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Vipul Naik founded the Open Borders website in March 2012. See also: Vipul Naik's personal statement Vipul Naik's description of open borders on his personal site Page about Vipul Naik on Open Borders

Slippery slopes to open borders

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One of the topics that came up at the Open Borders Bay Area Meetup (Sunday January 12) was the idea of slippery slopes towards open borders. My post is based on ideas raised in the discussions, but since the participants’ comments were largely off the record, I’ll take full responsibility (but not necessarily credit) for everything I write here.

Immediate, unconditional open borders, or even something fairly close to it, is unlikely to materialize in the near future. From a practical perspective, then, the best route to open borders is a long series of gradual steps. One key concern of people who have their eyes set on the end goal of open borders is that the first few steps should make future steps easy to achieve. A path that is ostensibly in the direction of open borders, but where the first few steps might lead to a shift backward (such as a nativist backlash that turns public opinion against more liberal migration) would be a bad path. A better choice would be a slippery slope: one where the initial steps may not necessarily look as “extreme” as open borders to the people who might object to them, but once those steps are taken, the next steps towards open borders become easier to accomplish. (UPDATE written after the post was drafted: Tyler Cowen’s recent post makes this type of backlash argument to explain a Swiss referendum to restrict immigration from the EU; see also responses from Bryan Caplan and Jason Brennan).

Some possible slippery slopes

  • Gradual expansion and merging of free migration zones: For instance, the EU is a free migration zone for European countries, and it is gradually adding countries. Suppose the United States and Canada created their own free migration zone, Southeast Asian countries created their own free migration zone, and a few free migration zones emerged in Africa and Latin America (South America). The US-Canada free migration zone could, after some time, add Mexico and the Caribbean Islands, and then merge with the South American free migration zone. The European free migration zone could eventually merge with the new unified American migration zone. Over time, as the threat of terrorism, and the subjective sense of the threat, receded more and more into the past, the Gulf states could merge with the European free migration zone. And so on, until eventually the whole world would be a free migration zone.
  • Gradual lowering of admissions standards for migrants: The idea here would be to begin with complete open borders for migrants who meet a particular skill level threshold or income threshold, and then to gradually reduce the threshold over time, either directly, or by failing to index for inflation, or by relying on global economic growth. A plausible argument for why this might work is that high-skilled and high-income migrants lead to fewer problems, both real and perceived, for natives, making the natives somewhat more pro-migrant (based on their experience interacting with migrants so far). It might therefore be easier to cross historical thresholds of migrant proportions in the population without any visible difficulties experienced by natives. Australia, Canada, and Singapore might be examples to look at, and it would be interesting to see the extent to which they avoid the nativist backlash phenomenon through an initial focus on high-skilled migration.
  • Gradual increase in quotas: Hard quotas in various migrant categories may be gradually expanded, and new categories that permit more general forms of migration may be added, initially with low numerical caps but with the caps steadily rising. Although this could in principle be huge, it doesn’t seem to have had much slipperiness historically in and of itself.
  • Family reunification, with a gradually expanding definition of “family”: Family reunification may begin small, with, for instance, the spouses or children, then it may expand to siblings, parents, or cousins, and finally it may expand to close friends or anybody whom a resident can provide some sort of sponsorship guarantee as a “personal acquaintance.” For a fixed definition of family, too, the amount of “chain migration” can be significant, and although insufficiently slippery to get to open borders all by itself, it can act as an amplifier to any other slippery tendencies. Quantitatively, this has been significant in both the US and Europe, and quite difficult to stop, even though governments have often attempted to crack down on various aspects of family reunification to prevent what they see as abuse.
  • A tariff/tax scheme with a gradually declining tariff or tax rate: A DRITI-type scheme that begins with high surtaxes and high mandatory savings, to a level that meets the concerns both of restrictionists and people who want the government to earn revenue. If the revenue-earning part of it goes well, that would create a strong impetus to create and expand the program, and lower the surtaxes and mandatory savings in order to attract more migrants and generate more revenue. Even though staunch restrictionists may oppose that second step, governments and the majority of voters may have become too addicted to the revenue streams and expanded economy size afforded by the program to backtrack from it. Over time, the rates would come down to the point that it would look more like a bureaucratic inconvenience than a program specifically designed to regulate migration. At this stage, general egalitarian concerns, or general philosophical views about taxation, may take over and lead to an abolition of the surtax and of the forced savings program.

