## Thursday, December 3, 2015

### Smith meet Jones

A while ago I wrote up a smorgasbord of policies that I thought could increase US economic growth, at least for a few decades, in "Economic Growth" (pdf, html here.) Noah Smith took me to task in a Bloomberg View column, complaining that I confused growth with levels,
...I want to focus on one bad argument that Cochrane uses. Most of the so-called growth policies Cochrane and other conservatives propose don't really target growth at all, just short-term efficiency. By pretending that one-shot efficiency boosts will increase long-term sustainable growth, Cochrane effectively executes a bait-and-switch.
As it turns out, the difference between "growth" and "level" effects in growth theory and facts is not so strong. Many economists remember vaguely something from grad school about permanent "growth" effects being different and much larger than "level" effects.  It turns out that the distinction is no longer so clear cut; "growth" is smaller and less permanent than you may have thought, and levels are bigger and longer lasting than you may have thought.

Along the way, I offer one quantitative exercise to help think just how much additional growth the US could get from the sort of free-market policies I outlined in the essay.

Part I Growth and Levels

China removed exactly the sort of "level" or "inefficiency" economic distortions that free-market economists like myself (and Adam Smith) recommend. What happened? Here is a plot of China's per capita GDP, relative to the US (From World Bank). In case you've been sleeping under a rock somewhere, China took off.
(Note: This blog gets picked up in several places that mangle pictures and equations. If you're not seeing the above picture or later equations, come to the original.)

Now, in the "growth" vs "level," or "frontier" vs. "development" dichotomy, China experienced  a pure "level" effect. Its GDP increased by removing barriers to "short-term" efficiency, not by any of the "long-term" growth changes (more R&D, say) of growth theory.

But "temporary" "short-run" or "catch-up" growth can last for decades.  And it can be highly significant for people's well-being. From 2000 to 2014, China's GDP per capita grew by a factor of 7, from $955 per person to$7,594 per person, 696%, 14.8% annual compound growth rate (my, compounding does a lot). And they're still at 15% of the US level of GDP per person. There is a lot of "growth" left in this "level" effect!

Lots and lots of people, even "liberals" in Noah's other false dichotomy, use the word "growth" to describe what happened to China, and would not belittle policies that could make the same thing happen here.

Part II. How much better can the US do?

But can liberalization policies have the same effect for us? Yes, you may say, China had scope for a big "catchup" growth effect. But the US is a "frontier" country. China can copy what we're doing. There is nobody for us to copy. Big increases in levels, which look like growth for a while, are over for us.

But are they? We know how much better China's economy can be, because we see the US. We see how much better North Korea's could be, because we see South Korea. (Literally, in this case.) How much better could the US be, really, if we removed all the distortions as in my growth essay?

"Distance to Frontier" overall measure of government interference:
The distance to frontier score...shows the distance of each economy to the “frontier,” which represents the best performance observed on each of the indicators across all economies in the Doing Business sample since 2005.
The individual measures are things like
Starting a Business, Dealing with Construction Permits, Getting Electricity, Registering Property, Getting Credit, Protecting Minority Investors, Paying Taxes, Trading Across Borders, Enforcing Contracts, Resolving Insolvency
(I used GDP data for 2013, and distance for 2014. That gave the largest number of countries.)

The US is $52,000 per year and a distance score of 82. China is$7,000 and a score of 63. The diagonal line is an OLS regression fit.

