Tyler, Noah, and Bob walk into a Chinese bar…

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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.

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

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

$\displaystyle \frac{y^{\ast}_t}{y_t} = 4.4 \ \ \ \ \ (2)$

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.

12 thoughts on “Tyler, Noah, and Bob walk into a Chinese bar…”

• Which is a completed different way of reconciling the issue. China may just have been making up the numbers. I cannot discount that at all.

• Riiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiight. ROTFL.

• That seems a bit ridiculous frankly. Assuming a 4% average (not maximum which implies an even lower average) growth rate from 1980 to 2015 implies that the current size of the Chinese economy is less than $750 billion USD (starting at ~$180 billion in 1980). Now compare this to the trade data. Remember trade data is NOT solely collected by the Chinese. Every country they trade with keeps it’s own import and export data so if the Chinese lie about how much they export, this can be easily countered by other countries simply showing “nope, we didn’t receive the imports you say we did.” The US alone claims that so far in 2015, $357 billion worth of exports has been received from China and this does not include the big months of November and December. Are you trying to saying that US imports from China ALONE are HALF of the Chinese economy? More if you’re only considering nominal data since China has tended to keep it’s currency weak for export encouragement? If you look at their total exports it’s over$2 trillion. China simply can’t cook it’s books at anywhere near the level you are asserting without it becoming blindingly obvious in the trade data!

And this isn’t to mention the huge construction projects, rapid military budget expansion, and huge overseas investments that become almost completely inexplicable with the growth rates you’re asserting. China is per capita poorer than North Korea if you’re right. In which case we should be hearing about all these Chinese migrants trying to escape to Kim Jong Un’s Worker’s Paradise rather than vice-versa.

No, the “Chinese Data is hugely faked” hypothesis is not something that really deserves serious consideration. I doubt they could even pull off a fudge of a single percentage point on their growth rate for very long before everyone notices “hey the Chinese trade data is looking really fishy here given US data” or “you know it’s odd that such a fast growing country doesn’t have a bunch of fast growing cities like Shanghai, Beijing, Tianjin, or Guangzhou.” GDP data is not easy to fake with a country closely connected to the world economy and the complaints that do get made seem to me to be cherry picking the weakest sectors of a huge, diversified, and complex economy.

• Yes, we could definitely use some trade data to calibrate the Chinese GDP data. I’m not saying that Chinese growth was only 4%, but I’ll admit to being suspicious about the run of 10% growth rates. My guess is that the real numbers are somewhat lower. How low? I don’t know, that’s the problem. I don’t discount the idea that 10% is wrong, but that doesn’t mean 4% is right.

• I have my doubts. Even an average 1% per year fudge make a huge difference in final GDP numbers over 35 years. For a country as big as China, assuming a 8% average growth rate rather than a 9% means their economy is $1 trillion smaller, which would mean the global economy basically loses a Canada. For such a globally connected economy as China, I think losing a Canada’s worth of value would be pretty obvious. I’m willing to entertain the idea that recently China has fudged some data, maybe for a year or so. And at that I’d still say probably to a small scale. But much more than that and I have my doubts. China’s government dreams of being an accepted major power. They can only do this if they can manage to expand their country’s economy and not get caught pulling frankly silly developing-world-despot tricks that are more about ego than real pragmatic gain. I think the problem with China is that the opinion of the zeitgeist on the country tends too much towards extremes. When China does well, people over hype it all too often forgetting that while China’s model might be decent enough for a poor, developing country, it’s almost assuredly a bad model for any country which currently has a per capita GDP of at least$20,000. When China’s doing less well, it’s not enough for a 3-4% trend growth rate slow down (just as they are finally reaching the lower end of middle income status) but it has to be a full recession. I don’t buy it. Not yet anyways.

1. What about the changes in human capital? China’s “investment” in literacy and high education, which would have started about 30 years before 1980, would have started paying noticeable dividends right around 1980. So if one used the Mankiw-(David) Romer-Weil version version of the Solow production function, the combination of a) past and continuing human capital investment and b) Solovian increased physical capital investment might not leave as much to be explained by ‘b”.

But I don’t doubt that “b” was huge. The Solow model asks us to assume that S = I. But it doesn’t require a lot of imagination to picture intense coordination problems in pre-1980 China. Beginning 1980 or so, perhaps I did begin to approximate S. That, per any growth model with a K component, would have resulted in a massive Solovian effect.

• If we think of human capital as accumulating like a stock (which we tend to do), then it fits within the whole idea of convergence explaining Chinese growth. The value of lambda (2% convergence parameter) is not based on there only being physical capital. It’s just pulled from the raw data on GDP growth rates, and reflects convergence due to any kind of capital accumulation (physical or human or any other kind).