Diversity and economic growth

The schools, they are a’changin’…from accountability to inclusion.  In the 1990s, policymakers wanted to boost productivity by compelling students to learn more skills, through rigorous testing.  Today, they worry that the tests were too hard, blocking under-privileged groups from good careers in medicine, science, engineering, and law.  To some degree, this is a debate about diversity, which I define as combinations of ideas.

We are told that new perspectives can solve complex problems. For once, an abstract approach may help.  Suppose that you have an idea, A, and I have another, B.  (A rare event for me.) Now someone adds a third idea, C. If we combine C with A and B, we will have three new ideas: C, AC, and BC. We have 6 ideas altogether, or 3! = 1 + 2+ 3. Generally, the total number of ideas is X! = 1 + 2 + … + X, where X denotes the latest idea. The marginal value of diversity is X, the number of new ideas. (By “marginal value,” I mean the value of one more idea.)  This rises in X. 

But the marginal cost of diversity also rises in X, because the growing complexity of the system of ideas becomes harder to manage.  One reason for the accountability movement was that schools had trouble educating such new groups of students as those for whom English was a second language.  

How much diversity do we want?  The usual answer today is that we want all that we can get. But it really depends on circumstances.  If the marginal value of diversity rises more rapidly than marginal cost and was higher than marginal cost to begin with, then, yes, the optimal amount of diversity is infinite.  This may be the case for problems cutting across many disciplines, such as the prevention of war.

Classroom rebel

But otherwise, the optimal amount of diversity is finite. Suppose that marginal cost rises more rapidly than marginal value.  Eventually, it will exceed marginal value. At that point, a little more diversity will impose a cost. Imagine teaching a classroom in which each student spoke a different language. 

In some cases, the optimal value of diversity may even be zero, because marginal cost always exceeds marginal value.  For example, if we are dealing with a simple problem such as adding two numbers, we need not add a poet to the team.

The accountability movement of the 1990s concerned the marginal cost of diversity.  Today's inclusion movement concerns its marginal value. Of course, we need a balance—specifically, concrete measures of value and cost.

In his 2021 book Rebel ideas, Matthew Syed argues that diversity creates knowledge by drawing together disparate points of view—an idea familiar from the economics of teams. If the contention is correct, more diverse populations should have higher rates of economic growth, because they know more about production. One can test the hypothesis by looking for a positive (and large enough) correlation across countries and time between the rate of GDP growth and the immigration rate—that is, the share of recent immigrants in the population. (GDP is gross domestic product, a measure of the size of the economy.)  In any event, the debate over diversity might benefit from more analyses and fewer anecdotes.

A final note: By diversity, I do not mean differences in traits that do not affect thinking, such as gender and skin color. I mean differences in ways of thinking.  For example, the native Spanish speaker may be harder to educate in an American classroom than a native English speaker; but she also brings a fresh perspective to problems in American history.  

—Leon Taylor, Baltimore, tayloralmaty@gmail.com

 

Note: Measuring the impact of diversity on economic growth

Using the Solow aggregate production function, a workhorse of macroeconomics, we can model the rate of economic growth as

Ydot(t) = a + b Kdot(t) + c Ldot(t) + d Tdot(t) + e(t)

where Y is output, K is physical capital, L is labor, T is technology, t denotes time, e is a disturbance term, and a, b, c, and d are parameters. "dot" denotes a rate of growth.

In theory, the growth rate of technology is a positive function of diversity D(t), measured as the ratio of recent immigration to the population:

D(t) = I(t) / P(t)

where I(t) is the number of immigrants at time t (or thereabouts) and P(t) is the population.

Substitute the instrument D for Tdot:

Ydot(t) = a + b Kdot(t) + c Ldot(t) + d D(t) + e(t) 

The test of diversity theory is whether d is positive.

 

Reference

Matthew Syed.  2021.  Rebel ideas.  New York: Flatiron.