Tag Archives: utilitarian case

Why I’m sticking with open borders, or, plucking the not-so-low-hanging fruit

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I started Open Borders: The Case about 2.5 years ago, in March 2012 (you can read the site story, my personal statement for the site, and some general background for my involvement with open borders). My active involvement with the site has reduced a lot since summer 2013, but it’s still the biggest single topic on which I semi-regularly write stuff for the general public. I have considered switching my attention to other topics such as drug policy (both recreational and medical), organ trading, economic freedom broadly construed, existential risks, cause prioritization in effective altruism, and animal welfare. However, I’ve decided to stick with open borders. This includes participation at the Open Borders Action Group, more blogging here, and other miscellaneous work. In this post, I’ll describe my reasons.

TL; DR

My reasons in summary form:

  1. My estimates for the value of open borders, or the extent to which we can realistically move to open borders, haven’t changed much.
  2. There are two countervailing, roughly canceling effects in terms of the extent of marginal impact of open borders advocacy, so on net that hasn’t changed much either.
  3. I am still well-positioned to help take Open Borders: The Case to the next level.
  4. Other causes, including the most promising ones, seem less promising than open borders.
  5. There is value to personal specialization. I’ve already acquired experience with thinking and writing about open borders, so I can do more by sticking to it.

Never give up
Cartoon showing the importance of not giving up. Source Moving Forwards Seminars

A quick review of the Drake equation

Before delving into the reasons, I’ll recall a framework I developed a while back in my Drake equation post. I wrote there:

$latex \text{Utility of a particular form of open borders advocacy} = Wxyz$

Here:

  • $latex W$ is the naive estimate of the gains from complete open borders (using, for instance, the double world GDP ballpark).
  • $latex x$ is a fudge factor to represent the idea that “things rarely turn out as well as we expect them to.” If we set $latex x = 0.1$, for instance, that’s tantamount to saying that, due to all the numerous problems that our naive models fail to account for, the actual gains from open borders would be only 10% of the advertised gains. The product so far, namely $latex Wx$, describes what we really expect the gains from open borders to be.
  • $latex y$ is the fraction to which the world can realistically move in the direction of open borders. The product $latex Wxy$ is total expected gain from however far one can realistically move in the open borders direction.
  • $latex z$ is the extent to which a particular effort at advocacy or discussions moves the world toward open borders, as a fraction of what is realistically possible. For instance, setting $latex z = 10^{-4}$ for Open Borders the website would mean that the creation of the website, and work on the website, has moved the world 1/10,000 of the way it feasibly could in the direction of open borders.

#1: My estimates for $latex W, x, y$ haven’t changed much

After a few years of reading, thinking about, and discussing open borders, my broad estimates of the gains from complete open borders, the fudge factor, and the extent to which we can realistically move in the direction haven’t changed. To some extent, my estimate for $latex W$ has fallen somewhat, but this is compensated for by an increase in $latex x$. I’ve moved in the direction of embracing lower estimates of the GDP gains from open borders, but also reduced my probability estimate of open borders being a total dud or having net negative consequences, so the fudge factor $latex x$ improves correspondingly. Open borders feels like a somewhat more known quantity. Moreover, the degree of uncertainty regarding consequences reduces further considering that we aren’t going to have complete open borders. Overall, I continue to believe that the product $latex Wxy$ falls somewhere between 500 million and 500 billion dollars, as I’d stated in my Drake equation post.

For a different take on the numbers, see Alexander Berger’s back-of-the-envelope calculations (that I excerpted in an Open Borders Action Group post). Berger’s summary estimate for the gains from open borders (included in an earlier table in that doc) offer the range $300 million – $3 trillion per year (middle estimate $150 billion) for what seems like the analogue of $latex Wxy$. This closely accords with my numbers, though Berger’s methodology is a little different and arguably more concrete and object-level.

#2: Two countervailing effects on $latex z$ approximately cancel each other

How has the $latex z$ value for Open Borders: The Case, and affiliated efforts, changed over time? There are two countervailing considerations:

  • Open Borders: The Case has exhausted some of the very low-hanging fruit. We now play a defining role on the subject: since at least the middle of 2014, and possibly earlier, we’ve topped web searches for open borders. In some ways, we’ve reached our asymptotic potential, and in many other ways, we’re at diminishing returns: even if additional effort yields positive returns, they’re not as high as the initial returns. One could argue that my very first 25 hours of work on the site, which led to this, had the highest return per unit time.
  • On the other hand, now that we’ve done the basic work of building out the case and collecting a community interested in debating the issue, each new post generates more discussion and can more quickly lead to better ideas. When I started blogging, there were only a couple other bloggers and a few commenters with whom we’d go back and forth. Just a year ago, we had about 900 likes on Facebook. Now we have over 1800, or about twice that number. The Open Borders Action Group launched in February 2014, and now has over 600 members and 20+ fairly active participants. Thus, we can quickly have discussions with 5-10 active participants without somebody needing to spend a couple of hours researching a post. And both our active participants and our readers include a fair number of people who might be able to influence the implementation of actual migration policies in different places in the world.

