Tuesday, May 6, 2014

Conservative economists assume what they want to prove, claim victory!



I have a new column out in Bloomberg looking at some arguments by conservative economists against Thomas Piketty's work on inequality. I stumbled last week across this post by Tyler Cowen, which Barkley Rosser helpfully put into context. Cowen claimed that we don't really need Piketty because several earlier studies "already give an explanation" for the observed wealth inequality. Really? It turns out, he suggested, that you don't need any stories about returns to investment growing faster than wages. Standard economic models have already shown that inequality may just be the consequence of simple things like differences in personal patience (rich having more, of course, and the poor less), or in the effects of random shocks to peoples' ability to earn over their lifetimes.

Really?

Having looked into it, I now think this is a perfect example of Chameleon Economics, as recently described so brilliantly by Paul Pfleiderer. You tuck some preposterous assumptions A into a model, derive some apparently interesting result X, and then hope that people will soon forget about A so you can go around saying "we've shown that X" holds. The preposterous assumptions A might even include an assumption that is essentially equivalent to X, so you've assumed the result you want to prove. This trick is the real basis of the papers that Cowen pointed to, but jeez -- the authors did such a good job of plastering their arguments over with 50 odd pages of technical mumbo jumbo that it took quite a lot of effort to see what they were up to. In the paper by Krusell and Smith, for example, you can read on and on in utter semi-conscious misery before you begin to find the real secret of what the authors have done, as they finally admit:

When the representative-agent model is altered only by adding idiosyncratic, uninsurable risk, the resulting stationary wealth distribution is quite unrealistic: there are too few very poor agents, and much too little concentration of wealth among the very richest. For this reason, we consider a version of the model with preference heterogeneity: agents have random discount factors, whose values have a symmetric distribution with a small variance and whose transition probabilities are such that the average duration, or life length, of a discount factor equals that of a generation. In this fashion, we incorporate genetic differences in the population that are passed on imperfectly from parents to children. We show that this model does succeed quite well in matching the key features of the wealth distribution.

In other words, they start out seeking an explanation for the unequal distribution of wealth -- why do some people have so much more than others? Ultimately, they find that this result tumbles directly out of their economic model, IF they make the assumption that some people in the model are more patient than others, and are therefore better at saving and accumulating wealth than others. There you go -- the whole result from that one assumption (plus some others)! Science advances! 

I'm reminded of the famous claim of the doctor in Moliere, explaining how opium induces sleep? "By virtue of a faculty," the virtus dormitiva, he said, "the nature of which is to put the senses to sleep." Fortunately, Moliere was writing comedy, not pretending to do science.

Anyway, how about the following for a funny coincidence. Courtesy of a kind invitation from Ole Peters, I'm spending May at the London Mathematical Laboratory, a small mathematics center in Central London. Last week we were discussing Piketty's book, which Alex Adamou, one of the researchers here, has been diligently working his way through. Ole boldly suggested that maybe we should try to get Piketty to come here and give a talk on the book, whereupon we all chuckled at the very idea, thinking it preposterous given the outrageous current demands on his time. Piketty seems to be on a worldwide tour of epic proportions.

Yet this afternoon we learned that, at the very moment of our discussion, Piketty was actually in the very same building, one floor above our heads, giving a talk to a public policy think tank! Had we been speaking a bit louder, he might have heard us!

39 comments:

  1. Pfleiderer probably has a point, but Krusell & Smith make no policy recommendations in their paper, which is really more on the theoretical side. In fact, their main contribution (in addition to novel computational methodology for solving these types of models - the "mumbo-jumbo", as you call it) can be interpreted as a negative result - adding idiosyncratic labor risk into standard model doesn't change results very much, so if you think heterogeneity matters, you need to have also something else going on. I think this is a valuable and nonobvious insight.

    As an illustration for "something else", they present an extension with stochastic time preference, but I don't think people take that as serious explanation for observed wealth inequality. More realistic way to obtain fat-tailed distribution of wealth is to introduce idiosyncratic risk into capital income as well, so that households face random multiplicative growth rate of their wealth, which leads to something like Pareto distribution in cross-section. Benhabib, Bisin & Zhu (2011) [1] is an example of such model in mainstream econ literature.

    [1] http://piketty.pse.ens.fr/files/BenhabibBisinZhu2011.pdf

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  3. Hi Ivan,

    As often with your comments, I agree very much with the core of what you say. Especially that a "more realistic way to obtain fat-tailed distribution of wealth is to introduce idiosyncratic risk into capital income as well, so that households face random multiplicative growth rate of their wealth." Absolutely. I'll have a read of the paper you mention from the mainstream economics literature. Thanks for the pointer. Conversely, I think you might find quite interesting a brilliant paper from the stat phys literature from 2000 by JP Bouchaud and M Mezard (here http://arxiv.org/abs/condmat/0002374). I did an earlier post on it (http://physicsoffinance.blogspot.co.uk/2014/02/is-inequality-approaching-tipping-point.html).

