Friday, May 6, 2016

Delong and Logarithms

Brad Delong posted a response to my oped on growth  in the Wall Street Journal. He took issue with my graph, reproduced here,

by making his own graph, here

He characterizes the difference between our graphs with his usual gentlemanly restraint,

"Extraordinarily Unprofessional!!:" "total idiocy" The University of Chicago and the Wall Street Journal Have Very Serious Intellectual Quality Control Problems

and so forth.

If you read Brad, you may wonder what skulduggery I used to make the plot. I will now reveal the dark secret. It's a clever Chicago-school mathematical trick:

Logarithms.

Now just how much of a sin is this? Well, growth theory is about growth, so it's pretty hard to do without logarithms. If thinking about percentage growth and running regressions with log income on the left hand side is a devious right-wing trick, I'm afraid we're going to have to throw out about 99% of growth theory and empirical economics, including much done by Brad's colleagues at Berkeley.

Furthermore, just look at the graph.  I invite anybody who has sat through a first-year econometrics class where they teach this devious technique to ponder my and Brad's plot, and think whether a level or a log fit is appropriate.

Brad raises one valid concern with all of empirical economics: Endogeneity. The graph is a correlation. How do we know that better ease of doing business causes better business, and not the other way around? In Brad's view, it is equally likely, I guess, that first a contry gets rich, and then it improves its laws and regulations.

I didn't mention this in the Journal, simply for lack of space (try to write anything in 950 words). In a previous blog post, here, I wrote a little bit about it.
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.)
(This post isn't hard to find. I linked to from my growth oped post. And if one is curious about "what does John have to say about endogeneity?" -- a rather obvious question, which I ask about twice at every seminar -- it is also possible to email me. )

That post goes on to survey a lot of academic literature on just how important good institutions are to economic growth.

But just think about it. Did North Korea or East Germany first get poor and then get bad institutions? Did the UK and US first get rich, and then develop our rule-of-law and property rights traditions? Is reverse causality at all a plausible explanation for the correlation? Just about every historical episode you can think of goes the other way.

Endogeneity is always an issue in economics, but Brad's case that I am too dumb to have even thought about it, or that this correlation obviously goes the other way,  does not hold up.

But apparently, Brad doesn't know about google, fact checking, or emailing for simple clarifications either. Otherwise he would know that I don't work at Chicago anymore, hardly a secret.

The notion that universities should practice "intellectual quality control" is interesting in this era of declining free speech. Brad, be careful what you wish for.  "Controlling" basic professional ethics may come first.

If anyone is still curious, I posted my data and program to my website, and this post describes it some more. I didn't clean it up well, as I never thought this would be controversial, but at least it documents what I did. Feel free to play with it as you wish.

Update: It's clear from many comments and the twitter storm that many readers, even trained economists, missed this basic point. My graph is an illustration of a conclusion reached by hundreds, if not more, papers in the academic literature. It is not The Evidence, or even particularly novel evidence. Were it so, standard errors, specification search, endogeneity, much better measures of institutions, etc. would be appropriate, as many suggest. My graph is just a quick graphical illustration of the conclusions of much growth economics, including much work by Jones, Acemoglu, Barro, Klenow, and many many others. Institutions matter to economic growth; bad governments have amazing power to ruin economies.  As always in writing, I should have made that clearer; but I thought this literature was familiar to the average economist-blogger.

Update 2: There is, I think, an important mis-specification in a regression of log income on the ease-of-doing business index, which Evan Soltas implicitly points out.  I referred to the index as "simple" and "crude" for this reason, but again it looks like this seemingly obvious point needs expanding.

The World bank's measure is mostly focused on the ease of starting small businesses. When we look at the regulatory sclerosis in the US, it is a much wider phenomenon, encompassing the tax code, social program disincentives, the  recent huge expansion of federal involvement in health and finance, general spread of cronyism, reduction in rule of law, and so forth. These affect large businesses as much or more than small businesses.

Clearly, as we look across countries, the ease of doing business is correlated with these wider legal and regulatory problems. Countries with bad institutions overall also have bad ease of doing business scores. But just as obviously, only fixing the ease of doing business indicators without fixing the larger legal and institutional failures that correlate with those indicators, won't do a whole lot of good, which is what Evan seems to find.