Reasons for continued slipping

  • Growing tangible benefits (real or perceived) feeding into growing support for more migration at the margin: People see tangible benefits from the expansion so far, and want to keep going further in that direction. This may be because the constituency that has been created by partial expansion of migration is more eager for further expansion than the original set of natives (for instance, recent migrants might favor more liberal migration policies — something that seems empirically borne out). It may be because people get addicted to the revenues from a DRITI-like scheme and feel the need to expand it.
  • Support for steady expansion as long as there are no tangible or major harms, based on a presumption that ceteris paribus, allowing more people to migrate is better: People don’t actually see much by way of tangible benefits, but they don’t see any tangible changes at all, so, given that they concede some sort of “presumption in favor of cautious expansion of migration as long as there are no visible drastic damages” they are happy to let it expand. Or perhaps the people aren’t even that aware of the exact state of things, but their representatives in government are willing to let migration gradually expand barring any unexpected developments.
  • Slippery slope in people’s perception of the forms of migration that morality or justice require should not be forbidden: Each step in the slippery slope changes people’s perception of the moral necessity of open borders. For instance, people may go from “it’s unjust to forbid somebody from migrating if they have family in the country or are fleeing persecution” to “it’s unjust to forbid somebody from migrating if they are going to be a net fiscal plus for the nation” to “it’s unjust to forbid somebody from migrating if they’re honest and hardworking” to “it’s unjust to forbid somebody from migrating unless it can be demonstrated that they pose a significant threat to the life and liberty of people in the country.”
  • Increasing share of the decision-making population that has a personal positive connection with migration: Migrants tend to be somewhat more pro-migration than natives (see the quote below), so increasing the proportion of migrants would increase the proportion of residents with pro-migration views. This may not have much effect alone, because migrants may be ineligible for direct participation in political decision-making, but they could influence the views of others they interact with. Natives who interact with migrants on a personal level may also become more pro-migration simply because of the “human face” of the issue, even if the migrants themselves don’t try to convince them. The children of migrants are also somewhat more pro-migration than natives. A caveat: the support for further migration may be limited to the migrant’s ethnic, racial, or religious group or socio-economic class.

The following quote from Bryan Caplan’s Cato Journal piece is relevant to the assertion made above about migrants having more pro-migration views:

Finally, there is at least one issue where immigrants are sharply more libertarian than natives: immigration itself. Materially, recent immigrants have the most to lose from additional immigration. Ottaviano and Peri (2008: 59) estimate that immigration from 1990–2006 depressed foreign-born workers’ wages by over 7 percent. But immigrants, like human beings generally, do not derive their political philosophies from material self-interest (Mansbridge 1990). The General Social Survey asks respondents to put their views on immigration on a 1–5 scale, with 5 being most hostile. People with two native-born parents have an average response of 3.9, with a
median of 4; people with at least one foreign-born parent have an average response of 3.1, with a median of 3. By way of comparison, people who call themselves “extremely liberal” have an average response of 3.3—versus 4.0 for the “extremely conservative.” People with foreign-born parents rarely favor open borders, but economists
and libertarians aside, no one is less opposed to immigration.

Reasons why we might expect slipping to not happen

Slipping is not an inevitability of nature. Without concerted effort, it may not happen. Some reasons:

  • It is very difficult to keep making changes steadily. In general, we should expect change in fits and starts.
  • As the proportion of migrants in the population reaches historically unprecedented levels, migration becomes a lot more visible as a phenomenon. Even with a moderate level of anti-foreign bias, people are likely to blame migration for any problems that arise. Also, appear to historical analogy fails to be a powerful argument for further expansion. The possibility of nativist backlash remains strong, and recent pushback to migration in the UK and Australia might be evidence of some natural limits in the amount of migration people will naturally tolerate given their current beliefs about how the world works.

Braking mechanisms

Braking mechanisms could matter for two reasons. First, we may be genuinely unsure of the extent to which open borders would be a blessing, even if we think it’s quite likely to be one. In this case, having a slope that slips by default, but that can be braked if things are turning out badly would be helpful. Just how much importance we place on a braking mechanism depends on what level of badness we deem sufficient to halt further progress. That level could vary between hardcore open borders advocates and people whose support for free migration is highly conditional to specific consequences.

Second, even if we (as open borders advocates) don’t believe that the braking mechanism would be necessary, others who are more skeptical of the change might be reassured by the presence of a braking mechanism. The braking mechanism would be like the chain passengers can pull for emergency-braking in some trains: it is rarely pulled, but its presence adds to the (perception of) safety (though the analogy also highlights that the braking mechanism may end up getting used for spurious reasons, just as miscreants misuse emergency brakes to get down wherever it’s convenient for them).

