for the estimation of parameters of interest in a model with endogenous, exogenous and correlated effects without information on the relevant linkages. Our identification analysis relies on usual assumptions on the nature of interactions found in, e.g., Bramoullé et al. [2009]. To obtain identification we further impose conditions on the density of links and repeated observation of outcomes for a given group of individuals. We provide an estimation strategy which we investigate via simulations and an empirical illustration.

**June 20, 2017**

**Frederic Vermeulen** (KU Leuven)

**Titel:** "Marital Matching, Economies of Scale and Intrahousehold Allocations"

**Abstract: **We propose a novel structural method to empirically identify economies of scale in household consumption. We assume collective households with consumption technologies that define the public and private nature of expenditures through Barten scales. Our method recovers the technology by solely exploiting preference information revealed by households' consumption behavior. The method imposes no parametric structure on household decision processes, accounts for unobserved preference heterogeneity across individuals in different households, and requires only a single consumption observation per household. Our main identifying assumption is that the observed marital matchings are stable. We apply our method to data drawn from the US Panel Study of Income Dynamics (PSID), for which we assume that similar households (in terms of observed characteristics like age or region of residence) operate on the same marriage market and are characterized by a homogeneous consumption technology. This application shows that our method yields informative results on the nature of scale economies and intrahousehold allocation patterns. In addition, it allows us to define individual compensation schemes required to preserve the same consumption level in case of marriage dissolution or spousal death.

**June 27, 2017**

t.b.a

**July 04, 2017**

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**July 11, 2017 **

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**July 18, 2017**

**Florence Nicol** (ENAC)

**July 25, 2017**

t.b.a