The regulatory program I outlined there and in the longer essay on growth (blog post herehtml here,   pdf here) went far beyond ease of doing business indicators, for just this reason.

Update 3: Or, seemingly obvious point #3 that seems to need an answer. A few commenters have questioned  how far "out of sample" one can go. At some point, yes, institutions are perfect and more income will not result from improving them. Where is that? 90? 100? 110? I don't know. But the local derivative is still high, no matter how you fit the "out of sample" points. If you don't think you can draw the line out to 100, going from 82 to 83 still has very large effects.

1. Wow! Nice response. Brad’s list of ciphers seems longer than usual, which makes your response more important than usual.

1. Thanks. Batten the hatches, you know what's coming.

2. I left off DeLong objection #4.

4. It is not reasonable to believe that China's per capita income grew 700% between 2000 and 2014. DeLong asserts that economists do not in general believe the official Chinese GDP statistics. You have not answered his complaint that you use Chinese growth as a central example in your WSJ article.

3. Take it up with the world bank, where I got the numbers. But for this point it doesn't really matter. Did Chinese per capita income grow 400%, or 700%, or 1000%? A modicum of freer markets lifted them from abject poverty to middle income status in less than a generation. This is one of the greatest improvements in human welfare ever. Sure they have a long way to go, including environmental issues. But it is an amazing transformation. It was not stimulus spending or monetary policy. And if you did not have data on other countries in front of you, you would have tut-tutted that it was all impossible looking just at Chinese data before 1980.

I don't get just how vitriolic this is. We know a lot of America is busted. We know how to fix it. We know that these things will improve growth, the only question being how much. Why is there so much attachment to the view that everything in American government policy is just perfect and you can't squeeze an ounce more growth out of it?

2. The comments on DeLong's blog are hilarious as always.

1. It is even more laughable the fact that the inconvenient comments are deleted.

3. When you google John Cochrane, it's not entirely obvious that you're at Hoover.

1. It's right there in the WSJ article DeLong is referencing.

"Mr. Cochrane is a senior fellow at Stanford University’s Hoover Institution"

2. Good points. Brad Delong is so wrong about where John Cochrane works these days.

4. what about when when your graph is unpacked from its log form as Noah Smith points out. The graph does look rather speculative.

http://noahpinionblog.blogspot.com/

Thanks

5. What's wrong with him?

6. I tend to be on the Keynesian side of debates but that was a good response to be fair...

7. delong's tone is annoying and impolite. But your choice of fit really isn't reasonable. If you are not going to use a linear fit, then a sigmoid of some kind that starts tailing off as the index keeps increasing would have been more appropriate. Of course, in keeping with style of wsj op-eds, your choice presents a more dramatic picture than reality. Which is unfortunate, because all this does is provides ammunition to those who say that conservatives are fundamentally unserious and resort to fudging the numbers to prove their points

1. Note John's lack of reply

2. Catch the update, read Hall and Jones and let me know what there is that I should still reply to.

3. I am not Anonymous, but after reading Hall & Jones and the update above I see nothing that suggests you have answered DeLong at all. Your conclusions go far beyond anything that Hall & Jones claim in their paper. It is true that they conclude that institutions matter a lot, but they do not quantify how much as you do - and DeLong does not disagree that institutions and ease of doing business matter. As I understand it, here are DeLong's objections:

1. You do not test your model in sample to see if it is correctly specified. If you do, the in sample data reject your model speciation. (Notice that while Hall & Jones use a log linear model, log linearity is the only similarity. You use different models, different data, and your conclusions are much more specific and DeLong is not objecting to log linearity in general. He objects that in your specific case the in sample data reject the log linear model specification.)

2. Your out of sample predictions depend critically on the log linear model to generate such stunning growth projections. DeLong objects to such projections as counterindicated by your own data and gives intellectual cover to an ideological position unjustified by science.

3. You pull a bait and switch. You use the World Bank Ease of Doing Business data to construct your model, but then suggest that the reforms advocated by Paul Ryan would result in the spectacular growth your model predicts if we could improve US EDB to 110. You provide no rationale to justify the implicit claim that the World Bank's measure Ease of Doing Business is in any way improved by implementing the proposals of Paul Ryan.

