Thinking about Costs and Benefits of Immigration

I find this a useful way to organise my thoughts about the costs and benefits of immigration. It may work for you too. I start out with a neutral benchmark, where immigration has neither costs nor benefits for the original population. Then I think of different ways in which that neutral benchmark could be wrong. This post is just a list (no doubt incomplete) of things that might create costs or benefits from immigration. I make no attempt to say which is bigger. It depends.

I am writing this mostly for non-economists. I should warn you that the economics of migration is not my area. I'm a macroeconomist, and most economists who specialise in immigration are microeconomists. This may give me a different perspective.

In case you think it matters: I migrated to Canada from the UK 40 years ago (and to Quebec from Ontario 30 years ago). This may influence my perspective.

And for what it's worth: I think that Canadian immigration policy is probably in the same ballpark as the right immigration policy for Canada. Though it is probably different for different countries.

The Neutral Benchmark. The country clones itself and becomes twice as big. Everything scales up in proportion. The supply of everything doubles, and the demand for everything doubles, so all prices (and wages) stay the same. Total output and income double, but output and income per capita stay the same. There are neither costs nor benefits for the original population.

I think that's a good place to start, but obviously a bad place to stop. What follows is a list of things we need to consider that might make it wrong.

Money and Say's Law. (I'm good at this stuff, and want to get it out of the way first.) If the stock of money in the country stays constant, we have a problem. There won't be enough money to buy double the quantity of goods, unless that money circulates twice as quickly (which is very unlikely to happen), or unless the dollar price of everything halves, so each dollar is worth twice as much as before (which may take a long time to happen and will cause other costs). If the supply of everything doubles when the population doubles, the central bank must ensure that the supply of money doubles too, otherwise demand won't double and immigration will cause mass unemployment. "Supply creates its own demand" (Say's Law) only works if the supply of money doubles along with a doubling of the demand for money. So we need a sensible response to immigration by the central bank.

Land. Doubling the population by immigration is not the same as annexing the identical country next door, because the stock of "land" (natural resources) stays the same. So the amount of land per person halves. Think about an agricultural economy, for example. Output rises if labour doubles, but the rise in output is less than double. So output and income per capita fall.

If the land is privately owned, by the original population, their average income per capita rises. But wages fall, and rents on land rise, and so the distribution of income changes; workers who own no land are worse off.

If the land is held in common, so the immigrants pay no rent to the original population, the original population is worse off.

It's much the same if the land is used for housing instead of agriculture. A doubling of the population causes house rents and prices to rise, so that real wages (adjusted for the cost of housing) fall.

Or the land could be used for national parks, that are held in common.

Capital. In the "short run", when the stock of capital is held fixed, capital (machines that make labour more productive) is just like land. So if you double the quantity of labour, holding capital fixed in the short run, output and income per capita fall, and wages fall. But unlike land, in the "long run" you can produce more capital by saving and investing, so eventually the stock of capital will double too, if the population doubles. And you can speed up the process by importing more capital from abroad. So we are back at my Neutral Benchmark, though it may take some time to get there if you can't import capital along with the immigrants.

Economies of Scale. That's when if you double all the inputs, output more than doubles. In this case, immigration causes output and income per capita to increase.

Non-Rival Goods. That's when it costs little or nothing to let an additional person consume a good that is already being produced. Like radio and TV broadcasts, or maybe national defence. So if the population doubles, the cost per person halves. It's like an extreme case of economies of scale.

National Debt [Update: and Assets]. If the population doubles, the pre-existing national debt halves on a per capita basis. It's like land held in common, except we are now talking about a common liability rather than a common asset. [Update: as Ralph Musgrave comments below, we must also consider the existing stock of publicly-owned capital assets, like roads and bridges, which are like land held in common. Those assets halve on a per capita basis.]

