2011
DOI: 10.2139/ssrn.1894610
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Bayesian Model Averaging and Weighted Average Least Squares: Equivariance, Stability, and Numerical Issues

Abstract: This article is concerned with the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals which implement, respectively, the exact Bayesian Model Averaging (BMA) estimator and the Weighted Average Least Squares (WALS) estimator developed by Magnus et al. (2010). Unlike standard pretest estimators which are based on some preliminary diagnostic test, these model averaging estimators provide a coherent way of making infer… Show more

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Cited by 23 publications
(14 citation statements)
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“…Keeping the institutional indicators as the focus parameters for the analysis, Bayesian averaging was conducted first on all regressors (focus and auxiliary) over a space of 2,097,152 possible models (1,048,576 possible models for each of the ROA and ROE specifications). The criterion for determining robust correlation with the outcome variable for the auxiliary regressors was suggested by De Luca and Magnus (2011), and involves retaining auxiliary variables which have an absolute value of t-ratios over 1 (which also satisfies the criteria that their two standard error confidence intervals do not include zero). This approach avoids the ad hoc rule of thumb of Kass and Wasserman (1995), which removes Bweak^variables (i.e.…”
Section: Baseline Specificationsmentioning
confidence: 99%
See 1 more Smart Citation
“…Keeping the institutional indicators as the focus parameters for the analysis, Bayesian averaging was conducted first on all regressors (focus and auxiliary) over a space of 2,097,152 possible models (1,048,576 possible models for each of the ROA and ROE specifications). The criterion for determining robust correlation with the outcome variable for the auxiliary regressors was suggested by De Luca and Magnus (2011), and involves retaining auxiliary variables which have an absolute value of t-ratios over 1 (which also satisfies the criteria that their two standard error confidence intervals do not include zero). This approach avoids the ad hoc rule of thumb of Kass and Wasserman (1995), which removes Bweak^variables (i.e.…”
Section: Baseline Specificationsmentioning
confidence: 99%
“…This approach avoids the ad hoc rule of thumb of Kass and Wasserman (1995), which removes Bweak^variables (i.e. those with a posterior inclusion probability of 0.5-0.75, see Eicher et al 2011), but has less predictive power than the Bmedian^model used by De Luca and Magnus (2011).…”
Section: Baseline Specificationsmentioning
confidence: 99%
“…As stressed by De Luca and Magnus (2012) standard econometric practice of using the same data for model selection (the choice of explanatory variables) and estimating -while ignoring that the resulting estimators are in fact pretest estimators -leads to false inference, since traditional statistical test theory is not directly applicable. Approaches to deal with this difficulty is the "extreme bounds analysis" (see Sturm and de Haan 2005;Hartwig and Sturm 2012) and the "Bayesian model averaging" (BMA) technique within a linear regression model (see Magnus et al 2010, andDe Luca andMagnus 2011). Here, the BMA technique is applied.…”
Section: _________________________mentioning
confidence: 99%
“…Thirdly, the number of potential predictors can be large, and this raises a serious statistical problem for model selection strategy. In the midst of uncertainty about the choice of the predictor variables to be included in the model, care should be To overcome this problem, model averaging techniques have been introduced (see Magnus and Durbin (1999); Danilov and Magnus (2004); Magnus, Powell and Prüfer (2010); De Luca, Giuseppe and Magnus (2011)). These techniques are unlike standard model estimators that are based on some pre-tests and post-tests for model estimation, thus, the techniques have a coherent way of making inference on the regression parameters of interests by taking into account the uncertainty due to both the estimation and the model selection steps.…”
Section: Introductionmentioning
confidence: 99%