The distance to frontier measure is highly correlated with GDP per capita. It tracks enormous variation in performance, from the abject poverty of $1,000 per year through the US and beyond. The correlation would be stronger if not for the outliers. In red, Libya and Venezuela are arguably countries with temporarily higher GDP than the quality of their institutions will allow for long. In green, Rwanda and Georgia may have reasons for temporarily low GDP among improving institutions. Cuba and North Korea are missing. Luxembourg, Kuwait, have obvious stories. And I did not weight by population; large countries seem to be closer to the line. Update: An attempt at nicer graph art. The countries are weighted by population. The dashed line is a weighted least squares fit, weighted by population. China is red, US is blue. Better? One might dismiss the correlation a bit as reverse causation. But look at North vs. South Korea, East vs. West Germany, and the rise of China and India. It seems bad policies really can do a lot of damage. And the US and UK had pretty good institutions when their GDPs were much lower. (Hall and Jones 1999 control for endogeneity in this sort of regression by using instrumental variables.) Too much growth commentary, I think, confounds "frontier" with "perfect." The US has good institutions, but not perfect ones. It takes forever to get a building permit in Lybia. It takes 2 years or more to get one in Palo Alto. It could take 10 minutes. We are not completely uncorrupt. Our tax code is not perfect. Property rights in the US are not ironclad. A lawsuit might take 10 years in Egypt. But it still could take 3 years here. (Disclaimer, all made-up numbers.) And so forth. So, the big question is, just how much greater "level" -- and how much China-like "growth" on the way -- could the US achieve by improving our good but imperfect institutions? The Distance to Frontier measure is relative to the best country on each dimension in the World Bank sample. So a score of 100 is certainly possible. I labeled that by a hypothetical country, "Frontierland" (FRO) in the graph. Perhaps we can do better. Even the best countries in the world are not perfect. Let's call the best possible institutions Libertarian Nirvana (LRN). How good could it be? If the US is currently 82, and the union of best current practices 100, let's consider the implications of a 110 guesstimate. Country Code Distance GDP/N % > US 20 year growth China CHN 61$7,000
United States USA 82 $53,000 Frontierland FRO 100$163,000 209 5.6
Libertarian Nirvana LRN 110 $398,000 651 14.8 The table shows China and the US along with my hypothetical new countries. Frontierland generates$163,000 of GDP per capita, 209% better than the US. If it takes 20 years to adjust, that means 5.6% per year compound growth. Libertarian Nirvana generates $398,000 of GDP per capita, 651 percent better than the US, a level effect which if achieved in 20 years generates 14.8% compound annual growth along the way. These numbers seem big. But there are no black boxes here. You see the graph, I'm just fitting the line. And China just did achieve nearly 20 years of 14% growth, and a 700% improvement. In a sense, the numbers are conservative. The US is above the regression line in the graph. By the regression line, our GDP per capita should only be$33,000 per capita. I extrapolated the regression line, not the current state of the US.

Summary: It is surprising that bad policies, bad institutions, bad ease of doing business, can do quite so much damage. Harberger triangles just don't seem to add up to the difference between $1,000 and$53,000 GDP per capita. But the evidence -- especially the basically controlled experiments of the Koreas and Germanys -- is pretty strong.

The converse must therefore also be true. If bad institutions and policies can do so much damage, better ones may also be able to do a lot of good.

This is admittedly simplistic. Growth theory does distinguish between "ideas" produced by the "frontier" country, that are harder to improve, and "misallocation", "development" of more efficiently using existing ideas. As traditional macroeconomics thinks about aggregate demand easily raising GDP until we run in to aggregate supply,  there is a point of superb efficiency beyond which you can't go without more ideas. I don't know where that point is. But uniting the existing best practices around the world in Frontierland is surely a lower bound, and an extra 10 percent doesn't seem horribly implausible.

Lots of other new research suggests that level inefficiencies are sizeable. For example, Chang-Tai Hsieh and Pete Klenow measure misallocation -- the extent to which low productivity plants should contract and high productivity plans should expand, largely by just moving people around (yes, I'm simplifying). They report from this source "Full liberalization, by this calculation, would boost aggregate manufacturing TFP by 86%–115% in China, 100%–128% in India, and 30%–43% in the United States." And this is just from better matches. They're not even talking about policies that raise TFP at all plants, like removing regulatory barriers.

Likewise, Michael Clemens argues that opening borders -- again better matching skills and opportunities -- would roughly double world GDP. That too is (as far as I can tell) based only on "level" calculations, not the "scale" effects of better ideas that growth theory (below) would adduce. But you'd get a lot of "growth" on the way to doubling the level!

Part III. Smith, meet Jones; Growth effects are smaller than you thought

Conversely, it turns out that "growth" effects are vanishing from growth theory. Levels are all we have -- but big levels, that take decades of "transitory" growth to achieve.

The crucial references here are Chad Jones' 2005 "Growth and Ideas" and 1995 "R&D based models of economic growth" and 1999 "Sources of U.S. Economic Growth in a World of Ideas" My discussion will pretty freely plagiarize.