#3: Open Borders: The Case will survive without me, but I can still contribute a lot to taking it to the next level

I was very active in the first 1.5 years of the site, and my job back then was to help grow the community and build the site and blog to the point where it could continue to run and grow without me. I worked hard to recruit people to the site who’d be willing and able to write great stuff (I’ve written a very long Quora answer on this). I think I’ve succeeded. I can have a busy week where I barely check in on the site, and there are still new blog posts and new draft posts, many new discussions on OBAG, and lots of site visitors. I could completely stop my involvement with the site and it wouldn’t collapse.

At the same time, there is so much more to do on this front. The world is still very far from open borders (this circles back to #2). Open Borders: The Case has established a niche that, while close to pre-existing libertarian-leaning blogging on the issue, is sufficiently distinctive. As John Lee wrote in an interview with Lis Wiehl:

The main thing which I think differentiates Open Borders from many other immigration advocacy groups is that we are the only ones who really take global freedom of movement seriously. It’s not merely that we champion it; it’s that we honestly ponder the question of how the world might be different — both for better and for worse — if people could freely choose where to travel, where to settle, and where to work or study.

[…]

Our mission is to offer a rational assessment of what the world would look like under open borders, and to articulate the case of why our governments and societies must respect the right to migrate (except in those extreme cases where infringement might be justified — just the same as with any other right).

The way things are going, we are establishing and solidifying our position as the premier place for philosophical analysis of the case for freedom of movement. Continued growth on this front would not be a laughing matter. But to actually get the world to open borders, so much more needs to be done. If we just keep posting and publishing stuff similar to what we’ve been publishing, we might continue to gain more adherents and grow traffic, but at the core, there won’t be progress.

Co-blogger Michelangelo recently asked about next steps for the open borders movement, and suggested we move in the direction of coming up with concrete actionable policy proposals, perhaps setting up a think tank to do so. In another recent post, I talked of the distinction between philosophers, wonks, and entrepreneurs and reframed Michelangelo’s suggestion as moving from a philosopher focus to a wonk focus.

Personally, I think a move in the wonk/entrepreneur direction is warranted, though I think of it a little differently. I think Open Borders: The Case should offer something so unique, so distinctive, that people feel wowed by it, and inspired to consider and work towards a world of open borders. We need to break new ground content-wise, combining in-depth exploration of the current realities of the world with our pro-open borders ideals, and coming up with stuff that’s captivating to read, whether it’s co-blogger Nathan’s lessons from slavery, co-blogger John’s takedown of the international refugee system, or my recent post on snakeheads as high-impact entrepreneurs. But there’s a lot more to do. It’s possible that such an evolution would occur even without me (some of my co-bloggers have done a great job with writing compelling material that breaks new ground, with no prompting on my part). But I do think that I could significantly accelerate the process, simply by being focused on it and pushing harder for it.

#4: The relative value of other causes

An affirmative decision to continue with open borders is also a decision against pursuing other causes, at least in the short term. A full evaluation would compare open borders with these other causes. And indeed, I think that open borders offers a lot more value than the other top contenders (this comports with Alexander Berger’s back-of-the-envelope calculations, where open borders has the largest upside by a huge margin and also the largest median case gain, though it’s tied for that status with other options).

I think the case for focusing on open borders over drug policy liberalization, free organ trading, economic freedom, and free trade is relatively clear. One might argue that now that a site on open borders has been created, there’s more low-hanging fruit in the other domains. This circles back to my point #2 and (to a lesser extent) point #1, so I won’t go in depth here. Moreover, I also think that, given its high potential, open borders continues to be relatively neglected (relative to drug policy, for instance). For instance, it’s relatively neglected among libertarians, as I’d discussed in these two posts.

The one economic freedom-related cause that I think offers high value and is relatively neglected is the economic freedom-related cause of allowing freer foreign direct investment. I’m mainly going by Bryan Caplan’s assessment of this cause as the most promising after open borders (see also this blog post by him). This is something I hope to investigate at greater depth. If its tractability proves extremely high, I might switch attention to it (i.e., it might have higher $latex x, y,z$ values to compensate for the lower $latex W$ value). Until then, I’ll stick to open borders.

#5: The value of personal specialization

When I first started Open Borders: The Case, my knowledge of migration-related matters was fairly shallow. Over the last few years, I’ve learned many things. Nonetheless, there still remains a lot to learn. If I start a website on a new topic, I’ll have to learn a lot about that topic. If, on the other hand, I continue working on Open Borders: The Case, I can build on the knowledge I’ve already acquired and be even more effective.

What open borders advocates and scholars of migration and development can teach each other

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I’ve recently been reading the scholarly literature on migration and development. In this blog post, I attempt to summarize my understanding of important ways in which researchers in the area are similar to and important ways that they differ from open borders advocates. Then, I’ll discuss what I think both sides can learn from each other.

For examples of the sort of things I’ve been reading, consider this 2007 report for the Department for International Development in the UK, this article on labor migration in India, the World Bank People Move blog, and the websites of KNOMAD and Migrating out of Poverty.

Who are the migration and development scholars who’ve explicitly endorsed radically freer migration?

Some scholars of migration and development are quite sympathetic to the logic of open borders, want the world to move as far as possible in that direction, and explicitly say so. One example is Michael Clemens. While he has expressed some terminological disagreement with “open borders” as a term, he accepts the basic moral logic, he’s all for the main aspects of open borders, and he supports moving as far in that direction as is feasible. Clemens is a co-creator of the place premium and income per natural concepts. He has raised the status in the economic development community of the idea that development is about people, not places. And he wrote the paper that prompted Bryan Caplan to come up with the double world GDP slogan. Note that Clemens isn’t famous solely as a migration researcher; he has also been at the forefront of critiquing some aspects of the Millennium Villages Project.

