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

Yves here. Note the comment at the end about how economic analyses or recommendations that don’t fit neatly into the stance of either party often wind up in a wasteland. My colleague Amar Bhide wrote a clever book, A Call for Judgment: Sensible Finance for a Dynamic Economy, that reasoned from Hayekian principles to conclude that financial markets needed to be regulated. It apparently made neither the right nor the left very happy.

By Mike Kimel. Originally published at Angry Bear

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.

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  1. PlutoniumKun

    I can see exactly why this sort of research is going to annoy a lot of people, with the result that its likely to be ignored. And the Caligula/Valens comparison is amusingly apt (I’d recommend that anyone follows that link to Angry Bear).

    Anecdotally, this rings true. My personal experience of living and working and travelling around immigrant communities is that the original origin/culture really matters, yet people are deeply reluctant to admit this. The only ones really willing to say it are the bigots, but they are often right for the wrong reasons. In much of Europe, immigration in the mid to late 20th century was dominated by a need for dying industries for an influx of cheap labour – textile mills in the north of England, transport and services in France, etc. Combined with a bit of colonial guilt, this meant an influx of people from very remote and rural areas in poor countries who were always going to struggle to assimilate. When you compare it to the relatively strict rules applied in (for example) Australia and Canada, the result was inevitably favourable to the latter.

    My own experience of living for years in an English midlands city with a very high immigration influx is that it has nothing to do with religion or ethnicity, everything to do with the individuals background and culture. Relatively well educated Indians and other Asians from high castes, or those from educated African backgrounds moved seamlessly into local society, their kids became English with ease (even if many English were reluctant to accept them). Those from poorer, less educated backgrounds from Africa and Asia struggled very hard. The first generation were often hardworking and kept their heads down. It seems always the second and third generation who really have difficulties and become marginalised.

    I find this a difficult topic, because having being an immigrant myself for much of my life (in two different countries), and with many good friends who are immigrants in my own country, my reflective instinct as a left winger is to defend immigration, both voluntary (i.e. people who just wish to move for their own professional/personal reasons), and refugees. And I tend to have a bias to see and identify the many benefits of a more diverse and cosmopolitan society – I love my mixed neighbourhood with its great Asian and African shops and businesses. But the evidence is out there that it can, if out of control, cause deep problems – and those problems tend to afflict those who are already disadvantaged. I think the biggest task for the left wing is to develop policies a language to discuss the topic without conceding to the bigots and racists.

    1. RabidGandhi

      What I get from both your comment and the OP is that accepting higher-income immigrants is more congenial to GDP growth than accepting lower-income immigrants. If this is the goal, then perhaps countries would do well to be more concise about their actual policies: you may come if you’re rich, but if you’re poor stay put (although this is explicit in many countries’ Golden Visa policies, eg Spain).

      IMO, this would make things a lot clearer, especially w/r/t the Identity Politics debate: we’re not anti-immigrant or racist; we’re anti-poor and classist. Meanwhile, by framing Trump/Le Pen/Farage as anti-immigrant instead of anti-poor, the public is deprived of the opportunity to debate the merits of having a wealth-based immigration system.

      1. PlutoniumKun

        Income may have been a part of it, but that’s not what I read from the article or from my experience. The pre-1960’s immigration to the US from Europe would have been overwhelmingly people arriving without much money. I know many, many Irish people who moved to the US in that period, and not one arrived with more than enough money for a few weeks rent, if that. Some would have had access to capital to set up a business, but it would have been from relatives already in the US.

        There are exceptions of course – many Asian immigrants from China post Mao and Vietnamese after the fall of Saigon did manage to bring capital with them (or had access to capital via relatives in Asia). My understanding of the research on this (there has been quite a lot of comparative work done – for example, comparing the relative success of different waves of Chinese immigration – but its usually by sociologists so its widely ignored) is that educational status is the key. Immigrants with skills and education usually do very well, especially if there isn’t an insuperable cultural barrier. Those without, struggle much more. It seems a reasonable extension from that, that the ‘wealth’ benefit for a country from immigration is far greater for educated or high skilled incomers.

