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Partial ML estimation for spatial autoregressive nonlinear probit models with autoregressive disturbances

ECONOMETRIC REVIEWS 2020年第5期39卷 437-475页

作者： Bille, Anna Gloria Leorato, Samantha Free Univ Bozen Bolzano Fac Econ & Management Bolzano Italy Univ Milan Dept Econ Management & Quantitat Methods Milan Italy

In this paper, we propose a Partial MLE (PMLE) for a general spatial nonlinear probit model, i.e., SARAR(1,1) probit, defined through a SARAR(1,1) latent linear model. This model encompasses both the SAE(1) probit and the more interesting SAR(1) probit models, already considered in the literature. We provide a complete asymptotic analysis of our PMLE as well as appropriate definitions of the marginal effects. Moreover, we address the issue of the choice of the groups (couples, in our case) by proposing an algorithm based on a minimum KL divergence problem. finite sample properties of the PMLE are studied through extensive Monte Carlo simulations. In particular, we consider both sparse and dense matrices for the true spatial model specifications, and cases of model misspecification given wrong assumed weighting matrices. In a real data example, we finally also compare our estimator with different MLE-based estimators and with the Bayesian approach.

关键词： Spatial autoregressive-regressive probit model nonlinear modeling SARAR partial maximum likelihood Marginal effects

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A quasi-Bayesian local likelihood approach to time varying parameter VAR models

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JOURNAL OF econometrics 2019年第1期212卷 286-306页

作者： Petrova, Katerina Univ St Andrews St Andrews Fife Scotland

The paper establishes a quasi-Bayesian local likelihood (QBLL) estimation methodology for a multivariate model with time varying parameters. The asymptotic validity of the resulting quasi-posterior distributions of the drifting parameters is proven in general and, in the special case of a Gaussian VAR model, a closed form time varying Normal-Wishart expression for the quasi-posterior distribution of the parameters is provided. In addition, this paper develops several Gibbs algorithms, which can sample from a VAR model with a mixture of time varying and time invariant parameters. The proposed estimators differ from existing state space approaches to VAR models in that they estimate parameter time variation nonparametrically, without imposing parametric stochastic processes on the parameters. The QBLL estimators are robust to misspecification of the state equation and exhibit good finite sample performance, even when compared to correctly specified parametric state space models, as illustrated by a Monte Carlo exercise. In addition, we demonstrate that the QBLL approach provides a remedy to the curse of dimensionality by accommodating large dimensional VAR systems and delivers improvements in the out-of-sample forecasts of key macroeconomic variables. Finally, the paper makes an empirical contribution to the literature on changing inflation dynamics in the U.S., presenting evidence of a fall in inflation persistence and volatility during the Great Moderation period. Crown Copyright (C) 2019 Published by Elsevier B.V. All rights reserved.

关键词： Time varying parameters Changing volatility Monetary policy Bayesian methods

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Data driven robust estimation methods for fixed effects panel data models

arXiv

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arXiv 2020年

作者： Beyaztas, Beste Hamiye Bandyopadhyay, Soutir Department of Statistics Istanbul Medeniyet University Istanbul Turkey Department of Applied Mathematics Statistics Colorado School of Mines GoldenCO United States

The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of outlying observations in panel data may often lead to biased and inefficient estimates of the model parameters resulting in unreliable inferences when the least squares (LS) method is applied. We propose extensions of the M-estimation approach with a data-driven selection of tuning parameters to achieve desirable level of robustness against outliers without loss of estimation efficiency. The consistency and asymptotic normality of the proposed estimators have also been proved under some mild regularity conditions. The finite sample properties of the existing and proposed robust estimators have been examined through an extensive simulation study and an application to macroeconomic data. Our findings reveal that the proposed methods often exhibits improved estimation and prediction performances in the presence of outliers and are consistent with the traditional LS method when there is no contamination. Copyright © 2020, The Authors. All rights reserved.