Another migration scholar who’s expressed considerable sympathy for the open borders position is Lant Pritchett. Pritchett co-authored the place premium paper with Clemens, and has also written a book advocating for freer migration. Pritchett is a renowned development economist who has done considerable work on many areas unrelated to migration, including the return to schooling worldwide and the relation between desired and actual fertility and the importance of contraception to fertility reduction.

How has the community of development scholars changed its views on migration?

I haven’t been able to get a very clear picture, but it seems to me that the international development community as a whole used to be more hostile to migration as a poverty reduction strategy, but they are now more open to it. The following are some general observations:

  • Brain drain was considered a major argument against migration among development scholars, but the balance of the evidence in recent years has moved scholars to the view that the problem is not severe, with many scholars believing that brain circulation and idea flows can be beneficial on net.
  • Historically, the dominant view in the international development community has been similar to the view of many mainstream moderate pro-immigration people that John Lee described here, namely, that migration is not natural, that barriers to it are natural, and that removing migration barriers creates an artificial subsidy encouraging people to move. They’ve also taken the view that suggesting migration as a solution to poverty is essentially a cop-out that accepts defeat in tackling the harder problem of how to get countries to develop. These views again seem to be declining somewhat. It’s more common now for development scholars to consider migration a legitimate part of a strategy that can facilitate improvements in the living conditions of people who migrate and people who stay behind.
  • Dilip Ratha’s work on remittances (see also this New York Times article) got people more interested in the idea that migration can benefit the people who are left behind. Robert Guest’s book on the importance of diasporas encapsulates the growing recognition among migration scholars of how migration can benefit people everywhere, not just those who migrate.

Some other people weighed in on the topic on the comments on this post on the Open Borders Action Group on Facebook.

How do the mainstream migration and development scholars differ from open borders advocates in their views and in their rhetorical emphasis?

In general, mainstream scholars of migration and development are quite similar to the mainstream moderate pro-immigration people John Lee described. In some respects, however, the scholars of migration and development come closer to the open borders position. In particular, compared to mainstream pro-immigration people, and perhaps even compared to some open borders advocates, they differ in these respects:

  • They have a clearer understanding of what poverty and wealth mean, and how rich and poor people are in different parts of the world. And they confront these facts on a regular basis in their work, so it’s harder for them to simply brush these under the carpet. Even somebody like Paul Collier, who wrote the book Exodus that took a lukewarm stance to migration, showed clear understanding and concern about just how big the differences in living standards are.
  • Even if they don’t use the term, they understand the concept of the place premium — the idea that an individual can improve his or her earnings just by crossing borders, with no change in skills, and that much of this improvement is attributable to differences in the value of what the person produces rather than a result of labor legislation or government redistribution.
  • They understand that governments often pander to nativist, citizenist, and territorialist sentiments to an extent that goes beyond what they think is morally appropriate, and also that the sentiments they are pandering to often rely on misguided economic logic. They themselves personally lean more universalist, sometimes in the additive utilitarian sense, sometimes in the egalitarian sense.
  • Even if they’re not themselves libertarians, the libertarian argument in favor of the right to migrate is something that stands out to them more than it does to moderate pro-immigration folks who haven’t thought much about international development. To them, it’s not just an armchair hypothetical. They are also aware of arguments based on human capabilities, even if they haven’t encountered the explicit framework.

On the other hand, they still differ from us “tear down the borders” folks:

  • Their more laser-like focus on poverty alleviation can make them seem somewhat lacking in moral qualms as they discuss issues of optimal migration policy, even when they favor freer migration.
  • Even when they do favor dismantling border controls or other regulations, they’ll frame it in language that suggests more government management of migration. For instance, a concrete recommendation like “get rid of Know Your Customer regulations that forbid migrants from opening bank accounts” would be framed as “facilitate migrant access to banking through reform in Know Your Customer regulations.”
  • Many of their recommendations are focused on strengthening existing patterns of migration that already exist, rather than on loosening border controls that could facilitate new patterns of migration. This may be partly because they’re too anchored to the status quo to consider radical changes. More defensibly, diaspora dynamics suggests that it’s easier to facilitate the expansion of existing migration patterns than create new ones.
  • Related to the preceding, migration and development scholars are a lot more focused on intranational migration as well as international migration among low-income countries and between low-income and middle-income countries.
  • For policy questions, migration and development scholars concentrate their energies on thinking about how to tweak existing systems rather than coming up with new systems from scratch (such as DRITI).
  • Migration and development scholars are very focused on other aspects of the welfare of migrants that are not directly related to open borders. These include migrant childrens’ access to schools, migrants’ access to government-provided and private sector services, and facilitation of communication between migrants and their relatives back home.

What can open borders advocates learn from migration scholars?