Comparative Advantage. One of the reasons that people trade, both with people from the same country and with people from other countries, is that different people are relatively better or worse at different things. (The other reason is economies of scale). But transport costs can make trade difficult, so it can be easier to trade if the people who trade move closer together. (Similarly, the Economies of Scale argument for immigration ultimately depends on transport costs.) And easier trade generally makes people better off.

[Update: Productivity and Terms of Trade. (Via Alex Tabarrok on Twitter). If the foreign people you buy from and/or sell to (your trading partners) immigrate, and become more productive and richer by immigrating (because your country has a better economic system), that may make you better off. Because the increased supply of the goods they produce means you pay a lower price for their goods or they pay a higher price for your goods. But this effect works the other way and makes you worse off if your competitors immigrate.]

Redistributive Taxation. If the immigrants are (or will be) more productive and have higher incomes than the original population, and so pay more taxes, this is a benefit to the original population. And the opposite if they are less productive and have lower incomes.

All The Other Things That Economists Normally Hold Constant Because We Aren't Very Good At Thinking About Them. If a doubling of the population caused a civil war, because the immigrants and original population had incompatible visions of how the country should be governed, that would obviously be a cost to the original population. And that cost might outweigh or nullify any of the other possible benefits listed above. And they might view surrender as even worse. That's an extreme case, of course. But it does remind us that countries are not just areas of land; countries are clubs of people. And some countries are richer than others, not just because they have more or better land, but because their social/cultural/economic/whatever institutions work better. And it is people who create and maintain those institutions. And those institutions may or may not change (for better or worse, in the eyes of the original inhabitants) as a result of immigration. It depends.

Not in the list, but something we should remember when trying to figure out whether the costs or benefits are bigger:

History is Biased. We can look at past experience to try to see whether immigration created net costs or net benefits. But we need to remember two sources of bias. The first bias is selection bias: countries normally try to prevent immigration if they think it will have bigger costs than benefits (and when they try and fail they call it "invasion" not "immigration"). So we tend to observe only that immigration that would be beneficial to the original population. The second bias is that history is written, in part, from the perspective of those who were immigrants themselves, or their descendants. If immigration changes a country, it may change what is considered a "cost" and what is considered a "benefit", and make it different from the past perspective of the original inhabitants. And the whole idea of a country is based on "We are all in this together", which is hard to reconcile with the idea that some of us shouldn't be here. Which makes it tricky to think about the costs and benefits of immigration.

Comments

[Ralph Musgrave]

While Nick does mention capital, he misses the point (also missed by almost every study of immigration I’ve seen) that there is a very large amount of publically owned capital (infrastructure etc) per head. That means that if that amount of that capital per head is to be held constant in the arrival of X new immigrants, the country as a whole has to sacrifice living standards so as to produce the extra infrastructure. (To be accurate, the important point here is immigration NET OF emigration.)

That is a big cost for the host country. Alternatively the host country just fails to invest in enough infrastructure, which means the host country bears a cost in terms in inadequate infrastructure (ring any bells?)

There is one study of this matter which puts the amount of that capital at £140,000 per head. See:

http://socialaffairsunit.org.uk/digipub/content/view/18/27/1/1/

I suspect that figure is an overestimate. But even if the true figure is much less, it is a pathetic failure on the part of most of those who have authored studies of the costs and benefits of immigration to have TOTALLY IGNORED that point.

[Nick Rowe]

Ralph: fair point. I did miss that. The existing stock of publicly-owned capital (net of public debt used to finance it) is like land held in common. Will update post.

[Roger Sparks]

An interesting post. Thanks for creating it.

When you discuss "capital", of course you are meaning tools used in the production of goods .

If we only think of hand tools, I would agree with your conclusion. OTOH, if we think of major installations (such as power generating plants) as being tools used in production, we can see that added immigration will stretch the demand on those resources. Yes, we might be able to build more over long periods of time, but the environmental resources supporting these plants also needs to be expanded, which may be impossible.

This observation makes me think that the additional stress on capital from immigration is not neutral but is negative for the original population.

