macro models taken at face value

I've been thinking a bit more about complete markets. Funnily, it was the first economic concept that I got in touch with in my math undergrad, although all I learnt about it back then was that it meant injectivity of the mapping from the probability space to the payoff space, which was good for throwing some measure theory at it.

Basically, in an economy with complete markets it is possible to costlessly write perfectly enforcible financial contracts on any current or future event and trade them on a competitive market. It's hard to explain in basic language, because it's pretty far from reality. If the world was a roulette game, then complete markets would be the existence of a competitive exchange in which a set of 37 assets are traded before each spin of the wheel, each paying off a fixed sum in the event that the roulette ball falls into the corresponding pocket.

The concept is applied quite pervasively in macroeconomics, international economics and finance, and forms the starting point for almost every analysis (at least that's what I've been taught). Imposing it has some very strong consequences. One is that, assuming standard preferences, consumption growth equalises among all agents. So consumption comoves perfectly between any two agents inside a country, and consumption per capita comoves perfectly across countries. In other words, the ratio of consumption per capita never changes across countries and within countries.

Of course, such a model prediction is just nuts. You needn't even look at data to know it won't fit. Just for fun, I made a few graphs anyway showing consumption per capita across countries. If two countries participate in complete markets, then the prediction is that the ratio of their consumption per capita is constant. So here are the relevant ratios of some countries with respect to Germany (sorry for the home bias in choosing a reference point). The data are in PPPs straight out of the Penn World Tables.

Here are some Western economies:

And some Emerging Markets:

Of course, consumption per capita relative to Germany is not constant (not within the Eurozone and not outside of it). A country like Singapore has caught up enormously while the difference to France has come down (if you believe the PWT of course).

Clearly, complete markets are not a good idea to describe long-run consumption growth across countries. I think that's mostly due to the implicit assumption that agents know, observe and can contract on exogenous shocks, whereas in reality we don't even know what those shocks are (see also my earlier post).

Unfortunately, complete markets lead to bad predictionsat business cycle frequency, too (see Heathcote & Perri ). And in closed-economy macro, they don't depict reality well either, since they essentially move a model towards a representative consumer environment which has been countlessly criticised (Noah Smith's latest post on the Euler equation is a case in point).

And yet, complete markets are the assumption you start with in macro and international macro. Why is that? The easiest answer is that it simplifies things in a model. It essentially allows you to have a representative consumer, which is more convenient for anyone who i) doesn't want to spend much time on getting a model started, ii) cares only about the supply side, or iii) wants to draw easy policy conclusions without distributional issues. In any case, you can focus on other things you want to analyse. That's a reasonable point of view: As economists, we produce models as stories to explain certain aspects of the economic sphere, and some models fit some purposes and others fit others. After all, we economists are not trying to have a unified theory that is consistent with all aspects of our data at once. Of course physics, the science we are said to envy, is aiming at exactly that, but that's different.

What I want to get at is that this scientific leap of faith is not particular to complete markets. As economists, we often build models to shed light on some aspect of the economy, complete of course with testing, calibrating, estimating against selected aspects of economic data. But the building blocks of these models, if taken at face value, provide many more predictions about the data than those we analyse, and a lot of them are completely at odds with the data! Calvo pricing, the exogenous TFP process, Modigliani-Miller, the Euler equation, default rates with credit frictions, the representative agent, the CRS production function, Nash equilibrium, even expected utility maximisation, you name it.

Now here's something odd: Sometimes, people use counterfactual model predictions to strike down a paper, and sometimes they are just okay with them. I cannot discern a pattern in this! It makes me feel I'm completely missing something in my field.

Take the attacks on New Keynesian models. Many people say these models aren't valid because they imply that individual firms change prices very infrequently, which is not true in the data. On the other hand, I have never seen anybody criticise a model because it has an Euler equation, although that also implies counterfactual model predictions on consumption growth. Is there a rule that justifies which type of counterfactual model predictions are acceptable and which aren't? Or maybe it's just okay as long as the paper is "convincing"?

