The Case for Formal Models

"Arguing in My Spare Time" No. 2.11

by Arnold Kling

August 14, 1999

May not be redistributed commercially without the author's permission.

I was re-reading Francis Fukuyama’s "The Great Disruption" on the airplane the other day, when the pilot came on to the speaker to announce that we were headed into "turbulence" near our Denver destination. (The next day, the storms to which he referred were the lead headline in the local newspaper.) He requested that all passengers return immediately to their seats and fasten their safety belts.

I glanced in the direction of the bathrooms, expecting to see people retreat unhappily from the queues to their seats. Instead, nobody moved from the aisle. On the contrary, additional people stood up and joined the lines. The pilot repeated his warning, this time more sternly, and still the queue for the lavatory did not diminish.

What I observed was a classic illustration of a central thesis of Fukuyama’s new book. I was witnessing the dramatic breakdown of hierarchical authority that has taken place since the mid-1960s. Thirty-five years ago, if you were on a plane and the pilot told you to sit down, then you SAT DOWN.

Many commentators, including myself, have suggested ways in which the information revolution has diminished the comparative advantage of bureaucracy and increased the advantage of trial-and-error innovation in the market. Fukuyama’s thesis is that this phenomenon is what has caused the breakdown in passenger discipline. The entrepreneurs keep getting up to go to the bathroom after the pilot tells them to fasten their seatbelts.

I do not mean for this essay to serve as a review of the entire book, which examines many interesting issues with great depth and breadth of erudition. All I will say is that if after reading "The Great Disruption" you do not find yourself bringing it up in conversation with your friends, then you need to make some new friends who have more intellectual curiosity.

The way that "The Great Disruption" motivated me to write an essay is that it made me appreciate the formal methodology that I was taught in economics. I am left with the feeling that I do not grasp Fukuyama’s model of the world. I found myself wishing that he would write up a few equations to make it easier for me to understand.

One of the key concepts in "The Great Disruption" is called "social capital." This sounds like an interesting concept. The term "capital" suggests something that depreciates and gets replenished, which relates to Fukuyama’s thesis that social order can be disrupted and restored.

Fukuyama says that social capital might be difficult to measure directly. Instead, he suggests that it is easier to use negative indicators to identify trends in social capital. He says that indicators of a decline in social capital include higher crime rates, higher divorce rates, and higher illegitimacy rates.

Something in the spirit of these negative indicators would be medical malpractice costs. Medical malpractice suits are expensive. They spawn malpractice insurance, which is costly. And they change doctor behavior in a way that may increase health care costs. If we had more trust and less malpractice litigation, this might lead to improved economic efficiency. However, as Fukuyama points out, we do not know what the alternative to private tort law might be. If the alternative is centralized regulation to control doctors, that regulation could prove to be even more costly than the malpractice system.

The foregoing suggests that the term social capital could very well describe something that relates to the costs of different institutional arrangements. But I still do not know what it means.

When economists talk about physical capital, they use equations involving output (Y), the capital stock (K), and next year’s capital stock (which I might call K*), and other algebraic constructs. All of this formal notation helps to clarify what we are talking about when we are talking about physical capital. In particular, it helps to sort out dynamics and causality.

The description of physical capital is dynamic, in that the stock of capital in one period is tied to the stock in the previous period. It would be valuable to sort out the dynamics of social capital, as well. For example, Fukuyama points out that if increased crime is due to family breakdown, then there should be a lag of about 15 years between an increase in the divorce rate and an increase in the crime rate. This is a dynamic relationship.

In addition to a theory that family breakdown causes crime, Fukuyama cites a theory that crime can cause family breakdown. Several mechanisms might cause crime to undermine families, including loss of trust and increased stress.

When non-economists encounter bi-directional causation, they seem to throw up their hands in despair of sorting out anything. Economists are used to that situation (price can affect supply, supply can affect price, etc.) We have a process called "identification," in which we write down all of the variables that are involved in a system. Some of the variables are exogenous to the cause-and-effect relationships, and these variables can be used to identify the processes at work in situations where causality is bi-directional. We can trace through the effect of a shift in an exogenous variable on the system as a whole.

Having a formal model of social capital might have resolved a basic question that troubled me:

If social capital is good for the economy (because it makes it easier for people to do business with one another), then why has the decline in social capital as shown by Fukuyama’s indicators not been harmful to the economy?

One solution might be this:

[1] Y = f (S, T)

Economic output, Y, is positively related to social capital, S, and advances in information technology, T.

[2] dS = g(T)

The change in social capital, dS, is negatively related to advances in information technology.

As long as the direct effect of information technology on output is sufficiently positive to offset the indirect adverse effect of the decline in social capital, advances in information technology can have positive economic effects with negative social effects.

Fukuyama’s view that disruptions to social order tend to be temporary can be expressed as saying that there is an equilibrium amount of social capital, S*, to which the economy tends to revert. Then S*-S is a measure of the amount by which social capital has been disrupted this period.

[2’] dS = g(S*-S, T)

Social capital will increase as an offset to disruption, while increases in technology may influence social capital in the other direction.

If equations [1] and [2’] represent Fukuyama’s thesis, then had he started out by presenting this simple formal model, it would have been much easier for me to follow the rest of the book. If not, then I still do not understand "The Great Disruption," and the case for using formal models may be even stronger.