Here are some things I believe open borders advocates should learn from migration scholars:

  • More attention to the actual experiences of poor people who migrate: Open borders isn’t purely about poor people, and in particular I believe that there will be a strong imperative for open borders even in a world without poverty. But certainly, freer migration should be an important part of the toolkit to end poverty, and the current state of world poverty considerably raises the importance of the issue. To the extent that open borders advocates are interested in the issue not just theoretically but at a practical level, a closer empirical look at how poor people fare under migration is warranted. Migration and development scholars spend a large part of their life thinking about poverty, and we can be inspired to spend at least a few hours on it.
  • More focus on intranational migration, migration between low-income countries, and migration from low-income to middle-income countries: Open borders advocacy can sometimes seem like too much speculation about something that doesn’t exist at all. And to an extent, that’s right: open borders across a huge place premium (of 5X or more) hasn’t happened. But it might be worth looking at the huge amount of migration that already exists and understanding its implications. While still arguing morally for open borders worldwide, we can focus more on understanding what already exists and making changes to it. Often, there is little reliable data and little interest among readers in such matters (such as Nepal and India, or North Korean refugees), simply because blog readers are highly likely to be in First World countries and are more aware of First World issues. But I think that pushing more in the direction of better understanding migration as it’s actually happening is worthwhile, even if it doesn’t make us popular. We can be inspired here by migration scholars, who have worked very hard to compile data and collect anecdotes to further the world’s understanding of migration.

What can migration scholars learn from open borders advocates?

I think migration scholars can also take a few lessons from open borders advocates:

  • The moral case for free migration matters. It’s the foundation of everything else. Make the case boldly wherever possible.
  • It helps to consider the radical proposal that is open borders, and ask just how far one can get there. Bold policy changes can be useful to consider, even if they aren’t possible to directly implement. It’s not good to stay anchored to the present all the time.
  • When advocating for reductions in government restrictions on migration, it may make sense to not obfuscate this with the “more government management of migration” language. Further, in cases where the optimal policy comes very close to complete deregulation, consider advocating complete principled deregulation instead of trying to target the specific optimal policy. Complete principled deregulation, even if not optimal on paper, leaves less room for governments to re-institute the counterproductive controls seen in current policy.

The photograph of an open borders campaigner at the top of this post was taken by Jonathan McIntosh at a rally in Los Angeles, California, and is licensed under a Creative Commons Attribution licence.

Doubling world GDP versus doubling utility: a technical note

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Carl Shulman, one of the most impressive people I know, pointed me to a blog post he’d written a couple of weeks ago titled Turning log-consumption into a measure of short-run human welfare. Carl brought to my attention that a passage in my recent post titled how far are we from open borders?, used ambiguous language. Specifically, he pointed out that the passage:

These same estimates also suggest that much of the gain in production – and consumption – would be experienced by the world’s currently poorest people, leading to a significant reduction in, and perhaps an elimination of, world poverty. If we take utility to grow logarithmically with income, then this distributional aspect argues even more strongly in favor of the idea that open borders would increase global utility tremendously.

might suggest that I’m saying that taking utility as logarithmic points in the direction of the proportional gain in utility being higher than the proportional gain in world GDP. That was not my goal. Rather, my goal was to say that, if we take utility as the sum of logarithms of incomes, then for a given gain in world GDP, the gain in global utility resulting from that gain in world GDP would be higher if inequality was also reduced than if it wasn’t. Explicitly, having the poor’s income increase four-fold and the rich’s income stay the same, with overall GDP doubling, would give a higher utility gain than having everybody’s income double.

That’s the quick clarification. But Carl’s post raises a number of other points about the use of logarithms for considering utility, and I want to talk a bit more about some of the issues raised. The upshot, based on my reading, is that the considerations Carl raises point in favor of life-saving interventions (such as combating malaria) over interventions (such as open borders) that improve the quality of life of an existing population. But within the class of interventions that improve the quality of life of an existing population, the relative value of open borders to other interventions is not affected by the considerations Carl raises. Note also that the calculations in Carl’s original post explicitly adopt a short-run perspective, although he is elsewhere on the record stating that long-run considerations should dominate. Finally, population ethics is a fraught subject and there are a large number of issues that are somewhat related to this blog post that I do not get into, such as the question of how to value the potential existence of nonexistent people. See Nick Beckstead’s Ph.D. thesis for a detailed discussion of the far future and a summary of the philosophical literature on population ethics.

The rest of the post is fairly technical — following it properly requires a basic knowledge of calculus-level mathematics, though you can skip the quantitative statements and just consider the verbal statements.

I will consider six cases of progressively increasing complexity.

Case 1a: If you just have one person: taking logarithms is a monotone transformation that translates ratios into differences

Let’s begin with the case that we’re looking at just one person’s income. We want to understand, roughly, how the person’s “utility” grows with his or her income. We know that the greater the person’s income, the higher the person’s utility. In other words, utility is an increasing function of income. This in and of itself is good enough to tell us whether a given change in income leads to an increase or decrease in utility. What it doesn’t do is allow us to compare different changes in income with different starting and ending points. In other words, simply knowing that utility goes up with income says that income can be used as an ordinal scale for utility, but doesn’t allow us to answer questions such as: would increasing income from $10,000 to $11,000 matter more or increasing income from $100,000 to $101,000?

The assumption that utility grows logarithmically with income is an assumption that allows us to make cardinal comparisons between different changes in incomes. If we take utility to be logarithmic in income, then the increase in utility is the logarithm of the ratio of the final income by the initial income. This allows us to now meaningfully say that increasing income from $10,000 to $11,000 results in a bigger utility gain than increasing income from $100,000 to $101,000, because the ratio in the former case (1.1) exceeds that in the latter case (1.01). Note that we don’t need to take logarithms to answer the question of what gain is greater: we can just compare the ratios themselves.

