scholarly journals INFERENCE IN INSTRUMENTAL VARIABLE MODELS WITH HETEROSKEDASTICITY AND MANY INSTRUMENTS

2020 ◽  
pp. 1-30
Author(s):  
Federico Crudu ◽  
Giovanni Mellace ◽  
Zsolt Sándor
Keyword(s):  
Simulation Study ◽  
Instrumental Variable ◽  
Finite Sample ◽  
Parameter Vector ◽  
Chi Square ◽  
Weak Instruments ◽  
Extensive Simulation ◽  
Many Instruments ◽  
Type Test ◽  
Finite Sample Properties

This paper proposes novel inference procedures for instrumental variable models in the presence of many, potentially weak instruments that are robust to the presence of heteroskedasticity. First, we provide an Anderson–Rubin-type test for the entire parameter vector that is valid under assumptions weaker than previously proposed Anderson–Rubin-type tests. Second, we consider the case of testing a subset of parameters under the assumption that a consistent estimator for the parameters not under test exists. We show that under the null, the proposed statistics have Gaussian limiting distributions and derive alternative chi-square approximations. An extensive simulation study shows the competitive finite sample properties in terms of size and power of our procedures. Finally, we provide an empirical application using college proximity instruments to estimate the returns to education.

Kernel Based Estimation for a Non-Homogeneous Poisson Processes

2013 ◽  
Vol 805-806 ◽  
pp. 1948-1951
Author(s):  
Tian Jin
Keyword(s):  
Air Pollution ◽  
Nonparametric Estimation ◽  
Simulation Study ◽  
Poisson Model ◽  
Poisson Processes ◽  
Finite Sample ◽  
Process Data ◽  
Homogeneous Poisson Process ◽  
Finite Sample Properties ◽  
Non Homogeneous Poisson Process

The non-homogeneous Poisson model has been applied to various situations, including air pollution data. In this paper, we propose a kernel based nonparametric estimation for fitting the non-homogeneous Poisson process data. We show that our proposed estimator is-consistent and asymptotically normally distributed. We also study the finite-sample properties with a simulation study.

scholarly journals Nonparametric Instrumental-Variable Estimation

2018 ◽  
Vol 18 (4) ◽  
pp. 937-950 ◽  
Author(s):  
Denis Chetverikov ◽  
Dongwoo Kim ◽  
Daniel Wilhelm
Keyword(s):  
Instrumental Variable ◽  
Estimation Methods ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Gasoline Demand ◽  
Tuning Parameters ◽  
Demand Functions ◽  
Instrumental Variable Estimation ◽  
Finite Sample Properties ◽  
Shape Restriction

In this article, we introduce the commands npiv and npivcv, which implement nonparametric instrumental-variable (NPIV) estimation methods without and with a cross-validated choice of tuning parameters, respectively. Both commands can impose the constraint that the resulting estimated function is monotone. Using such a shape restriction may significantly improve the performance of the NPIV estimator (Chetverikov and Wilhelm, 2017, Econometrica 85: 1303–1320) because the ill-posedness of the NPIV estimation problem leads to unconstrained estimators that suffer from particularly poor statistical properties such as high variance. However, the constrained estimator that imposes the monotonicity significantly reduces variance by removing nonmonotone oscillations of the estimator. We provide a small Monte Carlo experiment to study the estimators’ finite-sample properties and an application to the estimation of gasoline demand functions.

Many instruments: Implementation in Stata

2019 ◽  
Vol 19 (4) ◽  
pp. 849-866
Author(s):  
Stanislav Anatolyev ◽  
Alena Skolkova
Keyword(s):  
Instrumental Variables ◽  
Instrumental Variable ◽  
Simulation Experiment ◽  
Real Data ◽  
Projection Matrix ◽  
Consistent Estimation ◽  
Specification Tests ◽  
Weak Instruments ◽  
Many Instruments

In recent decades, econometric tools for handling instrumental-variable regressions characterized by many instruments have been developed. We introduce a command, mivreg, that implements consistent estimation and testing in linear instrumental-variables regressions with many (possibly weak) instruments. mivreg covers both homoskedastic and heteroskedastic environments, estimators that are both nonrobust and robust to error nonnormality and projection matrix limit, and parameter tests and specification tests both with and without correction for existence of moments. We also run a small simulation experiment using mivreg and illustrate how mivreg works with real data.

scholarly journals Distributional consistency of the lasso by perturbation bootstrap

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 957-964
Author(s):  
Debraj Das ◽  
S N Lahiri
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Bootstrap Method ◽  
Estimation Procedure ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Lasso Estimator

Summary The lasso is a popular estimation procedure in multiple linear regression. We develop and establish the validity of a perturbation bootstrap method for approximating the distribution of the lasso estimator in a heteroscedastic linear regression model. We allow the underlying covariates to be either random or nonrandom, and show that the proposed bootstrap method works irrespective of the nature of the covariates. We also investigate finite-sample properties of the proposed bootstrap method in a moderately large simulation study.

scholarly journals SUP-TESTS FOR LINEARITY IN A GENERAL NONLINEAR AR(1) MODEL

2009 ◽  
Vol 26 (4) ◽  
pp. 965-993 ◽  
Author(s):  
Christian Francq ◽  
Lajos Horvath ◽  
Jean-Michel Zakoïan
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Null Hypothesis ◽  
Nuisance Parameter ◽  
Time Series Models ◽  
Ratio Test ◽  
Finite Sample ◽  
Chi Square ◽  
Finite Sample Properties ◽  
Linearity Testing

We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the likelihood ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite-sample properties of the sup-tests are studied by simulations.

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