Suppose output is produced using labor $$L_Y$$ and a stock of ideas $$A$$ by $Y = A^\sigma L_Y$ New ideas are likewise produced from labor and old ideas, $\dot{A} = \delta L_A A^\phi$ where $$L_A$$ is the number of people working on ideas, often (but too narrowly, in my view) called "researchers." To keep it simple, suppose a fraction $$s$$ of the labor force works in research, $$L_A= s L$$ and that population $$L$$ grows at the rate $$n$$. The classic Romer, Grossman and Helpman, and Aghion and Howitt models specify $$\phi = 1$$. Then we have $\frac{\dot{A}}{A} = \delta s L$ and growth in output per capita is $g_Y \equiv \frac{\dot{Y}}{Y} -\frac{\dot{L}}{L} = \sigma \delta s L.$ Here you see the new growth theory promise: an increase in the fraction of the population doing research $$s$$ can raise the permanent growth rate of output per capita! This is a "growth effect" as opposed to those boring old "level effects" of standard efficiency-improving microeconomics.

But here you also see the fatal flaw pointed out by Jones. The growth rate of output should increase with the level of population. As world population increased from 2 billion in 1927 to 7 billion today, growth should have increased from 2% to 7% per year, per capita. The growth rate of output per capita should itself be growing exponentially! Substituting, we should see $g_Y = \sigma \delta s L_0 e^{nt}$ The problem is deep. The model with $$\phi = 1$$ gets all sorts of scale effects wrong. Not only has the population increased over the last century, the fraction engaged in R&D has increased dramatically. Integration, by which two economies merge and effectively double their populations, should double their growth rates. Yet frontier growth rates are quite steady, if anything declining since the 1970s.

Jones' solution is simple: How about $$\phi < 1$$? Let's think hard about returns to scale in idea-production
If $$\phi > 0$$, then the number of new ideas a researcher invents over a given interval of time is an increasing function of the existing stock of knowledge. We might label this the standing on shoulders effect: the discovery of ideas in the past makes us more effective researchers today. Alternatively, though, one might consider the case where $$\phi < 0$$, i.e. where the productivity of research declines as new ideas are discovered. A useful analogy in this case is a fishing pond. If the pond is stocked with only 100 fish, then it may be increasingly difficult to catch each new fish. Similarly, perhaps the most obvious new ideas are discovered first and it gets increasingly difficult to find the next new idea.
Or, maybe $$\phi=0$$ is a useful benchmark: each hour of work produces the same number of new ideas. But  $$\phi=1$$ is a strange case; each hour of effort produces the same increase in the growth rate of new ideas.

Solving the model for $$\phi \lt 1$$ the idea accumulation equation is $\frac{\dot{A}}{A} = \delta s L_0 e^{nt} A^{\phi-1}$ Let's look for a constant growth rate solution $$A_t = A_0e^{g_At}$$, $g_A= \delta s L_0 e^{nt} A_0^{\phi-1} e^{(\phi-1){g_At}}$ This will only work if the exponents cancel, $n+(\phi-1)g_A = 0$ $g_A = \frac{n}{1-\phi}$ The steady state output per capita growth is then $g_Y = \sigma g_A = \frac{\sigma n}{1-\phi}$ This change solves the problem: It's still an endogenous growth model, in which growth is driven by the accumulation of non-rivalrous ideas. There are still externalities, and doing more idea-creation might be a good idea itself. But now the model predicts a sensible steady growth in per-capita income.

The model no longer has "growth effects." Jones:
Changes in research intensity no longer affect the long-run growth rate but, rather, affect the long-run level of income along the balanced-growth path (through transitory effects on growth). Similarly, changes in the size of the population affect the level of income but not its long-run growth rate. Finally, the long-run growth rate
On reflection, this distinction isn't really a big deal. The model behaves smoothly, for any finitely long period of time or data, as $$\phi$$ approaches one. The "level" effects get larger, and the period of temporary "growth" in transition dynamics to a new level gets longer. Even a century's worth of steady growth can't easily distinguish between values of $$\phi$$ a bit below one, and the limit $$\phi=1$$ of permanent growth effects.

This should remind you of the great unit root debate. A model $$y_t = \phi y_{t-1} + \varepsilon_t$$ with $$\phi=1$$ has a unit root, and shocks have permanent effects. A model with $$\phi < 1$$ is stationary, with only transitory responses to shocks. But $$\phi=0.99$$ behaves for a century's worth of data almost exactly like $$\phi=1$$. So the difference between "permanent" and "transitory", like the difference between "growth" and "level" really is not stark.