[Nick Rowe]

Roger: yes. Those are all capital, but it depends on whether they are privately owned or owned by the government (common ownership). See Ralph's comment above, and my response.

[Toby]

Nick, how much does the analysis change if the migration is within a relatively integrated market such as Canada and the US? And what about NAFTA? The effect of migration across the border should then be more similar to migration within an area enclosed by a border. The net effect of migration should be smaller then, right?

[Bob Smith]

That's a very useful way of thinking about it. Thanks.

[Nick Rowe]

Toby: let me try to figure that out:

Ignore everything on my list except Comparative Advantage. With no transport costs, and Free Trade between Canada and the US, it wouldn't matter where anyone lived. Without Free Trade, everyone would move to the same country (it doesn't matter which one, but the larger country would always be more attractive) so they can trade. With Free Trade and transport costs, everyone would move to a single point which could be anywhere (remember we are ignoring Land).

So I think you are right.

[Lord]

And history is biased by time since growth occurs with or without immigration. Many will consider its effects not just on the country and original population but on the immigrants who will be generally better off or they wouldn't have immigrated, but how much the original population should value this is up to them, though some, the open borders people, deny they have any right to this at all.

[Nick Rowe]

Lord: yes, but that's more a question of counterfactual conditionals, which economists usually recognise as a problem with all evidence. We can't assume that *all* changes since the date any policy was changed are due to that policy change. Some of those changes would have happened anyway.

[Nick Rowe]

Thanks Bob! (I had to fish you out of the spam filter, again. Sorry.)

[Frances Woolley]

Nick, good post, thanks for writing it.

[Lorenzo from Oz]

Well done that man :)

[Lorenzo from Oz]

Here's another consideration: how does it affect the path of public policy? Unless the newcomers have exactly the same policy preferences as the current inhabitants, they will, over time, change the path of public policy in a way which presumably drifts further from the preferences of the current inhabitants compared to if they had not come.

Civil war is an extreme outcome, but there is a whole lot of other possibilities short of that.

Including, of course, targeting changes in the voter base to get desired effects: what Glaeser & Shleifer called "the Curley Effect". http://www.nber.org/papers/w8942

The literature on state capacity, internal conflict and state development is not very cheery when it comes to social diversity.
https://www.researchgate.net/publication/228466685_The_Political_Economy_of_Linguistic_Cleavages

[Nick Rowe]

Thanks Frances!

Lorenzo! What a coincidence! I have just spent the last hour reading your lovely blog. Such an intellectual, managing to keep so many things in your head at once (something that has always defeated me, like trying to read a Russian novel with too many characters).

Your point about public policy is right. And that is (presumably) a cost to the original inhabitants, because if they had wanted to change public policy in that direction they would have done it themselves. I expect I should have explicitly included that under my last point about social/cultural/economic/whatever institutions. But it's a more minor version of the sort of thing I had in mind. Personally, I think that stuff is the biggest potential cost of Open Borders. Countries exist for a reason, dammit! They aren't just random lines on a map (though some of them may start out a bit that way, and maybe suffer the consequences). Now immigrants do presumably partly self-select into countries whose policies and institutions they approve of, which helps. But sometimes feet and hands vote differently, or there's a collective action problem.

[Lorenzo from Oz]

Thanks Nick. Though it could be I am an intellectual bower bird, continually distracted by the next shiny thing :)

(I have a book contract with an actual commercial publisher to write a book on marriage, talking of matters broad.)

Institutional change is likely to be slower but deeper in effects. And possibly a bit less salient, precisely because it might be somewhat "lobster in slowly boiling pot", until it really isn't.

[Majromax]

I don't think that 'Comparative Advantage' is universally a gain from immigration.

Imagine that my English town instantly doubles in size from immigration of French people. For the sake of argument we can hold everything else constant-to-scale: the land built upon doubles, public infrastructure doubles, jobs and output double, etc. But we'll add one caveat now, that the immigrants are fully mixed.

