Human Capital and Conditional Convergence

In our previous videos, we showed how capital accumulation can generate growth in the short run, but in the long run, we always end up at a steady-state where all of investment is used to make up for depreciation. What about human capital? -- represented here by the labor force, "L", times their education level, "e." Well, there's no doubt that higher levels of education correlate with higher levels of economic output. But just like physical capital, human capital is subject to diminishing returns. The United States has a well-educated workforce, and that's good, but it's possible for a country to invest too much in education. It helps an economy to have some PhDs -- at least I hope it does.

But how much extra growth would we get if we required everyone to have a PhD? Probably not that much. It's a good investment to teach people to read and write and do some math, but would it pay to train everyone to understand the general theory of relativity? I don't think so. So, education is subject to diminishing returns. And what about depreciation? Yeah. Unfortunately, human capital -- it wears out too. Think about all of the current human capital in the world.

Where is it going to be in 100 years? Unfortunately, I know. First, we go into retirement, and after that, it's just depreciation, depreciation, depreciation. Moreover, it takes a lot of investment in schools and universities and time and effort to build human capital. At some point, we're going to need all of that investment just to keep the population as educated as it is now. So, the accumulation of capital, whether it's physical capital or human capital, it can only get us so far.

Now, let's turn to an important prediction of the Solow Model. Poor countries should grow faster than rich countries. Now, that's a pretty bold prediction. If it were completely true, then all poor countries -- they'd be catching up to the rich countries. And all countries would be approaching similar levels of steady-state output -- perhaps with some differences due to differences in savings rates. Now, as we saw before, there are growth miracles. Some countries like China and Korea -- they're clearly catching up. But there's also growth disasters. Countries like Nigeria and Argentina, which are falling further and further behind, or at least not catching up. Indeed, broadly speaking, over the last several hundred years, what we've seen isn't convergence, but divergence -- big time.

But let's step back and remember that the factors of production in the Solow Model -- they're just one piece of the puzzle. When it comes to explaining prosperity, we also need to remember the importance of institutions, the institutions that create the incentives to accumulate and to use the factors of production in socially beneficial ways. Two countries with really different institutions -- they're not going to converge. But, if we focus in on countries with similar institutions, then the Solow Model predicts that the poorer countries should grow faster, and all countries with similar institutions -- they should converge to similar levels of output. We call this "conditional convergence." Conditional on institutions and other factors being similar, we'd expect poor countries to grow faster.

Is it true? Let's take a look at the 20 founding members of the OECD, basically the Western developed economies. It seems reasonable to say that they've got similar institutions, so according to the Solow Model, they should have similar steady-state levels of output. Here we're going to plot the growth rate of these countries over 40 years on the vertical axis, and real GDP per capita in 1960 on the horizontal axis. Remember, the Solow Model predicts that the countries which were poorer in 1960 -- they should have grown faster over the next 40 years than the countries which were wealthier in 1960. And that's exactly what we see. The countries which were relatively poor in 1960 -- they grew faster than the countries which were relatively wealthy in 1960.

So, among countries with similar institutions, there is convergence -- conditional convergence. The Super Simple Solow Model, however, makes another prediction: zero growth in the steady-state. But clearly that's not what we see. The growth rates for the wealthier countries, they're lower than for the poorer countries, but they're not zero. The United States -- it's been growing consistently for 200 years, and we're still growing. That doesn't sound like zero growth at all. It's useful, however, to bring back the two types of growth that we discussed earlier: catching up; and cutting-edge growth. When you're catching up, when you're poor relative to your steady-state, that's when the Solow Model predicts that you grow quickly as capital accumulates. But then you slow down as you approach the steady-state. However, for the wealthiest countries in the world -- those are the cutting edge -- this model of capital accumulation, it fails to explain how you keep growing, albeit at a slower pace.

So how do we explain growth at the cutting edge? Well, let's not forget about our last variable: Ideas. Ideas is going to be the focus of our next video, and we'll see how new ideas can keep us growing on the cutting edge.