So where are we? There is no magic difference between permanent growth effects and one-time level increases. All we have are distortions that change the level of GDP per capita.

The big question remains: how bad are the distortions? Which ones have large effects and which are tolerable small effects? Endogenous growth theory still suggests that distortions which interfere with idea production, including embodiment of new ideas in productivity-raising businesses, will have much larger effects than, say, higher sales taxes on tacos. Just why is the correlation between bad government and bad economies so strong?  My essay just suggested getting rid of all the distortions we could find.

Part IV. Needless politicization

As I hope this extensive post shows, these questions are not political, and the subject of much deep current research.

Noah chooses to make this political. The quote again,
...I want to focus on one bad argument that Cochrane uses. Most of the so-called growth policies Cochrane and other conservatives propose don't really target growth at all, just short-term efficiency. By pretending that one-shot efficiency boosts will increase long-term sustainable growth, Cochrane effectively executes a bait-and-switch.
"Bad argument" may just mean that Noah is unaware of Jones' and related work. "Cochrane and other conservatives" is telling. Look at my profile. You don't find that word.  Open borders, drug legalization, and so forth are not well described as "conservative." I emailed Noah last time he used the word, so his inaccuracy is intentional.

"Pretending" "bait-and-switch" are unsubstantiated charges of intentional deception. And to call permanent increases in efficiency "short-term" is itself a bit of a stretch.

Even the New York Times, and many respectable "liberal" economists use the words "growth" to describe what has happened in China and to describe what "short-term" level effects could do for the US. From the Hilary Clinton Campaign website,
Hillary understands that in order to raise incomes, we need strong growth, fair growth, and long-term growth. And she has a plan to get us there.

Strong growth
Provide tax relief for families. Hillary will cut taxes for hard-working families to increase their take-home pay...

Unleash small business growth. ..She’s put forward a small-business agenda to expand access to capital, provide tax relief, cut red tape, and help small businesses bring their goods to new markets.

