Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach

Abstract

This paper examines the robustness of explanatory variables in cross-country economic growth regressions. It introduces and employs a novel approach, Bayesian Averaging of Classical Estimates (BACE), which constructs estimates by averaging OLS coefficients across models. The weights given to individual regressions have a Bayesian justification similar to the Schwarz model selection criterion. Of 67 explanatory variables we find 18 to be significantly and robustly partially correlated with long-term growth and another three variables to be marginally related. The strongest evidence is for the relative price of investment, primary school enrollment, and the initial level of real GDP per capita.

Variable Selection and Functional Form Uncertainty in Cross-Country Growth Regressions

“…We perform this joint treatment by extending the linear growth regression model to explicitly allow for multiple-regime parameter heterogeneity as suggested by new growth theory, while simultaneously addressing the variable selection problem by performing a Bayesian model averaging. Estimating the new models on the data set of Sala-i-Martin et al (2004) provides evidence of multiple-regime parameter heterogeneity of the type predicted by new growth theory and empirically documented by Durlauf and Johnson (1995) and Liu and Stengos (1999). In addition, we find that many of the explanatory variables indicated by the literature do not have robust marginal effects across countries when allowing for a more flexible model specification, contradicting the results of Minier (2007).…”

“…Following the tradition of the growth literature, as exemplified by Barro (1991), Levine and Renelt (1992), Sala-i-Martin et al (2004) and many others, we will consider linear regression models of the form…”

“…Similar to the analyis of Durlauf and Johnson (1995), they effectively split the sample based on explanatory variables, but instead of defining the splitting thresholds a priori they estimated them together with the regression coefficients. Using this approach, they performed Bayesian model averaging over the subset of variables found to be robustly correlated to growth by Sala-i-Martin et al (2004). Contrary to the results of Durlauf and Johnson (1995), Liu and Stengos (1999) and others they did not find much evidence for nonlinearity.…”

“…As an alternative method of providing robust inference, he proposed to instead look at the average result of the regressions, with each model receiving a weight proportional to its data likelihood. His follow-up paper (Sala-i-Martin et al, 2004) further developed this approach by deriving a new weighting method based on Bayesian model averaging. Another contribution using the concept of model averaging is Fernandez et al (2001b) who presented a similar analysis.…”

“…This ignores the fact that, through the quadratic and interaction terms, the 'robust' regressors may very well have marginal effects with different signs in different specifications, which makes her conclusions difficult to compare with the original LR results. Cuaresma and Doppelhofer (2007) extended the approach of Sala-i-Martin et al (2004) to allow for threshold effects in the model specification. Similar to the analyis of Durlauf and Johnson (1995), they effectively split the sample based on explanatory variables, but instead of defining the splitting thresholds a priori they estimated them together with the regression coefficients.…”