Assuming the U.S. chooses the physical productivity of skilled labour relative to unskilled labour, as in (4.6), I can compute levels of the physical productivity and quality of skilled labour for all other countries. The U.S. level of physical produc- tivity, µU.S., equals .99. This is interpreted as saying that 99% of all machines in
the U.S. are complementary with skilled workers. The result makes intuitive sense because we expect that almost all machines in the U.S. have to be complementary with skilled workers since almost all workers in the U.S. are skilled under the primary-completed definition. This is especially true since the U.S. is considered the world technology leader.
I find that the physical productivity and human capital embodied in skilled workers increases with per-capita income. Furthermore, the basic finding that skilled workers are relatively more productive in high income countries in Caselli and Coleman (2006) remains true after accounting for differences in embodied human capital. However, the gap in physical productivities across countries is now smaller, because some of the differences in the relative productivity of skilled workers is now accounted for by differences in embodied human capital.
Figure 4.1: Physical Productivity of Skilled Workers and Output (Primary)
Figure 4.1 plots the physical productivity of skilled workers,µj, against output
and unskilled workers (1.4, 1.2, 1.6, 1.8). It is clear that for all plausible values of the elasticity of substitution, the physical productivity of skilled workers, rel- ative to unskilled workers increases with output. High-income countries tend to adopt proportionally more machines which are complementary with skilled work- ers, and low-income countries adopt proportionally more machines complementary with unskilled labour. This result goes against the common idea that low-income countries may be unproductive because they adopt machines complementary with skilled workers, but not the unskilled workers who are abundant in these coun- tries. All countries do not adopt the same production techniques, and Caselli and Wilson (2004) provide evidence that types of machines imported in different coun- tries varies with skill level.
Figure 4.2: Embodied Human Capital and Output (Primary)
The estimates also show that the human capital embodied in skilled workers is higher in high-income countries. Figure 4.2 plots (the log of) embodied human capital against the log of output. Again, for all plausible values of the elasticity of substitution, embodied human capital is increasing in output. Thus high-income countries have better skilled labour quality, and use production techniques which make skilled workers relatively more productive.
Estimates of physical productivity and embodied human capital increase with income, because if physical productivities and embodied human capital are as- sumed to be the same across countries, (4.3) predicts very low skill premiums in high-income countries. To match observed skill premiums, the model implies that skill-abundant (high-income) countries must have more embodied human capital, or be relatively more physically productive with skilled workers. Recall that for
4.4. RESULTS 105 any given country, the human capital embodied in its skilled workers is chosen to match the estimate of the skill premium of its natives who are living in the U.S. Then the physical productivity of its skilled workers is chosen to the match the average skill-premium in that country, given embodied human capital.
In order to match higher skill premiums for immigrants from high-income countries, it must be that they have more embodied human capital. However, the higher human capital embodied in skilled workers from high-income countries does not completely explain why observed skill premiums in high-income (skill- abundant) countries are high. Hence, to match the average skill premium in these countries, it must be that the relative physical productivity of skilled workers is also higher. This explains why the data implies that the physical productivity and human capital embodied in skilled workers must be increasing with output. Fig- ures 4.11 and 4.12 show the same results for the secondary-completed definition of skilled.
It is interesting that rich countries have higher proportions of skilled workers, use skilled workers more physically productively relative to unskilled workers, and also have a higher quality of skilled workers. One might expect that the quality and quantity of skilled workers may be substitutes, or that the relative physical productivity of skilled workers may be substitutable with worker quality. These results call for a framework for understanding why the quantity, quality, and physical productivity of skilled workers are all complementary and increase with income.
At this stage, one might wonder whether the estimates of embodied human capital and physical productivities are consistent with other data. In order to test the validity of the model in terms of skill premiums, I investigate how the results match observed skill premiums for immigrants from different countries in Canada. I compute predicted skill premiums for natives of different countries living in Canada using estimates of the relative physical productivity of skilled workers and the observed skilled-unskilled labour ratio in Canada, combined with estimates of the human capital embodied in skilled workers for natives of different countries. The predicted skill premiums are then compared to those estimated from the data taken from Schoellman (2012).
The results are displayed in Figure 4.3 for all 3 definitions of skilled labour. The Figure plots predicted skill premiums against those estimated from the data, using an elasticity of substitution equal to 1.4. For all countries for which there are estimates of the skill premium in both Canada and the U.S., the model does a very good job of matching observed skill premiums in Canada, with Poland being an exception.21 The correlation coefficient is around .85 for all 3 definitions of skilled labour, and does not vary greatly using different elasticities of substitution. I believe this speaks to the validity of using (4.3) as a model of skill premiums across countries, and also the validity of using returns to education for natives of
21The skill premium does not exactly match observed returns for native-born Canadians in
Canada, because the physical productivity of skilled workers was chosen to match average returns in Canada.
different countries residing in a given country in order to understand differences in skilled labour quality.
Figure 4.3: Predicted Skill Premiums in Canada
Clockwise: Primary, Secondary, College