Economics as a subject is subject to fierce criticism these days. Most recently Paul Romer provoked a serious discussion around the usefulness of contemporary macroeconomics. I think the critique is justified. DSGE models need to be updated and banks as money creators should be included in the models. For reference, I recommend for example the following sources:

http://www.imf.org/external/pubs/ft/fandd/2016/03/kumhof.htm

http://www.bankofengland.co.uk/research/pages/workingpapers/2015/wp529.aspx

Ideally, economic business cycles should be modelled endogenously. This would mean that the system would produce oscillations inherently around perhaps some steady state. Contemporary DSGE models according to my knowledge are driven by external stochastic shocks. Maybe altogether better models can be developed, but I guess the point is that we need to have macroeconomic models that are ontologically sound and at the same time have microfoundations. This is no doubt very difficult.

However, today I am blogging about economic rationality and the theory of decision making in general. To me it seems that when people criticise economics, quite often one hears allegations of the type “man is not rational” “markets are not efficient or rational” or something of this sort. I would like to bring some structure into this debate here.

**Choice theory, utility functions and convex programming**

First of all, economic rationality is basically a set of axioms that we assume in order to establish a tractable model framework. This mostly means that if one wants to have for example a meaningful optimization scheme for consumer choice, we need to have a differentiable and therefore nice utility function so that we can try to find a constrained maximum and thus an optimal choice. Microeconomics is basically convex non-linear programming.

These axioms are technically what is called a total preorder induced by a binary (preference) relation on some set of alternatives. They are

- reflexivity
- totality
- transitivity

Basically we assume that all pairs of alternatives can be compared and that there are no loops. This notion of rational preferences does not say anything about moral good or what is to be pursued on ethical grounds. It is merely a reasonable set of assumptions for a decision maker. So economic rationality does not rule out anything like genocide or crime of what have you.

Armed with these and some topological considerations, one can represent the preferences of the decision maker with a nice utility function. Then one can proceed with optimization programme given material constraints.

**Choice under uncertainty**

When one assumes that the outcomes are uncertain, things get more difficult and interesting. First of all now we are making choices around some collection of probability spaces, so that we need to pick the right or the most suitable probability measure. In economics textbooks one usually talks about lotteries, but I think it is best to talk about random variables or probability measures.

So we assume the previous total preorder over the set of random variables/probability measures and we also assume additionally an axiom of independence and continuity (topology again). Enter John von Neumann. What we have is the expected utility paradigm. This theorem says basically that if the assume these axioms over random variables, the preferences can be ranked according to

Which is just the expected utility given a utility function u(.). So this is how a rational decision maker picks among things under uncertain payoff. This is quite useful. Only that is not empirically really accurate. According to data, people tend to deviate from this kind of EU -behaviour. We tend to overestimate the significance of events with small probability. So we expect too much and too little. For details, read e.g. the book “Thinking ,fast and slow” by Dr. Daniel Kahneman, a nobel laureate.

Maybe one should consider alternatives to EU-behaviour. This could be straightforward, as the representation can be established quite easily using some basic tools of linear vector spaces, like hyperplane separation/Hahn-Banach theorem and Riesz’s representation theorem in the case of Hilber Space. I’m aware of prospect theory, rank-dependent utility and dual choice theory by Yaari. Maybe one could still improve?

**Rational expectations, efficient markets and all that**

What about rational expectations and the efficient market hypothesis? Rational expectations is an assumptions that expectations are unbiased. So in other words we do not make systematic errors in forecasting. This seems plausible to me. EMH (efficient market hypothesis) in turn assumes that all information is already priced in financial assets. Plausible?

EMH does not imply that large deviations are precluded. Efficient market hypothesis is really about the price process being a martingale. So again, the expected price of tomorrow should be the same as today. Actually it is rather hard to assume otherwise because of arbitrage opportunities. If expected price was higher than todays, one should buy a lot, which would drive up the price today and vice versa. SO actually EMH is a rather plausible assumption.

So in other words, as long as the expectation exists, we can have EMH even with extreme events like non-integrable variance, like in the case of alpha-stable distributions.

Once again: extreme variation in prices does not imply that EMH is wrong.

**Rationality is not a moral statement**

In economics anyways. Rationality in economics is about being coherent and consistent. In economics, human behaviour is modelled through an optimizing entity. Think of dynamic programming and optimal control. The Bellman optimality criteria says basically that if one travels from A to C through B and the route is optimal, it implies that the route from B to C is also optimal. In game theory this is basically the same as subgame perfection. It is also backward induction in other instances. Economics is about optimizations as we are maximing profit or welfare or utility.

**Are we always selfish according to economics?**

In short: no. Economics only assumes usually a total preorder on the set of alternatives. This does not preclude in anyways choices where one gets utility from being unselfish. Again, economic rationality is about consistency.

There is however one interesting problem at the very foundations of economics. It is called the integrability problem. Basically the question is given some observed action/choice, can we construct a utility function for the decision maker that always makes the action rational? I guess this might be interesting for some scholars of philosophy of science.