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.

scholarly journals A NOTE ON THE EXACT SOLUTION OF ASSET PRICING MODELS WITH HABIT PERSISTENCE

2006 ◽  
Vol 10 (2) ◽  
pp. 273-283 ◽  
Author(s):  
FABRICE COLLARD ◽  
PATRICK FÈVE ◽  
IMEN GHATTASSI
Keyword(s):  
Asset Pricing ◽  
Rational Expectation ◽  
Closed Form Solution ◽  
Autoregressive Process ◽  
Form Solution ◽  
Estimation Methods ◽  
Finite Sample ◽  
Habit Persistence ◽  
Asset Pricing Models ◽  
Finite Sample Properties

This paper provides a closed-form solution to a standard asset pricing model with habit formation when the growth rate of endowment follows a first-order Gaussian autoregressive process. We determine conditions that guarantee the existence of a stationary bounded equilibrium. The findings are useful because they allow to evaluate the accuracy of various approximation methods to nonlinear rational expectation models. Furthermore, they can be used to perform simulation experiments to study the finite sample properties of various estimation methods.

scholarly journals Inference in nonparametric/semiparametric moment equality models with shape restrictions

2020 ◽  
Vol 11 (2) ◽  
pp. 609-636
Author(s):  
Yu Zhu
Keyword(s):  
Finite Sample ◽  
Confidence Sets ◽  
Dimensional Parameter ◽  
Inference Problem ◽  
Infinite Dimensional ◽  
Ascending Auctions ◽  
Shape Restrictions ◽  
Finite Sample Properties ◽  
Us Forest Service ◽  
Shape Restriction

This paper studies the inference problem of an infinite‐dimensional parameter with a shape restriction. This parameter is identified by arbitrarily many unconditional moment equalities. The shape restriction leads to a convex restriction set. I propose a test of the shape restriction, which controls size uniformly and applies to both point‐identified and partially identified models. The test can be inverted to construct confidence sets after imposing the shape restriction. Monte Carlo experiments show the finite‐sample properties of this method. In an empirical illustration, I apply the method to ascending auctions held by the US Forest Service and show that imposing shape restrictions can significantly improve inference.

scholarly journals TRUNCATED SUM OF SQUARES ESTIMATION OF FRACTIONAL TIME SERIES MODELS WITH DETERMINISTIC TRENDS

2019 ◽  
Vol 36 (4) ◽  
pp. 751-772 ◽  
Author(s):  
Javier Hualde ◽  
Morten Ørregaard Nielsen
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Relative Strength ◽  
Sum Of Squares ◽  
Monte Carlo Experiment ◽  
Time Series Models ◽  
Finite Sample ◽  
Generalized Polynomial ◽  
Finite Sample Properties ◽  
Deterministic Components

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to nonuniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components. Finite-sample properties are illustrated by means of a Monte Carlo experiment.

scholarly journals MODELING MULTIPLE REGIMES IN FINANCIAL VOLATILITY WITH A FLEXIBLE COEFFICIENT GARCH(1,1) MODEL

2009 ◽  
Vol 25 (1) ◽  
pp. 117-161 ◽  
Author(s):  
Marcelo C. Medeiros ◽  
Alvaro Veiga
Keyword(s):  
Asymptotic Properties ◽  
Monte Carlo Experiment ◽  
Type Model ◽  
Finite Sample ◽  
Financial Volatility ◽  
Proposed Model ◽  
Multiple Regimes ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood ◽  
Errors Estimation

In this paper a flexible multiple regime GARCH(1,1)-type model is developed to describe the sign and size asymmetries and intermittent dynamics in financial volatility. The results of the paper are important to other nonlinear GARCH models. The proposed model nests some of the previous specifications found in the literature and has the following advantages. First, contrary to most of the previous models, more than two limiting regimes are possible, and the number of regimes is determined by a simple sequence of tests that circumvents identification problems that are usually found in nonlinear time series models. The second advantage is that the novel stationarity restriction on the parameters is relatively weak, thereby allowing for rich dynamics. It is shown that the model may have explosive regimes but can still be strictly stationary and ergodic. A simulation experiment shows that the proposed model can generate series with high kurtosis and low first-order autocorrelation of the squared observations and exhibit the so-called Taylor effect, even with Gaussian errors. Estimation of the parameters is addressed, and the asymptotic properties of the quasi-maximum likelihood estimator are derived under weak conditions. A Monte-Carlo experiment is designed to evaluate the finite-sample properties of the sequence of tests. Empirical examples are also considered.

