# Tyler, Noah, and Bob walk into a Chinese bar...

I know that in internet-time I'm light-years behind this discussion, but Tyler Cowen recently put up a post questioning whether Chinese growth could be explained by Solow catch-up growth, and Noah Smith had a reply that said, "Yes, it could". I just wanted to drop in on that to generally agree with Noah, and to indulge in some quibbles.

Tyler says that

It seems obvious to many people that Chinese growth is Solow-like catch-up growth, as the country was applying already-introduced technologies to its development.

and Noah rightly says that this isn't what Solow-like catch-up growth is about.

Solow catch-up growth (convergence) is just about capital investment. That's the convergence mechanism. And that mechanism says that if you are well below your potential, you'll grow really fast as you accumulate capital rapidly. So the Solow story for China is that there was a profound shift(s) starting in the late 1970's, early 1980's that created a much higher potential level of output. That generates really rapid growth.

Does 10% growth make sense as being due to convergence? We can use my handy convergence-growth calculating equation from earlier posts to figure this out. In this case, Tyler was talking about aggregate GDP growth, so in what follows, ${y}$ represents GDP.

$$Growth = \frac{y_{t+1}-y_t}{y_t} = (1+g)\left[\lambda \frac{y^{\ast}_t}{y_t} + (1-\lambda)\right] - 1.$$

The term ${\lambda}$ is the convergence parameter, which dictates how fast a country closes the gap between actual GDP (${y_t}$) and potential GDP (${y^{\ast}}$). The rate ${g}$ is the steady state growth rate of aggregate output.

${g}$ might be something like 3-4% for China, the combination of about 2% growth in output per capita, along with something like 1-2% population growth. The convergence term ${\lambda}$ is around 0.02. We know that Chinese growth was around 10% per year for a while (not any longer). So what does ${y^{\ast}}$ have to be relative to existing output to generate 10% growth? Turns out that you need to have

$$\frac{y^{\ast}_t}{y_t} = 4.4$$

to get there. That is, starting in 1980-ish, you need Chinese potential GDP to be 4.4 times as high as actual GDP. If that happened, then growth would be 10%, at least for a while.

Is that reasonable? I don't know for sure. It's really a statement about how inefficient the Maoist system was, rather than a statment about how high potential GDP could be. GDP per capita in China was only about $220 (US 2005 dollars) in 1980. That's really, really, poor. A 4.4 fold increase only implies that potential GDP per capita was$880 (US 2005 dollars) in 1980. We're not talking about a change in potential that is ludicrous. There is a good reason to think that standard Solow-convergence effects could explain Chinese growth.

But not entirely. One issue with this Solow-convergence explanation is that growth should not have stayed at 10% for very long after the reforms. That is, the Solow model says that you close part of the gap between actual and potential GDP every year, so the growth rate should slow down until it hits ${g}$. That happens pretty fast.

After 10 years of convergence - about 1990 - China's growth rate should have been about 6.7%, and it was lower in the early 90's than in the 1980s. But after 20 years - about 2000 - China's growth rate should have been down to 5.3%. Yet Chinese GDP growth has been somewhere between 8-10% since 2000, depending on how you want to average growth rates, and what data source you believe.

So why didn't Chinese growth slow down as fast as the Solow model would predict? That requires us to think of potential GDP, ${y^{\ast}}$, taking even further jumps up over time. Somewhere in the time frame of 1995-2000, another jump in potential GDP took place in China, which then allowed growth to remain high at 8-10% until now. And now, we see growth in China starting to slow down, as we'd expect in the Solow convergence story.

I think I would take Tyler's post as being about the source of that additional jump'' in potential GDP that kept growth up around 8-10%. It may be that China had some kind of special ability to absorb foreign technology (perhaps just it's size?). But then again, in the late 1990's, China actively negotiated for WTO accession, which took place in 2001. Hong Kong also reverted to Chinese control in 1997. Both could have created big boosts to potential GDP.

We do not necessarily need to think of some kind of special Chinese ability to absorb or adapt technology to explain it's fast growth. Solow convergence effects get us most of the way there. Whatever happened in the 1990's may reflect some unique Chinese ability to absorb technology, but I'd be wary of going down that route until I exhausted the ability of open trade and Hong Kong to explain the jump in potential.

Okay, last quibble. In Noah's post, he said that we'd expect Chinese capital per worker to level off as they get close to potential GDP. No, it wouldn't! The growth of capital per worker will slow down, yes, but will settle down to a rate about equal to the growth rate of output per worker. The growth rate of capital per worker won't reach zero, if the Solow model is at all right about what is happening.