Basil Halperin

Essays — Basil Halperin

Essays


The Solow Model is overrated (for explaining catch-up growth)
July 10, 2024

Originally posted as a Twitter thread.


I think the Solow/neoclassical model is overrated *for explaining catch-up growth and convergence*

Some thoughts, as a prelude to a thread on Chinese growth accounting:


Let me frame the argument against Solow by appealing to the debate over the rapid growth of East Asian Tigers (Hong Kong, Singapore, South Korea, Taiwan) from 1960-2000:


1. Did the E. Asian Tigers grow fast because of rapid productivity improvement?

vs.

2. Was it merely Solow catch-up growth: poor countries start off with few machines...
...build more (“capital accumulation”)...
...and grow faster until they have enough machines (“convergence”)


Alwyn Young (1992, 1995) famously argued that the rapid growth of the East Asian Tigers was largely not due to productivity growth

Paul Krugman popularized this view in an influential Foreign Affairs article, “The Myth of Asia’s Miracle”, suggesting effectively zero TFP growth


From Young’s legendarily careful data work, it was argued Tiger growth was merely capital accumulation: Solow-style catch up growth

The growth accounting from Young (1995) – “the tyranny of numbers” – shows TFP growth explaining at most 30% of Tiger growth


That is: Hong Kong, Taiwan, S Korea, and especially Singapore simply started in 1960 with few machines and low education

The rapid growth merely came from building more machines and shuttling more kids through school – not from producing things more intelligently (TFP growth)


This Krugman-Young story is precisely the simple story of convergence of Solow!

Again: poor countries start off with few machines, then build more (“capital accumulation”) and so grow faster until they have enough machines (“convergence”)


This is the view of the E. Asian Tiger experience I had accepted, until recently

There are a few issues, with the overriding fact being that: growth accounting is actually just really hard. Empirically tough, but also conceptually

I’ll focus on a conceptual issue (“wonkish”)


Higher TFP causes capital accumulation:

If you get more productive, you want to (gradually) build more machines
=> AND those machines cause more growth

Should we attribute that higher growth to the machines, or to the productivity?


Traditional growth accounting gives credit for growth caused by that extra capital to capital itself

But it really makes more sense to give (long-run) credit to the higher productivity, which is itself causing the extra capital!


Brief Cobb-Douglas math for the curious (in logs):

Traditional growth accounting: Y = A + α⋅K + (1-α)⋅L

Instead: Y – L = (1/(1- α))⋅A + (α/(1- α))⋅(K – Y)

(See eg Klenow-Rodriguez-Clare 1997, or Jones 2016 sec 2.1)


So for example, Klenow and Rodriguez-Clare (1997) reanalyze the East Asian Tiger experience: properly accounting for TFP-induced capital accumulation + analyzing Y/L rather than Y

They find that TFP growth accounts for 50-75% of Tiger growth (!), except for Singapore


Briefly, another critique of the neoclassical (Young/Krugman) view is Hsieh (2002), who argues that the rate of return on capital didn’t fall in Singapore, as the neoclassical/Solow model would predict – implying higher TFP growth. This is the “dual approach” to growth accounting


[PART 2: an alternative view of catch-up growth]

Just from armchair theorizing, the Solow model view that faster catch-up growth is all due to capital accumulation feels a little odd, IMO


Do poor countries really grow fast because they’re just accumulating capital (building more machines, etc), a la Solow? Isn’t that kind of crazy?

A priori, aren’t poor countries also catching up by **importing technology**?

IMO the Solow model is plausibly... overrated 😎


Overrated, since Solow attributes fast catch-up growth entirely to temporarily high capital accumulation – and not at all to higher technological growth

Poor countries also have low productivity! Shouldn’t some of the catch-up growth come from simply imitating tech leaders?


(that^ tweet is the punchline of the thread!)


The first attempt (AFAIK) to model catch-up growth as being caused by technological diffusion, rather than Solow-style capital accumulation, was Barro and Sala-i-Martin (1997). The Acemoglu textbook ch. 18 also has a clear exposition

These models do what you would expect:


“Imitation is cheaper than invention”, so countries behind the frontier can copy ideas cheaply and grow TFP and GDP quickly

As they catch up in terms of TFP, it gets more expensive to copy ideas – you’re trying to imitate semiconductors instead of tractors – and growth falls


In the long run, all countries grow at the rate of the frontier – and the frontier is nicely determined exactly as in the canonical growth models


The framework matches the armchair view of historical catch-up growth – it is driven in part by poor countries getting more productive by copying technology

That said, obviously a lot of catch-up growth is ALSO surely due to Solow-style capital accumulation


A crude extrapolation is 50-50 on average: half productivity catch-up + half capital accumulation catch-up

I haven’t seen a paper doing the decomposition across all catch-up growth episodes (many papers look at all countries/times – mixing in BGP level differences, I think)


Maybe postwar Europe (which surely motivated Solow) – with the rebuilding after the destruction – was catch-up growth driven mostly by capital accumulation, not technology diffusion

(Though maybe not, based on this dirty cut adapted from Dietz Vollrath?)


Convergence is, obviously, a huge topic in the lit and I feel like there must have been more study of this / someone else must have framed the question this way:

“Is catch-up growth due to Solow-style capital accumulation vs. technology diffusion?”

References very welcome!




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