In defence of simplistic models

By Seamus Hogan 02/09/2013

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

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?
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

 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.