In this scenario, I'm a Brit. My friendly English baker down the street has relocated further away, and now I have a nearby French baker. Even though I can buy a baguette next door, I still want a scone – and I have to walk or drive further now to purchase it. The long-run result might mean that both bakers lose their distinctiveness, making equally-poor scones and baguettes to serve the local area.

I think this story generalizes wherever immigrants differ in some quality from natives: the fear is that whatever makes natives distinct will be diluted or lost. It's a cultural story that can be (but rarely is) told in economic terms. Or equivalently, why is it bad when someone moves from China to Vancouver, but not when they move from Sudbury to Toronto?

[Frances Woolley]

Majromax - "why is it bad when someone moves from China to Vancouver" - did you mean this to come out sounding the way it does? Even among those (of every ethnic origin) who complain about foreign buyers and empty condos and "starter castles" on prime Fraser Valley farmland, I think there are few who would be willing to state unequivocally that it's bad when someone moves from China to Vancouver.

Perhaps what you meant to say was something like, "if we're willing to say that it's bad when someone moves from China to Vancouver, why would we not also say it's bad when someone moves from Sudbury to Toronto."

Actually Canada's employment insurance program, which is much more generous to people living in high unemployment areas, and also the federal government's equalization program, which transfers funds from all taxpayers to residents of lower-income provinces, seem to be designed on the assumption that it *is* bad when someone moves from Sudbury to Toronto (or from Shediac to Calgary, in the case of equalization).

[Philo]

I believe your framework can be applied not just to migration into a country (international migration) but to migration into a state (province, region, Land, województwo, etc.), city, county, neighborhood, etc.

[Nick Rowe]

Majro: your scone/baguette example shows we need to think about land and location/transport costs at the same time. If land doubled, maybe the French bakers and their customers would settle in one area, and the English bakers and their customers settle in another area. It's like England and France joining together into one country. And if neither likes consuming anything the other produces, there are no gains from Comparative Advantage.

Majro and Philo: yes. It's a bit like the Optimal Currency Area question. Why should people a couple of kilometers north of the border use the Canadian dollar, and people a couple of kilometers south use the US dollar? Should there be One World Currency (like one world country)? If not, where exactly we draw the line is always going to be a bit arbitrary. But if we have more than one country (or currency) in the world, we have to draw a line somewhere, and treat people on one side of the line all the same, but differently to people on the other side of the line.

Frances: I read Majro the way you wanted him to say it.

[Majromax]

@Frances Woolley: I intended to portray a caricature of anti-immigration sentiment, mostly to highlight how it relates more to the "kind" of person (often with racial undertones) than there mere act of migration. Clearly my language was sloppy that my intended hypothetical did not come through, and your paraphrase is more accurate.

Regarding the transfers, I don't think the philosophy behind them is that it's *bad* when someone relocates for work, moreso that it's *regrettable* that they do so. Certainly nobody seemed to look at the boom of workers migrating to the oil patch with an aim to prohibit it, even though we see occasional opposition to immigration to Canada even for skilled workers.

@Nick Rowe:

If France and England merely adjoin, then I'm not sure we can say that immigration can really have taken place. But with the comparative advantage framework, we may also be able to look at it as a domestic version of 'gains from international trade.' There we understand that international trade produces winners and losers and sometimes compensation is necessary.

But rather than look at it as an 'optimal currency area' question, I look at it as more an 'optimal boundary of the firm', where culture shock produces an implicit set of transaction costs -- above involving me walking farther to get a scone.

[Nick Rowe]

Majro: Yep, the boundaries of the firm is another analogy. (Like all analogies, it sorta works and sorta doesn't.) Another one is 18 (or whatever) being the voting age. We treat people one side of the line totally differently to people just slightly on the other side. Like a mapping from a continuous variable into a discrete (or binary) variable.

[Pete Bias]

Ralph Musgrave and Nick,

How is immigration any different from natural born increases in populations? Do they have similar impacts on infrastructure? Are you suggesting that we don't have children because they are costly? Is it how fast immigration can infrastructure needs, whereas natural births have a 20-year window?
Something doesn't make sense.