关键词： Least squares approximations

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Penalized indirect inference

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JOURNAL OF econometrics 2018年第1期205卷 34-54页

作者： Blasques, Francisco Duplinskiy, Artem Vrije Univ Amsterdam Amsterdam Netherlands Tinbergen Inst Amsterdam Netherlands Coders Co Amsterdam Netherlands

Parameter estimates of structural economic models are often difficult to interpret at the light of the underlying economic theory. Bayesian methods have become increasingly popular as a tool for conducting inference on structural models since priors offer a way to exert control over the estimation results. Similarly to Bayesian estimation, this paper proposes a penalized indirect inference estimator that allows researchers to obtain economically meaningful parameter estimates in a frequentist setting. The asymptotic properties of the estimator are established for both correctly and incorrectly specified models, as well as under strong and weak parameter identification. A Monte Carlo study reveals the role of the penalty function in shaping the finite sample distribution of the estimator. The advantages of using this estimator are highlighted in the empirical study of a state-of-the-art dynamic stochastic general equilibrium model. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Penalized estimation Indirect inference Simulation-based methods DSGE

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Best subset binary prediction

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JOURNAL OF econometrics 2018年第1期206卷 39-56页

作者： Chen, Le-Yu Lee, Sokbae Acad Sinica Inst Econ Taipei Taiwan Columbia Univ Dept Econ New York NY 10027 USA Inst Fiscal Studies Ctr Microdata Methods & Practice London England

We consider a variable selection problem for the prediction of binary outcomes. We study the best subset selection procedure by which the covariates are chosen by maximizing Manski (1975, 1985)'s maximum score objective function subject to a constraint on the maximal number of selected variables. We show that this procedure can be equivalently reformulated as solving a mixed integer optimization problem, which enables computation of the exact or an approximate solution with a definite approximation error bound. In terms of theoretical results, we obtain non-asymptotic upper and lower risk bounds when the dimension of potential covariates is possibly much larger than the sample size. Our upper and lower risk bounds are minimax rate-optimal when the maximal number of selected variables is fixed and does not increase with the sample size. We illustrate usefulness of the best subset binary prediction approach via Monte Carlo simulations and an empirical application of the work-trip transportation mode choice. (C) 2018 The Author(s). Published by Elsevier B.V.

关键词： Binary choice Maximum score estimation Best subset selection l(0)-constrained maximization Mixed integer optimization Minimax optimality finite sample property

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Inference on trending panel data

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JOURNAL OF econometrics 2018年第2期206卷 282-304页

作者： Robinson, Peter M. Velasco, Carlos London Sch Econ London England Univ Carlos III Madrid Madrid Spain

Semiparametric panel data modelling and statistical inference with fractional stochastic trends, nonparametrically time-trending individual effects, and general cross-sectional correlation and heteroscedasticity in innovations are developed. The fractional stochastic trends allow for a wide range of nonstationarity, indexed by a memory parameter, nesting the familiar 1(1) case and allowing for parametric short-memory. The individual effects can nonparametrically vary simultaneously across time and across units. The cross-sectional covariance matrix is also nonparametric. The main focus is on estimation of the time series parameters. Two methods are considered, both of which entail an only approximate differencing out of the individual effects, leaving an error which has to be taken account of in our theory. In both cases we obtain standard asymptotics, with a central limit theorem, over a wide range of possible parameter values, unlike the nonstandard asymptotics for autoregressive parameter estimates at a unit root. For statistical inference, consistent estimation of the limiting covariance matrix of the parameter estimates requires consistent estimation of a functional of the cross-sectional covariance matrix. We examine efficiency loss due to cross-sectional correlation in a spatial model example. A Monte Carlo study of finite-sample performance is included. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Semiparametric panel data modelling Nonparametrically time-trending individual effects Nonparametric cross-sectional correlation and heteroscedasticity Spatial model Parametric fractional dependence Consistency asymptotic normality

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An integrated panel data approach to modelling economic growth

arXiv

引用

arXiv 2019年

作者： Feng, Guohua Gao, Jiti Peng, Bin Department of Economics University of North Texas DentonTX76201 United States Department of Econometrics and Business Statistics Monash University Caulfield EastVIC3145 Australia Department of Economics University of Bath BathBA2 7JP United Kingdom

Empirical growth analysis has three major problems - variable selection, parameter heterogeneity and cross-sectional dependence - which are addressed independently from each other in most studies. The purpose of this study is to propose an integrated framework that extends the conventional linear growth regression model to allow for parameter heterogeneity and cross-sectional error dependence, while simultaneously performing variable selection. We also derive the asymptotic properties of the estimator under both low and high dimensions, and further investigate the finite sample performance of the estimator through Monte Carlo simulations. We apply the framework to a dataset of 89 countries over the period from 1960 to 2014. Our results reveal some cross-country patterns not found in previous studies (e.g., "middle income trap hypothesis", "natural resources curse hypothesis", "religion works via belief, not practice", etc.). Copyright © 2019, The Authors. All rights reserved.

