6,059 research outputs found
Weighted-average least squares: Beyond the classical linear regression model
No full textThis paper introduces four new commands for the weighted-average least squares approach to model uncertainty: the hetwals command fits linear models with multiplicative forms of heteroskedasticity; the ar1wals command fits linear models with stationary AR(1) errors; the xtwals command fits fixed-effects and random-effects panel-data models with either i.i.d. or AR(1) idiosyncratic errors; while the glmwals command fits univariate generalized linear models. These commands extend the new functionalities of the wals command (version 3.0) introduced by De Luca and Magnus (2025a), and enlarge the classes of models that can be fitted by this model-averaging method. We also provide an illustration of the hetwals and glmwals commands by means of real data applications
Weighted-average least squares: Improvements and extensions
No full textThis paper presents version 3.0 of the wals command, which implements the weighted-average least squares estimator of Magnus et al. (2010, Journal of Econometrics 154, 139–153). Version 3.0 improves earlier versions of wals in several respects: a new syntax supporting factor variables, time-series operators, and weights; an enlarged set of prior distributions; extended quadrature methods for computing the posterior mean; new plug-in estimates of the sampling moments; simulation-based confidence intervals; and other options to control accuracy, computational speed, and output of wals. We also offer three new post-estimation commands: the predict command associated with wals; the lcwals command for estimating linear combinations of the parameters; and the margwals command for estimating smooth, possibly nonlinear, functions of the parameters at given values of regressors. Finally, we compare our new commands with two suites of Stata commands for tackling issues of model uncertainty
Weighted-average least squares estimation of generalized linear models
No full textThe weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model-averaging estimators when accounting for problems of uncertainty in the choice of the regressors. In this paper we extend the WALS approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models (GLMs). We study the large-sample properties of the WALS estimator for GLMs under a local misspecification framework, and the finite-sample properties of this estimator by a Monte Carlo experiment the design of which is based on a real empirical analysis of attrition in the first two waves of the Survey of Health, Aging and Retirement in Europe (SHARE)
Comments on “Unobservable Selection and Coefficient Stability: Theory and Evidence” and “Poorly Measured Confounders are More Useful on the Left Than on the Right”
No full textAbstract–: We establish a link between the approaches proposed by Oster (2019) and Pei, Pischke, and Schwandt (2019) which contribute to the development of inferential procedures for causal effects in the challenging and empirically relevant situation where the unknown data-generation process is not included in the set of models considered by the investigator. We use the general misspecification framework recently proposed by De Luca, Magnus, and Peracchi (2018) to analyze and understand the implications of the restrictions imposed by the two approaches
Weak versus strong dominance of shrinkage estimators
Full text linkWe consider the estimation of the mean of a multivariate normal distribution with known variance. Most studies consider the risk of competing estimators, that is the trace of the mean squared error matrix. In contrast we consider the whole mean squared error matrix, in particular its eigenvalues. We prove that there are only two distinct eigenvalues and apply our findings to the James-Stein and the Thompson class of estimators. It turns out that the famous Stein paradox is no longer a paradox when we consider the whole mean squared error matrix rather than only its trace
On the sensitivity of the usual t- and F-tests to covariance misspecification
No full textWe consider the standard linear regression model with all standard assumptions, except that the disturbances are not white noise, but distributed N(0, ?2?(?)) where ?(0)=In. Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are not interested in finding out whether ?=0 or not. Instead we want to find out what the effect is of possibly nonzero ? on the F-statistic itself. We propose a sensitivity statistic small phi, Greek for this purpose, discuss its distribution, and obtain a practical and easy-to-use decision rule to decide whether the F-test is sensitive or not to covariance misspecification when ? is close to zero. Some finite and asymptotic properties of curly or open small phi, Greek are studied, as well as its behaviour in the special case of an AR(1) process near the unit roo
Shrinkage efficiency bounds: An extension
Full text linkHansen (2005) obtained the efficiency bound (the lowest achievable
risk) in the p-dimensional normal location model when p≥3, generalizing an
earlier result of Magnus (2002) for the one-dimensional case (p=1). The classes
of estimators considered are, however, different in the two cases. We provide
an alternative bound to Hansen's which is a more natural generalization of the
one-dimensional case, and we compare the classes and the bounds
Weighted-Average Least Squares Estimation of Panel Data Models
No full textThis paper extends the weighted-average least squares (WALS) model averaging estimator to fixed-effects and random-effects panel data models with strictly exogenous regressors. We consider both the case where the errors are independent and identically distributed, and the case with first-order autocorrelation
Sampling properties of the Bayesian posterior mean with an application to WALS estimation
Full text linkMany statistical and econometric learning methods rely on Bayesian ideas. When applied in a frequentist setting, their precision is often assessed using the posterior variance. This is permissible asymptotically, but not necessarily in finite samples. We explore this issue focusing on weighted-average least squares (WALS), a Bayesian-frequentist `fusion'. Exploiting the sampling properties of the posterior mean in the normal location model, we derive estimators of the
finite-sample bias and variance of WALS. We study the performance of the proposed estimators in an empirical application and a closely related Monte Carlo experiment which analyze the impact of legalized abortion on crime
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