Pete Bias

[Nick Rowe]

Pete: short answer: because when people ask about the costs & benefits of immigration they are (usually) asking about the costs & benefits of immigration to themselves and their own kids. They care about their own kids, and want their kids to inherit citizenship of a country with good infrastructure and good everything else. And they (usually) view other citizens' kids in (roughly) the same way, following the "We (Canadians or whatever) are all in this together" idea that makes countries work. And it all breaks apart when they stop thinking like this, and view public assets as something that anyone can walk in a grab a share of. Why invest in the Club's assets, if anyone can demand membership of the Club and a share of the assets that the original members paid for?

OK, that was a slightly longer answer than I had planned!

[Pete Bias]

Hi Nick,
I'm still not buying yet. So, infrastructure increases are ok for "us" because we're "us." But aren't the infrastructure increases the same cost to society as they were before? We're just ok with it because it's "us"? So it boils down to whether we simply like it or not? Maybe. Works for goods and services. But, hmmmmm; still feels weak.
The usual economic argument assumes homogeneous blah, blah, blahs and you're not making that assumption (I think). So it's the "heterogeneity" of the people that makes it costly?
BTW, I feel the costs you're talking about; I just don't think this is the sound economic argument. Why not use the Friedman argument that immigration is fine until there is automatic welfare for those struggling. Then, unlimited immigration would produce potential unlimited costs. Maybe this is what Ralph means by infrastructure?

[Nick Rowe]

Pete: The idea is that we paid for it, so we (and our kids) get to use it. Having already paid for one hospital, that is just big enough for us (and our kids), we don't want to pay half the cost for a second hospital for them (and their kids) since they didn't pay half the cost of the first hospital. We would pay for 1.5 hospitals, they would only pay for 0.5 hospitals. And it's not just a fairness argument; the incentive to vote to invest in public assets would be a lot less too, if the original population has to pay 150% of the cost.

The way around it would be a one-time tax on immigrants to pay for existing stock of public assets (net of public debt). Or have all public assets debt-financed. But defining what is and is not a public asset is tricky. You *could* argue that "public assets" of a rich country = the NPV of the income differential between the rich country (that people want to immigrate to) minus the poor country (from where they want to emigrate). Like selling new shares (citizenship) in the country at a market price that people are willing to pay.

[rsj]

Nick,

You *could* argue that "public assets" of a rich country = the NPV of the income differential between the rich country (that people want to immigrate to) minus the poor country (from where they want to emigrate).

I think this works only if the immigrants bring a share of those assets with them. Otherwise, you would end up paying people in richer countries to come to you, which seems wrong, no? Especially if they came with nothing. The land, roads, education, and infrastructure remain in the old country. The fact that they came from a rich country doesn't really matter. What matters is that the denominator in assets/population just increased, so you would want

A'/(P+1) = A/P

or A' = A(P+1)/P = A(1 + 1/P)

so dA = A' - A = A/P

Thus they should bring with them the current assets per person of the target country, irrespective of the situation in the old country.

What I think you are referring to, is that the old country will also see A_old/P_old go up, also by A_old/P_old. So it could be the case that they would be willing to compensate those who leave by giving them A_old/P_old, as a type of cashout. And that hypothetical cashout could be used to defray the buy in for the new country. I think in this sense you mean to describe it as the difference, but there is no guarantee that the old country will give the cashout.

[Nick Rowe]

rsj: Hmm. You have a point there. That does seem wrong. Maybe paid to leave, by the rich country? Or paid to swap places? (It's early here, and my brain isn't working yet.)

Think it's like: If I want to buy shares in a company, I must either get someone to sell theirs, or pay for the company to invest more and issue more shares.

[Nick Rowe]

rsj: yes I think you are right in how you are thinking of it.

