The bottom half of Table 1 reports the average and standard deviation of the contribution of inputs and productivity to differences in output per worker. According to either statistic, differences in productivity across countries are substantial. A simple calculation emphasizes this point. Output per worker in the five countries in 1988 with the highest levels of output per worker was 31.7 times higher than output per worker in the five lowest countries (based on a geometric average). Relatively little of this difference was due to physical and human capital: differences in capital intensity and human capital per worker contributed factors of 1.8 and 2.2, respectively, to the difference in output per worker. Productivity, however, contributed a factor of 8.3 to this difference: with no differences in productivity, output per worker in the five richest countries would have been only about four times larger than in the five poorest countries. In this sense, differences in physical capital and educational attainment explain only a modest amount of the difference in output per worker across countries.

The reason for the lesser importance of capital accumulation is that most of the variation in capital-output ratios arises from variation in investment rates. Average investment rates in the five richest countries are only 2.9 times larger than average investment rates in the five poorest countries.

Moreover, this difference gets raised to the power a/(1 â€” a) which for a neoclassical production function with a = 1/3 is only 1/2â€”so it is the square root of the difference in investment rates that matters for output per worker. Similarly, average educational attainment in the five richest countries is about 8.1 years greater than average educational attainment in the five poorest countries, and this difference also gets reduced when converted into an effect on output: each year of schooling contributes only something like 10 percent (the Mincerian return to schooling) to differences in output per worker. Given the relatively small variation in inputs across countries and the small elasticities implied by neoclassical assumptions, it is hard to escape the conclusion that differences in productivity â€” the residual â€” play a key role in generating the wide variation in output per worker across countries.