Weighted-average Least Squares (WALS): Confidence and Prediction Intervals

Tinbergen Institute Discussion Paper 2021-038/III

d/SEAS Working Paper Forthcoming

42 Pages Posted: 10 May 2021

See all articles by Giuseppe De Luca

Giuseppe De Luca

University of Palermo - d/SEAS

J.R. Magnus

Vrije Universiteit Amsterdam, School of Business and Economics

Franco Peracchi

University of Rome Tor Vergata - Department of Economics and Finance; Einaudi Institute for Economics and Finance (EIEF)

Date Written: May 5, 2021

Abstract

We extend the results of De Luca et al. (2021) to inference for linear regression models based on weighted-average least squares (WALS), a frequentist model averaging approach with a Bayesian flavor.
We concentrate on inference about a single focus parameter, interpreted as the causal effect of a policy or intervention, in the presence of a potentially large number of auxiliary parameters representing the nuisance component of the model. In our Monte Carlo simulations we compare the performance of WALS with that of several competing estimators, including the unrestricted least-squares estimator (with all auxiliary regressors) and the restricted least-squares estimator (with no auxiliary regressors), two post-selection estimators based on alternative model selection criteria (the Akaike and Bayesian information criteria), various versions of frequentist model averaging estimators (Mallows and jackknife), and one version of a popular shrinkage estimator (the adaptive LASSO). We discuss confidence intervals for the focus parameter and prediction intervals for the outcome of interest, and conclude that the WALS approach leads to superior confidence and prediction intervals, but only if we apply a bias correction.

Keywords: post-selection estimators; adaptive lasso; frequentist model averaging; WALS; confidence intervals; prediction intervals; Monte Carlo simulations

JEL Classification: C11, C12, C18, C21, C52

Suggested Citation

De Luca, Giuseppe and Magnus, Jan R. and Peracchi, Franco, Weighted-average Least Squares (WALS): Confidence and Prediction Intervals (May 5, 2021). Tinbergen Institute Discussion Paper 2021-038/III, d/SEAS Working Paper Forthcoming, Available at SSRN: https://ssrn.com/abstract=3842430 or http://dx.doi.org/10.2139/ssrn.3842430

Giuseppe De Luca (Contact Author)

University of Palermo - d/SEAS ( email )

Viale delle Scienze, edificio 13
Palermo, 90124
Italy

Jan R. Magnus

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Franco Peracchi

University of Rome Tor Vergata - Department of Economics and Finance ( email )

Via di Tor Vergata
Rome, Lazio 00133
Italy

Einaudi Institute for Economics and Finance (EIEF) ( email )

Via Due Macelli, 73
Rome, 00187
Italy

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