SOME COUNTRIES PRODUCE SO MUCH MORE OUTPUT PER WORKER THAN OTHERS: Levels Accounting 2

With data on output, capital, and schooling, and knowledge of a and ф(-), one can calculate the level of productivity directly from the production function. It turns out to be convenient to rewrite the production function in terms of output per worker, y = Y/L, as
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where h = H/L is human capital per worker.

This equation allows us to decompose differences in output per worker across countries into differences in the capital-output ratio, differences in educational attainment, and differences in productivity. We follow David (1977), Mankiw et al. (1992) and Klenow and Rodriguez-Clare (1997) in writing the decomposition in terms of the capital-output ratio rather than the capital-labor ratio, for two reasons. First, along a balanced growth path, the capital-output ratio is proportional to the investment rate, so that this form of the decomposition also has a natural interpretation. Second, consider a country that experiences an exogenous increase in productivity, holding its investment rate constant. Over time, the country’s capital-labor ratio will rise as a result of the increase in productivity. Therefore, some of the increase in output that is fundamentally due to the increase in productivity would be attributed to capital accumulation in a framework based on the capital-labor ratio.

To measure productivity and decompose differences in output per worker into differences in capital intensity, human capital per worker, and productivity, we use data on output, labor input, average educational attainment, and physical capital for the year 1988.