        1. RabidGandhi

          My comment was based on this from you:

          Relatively well educated Indians and other Asians from high castes, or those from educated African backgrounds moved seamlessly into local society, their kids became English with ease

          which the OP mentions as well

          May [sic] 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.

          This makes me realise I have, perhaps erroneously, been assuming higher education/caste = wealthier, which is certainly not 100% correlated, but I would gander the correlation is very high. So my point should be that it’s not how much wealth an immigrant brings with her that matters, but rather so long as she has come from a wealthy class or at least has the trappings and customs of the wealthier classes.

          And this jives very much with my own experience (having lived in several countries myself). The upper classes have advantages that allow them to blend in with other upper class people: education, shared culture and languages, and oftentimes money. In my experience, the upper classes are far more open to accepting a declassé foreign brahmin than they are to accepting a dalit from their own country. Yet current immigration laws deny this very plain fact, discriminating based on borders instead of class lines.

          1. PlutoniumKun

            There is a lot of truth in that. We do of course, have a sort of international cosmpolitan elite these days who move seamlessly from Singapore to Bangalore to New York and London, and have far more in common with each other than with their country fellows. But I think there is more to it than this – many cultures do seem to slip into other countries much more easily than others – an obvious example historically is the Chinese, who seem to manage to settle in countries around the world without provoking much resentment (the exception being in 19th and early 20th Century US, when they were imported specifically as strike breakers).

            My own arguments about this are not so coherent because I haven’t really made my own mind up. My natural instinct is to be pro immigration and pro immigrant because of my own experiences. But the negative impacts on so many communities are becoming impossible to ignore (they have never of course been ignored by the communities themselves). The left have I think been successfully tied up in knots on this issue because they have taken the flack for defending immigration policies created by the capitalists, all because of a correct refusal to be drawn into racist policies.

  2. Bill Smith

    How different does it look like if you use the lowest marginal tax rate? Or the highest marginal tax rate – 10%?

  3. Starveling

    We need to cut off the immigration spigot for a while. Assimilation requires time- a few generations- and only works if there is pressure on the newcomers to adapt to prosper.

    Unlimited immigration creates friction, reduces assimilation (creating longer term ill effects that can lead to balkanization or dysfunction of the Hapsburg Austria-Hungary variety), makes any form of cohesion less possible among the working class, and a host of other issues.

    Also, regardless effects on GDP, more people equals more strain on roads, water supplies, productive ag land, suburban sprawl, environmental degradation, higher housing costs (as most immigrants don’t move to a patch of Montana Hi-Line but live in high COL states and areas), our health system, and others.

    I’m not saying the Hart-Cellar citizens need to go back, but we should stop making them for a while. Diversity is not strength- diversity is what is giving us Trump, Clinton, and might lead us to civil unrest someday. Cohesion and unity are strength- and the only way we are going to build up any of this is to force assimilation on the newcomers we already have.

    1. Adamski

      I do not think there is a slippery slope of unassimilated immigrants threatening social breakdown, at current levels. It being exploited by the right, yes. And I have sympathy with ppl who don’t know if immigration is good or bad for per capita incomes or not, but want to vote against it — just in case. Immigration policy should be made on the grounds of what will help the existing population. Immigration for humanitarian purposes should be limited to refugees and asylum seekers, in cooperation with other countries.

      But economic immigrants have no moral right to come. That’s to be judged on the effects on the host population only.

      1. Pelham

        Nationally there’s little evidence of social breakdown. But immigration is largely a local phenomenon, with refugees and poor immigrants tending to settle, or be settled in, some of the most out-of-the-way and hard-pressed communities across the country. There, it’s a different story. (Curiously, refugees are never settled in areas where upscale enlightened liberals live.)

        1. Starveling

          This is the part that gets to me- the people who push the hardest and signal the most on migration are the ones who are not touched by it. Flood our market with blue collar and manual laborers, bust the unions and close the factories, but don’t you dare touch the doctors/lawyers/10%’rs rackets.