4. Agree. Nothing is so unprofessional as not including a structural model, specification tests and robustness checks using different proxy variables in your 950-word op-ed in a newspaper.

8. Really nicely done, John. Represents Hoover eel in substance and style.

9. Did you not write: "If America could improve on the best seen in other countries by 10%, a 110 score would generate \$400,000 income per capita, a 650% improvement, or 15% additional growth for 20 years."
And: "And, following the fitted line in the chart, Frontier generates \$163,000 of income per capita"

Delong just undid the logs and got the same numbers. Your op ed was a model without logic. There is not much difference between a #1 ranking in #10, but a major difference between a 50th percentile and a bottom 10%.

10. You are not charting growth. You are comparing income in one year with "ease of doing business" in that one year. A semi-log chart has no business in that comparison. And, it is not at all clear that "ease of doing business" can sensibly be mapped to a meaningful scalar quantity.

Back when I was studying physics (before law school) they always told us to step back from the formulas and ask ourselves if the numbers we were getting made any physical sense. You should have stepped back and asked yourself if the number you were projecting made any economic sense: pretty clearly it does not.

Back when I was studying numerical analysis, they taught us about the dangers of extrapolating with any fitted curve. Extrapolating with a fitted exponential (which is what you are doing) is outside the bounds of any sort of sound or reliable practice.

You may not like Brad Delong's choice of words but ignore the style and on substance I would agree with Brad.

11. Of course business should easy to conduct, as a matter of human and commercial freedom and for practical reasons (like properity).

My only quibble is that I wish the John Cochranes of the world would give full-throated and frequent roar to the idea of abolishing property zoning and decriminalizing push-cart vending.

These are practical changes that could immediately increase real GDP and dramatically widen business opportunities for ordinary people.

1. Benjamin the real magic happens when we improve the flow of investment through financial deregulation. Just think how much more growth we have already thanks to shadow banking.

12. Wow, you've gotten destroyed on this one, and rightly so.

13. What this debate really shows is that you can get a PhD in Economics without having a clue of what's going on in the growth literature.

14. Logarithms and growth go together, of course, but what is plotted here is not growth, but GDP/capita, which has something to do with growth, but is not the same thing. And as you say, this graph is not proof, but illustration. Is it already well-established in the growth literature that GDP/capita has an exponential dependence upon "ease of doing business"? Is this to be found in Hail and Jones?

15. The frontier does seem way out of the data Range, and the log scale makes that fact a lot less visible. One IQR out in logs is 100% out in non log in this case. To state that a better score on EoB would double income per cap in one of the richest countries in the world ... Unlikely? Obviously, not a Country where it would not Help, but i'd expect diminishing returns. Or in stats: check stochastic frontier modelling.

16. This is a perfect example of teaching students how to validate regression models (log linear versus polynomial). Alas none of the bloggers seems to have done it... A leave-one-out or k-fold cross validation should provide a statistical argument for the more "correct" model specification.

17. What did you do to Delong? screw his wife or something? Otherwise, I don't understand this level of vitriol. It's a news article, not an academic study, making a simple non-controversial point. People need to get a grip.

1. It appears that his motives are political. He also mixes in economic justification to strengthen the legitimacy of his position.

That is the reason I believe he attacks the Chicago school, the WSJ and purposefully refers to Mankiw as Harvard.

John, if you are reading this comment. Please check the "favorite links" on the right side of your blog. It is still written "Booth School of Business Best business school, coincidentally my employer". Perhaps you should change it since you don't work in Chicago anymore.

18. What I dislike about the salt water economists is their answer to every problem is bigger and bigger government intervention into the market. As if the market is some sort of puppet that you can pull with a string. That's not real life.

Comments are welcome. Keep it short, polite, and on topic.

Thanks to a few abusers I am now moderating comments. I welcome thoughtful disagreement. I will block comments with insulting or abusive language. I'm also blocking totally inane comments. Try to make some sense. I am much more likely to allow critical comments if you have the honesty and courage to use your real name.