...Hillary’s New College Compact will invest $350 billion so that students do not have to borrow to pay tuition at a public college in their state. .. Boost public investment in infrastructure and scientific research. ... Hillary has called for a national infrastructure bank... She will call for reform that closes corporate tax loopholes and drives investment here, in the U.S. And she would increase funding for scientific research at agencies like the National Institutes of Health and the National Science Foundation. Lift up participation in the workforce—especially for women... No, that's not my essay, nor the Bush 4% growth website. There is the word "growth," all over the place, but only the scientific research might count as raising growth in the Noah Smith classificiation. Yet he does not include her among "conservative" economists displaying "bad arguments," "pretending," or "bait and switching." Enough. Shoehorning interesting economics into partisan political "conservative" vs. "liberal" categories is not a useful way to understand the issues here. #### 36 comments: 1. Great piece, John. Worth noting that the Doing Business indicators are controversial within the international community precisely because they do correlate so strongly. Not the usual vague fluff. Critics have already won a battle to water down the indicators of labor regulations. Good to call out how meaningful they are and credit their continuation. 2. Very interesting stuff. 3. "In green, Rwanda and Georgia may have reasons for temporarily low GDP among improving institutions." -Georgia and Kyrgyzstan's economies have sucked for over a decade. Belarus and Argentina have done better since 2005. 4. Nice and clear. 5. Very lucid and well written. I have no major objections to points I and III, although I would point out that endogenous growth models always have fundamental issues when it comes to determining which assumptions are correct, and how to map the data into the models and vice-versa, although I would, in this case, largely agree. However, I think you're going in a bit too strongly on point II. I understand and can definitely see what you're trying to suggest, that the improvements in the institutional framework in the US could result in large per capita gains, but I feel you are too quick to dismiss some the objections that you present. For one thing, I think you dismiss the possibility of reverse causality far too quickly. Yes, you do give us some compelling stories and if pressed between one or the other, I would probably think that institutions cause growth more than the other way round, but I imagine you're familiar with Glaeser, et al. (2004), among others, right? This is far from a settled issue, as far I can tell from my (admittedly, superficial) knowledge of the literature, and I have read convincing arguments that causality may run the other way round. Again, I'd probably agree with you on this, but it's a tricky issue. Furthermore, your exercise, whilst a very interesting one, stretches the counterfactual. Ignoring LRN, even Frontierland is a bit of a stretch. If you look at the individual aspects that compose the EoDB index, around 17% of the sub-items currently have no country at the frontier, which very much goes against the idea you're putting forth as what a representative country could be. And what I think is the trickiest problem, how sure can we be that further improvements to each individual aspects in which the US really will continue to exponential effects on growth as the trend suggests? The US is very much on the frontier (it is ranked 7th in the EoDB) and it's not so obvious that the benefits will accrue the same way. One simple way you could have a better idea about this would be to do the same graphs as you do above, but restricting it to countries that have a high enough level of income. Eyeballing it, it seems that there's more poor countries below the regression line and more rich countries above it, which suggests that the effect is diminishing, no? I.e., I suspect that the benefits get smaller, the richer you are, both in absolute and in relative terms... it'd be very interesting to try to think about this in a more formal setting. With respect to IV, you're right to say that these improvements have been subject to scientific scrutiny and it can be bad form to bring politics in these situations. But was he undue to characterize your policy positions as being closer to what is being proposed as priorities of the Republican party (i.e., "conservatives"), as opposed to the Democrats? I would suggest that no, even though he was incorrect and should have been much more careful at labelling you a conservative, specially since you have requested not to do so in the past. Let me ask you this, if he had written "Most of the so-called growth policies Cochrane propose, and that conservatives have prioritized, don't really target growth at all, just short-term efficiency.", would that have allayed your concerns with respect to that? As for the bait-and-switch, I agree with you that was uncalled for, as it does suggest a degree of deception, although I don't think he meant to imply that. Instead, having read a lot of what he's written and how much I think he admires you, I think he meant to suggest that you were, inadvertently, conflating growth and level effects, no more, no less. Regardless, it was inflammatory language, unnecessary and he should have used something else, if his intentions were as I read them (if he really meant it deceptively, he should really apologise). All in all, this was an excellent read, many thanks, particularly the summary of Jones. 6. I hate to be the guy that has to ask about the thing you said is obvious, what was is the story with Luxembourg, anyway? Is it just that it has a huge financial industry, relative to the size of its population? I've also heard that it's a statistical artifact of foreign workers commuting in from neighboring countries, but I've never been able to confirm that. 7. LOL, is this the state of the art in economic mathematics research? This is nothing more than what freshman electrical engineers study, or as found in Martin Braun's textbook on differential equations, see more here: https://en.wikipedia.org/wiki/Time_constant I guess some people with no knowledge of math might be impressed, and if those people are consumers of economist services then the math has proven its worth... 1. Wow... really, Ray? Are you trying to judge a discipline based on a blog post? It's like judging all hamburgers because you had one at a pub one-time. 8. Ray Lopez, let me remind you of Occam's razor. If there are two similar models but one is simpler, you should stick with that one. In fact, Romer, a reference in growth theory, recently criticised the excessive «mathiness» [1] in growth theory and economics in general. It is not that unfrequent to find a paper about macroeconomic dynamics where 4/5 consist of discussing the density of the Jacobian. Growth theory relies heavily on optimal control theory, which dates back to Pontyagrin and the Soviet Union (how funny). It should stay that way — using math as a language to describe and systematize the problem, instead of a bling-bling tool to impress others. Let's hope it continues that way. [1] - http://paulromer.net/wp-content/uploads/2015/05/Mathiness.pdf 1. Thanks Lopes. I found Romer's paper unconvincing, it's just the grumblings of an old man. Excerpt below. Does he realize the Solow growth model is premised on the Cobb's production function? That's one of the main assumptions, and if the data does not fit this stylized function then the model falls apart. There are other assumptions such as technology being exogenous, when clearly from my work in inventions I find you can 'engineer' an invention. However, Romer is right in that data (econometrics) is the future. It reminds me of in engineering, back before cheap and powerful computers, they tried to derive a 'closed form equation' to describe an engineering phenomena, which was a lot of work and often did not exactly capture the phenomena (though when it did, it was very powerful). Then computers got stronger and everybody moved to a finite element analysis numerical number crunching solution to engineering problems,which everybody uses today -RL Romer: “Piketty and Zucman ( 2014 ) present their data and empirical analysis with admirable clarity and precision. In choosing to present the theory in less detail, they too may have responded to the expectations in the new equilibrium: empir - ical work is science; theory is entertainment. Presenting a model is like doing a card trick. Everybody knows that there will be some sleight of hand. There is no intent to deceive because no one takes it seriously. Perhaps our norms will soon be like those in professional magic; it will be impolite, perhaps even an ethical breach, to reveal how someone’s trick works. When I learned mathematical economics, a different equilibrium prevailed. Not universally, but much more so than today, when economic theorists used math to explore abstractions, it was a point of pride to do so with clarity, precision, and rigor “ 2. You write:"... Does he realize the Solow growth model is premised on the Cobb's production function? That's one of the main assumptions, and if the data does not fit this stylized function then the model falls apart..." I studied with Solow and he never pretended all his partial differential equations actually had numerical solutions, whatever the production function being used. I didn't read Romer but I suspect he knows more about mathematical modeling than you do, whatever the field of application, economics or engineering. 9. The China/U.S. comparison should be in ppp dollars so China's GDP per capita in such a comparison is really$13,000 according to the World Bank and IMF. It doesn't change Cochrane's arguments at all but if looking at the red dot that is China on the graph, you should mentally raise it up a bit. So China's standard of living aside from a whole lot more pollution and a whole lot less free speech is 25 percent that of the U.S.

