$3600 to $4900 per capita range and then decline, with no commodity group peaking beyond $7000 per capita. This evidence suggests that although discovery might be part and parcel of the process of productive diversification, it does not seem to be a byproduct of shifting comparative advantage.

# _<Insert Table 3 here>_

One relationship that would seem important to control for in our test of the market failure hypothesis is scale. While not explicitly entering our model, it is possible that with a larger population, there would be a larger pool of entrepreneurs, leading to more experiments and a higher frequency of discovery. It is also possible that a larger pool of imitators, although increasing the social value of discovery, would reduce incentives for individual entrepreneurs to experiment, resulting in a lower frequency of discovery. Scale variables such as total population, working-age population, and number of person-years of education in the country were not found to be statistically significant in any test of our model, which is discussed in the following paragraphs.<sup>7</sup>

# _Testing the Model_

As motivated in section 2, our model serves as a test of the market failure hypothesis by examining how the relationship between the frequency of discovery, _D_ , and the returns to discovery, ~~π~~ , changes with barriers to entry, _α_ . As a measure of barriers to entry, we use a set of objective indicators rather than subjective surveys. These indicators are drawn from the World Bank’s _Doing Business_ database (World Bank 2004). Although only available for 2003, these are the best measures available of _α_ , and it is unlikely that the regulatory regime changed significantly during the sample period. Rather than arbitrarily selecting a single indicator, we construct an index based on five of them, encompassing costs and delays in starting a new business, enforcing contracts, and hiring employees. The indicators for registering a new business would be most appropriate if discovery is undertaken by new entrepreneurs, whereas the measures of labor-market rigidities would be most appropriate if discovery is the work of existing firms. It is not clear which is the case, which could also vary by country and by industry. Moreover, all these regulatory measures are highly collinear. A composite index of these variables is consequently the most appropriate measure, which we construct using principal components analysis. Nevertheless, the quality of the data corresponding to the variable on the costs of starting a new business across countries is notoriously weak. Consequently we test the robustness of our results reported below to the exclusion of that factor in the composite index.<sup>8</sup> Our measure of exogenous returns to export discoveries ( ~~π~~ ) is the annual growth of exports of the Leamer commodity export basket, excluding export goods identified as discoveries, minus the annual growth rate of non-export GDP. The growth of non-export GDP is netted out of our measure so that it more directly captures the returns to exports

> 7 Nor were measures of financial system development, initial exports, institutional quality, or infrastructure. 8 We thank Caroline Freund for pointing this out.

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