scholarly journals FRACTIONAL COINTEGRATION IN STOCHASTIC VOLATILITY MODELS

2008 ◽  
Vol 24 (5) ◽  
pp. 1207-1253 ◽  
Author(s):  
Afonso Gonçalves da Silva ◽  
Peter M. Robinson
Keyword(s):  
Stochastic Volatility ◽  
Latent Variables ◽  
Factor Model ◽  
Strong Dependence ◽  
Common Factor ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Finite Sample Properties

Asset returns are frequently assumed to be determined by one or more common factors. We consider a bivariate factor model where the unobservable common factor and idiosyncratic errors are stationary and serially uncorrelated but have strong dependence in higher moments. Stochastic volatility models for the latent variables are employed, in view of their direct application to asset pricing models. Assuming that the underlying persistence is higher in the factor than in the errors, a fractional cointegrating relationship can be recovered by suitable transformation of the data. We propose a narrow band semiparametric estimate of the factor loadings, which is shown to be consistent with a rate of convergence, and its finite-sample properties are investigated in a Monte Carlo experiment.

LOCAL INSTRUMENTAL VARIABLE METHOD FOR THE GENERALIZED ADDITIVE-INTERACTIVE NONLINEAR VOLATILITY MODEL ESTIMATION

2012 ◽  
Vol 28 (3) ◽  
pp. 629-669
Author(s):  
Michael Levine ◽  
Jinguang Li
Keyword(s):  
Instrumental Variable ◽  
Estimation Method ◽  
Estimation Methods ◽  
Financial Assets ◽  
Arch Model ◽  
Instrumental Variable Estimation ◽  
Interaction Terms ◽  
Variance Functions ◽  
Volatility Model ◽  
Instrumental Variable Method

In this article we consider a new separable nonparametric volatility model that includes second-order interaction terms in both mean and conditional variance functions. This is a very flexible nonparametric ARCH model that can potentially explain the behavior of the wide variety of financial assets. The model is estimated using the generalized version of the local instrumental variable estimation method first introduced in Kim and Linton (2004, Econometric Theory 20, 1094–1139). This method is computationally more effective than most other nonparametric estimation methods that can potentially be used to estimate components of such a model. Asymptotic behavior of the resulting estimators is investigated and their asymptotic normality is established. Explicit expressions for asymptotic means and variances of these estimators are also obtained.

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.

scholarly journals ADAPTIVE LONG MEMORY TESTING UNDER HETEROSKEDASTICITY

2016 ◽  
Vol 33 (3) ◽  
pp. 755-778 ◽  
Author(s):  
David Harris ◽  
Hsein Kew
Keyword(s):  
Long Memory ◽  
Score Test ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Large Power ◽  
Finite Sample Properties ◽  
Weighted Score ◽  
Unknown Form ◽  
Arfima Model ◽  
Asymptotically Efficient

This paper considers adaptive hypothesis testing for the fractional differencing parameter in a parametric ARFIMA model with unconditional heteroskedasticity of unknown form. A weighted score test based on a nonparametric variance estimator is proposed and shown to be asymptotically equivalent, under the null and local alternatives, to the Neyman-Rao effective score test constructed under Gaussianity and known variance process. The proposed test is therefore asymptotically efficient under Gaussianity. The finite sample properties of the test are investigated in a Monte Carlo experiment and shown to provide potentially large power gains over the usual unweighted long memory test.

ON THE LACK OF POWER OF OMNIBUS SPECIFICATION TESTS

2009 ◽  
Vol 25 (1) ◽  
pp. 162-194 ◽  
Author(s):  
J. Carlos Escanciano
Keyword(s):  
Dimensional Space ◽  
Monte Carlo Experiment ◽  
Finite Dimensional Space ◽  
Local Power ◽  
Finite Sample ◽  
Specification Tests ◽  
New Information ◽  
Finite Sample Properties ◽  
Von Mises ◽  
Consistent Tests

Designed to have power against all alternatives, omnibus consistent tests are the primary econometric tools for testing the correct specification of parametric conditional means when there is no information about the possible alternative. The main purpose of this paper is to show that, contrary to what is generally believed, omnibus specification tests only have substantial local power against alternatives in a finite-dimensional space (usually unknown to the researcher). We call such a space theprincipal space. We characterize and estimate the principal space for Cramér–von Mises tests. These results are some of the by-products of a detailed theoretical power analysis carried out in the paper. This investigation focuses on the class of the so-called integrated consistent tests under possibly heteroskedastic time series. A Monte Carlo experiment examines the finite-sample properties of tests and estimators of preferred alternatives. Finally, an application of our theory to test the martingale difference hypothesis of some exchange rates provides new information on the rejection of omnibus tests and illustrates our findings.

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