Estimating the Gini index for heavy-tailed income distributions

In the present paper, we define and study one of the most popular indices which measures the inequality of capital incomes, known as the Gini index. We construct a semiparametric estimator for the Gini index in case of heavy-tailed income distributions and we establish its asymptotic distribution and derive bounds of confidence. We explore the performance of the confidence bounds in a simulation study and draw conclusions about capital incomes in some income distributions.

Comparing Parametric, Nonparametric, and Semiparametric Estimators: The Weibull Trials

A simple example is used to show how the bias and standard error of an estimator depend in part on the type of estimator chosen from among parametric, nonparametric, and semiparametric candidates. We estimate the cumulative distribution function in the presence of missing data with and without an auxiliary variable. Simulation results mirror theoretical expectations about the bias and precision of candidate estimators. Specifically, parametric maximum likelihood estimators performed best, but must be “omnisciently” correctly specified. An augmented inverse probability weighted (IPW) semiparametric estimator performed best among candidate estimators that were not omnisciently correct. In one setting, the augmented IPW estimator reduced the standard error by nearly 30%, compared to a standard Horvitz-Thompson IPW estimator; such a standard error reduction is equivalent to doubling the sample size. These results highlight the gains and losses that may be incurred when model assumptions are made in any analysis.

Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach

We propose methods of estimating the linear-in-means model of peer effects in which the peer group, defined by a social network, is endogenous in the outcome equation for peer effects. Endogeneity is due to unobservable individual characteristics that inuence both link formation in the network and the outcome of interest. We propose two estimators of the peer effect equation that control for the endogeneity of the social connections using a control function approach. We leave the functional form of the control function unspecified, estimate the model using a sieve semiparametric approach and establish asymptotics of the semiparametric estimator.

Semiparametric efficient adaptive estimation of the GJR-GARCH model

In this paper we derive a semiparametric efficient adaptive estimator for the GJR-GARCH {(1,1)} model. We first show that the quasi-maximum likelihood estimator is consistent and asymptotically normal for the model used in analysis, and we secondly derive a semiparametric estimator that is more efficient than the quasi-maximum likelihood estimator. Through Monte Carlo simulations, we show that the semiparametric estimator is adaptive for the parameters included in the conditional variance of the GJR-GARCH {(1,1)} model with respect to the unknown distribution of the innovation.