The other important characteristic of an instrument is lack of correlation with the disturbance e. To satisfy this criterion, we must ask if European influence was somehow more intensively targeted toward regions of the world that are more likely to have high output per worker today. In fact, this does not seem to be the case. On the one hand, Europeans did seek to conquer and exploit areas of the world that were rich in natural resources such as gold and silver or that could provide valuable trade in commodities such as sugar and molasses. There is no tendency today for these areas to have high output per worker.

On the other hand, European influence was much stronger in areas of the world that were sparsely settled at the beginning of the 16th century, such as the United States, Canada, Australia, New Zealand, and Argentina. Presumably, these regions were sparsely settled at that time because the land was not especially productive given the technologies of the 15th century. For these reasons, it seems reasonable to assume that our measures of Western European influence are uncorrelated with e.

We measure distance from the equator as the absolute value of latitude in degrees divided by 90 to place it on a 0 to 1 scale.16 It is widely known that economies further from the equator are more successful in terms of per capita income. For example, Nordhaus (1994) and Theil and Chen (1995) examine closely the simple correlation of these variables. However, the explanation for this correlation is far from agreed upon. Kamarck (1976) emphasizes a direct relationship through the prevalence of disease and the presence of a highly variable rainfall and inferior soil quality. We will postulate that the direct effect of such factors is small and impose the hypothesis that the effect is zero — hence distance from the equator is not included in equation (4). Because of the presence of overidentifying restrictions in our framework, however, we are able to test this hypothesis, and we do not reject it, either statistically or economically, as discussed later in the paper.