          It annoys me to have the language of diversity/equality flogged and accusations of racism made when it is my neighbors who are having their oxen gored by these changes and not the well heeled.

      2. Jim

        How would you characterize the moral status of economic migrants who come to the US in significant part due to economic policies imposed on their countries by the US? The paradigmatic example is probably Mexican corn farmers, hundreds of thousands of whom were driven out of business because of NAFTA. However, the US is more generally responsible for pushing Mexico, Central America, and the Caribbean to develop precarious low wage export economies and dismantle supports for agriculture for internal consumption.

        I generally agree with your points that (a) immigration should be judged according to its impact in the host country and that (b) humanitarian immigrants should be given a preference over economic migrants. However, I think the line between humanitarian and economic is not always so clear.

        1. Vatch

          You make a good point, but there are additional complexities. It isn’t the “US” which imposes economic policies on other countries, it’s the US government, which is controlled by giant corporate executives and super rich individuals. The US residents who are most harmed by large scale immigration aren’t the corporate executives or billionaires. It is the lower and middle income people who suffer, as their wages either drop, or they lose their jobs. They also bear the brunt of tax increases to pay for schooling and new infrastructure for the rising population. The rich benefit from the lower wages that are paid as a result of the dilution of the job market.

          1. Vatch

            I just realized I said “giant corporate executives” instead of “executives of giant corporations”. I did not mean to imply that Jack the Giant Killer might be able to solve this problem. :-)

        2. fds

          it’s part and parcel. destruction of our and their industrial base. their migrants into our country is another barrier for labor organization. you are looking at it from a faux, limited factor moral perspective.

  4. Moneta

    Interesting how we can generate many multivariate narratives based on 1 single variable…

    My first thought was that immigration is a drag on GDP when your country is a net importer using its reserve currency to live an energy intensive developed world lifestyle.

  5. Dave

    Math formulas…the invisibility cloak of social policy.

    As a long term volunteer at a soup kitchen and after having spoken to many thousands of people, I have come to my own San Francisco Bay Area observations and have some more simple numbers for you.

    Union carpenters, plumbers and truck drivers, often minorities and some females, cannot “compete” against low wage imports from Mexico and Central America who work for approximately $10 to $20 an hour, often for cash. That puts downward pressure on retail clerk wages and allows some middle range businesses to expect work on weekends, nights and holidays. Overtime? Doesn’t exist in that universe.

    The Latin American and Caribbean migrants, legal and otherwise, (migrantslao), send something like $25 billion a year out of country to their home towns. That’s $25 Billion a year not subject to the Multiplier Effect of money circulating in our local economies. Blood sucking cash transferring parasites and other banking “services” extract a minimum fee of ten bucks per transaction, whether it’s $50 or $5,000 and often take far more from larger amounts.

    Spending? Used cars, used clothing, hand me downs, things “hauled away”, charity donations and items left behind in crowded apartments are what are used. Local charities, especially Catholic Charities, and soup kitchens provide free food. No local spending there, just a raising of the prices of used cars and driving apartment rents up.

    The migrantslao buy gasoline junk food and diapers, so I guess there would be a sales tax boost there.
    Yes, social security taxes are often withheld and never collected. According to Social Security, I have jobs right now in four California rural communities hundreds of miles apart. No, I can’t collect based on the fraudulent use of my number.

    “Legalization,” “Bringing people out of the shadows” through “immigration reform”, a.k.a. yet another amnesty, may allow more legitimate taxes to be collected but relative to the filing of per child tax credits for actual and unverifiable numbers of children back home in Latin America, that could be a net loss for the tax system and net gain for that new taxpayer.

    That slippery eel of economics, Milton Friedman said,
    “You cannot have a welfare society and open borders at the same time.”
    I will add to that,
    No one can reasonably expect to earn a livable wage in communities with an endless supply of immigrants, legal or otherwise.

