A simple calculation indicates that the ratio of standard deviations given in equation (11) is the correlation between measured and true social infrastructure, which we will denote rs s. Therefore, a lower bound on the correlation between measured and true social infrastructure provides a lower bound on as. It is our belief, based on comparing the data in Figure 2 to our priors, that the R2 or squared correlation between true and measured social infrastructure is no smaller than 0.5. This implies a lower bound on rs s of у/Л = .707.

With these numbers in mind, we will consider the implications of our estimate of /3iv = 5.14. Measured social infrastructure ranges from a low value of 0.1127 in Zaire to a high value of 1.0000 in Switzerland. Ignoring measurement error, the implied range of variation in output per worker would be a factor of 95, which is implausibly high. We can apply the ratio rs s = as/ag to get a reasonable estimate of the range of variation of true social infrastructure. The lower bound on this range implied by rs s = .707 suggests that differences in social infrastructure can account for a 25.2-fold difference in output per worker across countries. Alternatively, if there is no true endogeneity so that r§ s = .800, differences in social infrastructure imply a 38.4-fold difference in output per worker across countries. For comparison, recall that output per worker in the richest country (the United States) and the poorest country (Niger) in our data set differ by a factor of 35.1.

We conclude that our results indicate that differences in social infrastructure account for much of the difference in long-run economic performance throughout the world, as measured by output per worker. Countries most influenced by Europeans in past centuries have social infrastructures conducive to high levels of output per worker, as measured by our variables, and, in fact, have high levels of output per worker. Under our identifying assumptions, this evidence means that infrastructure is a powerful causal factor promoting higher output per worker.