There could be different senses of braking and reversal:

  • Outcome reversal: Additional migrants who have come in through the expansion so far are deported, bringing the situation as close as possible to how it would have been if the expansion had never occurred. Note: This isn’t intended to endorse such “outcome reversal” as either moral or even practically feasible; see the discussion below.
  • Policy reversal: The migration policy for new migrants reverts to what it was before we started slipping the slope, but people who already migrated under the temporarily more liberal migration policy are not forced to leave. A slight variant of policy reversal, that I call punitive policy reversal, would be where policy is not just reverted, but made even more strict than it was in the past until such time as we effectively have an outcome reversal. For instance, if quotas are doubled for the next three years, and people then want to reverse the effects, quotas may be set at zero for the three years after that, and then returned to current levels. Note that punitive policy reversal can accomplish outcome reversal only in cases where the original quota was nonzero, and is best suited to numbers-based increases rather than the addition of totally new categories of migration.
  • Policy freeze: The policy remains stuck at the new, expanded level, but further expansion becomes difficult.

(For the mathematically inclined, each sense references the derivative of the preceding one with respect to time).

(For an example of confusion that arose because of people in a conversation talking of reversibility in different senses, see the comments starting here).

Outcome reversal is nearly always difficult and often impossible to accomplish directly. Even if it were possible to force all the additional migrants to leave, the level of (visible) coercion and disruption necessary could give pause even to people highly critical of the expanded migration policy. Even those who wish to accomplish outcome reversal may end up suggesting the route of punitive policy reversal. Policy reversal is somewhat easier to accomplish if people feel the expansion has not worked well. Policy freeze, where further liberalization of migration is blocked, might be the easiest in so far as status quo bias argues in favor of it.

  1. Gradual expansion of free migration zones can be stopped by the participating countries, even though it would be relatively hard to undo an existing free migration zone. Outcome reversal is near-impossible, policy reversal is very difficult, but policy freeze is relatively easy.
  2. Gradual lowering of admissions standards can be stopped, and even reversed, if the results are deemed bad. Outcome reversal is near-impossible, policy reversal is of moderate difficulty (less so than with free migration zones), and policy freeze is relatively easy.
  3. Gradual increases in quotas can be stopped, and even reversed. Outcome reversal is near-impossible, policy reversal is of moderate difficulty (perhaps a little easier than with admissions standards, because “how to get in” is anyway a sufficient mystery that people don’t feel they are being deprived of something they were definitively promised), and policy freeze is relatively easy. Note that punitive policy reversal can be accomplished in principle in cases where the original quota was substantially greater than zero anyway, and would be easier than outcome reversal through deportation, but would still be pretty difficult.
  4. Family reunification would be difficult to undo. Outcome reversal would be near-impossible, policy reversal would be fairly difficult (though not impossible, and it might be easier to partially reverse at later stages), and policy freeze would be relatively easy.
  5. For tariff/tax schemes, a continued reduction in the tariff or tax rate will happen only if there is sufficiently high revenue (so that it’s a quantitatively significant source of revenue, making revenue considerations more important relative to other considerations) plus strong evidence to suggest that lowering the tax or tariff rate would attract even more revenue by increasing the “customer” base considerably. Here, outcome reversal is near-impossible, while policy reversal and policy freeze are relatively easy.

The type of braking mechanism available for the policy might be a consideration in the choice of slippery slope. If you’re fairly confident that the braking mechanism is more likely to be abused than used out of necessity, then it makes sense to choose a slippery slope where braking is harder. If, on the other hand, you anticipate that the initial stages could reveal information that could lead to the need to brake, it makes sense to choose a slippery slope where braking is easier.

The utility of different slippery slopes in relation to estimates of the global impact of open borders

In a recent post, I argued based on Carl Shulman’s post that, since existing estimates of the global economic impact of open borders rely on more people moving than may be realistic, estimates may have to be adjusted downward to 20-60%. Whether this affects the overall utility of a particular partial move towards open borders depends on whether that move is targeted at increasing numerical caps on how many people may move, or at removing other policy barriers to movement (whose effect in terms of the number of people that move at the margin might change once we correct our estimates). In the Drake equation language, we are interested in the product $latex Wxy$, and the downward adjustment of $latex W$ might be accompanied by different compensating adjustments for $latex y$ depending on the sort of measure. The sensitivity of expected utility to uncertain estimates of the global economic impact of open borders might be a consideration in comparing different slippery slopes.

Slippery slopes versus keyhole solutions

On this site, we’ve discussed keyhole solutions a lot. Some people might use “keyhole solutions” and “slippery slopes” interchangeably, but there is a difference:

  • A slippery slope involves a series of steps with each step liberalizing migration relative to the previous one, and with the end goal coming reasonably close to open borders. It represents a means or path.
  • A keyhole solution is a (typically policy-based) modification of pure open borders that addresses a significant real or perceived problem with open borders while disrupting open borders as little as possible. It represents an end goal.

