Our discussion starts from the premise that true simultaneity results in a positive correlation between the disturbance in our structural equation and social infrastructure. Recall that our system is:

Correlation of S with e arises from two sources. One is feedback controlled by the parameter 5. Provided the system satisfies the stability condition 5в < 1, a positive value of 5 implies that e is positively correlated with S. As we noted earlier, the natural assumption is that 5 is non-negative, since social infrastructure requires some resources to build, and log Y/L measures those resources.

The second source of correlation of S with e is correlation of n with e. Again, it would appear plausible that countries with social infrastructure above the level of the second structural equation would tend to be the same countries that had output per worker above the first structural equation. Thus, both sources of correlation appear to be non-negative.

On the other hand, as the reduced-form equation for S shows, measured social infrastructure is unambiguously positively correlated with the measurement error, v. Hence there is a negative correlation between S and the part of the disturbance in the first structural equation arising from measurement error, — ev.