The logarithm function is concave down, i.e., its second derivative is negative, so the average of the logarithms is less than the logarithm of the average. In other words, the gain in the logarithm for a given absolute gain in income is greater at lower income levels than at higher income levels. This can also be seen directly in terms of ratios as above: a $1,000 gain from $10,000 to $11,000 is larger as a proportional gain than a $1,000 gain the same absolute gain value) from $100,000 to $101,000.

There are two parameters to choose when setting up the logarithm-taking process, both of which are irrelevant for our purpose of comparing utility gains:

  1. The base to which logarithms are taken. Changing the base of logarithm from one value to another corresponds to a scaling transformation.
  2. The choice of “1” for income when taking logarithms, or equivalently, the choice of “0” for after taking logarithms, i.e., the income level whose logarithm we take to be zero. Changing this corresponds to a translation of the logarithmic scale, i.e., a change in the origin point.

Both choices are irrelevant for our main purpose: (2) is irrelevant because we are always looking at differences between points on the scale, so the location of the origin does not matter. (1) is irrelevant because we are comparing the differences with each other, not looking at their absolute magnitudes (in the same way as switching from meters to feet for length measurement will not change any of our fundamental analysis). (Technical note: We do need to impose the condition that the base of logarithms be greater than 1 for the analysis to hold, otherwise the scaling factor becomes negative and everything gets messed up).

A technical way of framing this is that we are treating the logarithm of income as an interval scale, i.e., a scale where it’s permissible to compare and take ratios of differences, but there is no natural zero, so it does not make sense to “double” a particular value of logarithm of income, nor does it make sense to add two values of logarithm of income. We can add, scalar-multiply, and take ratios between differences between logarithms of incomes, as these operations are invariant under the choice of origin. This is similar to how we treat temperature in practice: it does not make sense to add two temperatures and double a temperature, but we can perform the operations meaningfully on temperature differences.

However, once you delve deeper into physics, you discover that temperature actually does have an absolute zero and therefore can be measured on a ratio scale (the Kelvin scale being the standard choice in the case of temperature). If expressed in that scale, temperatures can legitimately be added and multiplied by scalars. Does there exist a similar natural choice of “absolute zero” for the logarithm of income? Not quite, but sort of. We now turn to some reasons for looking for such a zero.

Case 1b: Interpersonal utility comparisons

Let’s now consider the situation of comparing two people. We make the assumption not only that the utility functions of both are logarithmic in income, but also that the base of logarithms is the same. With these assumptions, we can compare an income change for one person to an income change for the other. If we also set an absolute zero for the log-income scale (i.e., a unit value for the income) for both the people (we could choose it to be the same for both) then we can also compare the income levels of the two people.

Case 1c: Considering the problem of zero income and non-existence

As income approaches zero, its logarithm approaches $latex -\infty$ (negative infinity). If we approximate death as switching to an income level of zero, then being dead corresponds to having a utility of negative infinity. This can pose problems when computing expected utilities in situations where there is a nonzero probability of death. Carl Shulman describes a standard way to get around the problem in his post. Explicitly, he suggests taking “subsistence income” as the absolute “1” for income, but with a twist: add a constant for the value of existing. Carl defines utility for a dead or non-existent person as 0, and utility for a living person as:

$latex s + \log(\text{income}) – \log(\text{subsistence income})$

where $latex s$ is the value of existence, and $latex \log(\text{income}) – \log(\text{subsistence income})$ is the additional value accrued from having income above the subsistence level. With this model, the effective “1” for income would be (subsistence income)/$latex b^s$ (where $latex b$ is the base of logarithms). People whose incomes are lower than that value have a negative value of existing. But in practice, we choose subsistence income and $latex s$ in a manner that nobody falls below subsistence income, let alone below (subsistence income)/$latex b^s$.

Once we have set up utility as a ratio scale as above, it makes sense to talk of the proportional change in utility. In particular, it makes sense to ask whether a given change in income causes utility to double, or more than double, or less. The answer to that would depend on the value of existence ($latex s$) and also on how far above subsistence income the person under consideration is. However, for reasonable choices, doubling income will lead to far less than a doubling of utility.

For instance, suppose we chose $latex b = 2$ as the base of logarithms, take subsistence income as $1/day, and take the existence value as $latex s = 5$. In this case, doubling income from $2/day to $4/day increases utility from 6 to 7, which is far less than doubling. Doubling income from $32/day to $64/day has an even smaller effect in terms of proportional utility gains: utility goes up from 10 to 11. (Technical aside: considering proportional gains in log-income is tantamount to taking differences of log-log-income.)

In fact, for a reasonably high choice of existence value, any change to the situation of an already existing person pales relative to a change that affects whether or not the person exists, such as birth and death. We’ll get back to this point once we consider the issue at the population level.

Case 2a: Getting multiple people into the picture, but abstracting away from the problem of people dying

We began by dealing with just one person who can earn different incomes, and then moved on to interpersonal utility comparisons, and also considered the possibility of death or non-existence, as well as . Let’s ignore the problem of death or non-existence right now, and consider a fixed population with more than one person.