关键词： Monte Carlo methods

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A fixed-bandwidth view of the pre-asymptotic inference for kernel smoothing with time series data

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JOURNAL OF econometrics 2017年第2期197卷 298-322页

作者： Kim, Min Seong Sun, Yixiao Yang, Jingjing Ryerson Univ Dept Econ Toronto ON Canada Univ Calif San Diego Dept Econ 9500 Gilman Dr La Jolla CA 92093 USA Univ Nevada Dept Econ Reno NV 89557 USA

This paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms. Based on the fixed-bandwidth asymptotic variance and the pre-asymptotic variance, we propose a heteroskedasticity and autocorrelation robust (HAR) variance estimator that achieves double robustness it is asymptotically valid regardless of whether the temporal dependence is present or not, and whether the kernel smoothing bandwidth is held constant or allowed to decay with the sample size. Using the HAR variance estimator, we construct the studentized test statistic and examine its asymptotic properties under both the fixed-smoothing and increasing-smoothing asymptotics. The fixed-smoothing approximation and the associated convenient t-approximation achieve extra robustness it is asymptotically valid regardless of whether the truncation lag parameter governing the covariance weighting grows at the same rate as or at a slower rate than the sample size. Finally, we suggest a simulation-based calibration approach to choose smoothing parameters that optimize testing oriented criteria. Simulation shows that the proposed procedures work very well in finite samples. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Heteroskedasticity and autocorrelation robust variance Calibration Fixed-smoothing asymptotics Fixed-bandwidth asymptotics Kernel density estimator Local polynomial estimator t-approximation Testing-optimal smoothing-parameter choice Temporal dependence

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MODEL-FREE INFERENCE FOR TAIL RISK MEASURES

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ECONOMETRIC THEORY 2016年第1期32卷 122-153页

作者： Xu, Ke-Li Texas A&M Univ College Stn TX 77843 USA

Understanding uncertainty in estimating risk measures is important in modern financial risk management. In this paper we consider a nonparametric framework that incorporates auxiliary information available in covariates and propose a family of inferential methods for the value at risk, expected shortfall, and related risk measures. A two-step generalized empirical likelihood test statistic is constructed and is shown to be asymptotically pivotal without requiring variance estimation. We also show its validity when applied to a semiparametric index model. asymptotic theories are established allowing for serially dependent data. Simulations and an empirical application to Canadian stock return index illustrate the finite sample behavior of the methodologies proposed.

关键词： STOCKS (Finance) FINANCIAL risk management econometrics SIMULATION methods & models NONPARAMETRIC estimation

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LM tests of spatial dependence based on bootstrap critical values

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JOURNAL OF econometrics 2015年第1期185卷 33-59页

作者： Yang, Zhenlin Singapore Management Univ Sch Econ Singapore Singapore

To test the existence of spatial dependence in an econometric model, a convenient test is the Lagrange Multiplier (LM) test. However, evidence shows that, in finite samples, the LM test referring to asymptotic critical values may suffer from the problems of size distortion and low power, which become worse with a denser spatial weight matrix. In this paper, residual-based bootstrap methods are introduced for asymptotically refined approximations to the finite sample critical values of the LM statistics. Conditions for their validity are clearly laid out and formal justifications are given in general, and in detail under several popular spatial LM tests using Edgeworth expansions. Monte Carlo results show that when the conditions are not fully met, bootstrap may lead to unstable critical values that change significantly with the alternative, whereas when all conditions are met, bootstrap critical values are very stable, approximate much better the finite sample critical values than those based on asymptotics, and lead to significantly improved size and power. The methods are further demonstrated using more general spatial LM tests, in connection with local misspecification and unknown heteroskedasticity. (C) 2014 Elsevier B.V. All rights reserved.

关键词： asymptotic refinements Bootstrap Edgeworth expansion LM tests Spatial dependence Size Power Local misspecification Heteroskedasticity Wild bootstrap

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