## Saturday, 31 August 2013

### In defence of simplistic models

This post on methodology is related to recent discussions about the role of maths in economics (Matt has a good summary with the relevant links here), but is actually response to a comment by Chris B over at SciBlogs to my initialpost on Labour’s proposed ban on non-resident ownership of houses. (Yes, this post is long overdue. Events have conspired to keep me away from blogging for a couple of weeks.)

Chris says:
You know, the more I think on it, the more dissatisfied I am with this thought exercise. If only because Seamus has seen fit to call it a “very simple model of the New Zealand housing market”. It realy isn’t . It’s simply a fictional market with certain highly abstract asserted properties. No more realistic or useful than the various maths exercises from my own university level economics classes.
Fair enough. I should have said a simple model to help think about the New Zealand housing market. The point of this post is to ask whether simplistic models can be useful. Note that such models are unrealistic by design. If I were writing an academic paper, I would have used a much more complicated model, and if writing a problem set for an undergraduate class, something only a bit more complicated. But this was a blog post, so the model was designed to be easily solveable in your head. (I hope that the maths exercises from Chris’ university-level economics classes were more involved than this one; if not he was severely short-changed by his university.)

In general, a simplistic model is designed to make one or two points by stripping away every piece of reality except a specific thing that you want to highlight. Some of the assumptions one makes in doing this are simply removing irrelevant reality in order to focus attention on the key aspect of the question at hand. Others are more like dogs that don’t bark in the night; seeing what happens when you assume away some aspect of reality highlights how important that aspect is. Chris lists a whole bunch of assumptions in my model. I won’t go into these in detail, but I would argue that they all fit into one of these two categories. Some, like the assumptions about homogeneous preferences and housing quality are just assuming away irrelevant reality. Others, like the assumption of inelastic supply are non-barking-dog assumptions. As I noted in my original post, when you relax this assumption, you make the case against bans on foreign ownership stronger.

The realism or lack thereof of a model is therefore not a criterion for judging a model’s success. A simplistic model can be criticised for one of three reasons:

a) the intuitive point that is laid bare when all other reality is stripped away is so obvious that the point doesn’t need to be made;
b) the model doesn’t actually illustrate the point being made; or
c) the point is actually wrong, and the model fails because it stripped away some highly relevant aspect of reality.

The third is not necessarily a criticism. If a model’s intuition can be changed by adding in some relevant piece of reality, the process of starting with a simple model and then relaxing the assumptions lays bare what the crucial step is for generating a particular conclusion and informs where one needs to look for empirical evidence supporting it.

Now, in my post, I was looking to make two points: The first was that the price of houses depends on the current and future expected stock of houses and the current and future expected demand for housing (i.e. the willingness of people to pay to live in houses); changing the rules on who is allowed to be non-occupier owners of houses should not change the price of housing absent a mechanism for the policy to affect demand for occupancy or the stock. The second point was that if speculation is pushing up the price of houses, it is only because house prices are expected to increase in the future; attempts to restrict speculation without dealing with the underlying drivers only delay the issue.

Now I don’t think you can say that my model fails on the ground of being too obvious, as so much public commentary on housing policy simply routinely ignores these two points. Whether the model is successful in illustrating the point is very much in the eye of the beholder. For the third criticism, I certainly can imagine relaxing assumptions to generate different conclusions and inform a debate about what is the more likely state of the world. Chris, however, would prefer to eschew the simplistic model altogether. In his words:
Plainly the exercise does not remotely resemble the New Zealand Housing market. Why, then, should we have any particular faith in our ability to extrapolate from the though exercise to what will happen in the real-world economy.
In what sense does the model not resemble the New Zealand housing market? The model has both renters and owner occupiers. It has owners of rental properties who earn investment income from the ownership. It has a future expected increase in the demand for housing, and in that world has landlords earning a below-market rate of return. All describe exactly, say, the Auckland housing market. Yes, the real-world economy has other things as well, but it is important to understand the simple models before adding complications. What is the alternative?  Chris’ conclusion is as follows:
Perhaps a better approach to arguing against the policy on economic grounds would be to identify other places where it has been implemented and talk about the impacts which have resulted. Potentially tricky to isolate the impacts of the policy from other confounding factors, but if it can be done, there’s the advantage of being able to present some empirical evidence against it.
Alternatively, perhaps we might drop the thought exercise entirely as extraneous and talk specifically about how we expect foreign buyers will react to future restrictions on their activities, consequences for investment decisions and the like.
Not so fast. How do social scientists isolate impacts from confounding factors? They use theory. That is, they have a model or competing models in mind that would be consistent with some observed correlations but not with others. And how can you learn anything about how foreign buyers will react to restrictions on their activities and what impact that reaction will have for the housing market, if you don’t have a view about how their behaviour relates to conditions in the housing market, how other people will respond to that reaction, etc.?

In other words, careful empirical and behavioural analysis rests on models, and complicated models rest on simplistic ones. Non-careful analysis, in contrast, rests on unstated models, models that are potentially self-contradictory or rest on assumptions that have assumed away relevant reality but have never been made explicit.