Slippery slopes and keyhole solutions could be related: the final stages of a slippery slope might resemble “open borders with a keyhole solution” and the initial stages might also be so described if “keyhole” is interpreted very generously. Also, some keyhole solutions with adjustable parameters (such as the surtax and mandatory savings parameters in DRITI) may lend themselves to a slippery slope: begin with highly restrictionist values of the parameters (so restrictionist that it would be a stretch to call it a “keyhole solution”), then gradually move the parameters in the direction of open borders.

PS: Also relevant is our moderate versus radical open borders page and Joel Newman’s blog post If Open Borders Are Instituted Gradually, What Should Be The Initial Number of Immigrants Admitted?
Thanks to Carl Shulman for helpful comments on a draft.

Open Borders the website: penetration with Internet libertarians

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This post was originally drafted in October and November 2013. I have kept the post largely as is, with some updates clearly marked as such. At the time of my late October 2013 editing round, the page had between 750 and 800 likes, it now has over 1000 (see historical Facebook data for more context).

Clarification: This post concentrates on the reach of “open borders” among “Internet libertarians” but I don’t intend to indicate that this is the only target audience for the site. So far, Internet libertarians, and people who are at the edges of that category, have been a major source of likes and engagement for the site. I expect that Internet libertarians will continue to have a high, but (proportionally) declining contribution to the like counts for the site.

A few weeks ago, I played around with Facebook Graph Search with the goal of trying to figure out how close Open Borders: The Case is to exhausting its potential target market among various segments of the world population. None of the findings were particularly surprising, but I think they’re still worth recording and sharing. The numbers here relate somewhat with my discussion of open borders and the libertarian priority list (part 1 here, part 2 here, part 3 pending). They also relate with the Drake equation-style estimation of the value of open borders advocacy. However, in this post, I’ll concentrate mostly on reporting the numbers, along with a bit of background on my prior speculation and my speculation after seeing the numbers.

My prior views

Prior to looking at these numbers, I had been of the view that there’s a broad category of person called “Internet libertarian” who likes websites that make arguments from libertarian premises, and that:

  • Of the category of “Internet libertarians”, a reasonable percentage (say 10%) would be in a position to like Open Borders: The Case if they came across the site and browsed it a decent bit. When I talk of “the site” I mean the site as it currently stands, without any changes being made to tailor to the audience. Note that my guess would be that about 50% of Internet libertarians would claim to be for radically freer migration in principle, but only about 20% would care about the issue sufficiently to be willing to publicly like our site.
  • My original estimate of “Internet libertarians” was that it would be something in the range of 50,000 (I was going off the estimates of how many people like mainstream libertarian-leaning websites and looking at the lower end of the range).

Combining the above, my original estimate was that there would be about 5,000 “Internet libertarians” who would be willing to like the site if they came across it and read it a bit. As of the time of writing this post, the website has between 750 and 800 Facebook likes. This suggests that there would be low-hanging fruit of about 4,000 people who would be willing to like the site more or less as is, but simply haven’t yet encountered the site (or have, but not for long enough or frequently enough to consider hitting the “Like” button).

My views after looking at the data

Although the numbers don’t definitively falsify the hypothesis, a close look at the numbers did lead me to update my model. My overall conclusion (POOTA numbers alert): is that one can subdivide libertarians into roughly three clusters (note that the clustering is quasi-arbitrary, and there is in reality a continuum, but it’s easier pedagogically to frame things in terms of clusters):

