The Solow Model and China

If you don’t know what the Solow model is, here is a great place to get started:

There are 11 videos in that series, and if you can spare the time, please watch all of them. Just two a day (they’re not more than 5 minutes each), and you’ll be done come the weekend.

But in effect, here is what the Solow model says:

  1. Output for a nation is a function of three (actually four) things:
    1. Capital (K): Buidings, ports, dams… infrastructure, basically.
    2. Education Augmented Labor (eL): The amount of hours that a person is able to put in to their work, but with the built in assumption that an educated person is likely to be more productive than a person without education.
    3. Ideas: Read the paragraph below to get a sense of what this means in practice.

Think about this blogpost that you are reading. I wrote it using my laptop, which is my capital. I will spend about an hour (that’s my plan, I’ll update you towards the end of this post about how well it worked out) writing it, and that’s the labor that I’ll be putting into this post. The fact that I have been “educated” in economics should mean that this post will be easier to write for me than, say, a gardener. The gardener could have written this post as well, of course, but it’s safe to assume that she would first have had to learn about the Solow model, and that, presumably, would have taken longer.

So that’s K and eL where the output (this blogpost) is concerned. But now think about it this way: what if another person, with a similar level of economics education as mine were to write this blogpost instead of me? Would that person have chosen this video, and these paragraphs to explain the Solow model? Maybe they would have recommended some other video, or some other podcast, or chosen to share details of an online textbook in which the Solow model is explained. That’s one way to think about ideas.

And so when you combine the capital (the laptop), the labor (the time I spend on this blogpost, given my education levels) and the ideas (what I choose to put into this blog post, and how), you get the output you’re reading right now.

What if I double the capital? Will the blogpost be done in half the time? Say I have an external monitor attached to my laptop – will two screens mean finishing the blogpost in half the time? It will save some time, but not by a factor of two, surely. Trust me, I have tried.

What if I double the labor? Hire an assistant to write this blogpost with me? The way I work, trust me, it will probably take longer! What if I go get a post-doc, to augment my education? Will that save me time? The hysterical laughter you hear in the background is the response of any PhD/post-doc student anywhere in the world, and that sound means a loud and resounding no.

In a sense, the Solow model asks these and related questions, and answers them using some graphs and equations. Except, of course, the Solow model does it for not one guy writing one blog, but for an entire nation at a time. There is no sense in me explaining the whole model over here, for it would be a case of me reinventing what is already a very good wheel. Please watch the videos.

But the Solow model is a remarkably useful way to get a handle on the long run growth prospects of a country. Is India likely to grow in the future? Well, is it going to add to its capital stock? Yes. Is it going to augment it’s stock of education augmented labor? Yes. Is it likely to produce more ideas than it is right now? Yes. And so the growth prospects for India look reasonably good.

Of course, there is more to the Solow model. All of this holds true given a strong and stable political system, well established rules of law, and strong and capable institutions. But so long as you believe that these are likely to continue to be so in the Indian case, you should be bullish on India.

What about, say, Japan? It has a capital stock that is more in need of replacement than new construction ( a feature of the Solow model that we have not discussed here, called depreciation), so it is unlikely that it will grow its capital stock too much. Here’s an example of what I mean. What about it’s stock of education augmented labor? Well, the news ain’t very good. Ideas? Trending upwards, but not by much. So if I had to bet on which country would grow more over the next twenty years, I would bet on India, not Japan.

Bear in mind that this is a model, and like all models, it is an imprecise abstraction of reality. So it is possible that at the end of the twenty year period, we find out that I am completely wrong. But if you think the Solow Model is a reasonably good model, you ought to bet the way I did.

So what about China?

Well, now, that’s a whole different story, and one that Noah Smith talks about in a recent blog post. Long story short, he doesn’t think China’s growth prospects are that great.

But the story is a little more complicated than that. The Solow model is a good model, sure, but it’s not as if the Chinese authorities/experts aren’t aware of the problem. And in his blog post, Noah looks at arguments put forth by two people who know a thing or two about China, and analyzes them critically.

The first argument is that sure, China’s demographics are on a downward trend, but what if we raised the retirement age for Chinese workers? Would that not solve the problem? Noah says no, probably not, because firms made of exclusively old folks isn’t necessarily a good idea. I wholeheartedly agree.

What about adding to China’s urbanization, and therefore its infrastructure? After all, China’s urbanization rate is “only” 64%. The inverted quotes around only in the previous sentence is because we, in India, are officially at 31%, but as in the case of China, it very much is a function of how you define urbanization. But similarly, in China, the urbanization rate is actually way more than 64%, and the Lewis turning point has already taken place in China, or will do so any moment.

And about ideas, well, China is an even more complicated story. Noah makes the point that China’s industrial policy is essentially a one-man army that is trying something that has never been tried before, and Noah is betting on it not quite working out. And given the events of the last year and a half or so, it is hard to disagree.

And so the Solow Model would probably tell you that China is unlikely to grow as fast in the near future as it did in the recent past, and even if you take into account potential adjustments, it likely will still be the case that China’s growth rate will start to plateau.

Please, read the entire post by Noah. But if you are a student of economics who has not yet met the Solow Model, begin there, and then get on to Noah’s post – your mileage will increase considerably.

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