I Just Ran Two Million Regressions

I Just Ran Two Million Regressions

MAY 1997 | XAVIER X. SALA-I-MARTIN
Xavier Sala-i-Martin's paper, "I Just Ran Two Million Regressions," addresses the issue of identifying robust variables correlated with economic growth. Building on Robert Barro's seminal work, Sala-i-Martin reviews the empirical literature that has identified numerous variables related to growth. However, the challenge lies in determining which variables are truly significant, as growth theories often lack clarity on the "true" regression model. Sala-i-Martin critiques the extreme-bounds test proposed by Ross Levine and David Renelt, which concludes that few variables are robustly correlated with growth. He argues that this conclusion may be due to the test's stringent criteria or the inherent variability in the data. To address this, Sala-i-Martin proposes a more nuanced approach that assigns a level of confidence to each variable rather than labeling them as "robust" or "nonrobust." The paper outlines two cases for computing the cumulative distribution function (CDF) of the estimated coefficients: when the distribution is normal and when it is not. In the normal case, the mean and variance of the distribution are used to compute the CDF. In the nonnormal case, the individual CDFs from each regression are weighted by the likelihoods to form the aggregate CDF. Sala-i-Martin estimates 30,856 regressions, totaling nearly 2 million, using 62 variables, including three fixed variables (initial income, life expectancy, and primary school enrollment) and 59 tested variables. He finds that 22 out of 59 variables are significantly correlated with growth, including regional, political, and religious factors. Notably, measures of government spending, financial sophistication, and various economic indicators do not show significant effects. The paper concludes that a substantial number of variables can be strongly related to growth, contrary to the pessimistic conclusion of the extreme-bounds analysis. This suggests that the empirical growth literature is more informative and robust than previously thought.Xavier Sala-i-Martin's paper, "I Just Ran Two Million Regressions," addresses the issue of identifying robust variables correlated with economic growth. Building on Robert Barro's seminal work, Sala-i-Martin reviews the empirical literature that has identified numerous variables related to growth. However, the challenge lies in determining which variables are truly significant, as growth theories often lack clarity on the "true" regression model. Sala-i-Martin critiques the extreme-bounds test proposed by Ross Levine and David Renelt, which concludes that few variables are robustly correlated with growth. He argues that this conclusion may be due to the test's stringent criteria or the inherent variability in the data. To address this, Sala-i-Martin proposes a more nuanced approach that assigns a level of confidence to each variable rather than labeling them as "robust" or "nonrobust." The paper outlines two cases for computing the cumulative distribution function (CDF) of the estimated coefficients: when the distribution is normal and when it is not. In the normal case, the mean and variance of the distribution are used to compute the CDF. In the nonnormal case, the individual CDFs from each regression are weighted by the likelihoods to form the aggregate CDF. Sala-i-Martin estimates 30,856 regressions, totaling nearly 2 million, using 62 variables, including three fixed variables (initial income, life expectancy, and primary school enrollment) and 59 tested variables. He finds that 22 out of 59 variables are significantly correlated with growth, including regional, political, and religious factors. Notably, measures of government spending, financial sophistication, and various economic indicators do not show significant effects. The paper concludes that a substantial number of variables can be strongly related to growth, contrary to the pessimistic conclusion of the extreme-bounds analysis. This suggests that the empirical growth literature is more informative and robust than previously thought.
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