  • A core (perhaps 2,000 people or so) of relatively hardcore libertarians — including people who work in academia, for think tanks, or for libertarian publications, and people who maintain active libertarian-leaning blogs — who are disproportionately likely to like many libertarian pages (including Open Borders). This core of people does not necessarily include only libertarian extremists. The people here may include anarcho-capitalists or moderate minarchists. It may range from social justice-loving bleeding-heart libertarians to dogmatic natural rights believers. The key feature of this core of people would be that they spend considerable effort researching, writing, or in other ways promoting libertarian ideas. Many of them may have jobs in academia or think tanks where libertarian writing is part of their professional work. The website’s penetration with this group of people seems fairly strong. I would guess about 25% of the people in this group (total: 500) would be willing to like Open Borders, and about half of those who would be willing to like it have already encountered it and liked it (total: 250). Update: As of February 2014, I think we have covered about 70% of such potential likers.
  • A much larger pool of people (about 50,000 by my estimate, based on feedback from some others) who like reading libertarian material on the Internet and occasionally comment on libertarian websites. Not all of these people need identify with the label of libertarian: many of them may consider themselves free-market liberals or free-market conservatives or perhaps “fiscally conservative, socially liberal” and some may even oppose key tenets of libertarianism. But they do engage regularly, and at least in some cases actively (for instance, by leaving comments on blogs), with libertarian content on the Internet and in real life (for instance, by attending local Students For Liberty events or going to Cato talks). My guess is that of this group, perhaps 5% or so would be willing to like the Open Borders website as is if they saw it (total: 2500), and we have probably penetrated about 10% of this market (about 250 people).Update: My guess is that we may have gone up to about 15% of the people in this group.
  • An even larger pool (about 150,000 by my estimate) of people who like libertarian websites on Facebook and occasionally read libertarian blogs but aren’t really into closely following them. I expect that only about 1% (total: 1,500) or so would like the Open Borders website, and perhaps about 5% of the people in that group have liked the site already (total: 75). Update: My guess is that we are now at 7-8% of this group.

Note that the numbers I provided in this paragraph are very rough guesstimates based on the numerical intuition I acquired after compiling the numbers below. I certainly did not derive the numbers using any sort of mathematical procedure from the data.

Note also that this should not be taken to construe that the site’s long-term appeal among “libertarians” is limited to the ~4,500 or so people that my above guesstimates suggest would like it if they saw it today. As the site gets redesigned to have more visual appeal and as the ideas become more mainstream within libertarian circles, the number of people who like it may go up. But that’s not low-hanging fruit — it requires site redesign effort and effort in making open borders more mainstream within loosely libertarian circles.

Data based on Facebook Graph Search

A few limitations of graph search worth keeping in mind:

  • Due to privacy settings, some people may not appear in the lists, even though they do affect the counts. Thus, the manual counting for the “Fewer than 100 people” cases is in most cases an underestimate.
  • Facebook does not provide exact counts, instead generally saying “fewer than 100 people” or “more than 100 people” if the number of people is more than (about?) 15.

Below is a partial list of libertarian Facebook pages that had more than 100 common likers with Open Borders as of October 26, 2013.

Page Number of likes as of October 26, 2013 Link to Facebook Graph Search query for intersection
Economic Freedom 297,158 intersection
Independent Institute 246,138 intersection
LearnLiberty 245,830 intersection
Cato Institute 186,186 intersection
Reason Magazine 109,485 intersection
Students for Liberty 98,135 intersection
Mises Institute 87,911 intersection
Libertarianism.org 72,953 intersection
EconLib 41,341 intersection
Institute for Humane Studies 31,774 intersection
Skeptical Libertarian 21,935 intersection
Mercatus Center 18,405 intersection
Bleeding-Heart Libertarians blog 5,191 intersection

Here is a list of websites I checked that had less than 100 likes in common with Open Borders: The Case as of October 26, 2013. For those where the intersection is now estimated as over 100, I have indicated that parenthetically. For others, a guesstimate of the new value is provided.

(now about 60)

Page Number of likes as of October 26, 2013 Size of intersection as of October 26, 2013, along with link to Facebook Graph Search query (parenthetical value is estimate as of February 8, 2014)
Punk Rock Libertarians 58,998 35 (now more than 100)
Libertarian Troll 8,208 17 (now about 30)
Center for a Stateless Society 6,059 50 (now more than 100)
Cafe Hayek 5,018 53 (now more than 100)
Liberty Fund 1,319 40 (now about 50)
Future of Freedom Foundation 485 39

Multiple intersections (main information October 26, 2013, updated information February 8, 2014):

  • The intersection with the three most liked libertarian pages in the list was fewer than 100 people (it is now more than 100 people).
  • On the other hand, the combined intersection with the Cato Institute, Reason Magazine, and the Independent Institute was more than 100 people. All three of these are relatively famous libertarian pages.
  • The combined intersection with EconLib and Bleeding Heart Libertarians was fewer than 100 people, with 40 visible search results (now, about 56 visible search results).

I noticed from the above that the intersections with much smaller and more hardcore libertarian pages are not that much smaller than the intersections with relatively more widely liked pages. This suggests that our likers have a significant fraction of “movement libertarians” — people who have strong commitment to libertarian ideas and for whom it may even be part of their professional work. To test this hypothesis, on November 3, I considered intersections with people who had ever worked at a number of libertarian places. Note that many people don’t fill out their employer information on Facebook, so these numbers are all almost certainly underestimates.

