以前、アンドリュー・ゲルマンピーター・ドーマンの効用理論批判を取り上げたことがあったが、その両者の最近のやり取りがゲルマンのブログで紹介されている。エントリには「計量経済学統計学の違い:変動する介入効果から効用に至るまで、経済学者は不変のモデルを好むようだが、統計学者は変動する方が安心する(Differences between econometrics and statistics: From varying treatment effects to utilities, economists seem to like models that are fixed in stone, while statisticians tend to be more comfortable with variation)」という長いタイトルが付けられている。

やり取りは、ある特定の変動に焦点を当てがちな経済学者の傾向についての議論から始まっている。ドーマンが、最近階層モデル(hierarchical modeling)でリスク分析をしたところうまくいったが、計量経済学に何十年も携わってきたにも関わらず、階層モデルなるものをこれまで知らなかった、と書いたのに対し、ゲルマンは次のように答えている。

...it’s my impression that economists are trained to focus on estimating a single quantity of interest, whereas multilevel modeling is appropriate for estimating many parameters. Economists should care about variation, of course; indeed, variation could well be said to be at the core of economics, as without variation of some sort there would be no economic exchanges. There are good reasons for focusing on point estimation of single parameters—in particular, if it’s hard to estimate a main effect, it is typically even more difficult to estimate interactions—but if variations are important, I think it’s important to model and estimate them.


I’ve been mulling the question about economists’ obsession with average effects and posted this on EconoSpeak. I could have said much more but decided to save it for another day. In particular, while the issue of representative agents has come up in the context of macroeconomic models, I wonder how many noneconomists — and even how many economists — are aware that the same approach is used more or less universally in applied micro. The “model” portion of a typical micro paper has an optimization model for a single agent or perhaps a very small number of interacting agents, and the properties of the model are used to justify the empirical specification. This predisposes economists to look for a single effect that variations in one factor have on variations in another. But the deeper question is why these models are so appealing to economists but less attractive (yes?) to researchers in other disciplines.


There is the so-called folk theorem which I think is typically used as a justification for modeling variation using a common model. But more generally economists seem to like their models and then give after-the-fact justification. My favorite example is modeling uncertainty aversion using a nonlinear utility function for money, in fact in many places risk aversion is _defined_ as a nonlinear utility function for money. This makes no sense on any reasonable scale (see, for example, section 5 of this little paper from 1998, but the general principle has been well-known forever, I’m sure), indeed the very concept of a utility function for money becomes, like a rainbow, impossible to see if you try to get too close to it—but economists continue to use it as their default model. This bothers me. I don’t think it’s like physicists starting by teaching mechanics with a no-friction model and then adding friction. I think it’s more like, ummm, I dunno, doing astronomy with Ptolemy’s model and epicycles. The fundamentals of the model are not approximations to something real, they’re just fictions.


So my deep theory goes like this: the vision behind all of neoclassical economics post 1870 is a unified normative-positive theory. The theory of choice (positive) is at the same time a theory of social optimality. This is extremely convenient, of course. The problem, which has only grown over time, is that the assumptions needed for this convergence, the central role assigned to utility (which is where positive and normative meet) and its maximization, either devolve into tautology or are vulnerable to disconfirmation. I suspect that this is unavoidable in a theory that attempts to be logically deductive, but isn’t blessed, as physics is, by the highly ordered nature of the object of study. (Physics really does seem to obey the laws of physics, mostly.)
I’ve come to feel that utility is the original sin, so to speak. I really had to do some soul-searching when I wrote my econ textbooks, since if I said hostile things about utility no one would use them. I decided to self-censor: it’s simply not a battle that can be won on the textbook front. Rather, I’ve come to think that the way to go at it is to demonstrate that it is still possible to do normatively meaningful work without utility — to show there’s an alternative. I’m convinced that economists will not be willing to give this up as long as they think that doing so means they can’t use economics to argue for what other people should or shouldn’t do. (This also has connections to the way economists see their work in relation to other approaches to policy, but that’s still another topic.)
And I’ve been thinking more about your risk/uncertainty example. Your approach is to look for regularity in the data (observed choices) which best explains and predicts. I’m with you. But economists want a model of choice behavior based on subjective judgments of whether one is “better off”, since without this they lose the normative dimension. This is a costly constraint.
There is an interesting study to be written — maybe someone has already written it — on the response by economists to the flood of evidence for hyperbolic discounting. This has not affected the use of observed interest rates for present value calculation in applied work, and choice-theoretic (positive) arguments are still enlisted to justify the practice. Yet, to a reasonable observer, the normative model has diverged dramatically from its positive twin. This looks like an interesting case of anomaly management.

この両者のやり取りについてデロングがEquitableブログで以下のようにコメントしている(H/T Economist's View)。

  • 期待効用の意思決定理論は規範的なものであり、実証的なものではない、と理解している。それは、リスクのある環境で目的を達成するために人々がどのように行動すべきかを示すものであり、どう行動するかを示すものではない。期待効用の意思決定理論を人々に教える意味は、確率が分かっている少額の賭けについては人々はリスク中立的であるべき、ということを知らしめる点にある。教える手順は以下の通りとなる。
    1. 人々は少額の賭けについてリスク中立的ではない。
    2. 合理性に関する基本的な考察を取り入れると、目的達成のためには少額の賭けについてリスク中立的であるべき、ということになる。
    3. 従って人々は少額の賭けについてリスク中立的であるべき、ということになる。
    4. 他人を相手に賭けをしている際には、賭け金が少額といえどもリスク回避的になるべきではない。賭けの相手の引き受け手がいるということは自分の主観的確率が偏っていることを意味し、主観的確率に基づく期待効用の意思決定理論は自らの偏りに関する情報を織り込んでいないため、あらぬ方向に導いてしまう。
    5. 自然を相手にした少額の賭けについてもリスク中立的に行動すべきか――そうすることが不安、延いては不幸な感情をもたらすとしても――という問題については未だ回答が無い。
      • デロング自身は、不安や不幸という感情を持たないように自分を訓練し、リスク中立的たるべき、と考えている。
  • 人々が実際にベイズ的な期待効用に基づく意思決定を行っていないにも関わらず、そうした経済主体の参加するものとして市場をモデル化することについて、経済学者の考え方は以下の三つに大別される。
    1. その問題について考えたことさえない。
    2. 個人が期待効用に基づく意思決定を行っていないとしても、組織は、認知に関する制度や手続きによって、期待効用に基づく意思決定者のように振る舞う。
    3. 市場の失敗は個人が期待効用の意思決定理論に沿わず、それを補填する制度も存在しないことから起きる。
  • 第三の考え方をする経済学者がごく少数に留まり、第二の考え方をする経済学者が存在する、という事実によって、ゲルマンが経済学をプトレマイオス天文学に喩えたことにデロング自身も100%同意する。