10. http://mungowitzend.blogspot.com/2015/12/isomorphic-mimicry-run-amok-john.html

11. Definitely a good item for discussion in my class.
Noah's approach has become: look at every topic through a political lens, draft a few disparate thoughts that can impress the general reader, but do not pass muster with those that actually know the economics of those issues. When called on the carpet, dismiss critics as "conservatives" or bad guys. He is certainly learning his approach from the Master!
Cheers.

12. My jaw just dropped open at the line "Let's look for a constant growth rate solution", and the following lines seem to indicate that you (or Jones, whatever) take the g_A at which exponents cancel as the resulting value because, well, that's the value at which exponents cancel and a constant growth rate solution results! What sort of justification is that? It is true that at this particular value of g_A the exponent is *a* solution to the differential equation you are investigating, but it is a singular solution whereas the general solution is proportional to (C-t)^{1/(1-phi)} and may be divergent depending on initial conditions.

1. This is a blog post summary, not a journal article of novel research. Go read the Jones references, if you find his math incomplete come back.

13. A very persuasive essay. Regarding needless politicization, however, I think Cochrane reacts too strongly. Maximization of efficiency is a well-known preoccupation of conservative economists (think Milton Friedman) and also of Cochrane, just as enhancement of social welfare is a well-known preoccupation of liberal economists. The left-right ideological model borrowed from political science, however dichotomous and over-simplistic it may be, seems entirely apt to me here. We know the mind of Cochrane through what he writes, and his writings are certainly conservative.

1. I do have a written record. It doesn't seem to me you're doing a very good job of reading. These points are directly contradicted even in this blog post.

2. I think it might help to separate two factors in this argument: (1) the politics and (2) the polemics.

I agree with Cochrane that here Noah Smith had engaged in the latter, and for this Cochrane's irritation with Smith is understandable.

For the remainder, I stand by what I said. Macroeconomics is politicized, suffused by ideology, and the preoccupation with growth and efficiency as social priorities is certainly a large part of right-wing economic thinking.

3. LOL - "... preoccupation with growth and efficiency as social priorities is certainly a large part of right-wing economic thinking".

What else can macro-economists credibly focus on but "growth and efficiency"? The rest is just value judgments about what is good or bad. That is philosophy, not economics.

14. I read your Economic Growth essay last month and I found it so uplifting and cogent that it made my entire day! I have convinced most of my co-workers to read it.

I find the pigeonholing of interesting economic phenomena into “liberal” or “conservative” terribly disappointing and unhelpful in mainstream economic writing. It flies in the face of searching for truth as near as we can find it. Our growth problems are too important to dismiss through the lens of which team you're on.

Thank you for helping us to understand the issues better, what possible solutions might exist, and more importantly, highlighting the seriousness of growth problems.

15. As usual, I agree with John Cochran. But what I always find lacking is frank discussion of policies.

Can we outlaw single-family detached housing districts and all other property zoning? That would boost growth. So would cutting "national security" spending by three quarters. Eliminating rural subsidies is a great idea.. Wiping out the VA would and eliminating the ethanol fuel program.

Bring it on....hey, who is on?