    1. Felix_47

      So true but we cannot allow the rest of the world to starve and life in Honduras or Africa or the Indian subcontinent is a disaster getting worse every day given the birth rate. How about providing a guaranteed minimum income to everyone in the world? It sounds crazy but it is a lot cheaper than what we are doing now which is unlimited immigration, as a practical matter, to the US and Europe. Not only that we might foment peace in the Muslim world and with the defense money we save we could fund it. We spend a trillion per year of defense if one counts VA and NSA and security and Homeland Security. Realistically, there never will be meaningful jobs for the vast mass of humanity as automation progresses. Why hire an illiterate Afghan who brings a wife and six kids when I can do the job with a machine a lot cheaper?

      1. Dave

        OK Felix, then why bring an illiterate Afghan with six kids into the U.S., or any equivalent from closer? How does that help us?
        Many charities can help feed these people, what’s the point of destroying our middle class to do so?
        Just how much are you willing to lower your wages to help boost the wages of a Honduran migrantlao who is fleeing Hillary’s coup?
        Let’s solve the problems inside our own border before we try and fix the world.

      2. Vatch

        Providing a minimum guaranteed income to everyone in the world is a pretty big project. Perhaps we should wait to see how minimum guaranteed income works in the U.S. before applying it to billions of people in other countries. Will the people who control the country even consider such a program? Also, I hope your plan for a guaranteed income would be limited to those people who only have two or fewer children. Since you mentioned the birth rate, I suspect you would want it to have that limitation.

  6. zapster

    The timing is suspect as well. In the 70’s Reagan started dismantling the unions, financial deregulation came along in there, culminating in NAFTA, etc. How much of this effect is from immigrants walking into a situation where labor was already being clobbered anyway?

  7. McWatt

    There are just too many people here. San Francisco is now like New York and New York is like New Delhi, crowded. My two most recent tenants are from Iran and India. I have no idea if they are here legally or not. No one does, probably not even INS. We need to get back to managed immigration for all people who want to come here. Most arrivals are just walking through airport customs and not looking back. All segments of our society need to get back to a legal basis; immigration, federal government, state government and local government. I don’t think any of these are following any laws other than those that generate revenues for them.

  8. Jeremy Grimm

    Is it wrong to ask what is the purpose of or intent for immigration? Of course the next question has to be what is the stated intent and what is the hidden purpose for immigration? I think these questions deserve answers before getting too deep into questions whether immigration increases GDP or not. The framing of immigration in terms of GDP contains a little too much acceptance of the neoliberal ideas of making everything a matter of markets. And what about the underlying assumption built into the GDP question that somehow growth in GDP is good for the country? Good for everybody? Good for some? And one more question — why does immigration come up so often for discussion in our politics but somehow the discussion often reverts to questions of GDP?

    Many people fear other people who think or act differently — whether the others are immigrants or just different. In the new world of work many of us fear for our livelihoods and large influxes of new people coming in — whether immigrants or not — do little to allay our fears. Most people in our country take pride in and enjoy the many new things immigrants bring with them — much as we are annoyed or grow angry about other things they bring. I like to believe the U.S. is more open than most countries to new things and new people and new ways of doing things. But our country is old enough to have definite ideas about how things should be done and what things should not change although we disagree about many of the particulars.

    Too much is lost when we take the discussion to a question whether immigration gooses up the economy or drags it down. If nothing else the issue ignores too much of the how and who benefits.

    1. Jeremy Grimm

      Maybe refugees could be thought of as an economic externality of wars — an externality the economic sectors who profit from wars. Economic immigrants are an externality of predatory economic sectors who profit from the resources and production they squeeze out of other countries. The whole problem could be solved by finding ways to repair the market mechanisms.

  9. Beverly Mann

    Just wondering why in this type of discussion it’s rarely mentioned that there are virtually no immigrants or second- or even third- generation Americans in Appalachia, the poorest region of this country (by far, I believe), and in the rural South.

    Any ideas, folks?

    Also wondering why anyone would simply accept the conclusion of this blog piece that since post-1965-Immigration Act immigration correlates with slower growth, the main or sole cause of the slower growth is the result of the 1965 Immigration Act. As if there are not a slew of other possible causes of it, none of which Kimel attempts to eliminate as a possibility. Much less does he attempt to eliminate ALL of them.

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