To examine the quantitative importance of differences in social infrastructure as determinants of incomes across countries, we hypothesize the following structural model:

where S denotes social infrastructure and X is a collection of other variables.

Several features of this framework deserve comment. First, we recognize explicitly that social infrastructure is an endogenous variable. Economies are not exogenously endowed with the institutions and incentives that make up their economic environments, but rather social infrastructure is determined endogenously, perhaps depending itself on the level of output per worker in an economy. Such a concern arises not only because of the general possibility of feedback from the unexplained component of output per worker to social infrastructure, but also from particular features of our measure of social infrastructure. For example, poor countries may have limited ability to collect taxes and may therefore be forced to interfere with international trade. Alternatively, one might be concerned that the experts at Political Risk Services who constructed the components of the GADP index were swayed in part by knowledge of income levels.
Second, our specification for the determination of incomes in equation (4) is parsimonious, reflecting our hypothesis that social infrastructure is the primary and fundamental determinant of output per worker. We allow for a rich determination of social infrastructure through the variables in the X matrix. Indeed, we will not even attempt to describe all of the potential determinants of social infrastructure — we will not estimate equation (5) of the structural model. The heart of our identifying assumptions is the restriction that the determinants of social infrastructure affect output per worker only through social infrastructure and not directly. We test the exclusion below.

Our identifying scheme includes the assumption that EX’e = 0. Under this assumption, any subset of the determinants of social infrastructure constitute valid instruments for estimation of the parameters in equation (4). Consequently, we do not require a complete specification of that equation. We will return to this point in greater detail shortly.

Finally, we augment our specification by recognizing, as discussed in the previous section, that we do not observe social infrastructure directly. Instead, we observe a proxy variable S computed as the sum of GADP and the openness variable, normalized to a [0,1] scale. This proxy for social infrastructure is related to true social infrastructure through random measurement error:
where v is the measurement error, taken to be uncorrelated with S and X. Without loss of generality, we normalize ф = 1; this is an arbitrary choice of units since S is unobserved. Therefore,

The coefficient в will be identified by the orthogonality conditions EX’e = 0. Therefore, both measurement error and endogeneity concerns are addressed. The remaining issue to discuss is how we obtain valid instruments for GADP and our openness measure.