16. John Cochrane was right the first time: growth is derives endogenously from technical progress.

Work over the past 20 years firmly establishes three things: (1) semi-endogenous growth theory is wrong, (2) the data cannot reject the 2nd-generation endogenous growth model, and (3) in the latter, growth has no inherent tendency to stop.

The crucial equation of Jones’s model is

where A is productive efficiency and b<1. Dividing by A gives

The exponent b-1 of A on the right side is negative, so the right side goes asymptotically to zero if L is constant, driving growth to zero and implying that growthcan be sustained only if L grows.

The 1st-generation endogenous growth equation for technical progress is

which gives

As John notes, the dependence of growth on L (the well-known scale effect) is counterfactual.

Unfortunately for semi-endogenous growth, its growth equation also is inconsistent with the data: growth of income per capita is not systematically related to population growth. Indeed, the very graph that Jones used in his original article (JPE 1995) on semi-endogenous growth contradicts the theory it motivates: (1) the growth rate of A has been roughly constant and (2) the number of scientists in R&D has increased roughly linearly. A linear increase in scientists means the *growth rate* of scientists has been falling. In Jones’s model that means the growth rate of A should fall, but Jones’s own Figure 1 shows that did not happen.

Fortunately Peretto (JEG Dec1998, JME 1999), Dinopoulos and Thompson (JEG 1998), and Howitt (JPE 1999) have produced better theory, the 2nd generation endogenous growth model, with superior microeconomic foundations and that passes an array of tests that reject semi-endogenous growth. Its growth equation is

where m depends on underlying parameters, including policy parameters. There is no dependence on L and no tendency for the growth of A to die.

A substantial empirical literature pits semi-endogenous growth against 2nd-generation fully endogenous growth. 2nd-gen theory wins hands down. See Laincz & Peretto (JEG 2006); Ha & Howitt (JMCB 2007); Madsen (EconLett 2007, JEG 2008, JME 2010); Madsen, Saxena, & Ang (JDevEcon 2010); Madsen, Ang, & Banerjee (JEG 2010); Ang & Madsen (REStat 2011); and Madsen & Timol (REStat 2011) and other work cited therein.

2nd-gen growth theory has many policy implications that differ markedly from its rivals. One example is taxes. In 1st-gen theory, taxes reduce growth rates, but the evidence show tax effects that are weaker and less one-sided as 1st-gen theory predicts (Stokey and Rebelo, JPE 1995). Taxes have no growth effect at all in semi-endogenous theory because growth is driven entirely by population growth. In 2nd-gen theory, some taxes reduce growth, some increase growth, some have ambiguous effects, and some have no effects. A dividend tax, for example, increases growth. The tax reduces profit and so reduces the number of firms. There is no direct effect on the return to R&D but does have an indirect effect: by reducing the number of firms, it raises the rate of return to the firms that remain. There are fewer firms serving the economy, so they have a higher return to their activities. Thus a dividend tax will raise, not lower, the growth rate. (Peretto, JET 2007).

The economics of growth is a fascinating interplay of the economics of industrial organization and general equilibrium dynamics. 2nd gen theory is the nexus that shows how the two are tied together.

Anyone interested in understanding economic growth should meet Peretto, Dinopoulos and Thompson, Howitt, Madsen, and others.

1. Thanks for the great comment. Minor note, "growth can be sustained only if L grows" is not quite true; if L is constant you still get linear increases in output / capita. Not exponential, but not constant. Jones 2005 review has a response to "2nd generation" models.

2. The first part of John Cochrane’s reply to my comment seems to refer to transitional growth, which I did not discuss. John refers to linear increases, which is transitional growth that goes asymptotically to zero. In Jones’s semi-endogenous growth model, the balanced growth rate (i.e., steady-state growth rate) is zero in the absence of population growth. Along its adjustment path, the economy’s growth rate therefore should fall toward zero. We have not observed any such behavior in the growth rate in the world for 1000 years (Maddison 2001). Also, as I said in my comment, there is no correlation between the growth rates of income and population, contrary to the basic equation of Jones’s model.

The second part of John’s reply refers to Jones’s 2005 chapter in the Handbook of Economic Growth, which briefly mentions 2nd-generation growth theory. Jones’s discussion ignores the important issues, emphasizing instead red herrings.

