On the effect of prior assumptions in Bayesian model averaging with applications to growth regression This article was published online on 30 March 2009. An error was subsequently identified. This notice is included in the online and print versions to indicate that both have been corrected l6 Apr... (original) (raw)
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Journal of Applied Econometrics, 2009
This paper examines the problem of variable selection in linear regression models. Bayesian model averaging has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. The paper analyzes the effect of a variety of prior assumptions on the inference concerning model size, posterior inclusion probabilities of regressors and on predictive performance. The analysis illustrates these issues in the context of cross-country growth regressions using three datasets with 41 to 67 potential drivers of growth and 72 to 93 observations. The results favor particular prior structures for use in this and related contexts.
2008
Abstract. We consider the problem of variable selection in linear regression models. Bayesian model averaging has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. We examine the effect of a variety of prior assumptions on the inference concerning model size, posterior inclusion probabilities of regressors and on predictive performance. We illustrate these issues in the context of cross-country growth regressions using three datasets with 41 to 67 potential drivers of growth and 72 to 93 observations. Finally, we recommend priors for use in this and related contexts.
Journal of Applied Econometrics, 2009
Bayesian model averaging (BMA) has become widely accepted as a way of accounting for model uncertainty, notably in regression models for identifying the determinants of economic growth. To implement BMA the user must specify a prior distribution in two parts: a prior for the regression parameters and a prior over the model space. Here we address the issue of which default prior to use for BMA in linear regression. We compare 12 candidate parameter priors: the Unit Information Prior (UIP) corresponding to the BIC or Schwarz approximation to the integrated likelihood, a proper data-dependent prior, and 10 priors considered by Fernandez et al. (2001b). We also compare the uniform model prior to others that favor smaller models. We compare them on the basis of crossvalidated predictive performance on a well-known growth dataset and on two simulated examples from the literature. We found that the UIP with uniform model prior generally outperformed the other priors considered. It also identified the largest set of growth determinants.
Jointness in Bayesian variable selection with applications to growth regression
Journal of Macroeconomics, 2007
We present a measure of jointness to explore dependence among regressors, in the context of Bayesian model selection. The jointness measure proposed here equals the posterior odds ratio between those models that include a set of variables and the models that only include proper subsets. We illustrate its application in cross-country growth regressions using two datasets from the model-averaging growth literature.
Unraveling the fortunes of the fortunate: An Iterative Bayesian Model Averaging (IBMA) approach
Journal of Macroeconomics, 2007
We investigate country heterogeneity in crosscountry growth regressions. In contrast to the previous literature that focuses on low-income countries, this study also highlights growth determinants in high-income (OECD) countries. We introduce Iterative Bayesian Model Averaging (IBMA) to address not only potential parameter heterogeneity, but also the model uncertainty inherent in growth regressions. IBMA is essential to our estimation because the simultaneous consideration of model uncertainty and parameter heterogeneity in standard growth regressions increases the number of candidate regressors beyond the processing capacity of ordinary BMA algorithms. Our analysis generates three results that strongly support different dimensions of parameter heterogeneity. First, while a large number of regressors can be identified as growth determinants in Non-OECD countries, the same regressors are irrelevant for OECD countries. Second, Non-OECD countries and the global sample feature only a handful of common growth determinants. Third, and most devastatingly, the long list of variables included in popular crosscountry datasets does not contain regressors that begin to satisfactorily characterize the basic growth determinants in OECD countries.
Mixtures of -priors for Bayesian model averaging with economic applications
Journal of Econometrics, 2012
This paper examines the issue of variable selection in linear regression modeling, where there is a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset. In this context, Bayesian Model Averaging presents a formal Bayesian solution to dealing with model uncertainty. The main interest here is the effect of the prior on the results, such as posterior inclusion probabilities of regressors and predictive performance. The authors combine a Binomial-Beta prior on model size with a g-prior on the coefficients of each model. In addition, they assign a hyperprior to g, as the choice of g has been found to have a large impact on the . The authors may be contacted at M.F.Steel@stats.warwick.ac.uk and eley@worldbank.org .
Mixtures of g-priors for Bayesian model averaging with economic applications
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This paper examines the issue of variable selection in linear regression modeling, where there is a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset. In this context, Bayesian Model Averaging presents a formal Bayesian solution to dealing with model uncertainty. The main interest here is the effect of the prior on the results, such as posterior inclusion probabilities of regressors and predictive performance. The authors combine a Binomial-Beta prior on model size with a g-prior on the coefficients of each model. In addition, they assign a hyperprior to g, as the choice of g has been found to have a large impact on the . The authors may be contacted at M.F.Steel@stats.warwick.ac.uk and eley@worldbank.org .
Journal of Applied Econometrics, 2008
This paper takes a fresh look into Africa's dismal growth performance by using the Bayesian Model Averaging (BMA) methodology. We estimate the posterior probability of a large number of potential explanatory variables and cross-country regression models. In large, we find that determinants of growth in Africa are strikingly different from the rest of the world. In addition, growth regression models that best explain global growth do poorly in explaining African growth, and conversely.
Bayesian Model Averaging and Forecasting
2011
This paper focuses on the problem of variable selection in linear regression models. I briefly review the method of Bayesian model averaging, which has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. Some of the literature is discussed with particular emphasis on forecasting in economics. The role of the prior assumptions in these procedures is highlighted, and some recommendations for applied users are given.
8. Bayesian model averaging and forecasting
This paper focuses on the problem of variable selection in linear regression models. I briefly review the method of Bayesian model averaging, which has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. Some of the literature is discussed with particular emphasis on forecasting in economics. The role of the prior assumptions in these procedures is highlighted, and some recommendations for applied users are given.