Libertarian institution or publication Number of people who like Open Borders and have ever worked for this institution or publication (link to Facebook Graph Search query) (numbers as of November 3, 2013)
Cato Institute 6 people
Reason Magazine 1 person
The Independent Institute 1 person (but this is an underestimate relative to what I know)
Students for Liberty 3 people
Institute for Humane Studies 3 people
Ludwig von Mises Institute 1 person

Although these numbers do not seem to work out to very high values, anecdotal evidence of the relatively high degree of commitment to libertarianism of people who like the site seems to bolster the hypothesis.

Penetration rates for blog subcultures

Libertarians are not a homogeneous group. There are different subcultures within libertarianism, and each subculture has a slightly different typical mix of blogs followed.

Currently, Open Borders has been mentioned in a number of libertarian blogs, but to widely varying degrees. Here’s my sense of things, based on data collected at the external coverage page (Update February 2014: I expect each of these to have moved up a couple percentage points, but not significantly, since Open Borders did not receive much additional coverage in the blogs listed below)

Libertarian (or libertarian-leaning) blog Extent to which it’s mentioned Open Borders Estimate of penetration: (number of regular or semi-regular readers who have liked Open Borders)/(number of regular or semi-regular readers who would like Open Borders if they visited the site), expressed as a percentage
EconLog 1 post about the site, 4 links to site posts with substantive discussion, about 5 other links to site posts, plus 2 posts about EconLog blogger Bryan Caplan’s guest posts on Open Borders 80-90%
Volokh Conspiracy 1 post linking to a page on the site, 1 post about a guest post on the site by the author Ilya Somin 30-40%
Cafe Hayek 2 posts mentioning the site in link roundups. 20-30%
Bleeding Heart Libertarians 1 post mentioning a substantive post 20-30%
Marginal Revolution 2 brief mentions of the site, 1 brief mention of a post on the site 5-10% (update: now 10-15%)

Implications of embracing low-end estimates of the global economic impact of open borders

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Carl Shulman’s recent post on upward and downward biases in the double world GDP estimates, as well as Nathan’s (forthcoming) post proposing his own model, led me to start thinking about the extent to which the case for open borders is tied to uncertain claims about the economic effects, and whether pushing the “double world GDP” idea as a slogan is epistemically unsound.

One can make a case that high estimates of the global effect of open borders have value in getting people initially interested in the subject, and that once they’re sufficiently invested they will not change their mind even if they learn that the estimates were too high. Indeed, something similar seems to have happened with the growth of the effective altruism movement: initial estimates of the money you needed to donate to save a life were in the range of a few hundred dollars, whereas current estimates are over 2000 dollars, and still rising. Jacob Steinhardt described this in his critique of effective altruism:

The history of effective altruism is littered with over-confident claims, many of which have later turned out to be false. In 2009, Peter Singer claimed that you could save a life for $200 (and many others repeated his claim). While the number was already questionable at the time, by 2011 we discovered that the number was completely off. Now new numbers were thrown around: from numbers still in the hundreds of dollars (GWWC’s estimate for SCI, which was later shown to be flawed) up to $1600 (GiveWell’s estimate for AMF, which GiveWell itself expected to go up, and which indeed did go up). These numbers were often cited without caveats, as well as other claims such as that the effectiveness of charities can vary by a factor of 1,000. How many people citing these numbers understood the process that generated them, or the high degree of uncertainty surrounding them, or the inaccuracy of past estimates? How many would have pointed out that saying that charities vary by a factor of 1,000 in effectiveness is by itself not very helpful, and is more a statement about how bad the bottom end is than how good the top end is?

People who may have been attracted initially by the lowball estimates have generally tended not to leave, perhaps due to an endowment effect or status quo bias, or because they found more compelling and robust reasons to stay once they became effective altruists.

On the other hand, “too-good-to-be-true” estimates can also make it difficult to get people to take the cause seriously in the first place, and can also lead to people getting disillusioned once they realize the estimates won’t work, thereby throwing out the proverbial baby with the bathwater. As Carl Shulman wrote in the context of effective altruism estimates:

Mainly, I think it’s bad news for probably mistaken estimates to spread, and then disillusion the readers or make the writers look biased. If people interested in effective philanthropy go around trumpeting likely wrong (over-optimistic) figures and don’t correct them, then the community’s credibility will fall, and bad models and epistemic practices may be strengthened. This is why GiveWell goes ballistic on people who go around quoting its old cost-effectiveness estimates rather than more recent ones (revisions tend to be towards less cost-effectiveness).