Semi-endogenous growth theory consists of a reduction of the exponent of A in the Adot equation from 1 to a value less than 1. The reduction is an ad hoc attempt to eliminate the scale effect. It treats symptom without fixing the cause (an inadequate treatment of firm entry), leaving intact other problems with 1st-generation theory and introducing problems of its own. It also is inconsistent with much of what the IO literature tells us about R&D. In contrast, second-generation endogenous growth theory fixes the underlying problem in a way that is consistent with the IO literature, giving the theory a solid microeconomic foundation.

Instead of discussing those issues, Jones brushes aside 2nd-generation growth theory on the grounds that it is “very fragile.” By that he means that results change if the exponent on A on the right side of the 2nd-generation model’s Adot equation is not 1 but rather is less than 1. By Jones’s logic, the equations for radioactive decay (Ndot = -aN), the rate of nuclear fission (Ndot = aN), the dissipation of heat (Ndot = -r[T-N]), and the growth of bacteria (Ndot = aN) are all “very fragile” and should be discarded in favor of formulations in which N on the right side is raised to an arbitrary power x. Try telling that to the physicists and biologists!

Choosing between the competing theories of growth comes down to a matter of evidence. Which theory fits the data better? As I explained in my comment, a large battery of tests has been decisive on that score: the semi-endogenous model is resoundingly rejected and the 2nd-generation model is not. The two theories have several opposing implications. In every case formal tests reject semi-endogenous theory and fail to reject 2nd-generation theory. There even is evidence (Ulku, Applied Economics 2007) that the exponent in question has a value that is statistically indistinguishable from one.

The extensive empirical evidence can be summarized simply: semi-endogenous growth theory is a scientific failure, and 2nd-generation growth theory is a scientific success.

3. "there is no correlation between the growth rates of income and population, contrary to the basic equation of Jones’s model"

In my understanding, these models do not treat different economies as operating in isolation. Ideas spread across the world.

4. Ideas do flow across borders, but only to a limited extent because those of practical value (i.e., the ones that improve productivity) usually are either patented or proprietary. More important, though, is that we have clear cases where countries were virtually isolated from the rest of the world, had high population growth rates, and had very low growth rates of income per person: India and China before 1980. Also, the swings in world population growth rates do not match the growth of world income per person over the last 300 years. Furthermore, the semi-endogenous growth model has other testable implications that have been solidly rejected by formal tests that the 2nd-generation endogenous growth model passes.

5. Having done some research in the field of growth, I am inclined to agree with John Seater. There is a lot of empirical evidence (just to name a few: Zachariadis, 2003; Ha and Howitt, 2007) showing that endogenous models perform much better than semi-endogenous models. Jones' response is that transition paths from one steady-state to another are so long that there are indistinguishable from growth effects, and that the lack of correlation between population growth and productivity growth in cross sections and time-series may be due to the flow of ideas. The problem is that Jones' theory then becomes untestable. Moreover, for practical matters it also becomes irrelevant.

On topic, I think that whether the separation between level and growth effects is important depends on the size of the level effect and the duration of the transition path, which in turn depends on the policy under examination. If someone argued that raising the investment rate in physical capital can accelerate growth in South Korea, which already has a high capital-labor ratio, I would probably take issue because I would not expect the effect to be very long-lasting. But, I would not feel the same way if the claim was about investment in R&D. So I think it is a case-by-case issue. Yes, China's accelerated growth has been long-lasting, but China started very far from the frontier. In any case, even level effects are too important to ignore.

6. Just to add, this is not to say that I am not disappointed by Noah's attempt to politicize this issue.

7. "Level effects", as depicted, are definitely more important and easier to adopt by developing countries. I widh that would be even more obvious. Also, good ideas are everywhere nowadays. One should not neglect how musch entrepreneurial work (and institutional setup creation) is needed to make them reality. Think Google and driverless cars ...

8. The opposite strikes me as more probable - think of the problems of Greece imposing structural reforms, for instance - and that's why I disagree with the idea promoted by prof. Cochrane and others that removing borders will allow for a better match between skills and opportunities.

A warning: the European gypsies, also known as Roma, 14 centuries after their arrival in Europe still have DNA indistinguishable from DNA of current inhabitants of the Pakistani province of Sindh. Others had no problem getting assimilated so this border abolition project might usefully be placed on hold until the risks are better understood.

17. John, what do you predict will be the best parts of president Trump's economic policies? Did you hear him tonight? Lol...

18. I'm quite sure to find more efficient ideas.