The goal is to consider two different income configurations for this population, and compare them to find out which one is better. Now, at the individual level, the knowledge that utility is increasing in income was enough to say which of two income levels is greater, and the logarithmic assumption was necessary only to answer the question of how differences compared. However, in order to effectively aggregate the individual data, we do need to use a cardinal scale. In this case, since utility is assumed to be logarithmic in income, the “total utility” is the sum of all log-income values. We can then compare these totals across different configurations. Note that this case relies, albeit indirectly, on our being able to execute interpersonal utility gain comparisons (the case 1c above), and that reliance is reflected in our choice of using the same base for logarithms for all members of the population.

Now, although we are taking the sum, we are still using only the interval scale properties, and in particular, the location of the zero does not matter. This is because we are adding the same number of terms (corresponding to the members of the population) in all configurations. If we shift the location of the “zero” then that affects our “sum of log-incomes” for all configurations by an equal amount. Perhaps a better way to think than the sum is the average, for which the conclusion is clearer.

If open borders were to double every individual’s income, it would increase the average value of log-income by $latex \log 2$ and it would increase total utility by $latex \log 2$ times the population size. If, however, open borders doubled world GDP with its effect concentrated on people with low incomes, it would increase the average value of log-income by more than $latex \log 2$ (this follows from the remarks made in the discussion of Case 1a about the logarithm function being concave down).

The above is the situation that I consider by default and that is the context in which the quoted passage from my earlier post was written.

Case 2b: Comparing different populations

The remarks above continue to apply to the case of comparing improvements for different populations, including populations of different sizes, with the following catch: unless we fix an absolute zero, we can only compare changes in one population with changes in the other population. We cannot compare the absolute level of one population against the absolute level of the other, except in the following cases:

  • If both populations have the same size, we can compare absolute utility levels for the populations with one another assuming they have the same absolute zero, but we do not need to specify this absolute zero.
  • If the populations have different sizes, we need to specify absolute zeros for both populations in order to compare their absolute utility levels.

Case 2c: How the absolute zero allows us to compare absolute levels for different populations and introduce the possibility of death

If we embrace the model used by Carl described in Case 1c, we can tackle both the situation of comparing different populations and dealing with the problem of a nonzero probability of death. In this context, it actually does make sense to ask questions such as:

  • What is the ratio of the utility levels of two different populations?
  • What is the ratio of the utility levels of two different configurations for the same population?
  • What is the expected utility gain for a population in a scenario (where there is a nonzero probability of death or new births in the population)?

In this context, therefore, it makes sense to ask whether doubling world GDP would indeed double utility. The general answer would be that it falls far short of doing so, even if the gains are concentrated on the poorest people. This is for the reasons already discussed in Case 1c: for any individual, doubling income has a far smaller effect on utility than doubling. Note that the gains being concentrated on the poorest people still has more effect on utility than having the gains evenly distributed or concentrated on the richest people, but that “more” still isn’t sufficient to cause doubling.

The main reason why open borders gets to look a lot worse from the point of view of the ratios of utility levels than otherwise is simply that existence itself carries huge value, and open borders, by simply moving people, doesn’t add value commensurate with the value of existing. But this argument applies generally: for a reasonably high estimate of the value of existence, any measure that makes an existing population somewhat better (without increasing births or eliminating deaths) would look a lot worse than a measure that increased the size of the population. In fact, from the existence value perspective, there’s very little that’s more promising than pro-natalism and mortality reduction — which could range from combating malaria to ending aging. Thus, the comparative analysis of open borders with most other typically considered interventions, except interventions that directly and significantly affect mortality, still points strongly in favor of open borders.

With that said, it’s worth noting that it’s likely that, by reducing poverty, open borders would reduce child mortality and increase life expectancy worldwide, and therefore could also increase global utility more greatly through that channel than the GDP estimates indicate. Also, the effects on global population growth would need to be considered: it’s likely that open borders would lead to a short-term increase in population (as first-generation migrants resemble the fertility rates of their source countries but would have lower mortality rates), meaning a significant gain in utility, but within a few generations, migrants would assimilate to native fertility rates, which may well mean lower world population than in the status quo scenario. The effect of open borders on long-term demographic trends is an important topic but is outside the scope of the current post.

Open borders advocacy: a Drake equation

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The Drake equation is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy. The idea is to express the number of such civilizations as a product of quantities in a manner that’s true by definition, but also such that one can talk somewhat more intelligently about estimating the individual factors than one can talk about directly estimating the number of active, communicative extraterrestrial civilizations. XKCD has poked fun at the Drake equation in at least two comics. Viewed as an exercise aimed at obtaining precise actionable estimates, the Drake equation is probably futile. But viewed as a way to start thinking about the problem, it is arguably useful. The main reason it’s bad for estimation is that the multiplicative nature of the model means that the huge uncertainty in measurement for each of the factors is also multiplicative, leading to a gigantic uncertainty in the overall estimation.