I have listed above some of the strategic pros and cons of embracing overly optimistic estimates, but I am personally more interested in the epistemic question of the extent to which the case for open borders, or for migration liberalization in general, hinges on the magnitude of the estimates, and what a reasonable case for open borders, and for open borders advocacy, might be in the lowball scenario.

Let’s first look at the lowball scenario. Here is a back-of-the-envelope calculation that Clemens does in his literature review paper (Pages 84-85) (emphasis mine):

Should these large estimated gains from an expansion of international migration outrage our economic intuition, or after some consideration, are they at least plausible? We can check these calculations on the back of the metaphorical envelope. Divide the world into a “rich” region, where one billion people earn $30,000 per year, and a “poor” region, where six billion earn $5,000 per year. Suppose emigrants from the poor region have lower productivity, so each gains just 60 percent of the simple earnings gap upon emigrating—that is, $15,000 per year. This marginal gain shrinks as emigration proceeds, so suppose that the average gain is just $7,500 per year.
If half the population of the poor region emigrates, migrants would gain $23 trillion—which is 38 percent of global GDP. For nonmigrants, the outcome of such a wave of migration would have complicated effects: presumably, average wages would rise in the poor region and fall in the rich region, while returns to capital rise in the rich region and fall in the poor region. The net effect of these other changes could theoretically be negative, zero, or positive. But when combining these factors with the gains to migrants, we might plausibly imagine overall gains of 20–60 percent of global GDP.

This 20-60% comes under assumptions that I think would seem reasonable to many critics of migration. For instance, it largely accords with the assumption of no closing of the skills gap between migrants and natives. Also, it doesn’t consider the long term (the children of migrants getting better education and therefore having more human capital than their counterfactuals in the home country). So it does not rely on beliefs about the closing of skill level and achievement gaps, which are controversial among many critics of migration. In particular, if you believe in intergenerational persistence of these gaps, the above estimation exercise should still seem reasonable to you. The only thing the above doesn’t account for is a radical form of killing the goose that lays the golden eggs (note that the lower end of the 20-60% estimate already accounts for moderate forms of goose-killing, as the original point estimate is 38%). So, setting such radical goose-killing aside for now as an important possibility worth separate investigation, let’s look at the 20-60% estimate. What would it mean?

The pessimistic end of the estimate, 20%, is still more than three times the total of the highest literature estimate of the gains from removing trade barriers and the gains from removing barriers to capital mobility (4.1% + 1.7% = 5.8%) among the papers cited by Clemens. So, free labor mobility still has higher upside — even with these pessimistic assumptions — than free trade.

But even though there’s bigger upside, the margin isn’t that huge. If you had originally believed that open borders would double world GDP, but you then revised the estimate downward to 20%, that would mean that the extent to which open borders advocacy is a compelling cause would reduce, ceteris paribus. However, there are a few countervailing considerations, even if you embrace the lowball estimate.

To help explain this, let me look at my Drake equation-like estimate of the social value of open borders advocacy. I expressed the value as a product:

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

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.

Now, note that we have at least two ways that a decline in $latex W$ might be compensated for:

  • Compensating increase in $latex x$: This would be tricky to argue, because we need to show that our current belief of how realistically our new model accounts for stuff is better than our past belief of how the old model accounted for stuff. In other words, if our original estimate of $latex x$ was based on the knowledge that that model is as crude as it turns out to be, then when we adjust $latex W$ downward and thus make our model realistic, we can compensatingly adjust $latex x$ upward. The effects would approximately, though not exactly, cancel out.
  • Compensating increase in $latex y$: In the specific case at hand, in fact, these arguments do apply. The main source of overestimation in the models predicting huge gains in world GDP is the large number of people that would need to move. Adjusting those numbers alone would get us in the 20-60% range. But, to the extent that this is true, the fraction in which we can move in the direction of open borders might also increase: if open borders involves “only” 300 million people moving instead of 3 billion, then allowing 30 million people to move moves us 10% (0.1) of the way to open borders, rather than 1% (0.01). Again, whether or not $latex y$ gets compensated in practice depends on whether we were aware a priori of the large numbers of people that the model needs to move — if we weren’t, then the adjustment might not happen.
  • Compensating increase in $latex z$: If open borders, or partial moves in that direction, aren’t as radical as they seemed, maybe partial advocacy efforts in that direction are more likely to move us toward them. We should be careful not to double-count this against $latex y$, though — if we’ve already made the adjustment for $latex y$, we probably don’t need to make the adjustment for $latex z$.

