About two months ago, I wrote a post about the weird lack of economic convergence in the G7 -- Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States. Neoclassical growth theory suggests that countries with similar economic institutions, levels of investment, and population growth (e.g., the G7) should all converge to similar levels of labor productivity. The fact that this doesn't happen, or has stopped happening for different countries at different times (Canada in the 1980s, Japan and Italy in the 1990s, the UK since 2010), flies in the face of the 'absolute convergence' hypothesis.
Unlike the evidence against absolute convergence from other countries, however, members of the G7 haven't been diverging from each other in terms of GDP per capita over the last few decades, per se. Instead, there seems to be something affecting the level of each countries productivity over time. In terms of GDP per hour worked, the UK is consistently around 75% as productive as the US, Japan is about 65% as productive, and Germany and France roughly match the US. The Solow model does have predict some variability in productivity levels based on the savings rate, the population growth rate, and depreciation. However, all of these differences should be controlled for if you look at total factor of productivity, which is what I tried to do in my previous post. Long story short, the Solow model fails almost entirely in explaining productivity differences across the G7.
Economists from the '90s are probably screaming right now that I should look at human capital and test for convergence conditional on that. My issue with looking at human capital is that 1) nobody even knows what it is and 2) the way it's used in theories is really strange. For instance, in the paper I linked above, Mankiw et al famously model human capital as just another kind of capital in a Cobb-Douglas production function and then assert that it accumulates in the same way are normal capital, i.e. through saving/investment. They then assert that the savings rate for human capital is equal to the share of the working age population that is in school (even though in their model human capital investment is a portion of income).
Still, the idea of conditional convergence is intriguing, so why not regress growth from 1981 to 2015 on the initial level of productivity and some crude measure of human capital (percentage of population with a post-secondary degree)? For the heck of it, let's throw in R&D spending as a percentage of GDP.
Interestingly enough, the fit is actually astonishingly good, especially considering that I only used data from seven countries. I was also surprised to see that the (statistically insignificant) coefficient on tertiary degree attainment is negative. There's probably a better measure of 'human capital', but I still think there's something strange about using anything as a proxy for an inherently unmeasurable theoretical construct.
If you exclude the education variable, then the results are as follows:
The coefficient of R&D spending does change, but the main result here is consistent: strong support for the hypothesis that productivity in the G7 converges conditional on R&D spending. The equation that I tested was
growth from 1981 to 2015 = a * GDP per hour in 2015 + b * average R&D spending from 1981 to 2015 + c
All values are relative to the US, so you can predict the relative level of GDP per hour in the long run by plugging in a value R&D spending and then solving for GDP per hour. Assuming a level of R&D spending equal to the US, the regression predicts complete convergence: 43.1548/0.4155 ≈ 104% of US productivity.
Alternatively, you can compare actual productivity in 2015 to productivity predicted by the model and a counterfactual with R&D spending equal to the US:
This approach predicts actual productivity levels surprisingly well (removing R&D spending from the regression reduces the r-squared value to 0.522). It also seems to suggest that Japan's low productivity levels should be of no surprise; it just started from such a low level that we should expect it to take a while longer to converge completely. Similarly, Canada, Italy, and the UK look to be suffering simply from low R&D spending.
Even though R&D does appear to explain productivity differences in the G7, I am hesitant to say I've solved my puzzle yet. Looking specifically at Japan, it's period of high growth occurred when R&D spending was low, and subsequently higher R&D spending has coincided with lower growth. Another problem is the tiny sample size. Seven countries is far too small to make any serious conclusions (if I calculated correctly, the standard deviation on the estimate for the amount of convergence in the long run is 35.2). So I end this post barely more sure of what causes productivity differences between developed countries than I was two months ago, but maybe a slightly better idea of where to go from here.
Unlike the evidence against absolute convergence from other countries, however, members of the G7 haven't been diverging from each other in terms of GDP per capita over the last few decades, per se. Instead, there seems to be something affecting the level of each countries productivity over time. In terms of GDP per hour worked, the UK is consistently around 75% as productive as the US, Japan is about 65% as productive, and Germany and France roughly match the US. The Solow model does have predict some variability in productivity levels based on the savings rate, the population growth rate, and depreciation. However, all of these differences should be controlled for if you look at total factor of productivity, which is what I tried to do in my previous post. Long story short, the Solow model fails almost entirely in explaining productivity differences across the G7.
Economists from the '90s are probably screaming right now that I should look at human capital and test for convergence conditional on that. My issue with looking at human capital is that 1) nobody even knows what it is and 2) the way it's used in theories is really strange. For instance, in the paper I linked above, Mankiw et al famously model human capital as just another kind of capital in a Cobb-Douglas production function and then assert that it accumulates in the same way are normal capital, i.e. through saving/investment. They then assert that the savings rate for human capital is equal to the share of the working age population that is in school (even though in their model human capital investment is a portion of income).
Still, the idea of conditional convergence is intriguing, so why not regress growth from 1981 to 2015 on the initial level of productivity and some crude measure of human capital (percentage of population with a post-secondary degree)? For the heck of it, let's throw in R&D spending as a percentage of GDP.
If you exclude the education variable, then the results are as follows:
growth from 1981 to 2015 = a * GDP per hour in 2015 + b * average R&D spending from 1981 to 2015 + c
All values are relative to the US, so you can predict the relative level of GDP per hour in the long run by plugging in a value R&D spending and then solving for GDP per hour. Assuming a level of R&D spending equal to the US, the regression predicts complete convergence: 43.1548/0.4155 ≈ 104% of US productivity.
Alternatively, you can compare actual productivity in 2015 to productivity predicted by the model and a counterfactual with R&D spending equal to the US:
| Country | Productivity | Prediction | Counterfactual |
|---|---|---|---|
| Canada | 76.915034 | 81.727441 | 94.292790 |
| France | 94.021332 | 89.476058 | 95.644441 |
| Germany | 93.728856 | 93.321678 | 94.395491 |
| Italy | 75.604129 | 75.233253 | 96.770322 |
| Japan | 65.538401 | 66.124831 | 63.949169 |
| United Kingdom | 75.644250 | 73.969879 | 83.190180 |
| United States | 100.000000 | 101.604800 | 101.604800 |
This approach predicts actual productivity levels surprisingly well (removing R&D spending from the regression reduces the r-squared value to 0.522). It also seems to suggest that Japan's low productivity levels should be of no surprise; it just started from such a low level that we should expect it to take a while longer to converge completely. Similarly, Canada, Italy, and the UK look to be suffering simply from low R&D spending.
Even though R&D does appear to explain productivity differences in the G7, I am hesitant to say I've solved my puzzle yet. Looking specifically at Japan, it's period of high growth occurred when R&D spending was low, and subsequently higher R&D spending has coincided with lower growth. Another problem is the tiny sample size. Seven countries is far too small to make any serious conclusions (if I calculated correctly, the standard deviation on the estimate for the amount of convergence in the long run is 35.2). So I end this post barely more sure of what causes productivity differences between developed countries than I was two months ago, but maybe a slightly better idea of where to go from here.
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