Here’s my Drake-like attempt:

$latex \text{Utility of a particular form of open borders advocacy} = Wxyz$

Here:

  • $latex W$ is the naive estimate of the gains from complete open borders (using, for instance, the double world GDP ballpark).
  • $latex x$ is a fudge factor to represent the idea that “things rarely turn out as well as we expect them to.” If we set $latex x = 0.1$, for instance, that’s tantamount to saying that, due to all the numerous problems that our naive models fail to account for, the actual gains from open borders would be only 10% of the advertised gains. The product so far, namely $latex Wx$, describes what we really expect the gains from open borders to be.
  • $latex y$ is the fraction to which the world can realistically move in the direction of open borders. The product $latex Wxy$ is total expected gain from however far one can realistically move in the open borders direction.
  • $latex z$ is the extent to which a particular effort at advocacy or discussions moves the world toward open borders, as a fraction of what is realistically possible. For instance, setting $latex z = 10^{-4}$ for Open Borders the website would mean that the creation of the website, and work on the website, has moved the world 1/10,000 of the way it feasibly could in the direction of open borders.

The restrictionist or pessimist might well view $latex x$ as a negative number, making open borders advocacy a great disservice to humanity. For our purposes, however, we’ll consider estimates where the values are positive, yet sufficiently small as to account for considerable uncertainty. Let’s say that, for the Open Borders website, the numbers look as follows, with the numbers in US dollars (note that of the four numbers, $latex z$ is the only one that requires particular knowledge of the Open Borders website):

$latex W = \$ 50 \text{ trillion}, x = 0.01, y = 0.001, z = 0.0001$

The 50 trillion figure can be calculated as just one year’s gain based on the double world GDP estimates. Note that there are some complications when considering potential delays in opening borders, as well as discount rates for the future and economic growth in the future. But since the starting numbers are anyway very rough guesses, there’s not much point in trying to do a very elaborate estimation exercise to calculate $latex W$ (for what it’s worth, I did some estimates based on assumptions about discount rates and economic growth, and I got a figure of about twice that much in expected value even if open borders are delayed by several years and the gains are slow to arrive and temporary). Note also that the fudge factor $latex x$ of 0.01 is essentially taking a very pessimistic view of the estimation exercise, by claiming that 99% of the claimed gains will not in fact materialize, or will be canceled by other losses.

With these numbers, the value of the website comes out to 50,000 US dollars. That’s not huge, but it’s about the same order of magnitude as the cost of time spent on the website (about 1500-2000 hours). With these numbers, therefore, the site just about breaks even in terms of social value generated versus time spent.

Here’s an optimistic version of the numbers:

$latex W = \$ 50 \text{ trillion}, x = 0.1, y = 0.1, z = 0.0001$

With this view, the naive estimate overstates the gains, but only ten-fold, it’s also possible for the world to realistically move 10% of the way toward open borders, and Open Borders the website has moved the world 1/10,000 of the way toward the theoretically possible limit. With these numbers, the expected value of Open Borders comes to about $50 million.

Obviously, the above estimation exercises are very naive, and there’s a sense in which this might feel like Pascal’s mugging. The key point that emerges here, though, is that the position yes, open borders would have gains, but the gains from what’s realistically possible in that direction are too small to be worthwhile isn’t a very tenable position. Open borders is a radical proposal — for better or worse. To arrive at such a position, you’d need to have $latex x,y,z$ all very small — but still positive. If you’re coming that close to zero, then you might as well offer some good reason why you don’t go all the way to zero — or beyond, to the negative territory. If the restrictionist position were right, then, it would entail showing at least one of these (or more precisely, an odd number of these, but never mind that):

  • $latex x$ is zero or negative: Economists have badly estimated not just the magnitude, but rather, the sign of the effect of open borders. The best attempts in the direction of demonstrating that the expected sign is negative is the killing the goose that lays the golden eggs argument. And while I think there’s considerable plausibility to that argument, and it may well point toward certain keyhole solutions being desirable, I am not convinced that these come anywhere near toggling the expected sign of the gains from open borders.
  • $latex y$ is zero or negative: It’s impossible to move in the direction of open borders at all.
  • $latex z$ is zero or negative: Open borders advocacy (or at any rate, the specific advocacy effort being considered) hurts the move toward open borders more than it helps. Tyler Cowen took this sort of approach in his recent blog post that generated considerable response (including from Nathan and John).

An alternative position is that we just don’t know enough to even estimate the signs of the quantities, and that more research is needed. I certainly agree about the need for more research, and I think a strong case could be made for an agenda that focuses extensively on research before clearly coming down on one side or another, while favoring continued experimentation with liberalization and keyhole solutions at the margin. But what’s not justifiable is the absolute certainty that many people seem to have that the status quo is approximately optimal, or that radical liberalization of movement simply isn’t a paradigm worth investigating because the gains are too small.

Gains from migration: GDP versus surplus

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A couple of days back, I wrote a blog post titled the story behind the “double world GDP” estimates. Yesterday, I chanced upon a blog post by Michael Clemens titled Do the Gains from International Migration “Go to the Immigrants”? (do read that — it makes a lot of points which I make in a slightly different way in this post). And reading that, I now think that some of what I said in my original blog post was, although not quite wrong, misleading.

GDP is roughly calculated by adding up the (price times quantity) of all final goods and services produced within a country’s domestic territory in a calendar year. World GDP is the sum of the GDPs of all nations. In the previous blog post, I tried to get into the story behind the double world GDP estimates. My overall statement was that the gain is seen largely through a direct effect in an increased value of production of the migrants themselves. This increase is not due to an increase in the skills of the migrants (though that might also eventually occur) but rather, is due to the place premium, whereby the exact same worker with the exact same skills produces more values, and gets paid more, in some places than others. That “more value” could be due to higher total factor productivity. Or it could simply be because the job the migrant does is more valued. For instance, a nanny in the United States may earn more than a nanny in India, because parents in the United States have more to gain by leaving their babies in a nanny’s hands and going to work instead.