A couple of additional notes:

  • All the estimates ($latex x$, $latex y$, and $latex z$) are highly speculative. Combined with the fact that these estimates are related to our estimates for $latex W$ and the methods we used to arrive at those estimates, there’s a lot of room for fudging and very little that can be said conclusively. The order of magnitude of decline in our gain estimate (from 100% of current world GDP to 20%) is only a decline by a factor of five, so our estimates of utility go down by only one order of magnitude, whereas the range of uncertainty is about three orders of magnitude (the range I gave in the original blog post for the Open Borders website was $50,000 -$50,000,000).
  • That said, it would be surprising if the decline in $latex W$ were accompanied by no decline in the overall utility of the form of open borders advocacy. That could happen, based on the considerations listed above, but we should have a prior against it happening. Remember the one-penny proof whenever you’re tempted to believe that a specific change in the estimate of one value will not affect the estimate of another value that it is in general related to.

UPDATE: Diaspora dynamics might reconcile low short-run estimates of how many would move with large long-run estimates of the same. For more, see here.

Public schooling for immigrants’ kids — why’s it a problem?

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One of the common complaints of critics of migration is the welfare state/fiscal burden objection, or more specifically, the observation that migrants impose a net fiscal burden on the receiving countries. In many countries, such as the United States, migrants’ access to means-tested social safety nets is restricted, and it could in principle be restricted further. Perhaps for this reason, one of the main items that contributes to the “cost” side of the fiscal ledger for migrants is the cost of free (i.e., government-funded) schools for the children of immigrants. In this post, I’ll take a closer look at the objection in light of a few different possible belief systems regarding how education must be funded.

In one important respect, however, the specifics of the belief systems are irrelevant to my broader point. In each case, I will consider a possible general principle, and then note the tension between that principle and a differential treatment of migrants and natives. In other words, for each position on the purpose and funding of education, I am questioning what Sebastian calls the moral relevance of countries while applying that principle.

Education as private good that should be funded privately

On this view, schooling and education should be paid for privately, either by the student, or the parents, or through private philanthropy, or educational loans. If you take this view, then it would be correct to view the cost of schooling immigrants’ kids in government schools as a subsidy from the government to the immigrants. But there is nothing in this view that distinguishes immigrants’ kids — the same rules apply for natives. People who take this view should be advocating the separation of school and state, not complaining about immigrant consumption of schooling alone.

Education as state investment or social investment

According to this view, which is more widely held, the state invests in the schooling of children, helping them acquire human capital, and then recoups its investment in the form of taxes when the children become adults. By this theory, it’s not immigration that we should be concerned about, it’s emigration — the worry should be that kids will consume schooling, then emigrate to other countries and enrich those other countries with the human capital they acquired (incidentally, this concern has been voiced, but largely in the context of brain drain from underdeveloped countries). As long as the kids plan to live and work in the same country after completing their schooling, the fact that they’re immigrants should not cause any worry (and incidentally, this also provides a purely pragmatic “cost-recovery” argument against deportation — why deport people after having invested in their education, before the investment can be recouped?). At any rate, comparing the money that the state spends on the kids with the fiscal contributions of the kids’ parents seems at odds with this theory. If one really believed that the money spent on children’s education should be related to their parents’ (rather than their own) fiscal contributions, one should probably revert to some form of the private parent-funded view of education.

Another related point is that in many places, such as the United States, educational funding is at the state and local rather than national (federal) level, so that even if people stay within the country, they may move to another state. This points in the direction of being concerned not only about immigrants, but also about natives who are likely to move between states. Given that a lot of natives, particularly those at higher skill levels (and hence, the people likely to have higher incomes and pay higher taxes), spend their adult lives in a different state than where they spend their childhood, this is a big problem for the “education as investment” theory.

Yet another point may be that educational investment for certain kinds of students simply doesn’t yield a good return on investment, and immigrants are disproportionately represented in those categories. But if you believe that, you should advocate curriculum reform, introduction of vocational education, an end to compulsory schooling, and/or more stringent performance criteria for eligibility for government-funded schooling, not complain about immigrant overuse of educational resources.

Education as moral right

This view is also widely held. According to this view, all members of the community deserve an education, regardless of whether it helps make them economically productive. However, there is a tension between the language of moral rights and the concern that people should coercively be prevented from using the resource. One has to have a very strong citizenistic view to believe that this right extends to citizens. However, even to the extent that it applies only to citizens, many of the children of immigrants whose schooling is considered a downside of immigration are either already citizens or are on a path to citizenship. Perhaps there is currently uncertainty as to whether they will eventually become citizens, or perhaps you believe that they should not become citizens. Nonetheless, childhood is a uniquely optimal period for providing education. This suggests that, if there’s a reasonable probability of their becoming citizens, and if education is indeed a moral right, then educating the children of immigrants is morally required.

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.