# How Does Diversity Affect Economic Growth?  A Look at Data on Immigration, Tax Rates and Real GDP per Capita

### Authored by Mike Kimel

In this post, I will explain the annualized growth rate in real GDP per capita using tax rates and the percentage of the population that is foreign born using data for the United States.  The data shows the following:

A. the tax rate that maximizes economic growth is higher than you think
B. immigration from countries with advanced economies whose population resembles the US correlates with faster economic growth over subsequent years
C. increasing rates of immigration from countries with diverse populations does not correlate with faster future economic growth

You can skip ahead to the results of the regression if you want.  Otherwise, if you care about the details, here goes…

I used to occasionally write posts where I would build models based on fitting models of the following form:

growth in real GDP per capita, t to t+1 = f(tax rate at t, tax rate squared at t)

In that formulation, tax rate = top marginal income tax rate.  The quadratic form allows us to find a tax rate that maximizes growth rates if the real world has such a thing (which, happily, it does as we will see below).

More recently, I have been looking at how immigration has affected the economy.  In particular, I had a few posts looking at this relationship:

job growth, t to t+10 = f(foreign born % at t)

Why the ten year look-ahead?  To be frank, I just got tired of arguing with readers about causality.  Comparing X today to Y over the next ten years puts a halt to chicken and egg arguments tout suite.

I’ve also had a few essays speculating about the effect of changes in immigration law in 1965 on the economy but in those posts, I relied only on logical and not on data.

In this post, I want to combine those three (well, really two and a half) issues. I will fit the following model:

1. Dependent variable:  annualized growth in real GDP per capita, t to t+10
2. Explanatory variables i and ii are tax rate and tax rate squared, both at time t
3. The next explanatory variable is the % of the population that is foreign born at time t.   But…  if immigration, and its impact on the economy, changed as a result of the 1965 Immigration Act as I’ve stated in earlier posts, what we really need is two variables:
3a.  Foreign Born as a % of the Pop Until 1965 (and zero otherwise)
3b.  Foreign Born as a % of the Pop After 1965 (and zero otherwise)

Tax rates came from the IRS’s historical table # 23.  The foreign born percentage was obtained from the Migration Policy Institute (MPI).  The MPI’s data originated with the Census, but they organized it a bit better so I downloaded it from them rather than the Census.  Data is available in ten year increments from 1850 to 2010, and annually from 2010 to 2015.   I annualized the decennial data by simply assuming a linear annual change between every tenth year’s figures.

The entire set of data was organized in Excel, but the regression itself was run in R.  The output (click on figure for larger size) appears below:

The first thing to note is that the model explains about half of the variation in the ten year economic growth rate.  Not bad for tax rates and immigration alone.

Next, the coefficient on tax rates is positive, the coefficient on tax rates squared is negative, and both are significant.  (That’s the quadratic relationship mentioned earlier.)  If you do the math, it turns out that the rate that maximizes the ten year annualized growth in real GDP per capita is 55%. This is about what most of my previous estimates over the years have come up with as well.

Moving on, the next variable is the percentage of the population that is foreign born in years prior to 1965.  That variable is positive and significant even at the 1% level.  In plain English, before 1965, more immigrants -> faster economic growth.

But the next variable is problematic, and spits out a result that is, at a minimum, politically incorrect. That variable, the percentage of the population that is foreign in years after 1965 is negative though not quite significant.  If we are worried about being reported by the neighbors, we could with a straight face, stop here and state from this that immigration has not not affected growth since 1965.  For the moment, let’s do that.

The coefficients and relative significance of the last two variables essentially restate what I have been writing in the last few weeks.  As a result, I can explain what is going on by more or less plagiarizing myself.  So, at a high level, why does pre-1965 immigration clearly boost economic growth and post-1965 immigration clearly not?  As I noted in earlier posts, from 1921 to 1965, about 70% of the immigrants came from Germany, Great Britain and Ireland.  The 1965 Immigration Act was designed to allow more immigration from the rest of the world.

Before 1965 immigrants would have fit in more seamlessly. After all, the US had been strongly shaped by previous immigrants from the very same countries where the new immigrants had just left.  Furthermore, most of the people the immigrants would encounter in their new land would have experience with other immigrants from the same culture. Additionally, in the last century technology was an important driver of growth, and the countries which supplied the most immigrants before 1965 also happened to be fairly technological advanced countries.  One more thing to keep in mind – the percentage of the population that was foreign born shrunk steadily from close to 12% in 1929 to about 5% in 1965.

Since 1965, of course, the story is very different.  The foreign born population has been increasing, reaching 13.5% in 2015.  Post-1965 immigrants have been far more heterogeneous in ethnic composition and skillset than the earlier group.  May have come from poorer, less technologically advanced societies.  Some have cultural traits that are not entirely compatible with accepted norms in the US which results in a variety of frictions.

My guess, from the results, is that if more granular data was available on post 1965 immigration (say, by country of origin, or better still, by education level and education quality), it would turn out that some subsamples of post 1965 immigration had positive and significant effects on growth, but proportionately larger subsamples would have negative and significant coefficients.  I will dig a bit harder to see if I can find data that can confirm or repudiate my guess.

A few closing comments.  Given the election is coming up, it is worth noting that Hilary and Trump are on opposite sides of both the tax and immigration issues.  Hilary’s proposed tax changes are likely to generate faster economic growth, Trump’s proposed tax changes are likely to slow the economy.  On the other hand, Trump’s immigration proposals (to the extent that they can be coherently defined) suggest an interest in pre-1965 style policies.  Hilary, though, will probably accelerate the path we are already following.

For what it is worth, both tax and immigration policies have consequences.  However, it is easier to change direction, or to reverse the effects of earlier policies if those relate to the fiscal rather than the immigration arena.  That’s why the Roman Empire could survive crazy behavior by madmen like Caligula and Nero, but one mistake by a dry technocrat like Valens led inexorably to the sacking of Rome.

In future posts, I will try to understand what some of the impediments have been to integration of post-1965 immigrants.  I am also interested in whether and how those impediments can be reduced.

Finally, as always – if you want my data, drop me a line at my first name (mike) dot my last name (kimel – and that’s with one m, not two) at gmail which of course is followed by a dot com.  I’d be happy to share my Excel spreadsheets and if you want it, the trivial amount of R code that went into this.  If you contact me within a month of this post going up, I’ll send it to you.  Beyond that, I will probably send it to you but no guarantees.  I reserve the right to have my computer stolen, go into a coma, move on with my life, etc.  But of course, the data is pretty easy to recreate.

One postscript…  This post kind of reminds of me of Presimetrics, the book I wrote with Michael Kanell.  I like to think the book never found an audience because we went where the data took us, rather than towing either the Republican or the Democrat Party lines.  As a result, some of the results we presented were in line with Republican beliefs, and some with Democrat beliefs, but neither side could embrace the results.  Had we been smart enough to be partisan hacks, perhaps the book would have sold much better.