One candidate for a rule could be that counterfactual predictions are okay as long as they're "microfounded". I'm not sure what microfoundations are but I think it means that a model outcome is the result of agents' choices in some constrained optimisation problem in which there is no a priori restriction on choices, only a weighing of costs and benefits. Is this the right way to go? There has been a formidable exchange of views on this position recently (e.g. here, here and here); in any event, the complete markets predictions would pass this test.

Another rule could be that models delivering counterfactual predictions are acceptable if the predictions would actually be accurate under some ideal conditions. That is a very powerful argument, and part of the bread and butter of natural sciences. One standard comparison is to the concept of gravity in elementary physics. The theory states that the gravitational force is such that any object is pulled towards the ground with constant acceleration. In particular, a feather and a cannonball thrown horizontally from the same height are predicted to reach the ground at the same time. That's of course completely at odds with what we usually observe, but it is only so because of air friction (and, as I just learned from Wikipedia, buoyancy). In a vacuum, the "model prediction" fits the data perfectly. So it makes sense to start from the constant acceleration model and then factor in other effects afterwards, which involve more complex calculations.

In the same way, we can argue that consumption behaviour under complete markets, or the representative agent Euler equation etc., would be accurate depictions of reality in an idealised economic setting. Then, if we want to make predictions for the world we live in, we start from there and incorporate all kinds of frictions. Such is indeed the agenda of a good part of  macroeconomics, where entire research programmes study how to extend the standard neoclassical models by including heterogenous agents, occasionally binding borrowing constraints, private information, endogenously incomplete markets, rational inattention and much more.

But it's not so clear whether this is a good strategy in economics, even if it is successful in physics. There, we can actually create the idealised conditions and do experiments - we can generate a vacuum and test constant gravitational acceleration - or in their absence we can make repeated experiments to measure the deviation from the prediction and find regularities in that. This is difficult to do in economics, and particularly macroeconomics, where we can rarely do experiments. As a consequence, the idealised conditions and the predicted behaviour are often not the product of experimental research but of some axiomatic approach, like expected utility maximisation or Nash bargaining. To my taste, the justification that the data don't fit because of some missing "friction" becomes a bit weak.

But there is still a very pragmatic merit to thinking in these terms: They provide a common, simple framework that we can use to start thinking about things. We as economists might not understand every paper with its particular setup, but we all understand complete markets, and so we can exchange ideas starting from there. And when we want to analyse a new problem, we have a baseline from which to start exploring. In this sense, we're functioning a bit like an expedition into some unknown land: we build a basecamp where we are comfortable and safe, and then explore the territory from there. When we get stuck and the terrain becomes too difficult, we can always return to the basecamp to devise a new strategy and try again the next day. That way, when we want to think about inflation inertia, we can start with Rotemberg or Calvo pricing and develop our ideas from there, even if we don't think it's a good description of the world - at least it's a starting point. I can see nothing wrong with this approach. The only caveat with it is that we have to be ready to move our basecamp as we explore our territory further. There is no guarantee that the initial spot we picked will remain ideal forever (it might only be a local optimum, so to say). I guess that is what behavioural economists are trying to convince the rest of the profession of for some while now. They yet have to show that their "basecamp" is the more useful one, but usefulness should really be the main criterion. To use a really heavy-handed analogy: You can perfectly describe the motions of planets using a geocentric system by putting in lots and lots of frictions. But what people eventually discovered was that it is much easier to start from a heliocentric system, for which you need much fewer "frictions" to get rid of counterfactual predictions. Of course moving that basecamp wasn't particularly easy either.

In any case, criticising fundamental building blocks is easy, but coming up with alternatives is hard.  The alternatives to the neoclassical DSGE "basecamp" that are out there are obscure and/or unwieldy (naturally, since the status quo has been worked on more). Certainly, I don't really have the competence to plant a new basecamp. Nor would it be wise to start working on that: First I have to finish my PhD...