Using and Misusing Mathematical Models

by Dave Schuler on February 5, 2010

This morning I want to make a brief comment about Paul Krugman’s column for today, not because I necessarily disagree with it but in order to reflect on the use and misuse of mathematical models in economics or anything else for that matter. Dr. Krugman observes:

These days it’s hard to pick up a newspaper or turn on a news program without encountering stern warnings about the federal budget deficit. The deficit threatens economic recovery, we’re told; it puts American economic stability at risk; it will undermine our influence in the world. These claims generally aren’t stated as opinions, as views held by some analysts but disputed by others. Instead, they’re reported as if they were facts, plain and simple.

Yet they aren’t facts.

That’s quite right. They aren’t facts. They’re conclusions drawn from some combination of mathematical models of the economy, observed facts, and, probably, intuition into people’s behavior. And when Dr. Krugman continues:

Let’s talk for a moment about budget reality. Contrary to what you often hear, the large deficit the federal government is running right now isn’t the result of runaway spending growth. Instead, well more than half of the deficit was caused by the ongoing economic crisis, which has led to a plunge in tax receipts, required federal bailouts of financial institutions, and been met — appropriately — with temporary measures to stimulate growth and support employment.

The point is that running big deficits in the face of the worst economic slump since the 1930s is actually the right thing to do.

that isn’t a fact, either. It’s another conclusion derived from mathematical models, observed facts, and different intuitions into human behavior.

You may have seen the graphs, produced by President Obama’s economic team, showing what unemployment would have been in 2009 and 2010 without the spending package they supported and with the spending package they supported. Their predictions were wrong both in amplitude (how high unemployment would get) and frequency (the period over which unemployment would continue to rise). The most obvious conclusion from that is that their models were wrong.

However, continuing to refer to these models as if they were facts is even more wrong. Taking a single set of incorrect assumptions and deriving two sets of incorrect numbers from them, varying one parameter, tells you exactly nothing about the underlying reality.

I don’t know if deficit spending is an effective means of stimulating economic growth or not. It’s certainly what I was taught when I took economics. It’s not the model that determines whether it’s right or wrong but the underlying facts. It may be possible that the optimal deficit spending package implemented with perfect timing could have the predicted effect, real deficit spending packages implemented in real timeframes don’t. It’s the facts that determine that not the models.

In a few minutes the Bureau of Labor Statistics will be presenting us with more facts or something approximating facts: last month’s unemployment figures. Ignore the models and consider the facts, whatever they may be.

{ 8 comments… read them below or add one }

Andy February 5, 2010 at 7:56 am

And fear-mongering on the deficit may end up doing as much harm as the fear-mongering on weapons of mass destruction.

Oh my…..

Drew February 5, 2010 at 10:10 am

Although its true that deficit spending/total debt concerns are not “facts,” one would do well to beware the bond market, and observe the current situation in Greece, and the concerns about Japan as it edges into a non-saver country.

Further, take a look at our total debt to GDP, which includes the off balance sheet items.

Dave Schuler February 5, 2010 at 10:17 am

Reminds me of James Carvell’s wisecrack that when he died he wanted to come back as the bond market so everybody would be afraid of him.

In all seriousness the bond market tells us two things. First, it’s a measure of how people are seeing long term prospects. That’s subjective. But it’s also an objective measure of how expensive it will be for governments and other institutions to raise money. Neither look particularly rosey right at the moment.

Drew February 5, 2010 at 1:16 pm

I’m not sure the bond market is as subjective a view of long term prospects as you say. Debt financing of the national debt is really no different than refinancing a corporate loan. And there, as in public finance, a quantitative assessment of the need vs the available funding is made.

Now I know that public financing has more options than private. But we are getting way down the curve not just on what the rate required to attract capital might be, but on absolute availability.

Andy February 5, 2010 at 7:06 pm

I remembered this 2003 Krugman post just a few minutes ago and looked it up. Read them side-by-side or one after the other. The only conclusion I can make is that Krugman doesn’t bother to read what he’s previously written on a topic.

Steve Verdon February 5, 2010 at 7:12 pm

Models are nothing more than tools for trying to understand the world around us. As such they are invaluable tools, but they are limited tools just as a hammer is invaluable, but also limited.

Consider this part,

I don’t know if deficit spending is an effective means of stimulating economic growth or not. It’s certainly what I was taught when I took economics. It’s not the model that determines whether it’s right or wrong but the underlying facts. It may be possible that the optimal deficit spending package implemented with perfect timing could have the predicted effect, real deficit spending packages implemented in real timeframes don’t. It’s the facts that determine that not the models.

The model is mis-specified, or its assumptions are not being taken into account. If the model abstracts from political “gaming” then the model is going to give the wrong answer. The people who came up with the model and those who are considering basing policy on it, need to take into consideration this simplification. The model doesn’t include the political dimension and that there could be things like obstructionism, pork barrel polticking, etc. As such, it is an idealization: in a perfect world this is the best result…we live in an imperfect world and the results of the model are unlikely to obtain.

Ignore the models and consider the facts, whatever they may be.

No, this is wrong. We have to evaluate the efficacy of models in light of the facts. Ideally what we want to know is the following:

Is a given model true? How do we determine this? One approach is via the language of probability:

Prob(M1|Facts)

We can use Bayes theorem to come up with:

Prob(M1|Facts) = Prob(Facts|M1)*Prob(M1)/Prob(Facts)

In other words how likely are the facts given model 1 is indeed true times our initial guess at the probability of model 1 being true, divided by the probability of the facts being true in general. If the facts result in

Prob(M1|Facts) > Prob(M1) then that indicates support for the model. It can even be generalized so that we can compare Prob(M1|Facts) vs. Prob(M2|Facts) and so forth.

Ignoring the models means you have no framework whatsoever in which to evaluate the implications of the facts–i.e. data. You NEED both!

Dave Schuler February 5, 2010 at 8:14 pm

Believe me, Steve, I understand the nature and usefulness of mathematical models. I developed my first computerized mathematical model more than 45 years ago.

However, observation is key and you need to evaluate your model against the data not the other way around.

Steve Verdon February 8, 2010 at 11:57 am

However, observation is key and you need to evaluate your model against the data not the other way around.

I know that is what I just said as well, but this does not mean ignore the models and look only at the facts. We need both.

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