Nonlinearities and Robustness in Growth Regressions

Abstract

Much economic growth research has been devoted to determining the explanatory variables that explain cross-country variation in growth rates. A frequently cited problem with this literature is that the number of potential growth regressors is vast, potentially exceeding the number of countries available for study. Thus, researchers are faced with the task of arbitrarily specifying which explanatory variables to include in their growth regressions, raising concerns about how confident we can be in their results. These concerns were magnified by the influential paper of Ross Levine and David Renelt (1992), in which they employ a variation of Edward E. Leamer's (1983) extreme bounds analysis to test the robustness of conventional growth regression coefficients to changes in the set of conditioning variables. They conclude that the results of this literature are extremely fragile, with the only robust determinants of growth being physical capital investment, initial income, and secondary school enrollment. In contrast, they demonstrate the fragility of a host of fiscal, monetary, and trade policy variables, as well as measures of political and economic stability and economic distortions.There have been two main responses to their findings. The pessimistic response has been to conclude, given the lack of a reliable statistical relationship between conventional macroeconomic indicators and growth, that cross-country growth regressions cannot tell us anything about growth. The more optimistic response has been to argue that the extreme bounds analysis of Leamer (1983) is excessively stringent, requiring the coefficient estimate of interest to be statistically significant in all specifications. Thus, other researchers have proposed alternative, less stringent, approaches to robustness in the growth context (e.g., Xavier X. Sala-iMartin (1997) andGernot Doppelhofer, Ronald I. Miller, andSala-i-Martin (2004)).

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

“…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). Our results offer some new insights into the form of the parameter heterogeneity in the growth data and we discuss its connection to phenomena like the natural resources curse.…”

“…Most recent work on growth regressions has focused on the selection of explanatory variables to include in this model (Fernandez et al (2001b), Sala-i-Martin et al (2004)) or on the specification of countryspecific parameters (Kalaitzidakis et al (2000), Minier (2007), Paap et al (2005), Basturk et al (2010), Maasoumi et al (2007)). A rigorous regression analysis of cross-country growth data should simultaneously take into account both of these sources of uncertainty.…”

“…Indeed, the majority of the literature dealing with these issues in growth regressions builds on the Bayesian framework (e.g. Levine and Renelt (1992), Sala-i-Martin (1997), Fernandez et al (2001b), Sala-i-Martin et al (2004), Minier (2007) and many others).…”

“…To the author's knowledge, Minier (2007) and Cuaresma and Doppelhofer (2007) are the only attempts to date at combining both sources of uncertainty in an analysis. Minier (2007) investigated the influence of nonlinearities in the fragile variables of LR by repeating their analysis, but subsequently introducing quadratic and interaction terms into the specification as well as allowing for different growth regimes by splitting the sample according to initial conditions.…”

“…Minier (2007) investigated the influence of nonlinearities in the fragile variables of LR by repeating their analysis, but subsequently introducing quadratic and interaction terms into the specification as well as allowing for different growth regimes by splitting the sample according to initial conditions. By doing so, several more variables relating to fiscal policy appeared robust in her specification compared to the original LR analysis.…”