On the other hand, a utilitarian or welfare-based analysis looks, not at price times quantity, but at the social surplus: difference between the reservation prices of buyer and seller, multiplied by (or rather, integrated over) the quantity. Graphically, it’s the area of a certain “triangle” between the demand and supply curves. Part of the social surplus is captured by the buyer, and part of it by the seller.

For any individual economic transaction, the social surplus can tell a very different story from the “GDP contribution” of that transaction (examples below). At a macro level, I think GDP offers a reasonable approximation to “utility” concepts, but it’s mathematically different.

Why is this relevant? As I said in my previous post, most of the GDP gain from migration is due to the increased value of production of the migrants — though there are also secondary occupational mix effects (see this paper by Dixon and Rimmer, for instance, or more general discussion at the suppression of wages of natives) where natives are relieved of some aspects of their jobs by immigrants and can switch to other jobs that create more value. However, even ignoring the occupational mix issue for the moment, the claim that the GDP gain is mostly registered to the migrant is quite different from the claim that the social surplus is largely captured by the migrant. Certainly, the claims are related, but they aren’t the same. I will make four points to clarify this.

  • Consumer surplus: When Apple introduces a new iPhone, the gains in world GDP are registered to Apple and their suppliers, manufacturers, retailers, and employees. There may also be some compensating losses as other phone manufacturers lose out on buyers. However, the welfare gains are experienced not just by phone producers, but by phone consumers — aka all iPhone users. They’re the ones, after all, who are buying the phones, which means that they value the phone at least as much as Apple prices them. It’s the same story with migrant labor — the welfare gains go to the migrants, their employers, and all the customers of their employers who benefit from the employer’s ability to hire better or cheaper labor in the form of better quality or lower prices.
  • Shifting of non-economic activities into the economic realm: This is a somewhat complicated point. The key idea is that part of the gain to world GDP will happen because non-economic activities return to the market. For instance, suppose I value my time spent cleaning up my apartment at $18. I value a clean apartment at $20, but the cheapest cleaning service costs $25. So, I choose to clean my apartment myself, getting a private surplus of $2, but there is no economic transaction. Now, suppose an immigrant arrives, who would be willing to clean my apartment for $11 or more. We negotiate and agree to a price of $14. The immigrant gets a surplus of $3, and my surplus is $6. My surplus has gone up by $4 (from an original of $2). But the GDP shows a gain of $14 corresponding to the shifting of the activity into the market realm.

    A slight variant of this example — one where I value my own time spent cleaning the apartment more than $20 — would result in a situation where an apartment I would leave dirty getting cleaned up, so my social surplus went from zero (leaving the apartment dirty) to $6. In this variant, non-activity is replaced by activity. But in the original example, non-economic activity is being replaced by economic activity.

    In both versions, though, we see that the GDP gain is much larger than the social surplus created. Does this mean that “double world GDP” estimates are gross overstatements? Not quite. Social surplus as a concept here makes sense for a single transaction with a fixed backdrop, and it’s not easy to generalize macroeconomically. Further, the “double world GDP” estimates are proportional estimates, and so even if you say that GDP vastly overstates social surplus, the overstatement is prima facie likely to be proportional. To actually provide an argument against, you’d need to show that the kind of gains to world GDP that would accrue from migration are not the kind that tend to increase social surplus that much in proportional terms.

  • Occupational mix: Combining the occupational mix idea and the “cleaning my apartment” hypothetical: whether there are further increases in GDP depends on what I do with the time I’ve freed up by having somebody else clean the apartment. Do I use it for activity that would show up as economic production? Do I use it to consume more goods and services that would show up in somebody else’s production statistics? Or do I use it to just relax without producing or buying anything? In the first two cases, there will be a secondary effect of GDP gain from whatever activity I undertake instead of cleaning my apartment. In the third case, there is no secondary effect on GDP.
  • Intra-family transfers: If the income of the parents in a family goes up, does that mean that the gains go “only to the parents” and not to the children in the family? Probably not. The increased parental income probably means gains for the children as well in material and other terms. The key here is intra-family transfers. Certainly, many parents are not completely altruistic regarding their children (though some are more than altruistic), so the extent of intra-family transfers can be debated, but the phenomenon does exist. The same argument can be made regarding cases where only one parent is earning an outside income — in this case, increases in this parent’s income are likely to improve the standard of living of everybody in the family, and the way in which the gains are distributed remains an empirical question. The analogous phenomenon in the context of migration is in terms of remittances. Note, however, that as far as the GDP gain is concerned, the gain is registered only to the person who actually works and/or migrates, not to the other family members who share in the benefits.

So the overall welfare analysis, as we’ve just seen, is a lot more complicated than the GDP contribution analysis. Again, even in a welfare analysis, I think it would still be true that “most of the gains go to the migrants” — though less sharply so than for a GDP contribution analysis. The benefits to migrants are at the heart of the utilitarian case for open borders. However, even after you take out “most” of a doubling of world GDP, there’s still a lot left in terms of benefits to immigrant-receiving countries, benefits to immigrant-sending countries, and global benefits.