The main specification in Table 2 reports the results from instrumental variables estimation of the effect of a change in social infrastructure on the log of output per worker. Four instruments are used: distance from the equator, the Frankel-Romer predicted trade share, and the fractions of the population speaking English and a European language, respectively. The point estimate indicates that a difference of .01 in social infrastructure is associated with a difference in output per worker of 5.14 percent. With a standard error of .508, this coefficient is estimated with considerable precision.

OverlD Test Coeff Test
Social p-value p-value
Specification Infrastructure Test Result Test Result <7e
1. Main Specification 5.142 .256 .812 .840
(.508) Accept Accept
Alternative Specifications to Check Robustness
2. Instruments: 4.998 .208 .155 .821
Distance, Frankel-Romer (.567) Accept Accept
3. No Imputed Data 5.323 .243 .905 .889
79 Countries (.607) Accept Accept
4. OLS 3.289 .002 .700
(.212) Reject

The second column of numbers in the table reports the result of testing the overidentifying restrictions of the model, such as the orthogonality of the error term and distance from the equator. These restrictions are not rejected. Similarly, we test for the equality of the coefficients on the two variables that make up our social infrastructure index, and this restriction is also not rejected.

The lower rows of the table show that our main result is robust to the use of a more limited set of instruments and to estimation using only the 79 countries for which we have a complete data set. In results not reported in the table, we have dropped one instrument at a time to ensure that no single instrument is driving the results. The smallest coefficient on social infrastructure obtained in this robustness check was 4.93.

Our estimate of в tells us the difference in log output per worker of a difference in some exogenous variable that leads to a difference in social infrastructure. The point estimate indicates that a difference of .01 in social infrastructure, as we measure it, is associated with a difference in output per worker of a little over 5 percent. Because we believe that social infrastructure is measured with error, we need to investigate the magnitude of the errors in order to understand this number. We need to determine how much variation there is in true, as opposed to measured, social infrastructure across countries.