    I would be interested in your views. From a logical point of view, this paper isn't saying that "this is the cause of wealth inequality" in our world. Rather, it's saying that "we shouldn't be surprised to see such inequality because it ought to emerge out of the most basic aspects of how our economies work," with random multiplicative growth playing a key role (as you suggested).

    I guess what I found so irritating about the Krusell and Smith paper is that they didn't present their results as the valuable negative result (as you suggested they might have), but instead suggest that the "genetic differences" they assume in their model "does succeed quite well in matching the key features of the wealth distribution." It's all to easy to read that as "we've shown that the rich may just be genetically superior." [I'm not saying that these authors went that far, but their language puts the paper out there for others to interpret that way.... one of my Bloomberg commenters suggested as much -- the poor are simply "genetically dumber."

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  4. Ivan,

    I've had a brief look at the paper. Looks interesting. I'm glad they at least cite the physics literature (perhaps because of interaction with Xavier Gabaix, who has worked with Gene Stanley on econophysics stuff), although they pretty quickly dismiss it as lacking microfoundations. It seems like their conclusions (judging from the abstract alone) are pretty much like those in the Bouchaud-Mezard paper, i.e. taxes of various sorts can make wealth more equal (although I can't yet be sure, and I think their model has some aspects which are significantly different from the Bouchaud-Mezard work).

    More importantly, I wonder what you think about something else. If you've read at all the various critiques of the Piketty argument, you'll see that the focus on his claim that r > g in the recent past, and perhaps in the future. It seems to me that the key role of random multiplicative growth of capital in creating wealth inequality implies that it is quite easy to get increasing wealth inequality even if r = g, i.e. that this part of Piketty's argument really isn't necessary. Even if r = g, ff the processes in the economy involving multiplicative returns to capital become more important, i.e. if a larger fraction of overall economic activity is bound up with this kind of stuff, rather than wages, then you're going to get more inequality. R > g might well be sufficient for more inequality, but is by no means necessary. I wonder what your thoughts are on that.

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  6. I agree that speaking about "genetic" (even if not meant literally) differences in context of wealth inequality is not the most fortunate choice of language.

    I think I looked briefly at Bouchaud paper already before. I'm not familiar enough with this literature to judge how novel or influential it is. It seems that they make quite a few simplifying assumptions, and I suspect if those were translated into economics terminology you and other critics might find them just as questionable as you find assumptions in mainstream economic models. For example, symmetric agents that spend constant share of wealth on buying different types of stuff would be "ex-ante identical agents with Cobb-Douglas preferences" in econospeak.

    And yeah, they don't have any microfoundations. I'm no freshwater purist, but I think that deriving, or at least motivating behavior from some underlying principles is valuable if one wants to speak about policy. E.g. if government made substantial changes to taxes, one could use Bouchaud model to see how that would affect wealth distribution, if people's decision rules didn't change - but how realistic is that?

    I haven't read Piketty's book, so all my knowledge comes from reading some reviews. As I understand it, in the models we discussed, the distribution is fat-tailed due to the multiplicative growth, but otherwise its shape (e.g. top 1% wealth share) is constant over time. But I had the impression that central part of Piketty's story is not only that there is inequality, but that if r > g, wealth distribution becomes more concentrated (i.e. the tail becomes heavier, or pareto coefficient becomes lower) over time due to the inherent underlying dynamics of capitalism. My guess (could be wrong) is that to get such dynamics, one must have more explicit asymmetry across people - e.g. if there are two "classes", only capitalist class earns capital income, and wealth distribution is more unequal across capitalists than across workers, then if share of capital income goes up, the overall distribution will shift more towards inequality.

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    Replies
    1. Hi Ivan,

      I'm sure you have more important things to spend your time on, but I'm hoping you might help me clear up something in that Benhabib et al. paper you mentioned. I understand the general argument of the paper, but the authors also discuss the results of various "simulations" they've done - here I'm having a hard time figuring out precisely what they have done. My initial expectation was that they started with some random initial distribution of wealth (over some large number of individuals) and then propagated this forward using their stochastic process with, at each time step, a multiplicative (alpha) and additive (beta) component. After a large number of generations, presumably, they find convergence to a stable distribution. But I can't find anywhere in the paper any mention of the number of generation required to achieve convergence, or other such details, which makes me think that I'm misinterpreting "simulations." Are they instead just illustrating their theorems in several specific cases? I realize, of course, that this part of the paper may not be perfectly clear to you either, but if you have any ideas I'd love to hear them...

