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.

Vipul Naik

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