      Delete
    2. Yes, I think that's what they are doing - simulate a panel of households for a long time, then look at distribution at the end (when it should be close to the true ergodic distribution). I noticed they have posted replication files at

      http://www.econometricsociety.org/suppmat.asp?id=286&vid=79&iid=1&aid=5

      with some Matlab files that should run the simulation, but the code is not exactly clear either :)

      Delete
    3. So when they compare e.g. different tax regimes, they're really looking only at two stationary distributions, not at any transition dynamics. Transition should be easy to simulate too, but I guess they didn't do it because the model is rather simple, so that precise quantitative results about short-run dynamics might be hard to accept as reliable.

      Delete
    4. Thanks. I can't say that the description file is hugely enlightening! Unfortunately, I also don't have easy access to matlab to run the other files to see what happens.

      However, the more I look at this paper, the more it also begins to look to me like one of Pfleiderer's Chameleon models, or at least going in that direction. Let me explain why. The model claims to study how random multiplicative returns on wealth (capital risk, as they put it) can generate large inequality, including a fat tailed distribution of wealth, much like that seen in reality. A priori, I think that's a pretty weak claim -- since we've had stylized models showing this for essentially half a century. However, I recognize that the authors want to insert some microfoundations so they can make arguments about how policy steps will influence the probability distribution of the multiplicative returns (alpha, in the model). I assumed this is what they had done, using plausible values for the yearly multiplicative returns and showing that this dynamics rapidly leads to a highly skewed wealth distribution.

      BUT now I don't think this is what they have done at all. In fact, I believe they have more or less inserted into the model the very wealth differences they initially set out to explain. If you look at the key equations [5 and 6] in their Appendix A, it turns out that they select a random return, r, for each individual. But they assume this remains fixed for an entire generation. Their footnote 41 gives the values they use for the returns in their simulations. Using the first set of these, I calculated that the multiplicative factors alpha are 0.06 (with probability 80%), 0.21 (prob. 12%), 0.50 (prob. 7%) and 4.4 (prob. 1%). So, in one generation, they make the wealth of 1% of the population increase by a factor of nearly 100 relative to 80% of the population; another 7% of the population has their wealth amplified by a factor of about 10 relative to that 80%. It's no wonder at all that you rapidly get lots of inequality. In essence, they've shown that in a model in which it is assumed that the wealth of 1% grows about 100 times faster than the bulk of the population -- and where this imbalance persists over generations -- you end up with lots of inequality. I'm not convinced this was at all worth doing.

      Moreover, I'm quite suspicious of these values they chose for the alphas in their simulations. Why this artificial choice of 4 values? Where did the 0.32 come from? I suspect they chose this to make the distribution come out right, but then this just seems like adjusting the parameters on an arbitrary model to fit the data.

      I can't help but also note that it's rather disturbing that while they have various key parameters in the model defined to either two or even just one significant figure (T=45, rho = 0.04), they then report values of the tail index in their experiments with four significant figures!! That's not good, to say the least.

      Am I missing something? I tried to like this paper. I thought they were going to show how, with plausible assumptions in the year-to-year fluctuations in returns, even fairly small fluctuations can over time lead to huge wealth differences. Instead, they've shown that big differences in generational returns can lead to lots of inequality, which is quite obvious. At least that's what I've been able to get out of the paper.

      Delete
    5. Yes, rate of return is constant for the whole length of a generation (45 years). So if you get high realization of return, over the 45 years you accumulate lot of wealth and thus wealth of your heirs will rise a lot. On the other hand, there are many generations/families alive at each point in time, each born at different point of the 45-year window, and each having its own rate of return, so there's also a cross-sectional inequality at each moment (i.e. their results are not limited only to the long, "generational" timescale).

      I believe the parameters are taken mostly from other studies (beginning of section 5), they don't pick them just to match the distribution (which would kind of defeat the point). Anyway, sure the paper has limitations and leaves space for further extensions, but then which paper hasn't?

      I recently came upon another paper (not yet published): http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2322845 , which seems to do a similar thing in a lot more general (but still pretty neoclassical) model, so you may like it more. (also, the author, A. Toda, seems to have a previous publication on power laws at Phys. Rev. E).

      BTW, as a published writer/journalist I guess you could just try to ask these people directly if you have questions :)

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  8. Just let inflation rise to 10% for 10 years and inequality is gone.

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