But my mind is stuck between two types of "technology": a sorta Leontieff technology, where it's strictly one hospital bed per sick person, and extra beds are waste; a sorta Smooth technology, where 100 metres of road per car is ideal, but there's only small net costs of having 99 or 101.

It's still early here.

[rsj]

where 100 metres of road per car is ideal, but there's only small net costs of having 99 or 101.

So Let's say in the absence of population change, the optimal asset intensity (A/P) is some target value. Then the cost function will be quadratic near the equilibrium (where the first derivative is zero). For small shifts of the equilibrium -- say because the parameters of the model change -- it's always much more efficient to pay someone to compensate them for the utility loss than it is to move to the new equilibrium. But that only works for one time changes. If we did that for many changes, we would find that the quadratic costs start to climb and exceed the cost of moving to the new equilibrium as you keep deviating away form it.

Therefore if we allowed people to pay the cost of the loss function, rather than the cost of shifting to the equilibrium, this would be an arbitrary shifting of costs. If a batch of immigrants happened to arrive when the asset intensity was at equilibrium, then these immigrants would, instead of keeping you at equilibrium, compensate you a very small amount. Then the next batch would need to pay for adding enough assets to cover the first batch and its own, because the quadratic compensation costs is now higher than the cost of tracking the equilibrium. It seems to me that the second batch is being treated unfairly, as it is subsidizing the first.

In any case, when looking at the long run trend, you don't care too much whether every other generation is subsidizing the other, you can assume that each generation is paying an average cost equal to keep asset intensity tracking the equilibrium.

[Nick Rowe]

rsj: I think that's a good way of looking at it. But I'm not sure if your last sentence is right, except when r=g and both are constant forever, which gets us into that whole Ponzi thing! (Compare two otherwise identical economies, both growing through immigration at rate g: the first debt-finances so pays rA/P in taxes per capita; the second pays up front so pays gA/P in taxes per capita.)

[Nick Rowe]

Think I'm gonna hafta write a post on this (comments by Ralph, Pete, and rsj, and my responses).

[Pete Bias]

Hi Nick,

Liking it more, but wonder if it's much different from a population explosion that society was unprepared for. We older folk still need to build roads and hospitals and not get much return. Isn't that similar to the immigration idea?
rsj is on to something, but it seems to me any increases in population put a burden on the infrastructure and increase the cost burden to the rest of society. That is, any new children (or at least new children increasing at a higher rate) put a burden on me that will increase my taxes. Following rsj's approach, some of us increase A in keeping with our children. But some of us don't and let others 'foot the bill.' The 'foot the billers' seem a lot like immigrants. No?

[Nick Rowe]

Pete: If they are our kids, and we care for them, and we chose to have lots of kids, presumably that's all OK.

But we can compare immigration to a case where half the population of a country has twice as many kids as the other half. The latter have to pay extra to build the schools for the former's kids. The latter might insist the former pay more (or debt-finance the schools so the kids pay), or restrict their number of kids, or might just say "We're all in this together".

[Majromax]

@rsj:
> I think this works only if the immigrants bring a share of those assets with them.

Immigrants do bring their human capital. This can be anything from a moderate benefit to a huge benefit depending on whether the production function has network effects. Politically speaking, this is also why there's different/more muted opposition to immigration of educated and skilled workers compared to 'unwashed masses'.

@Pete Bias:
> That is, any new children (or at least new children increasing at a higher rate) put a burden on me that will increase my taxes

The situation is more complicated with public pensions.

There's also an impact on private fixed capital and land. If a country has negative population growth, then the NPV of land is lower -- the future would have more land per capita so the value of the marginal acre would fall. If immigrants (or children) are supposed to purchase their per-capita share of capital from existing owners, then some form of population growth keeps prices from collapsing. The private benefit to landowners may outweigh a modest public cost.

[rsj]

@Majormax,

Yes, immigrants bring human capital and they also can bring money. It's no wonder that many nations have things like investor visas as well as point systems. All of this makes sense.

But I worry about a false sense of precision, because the greatest thing that immigrants bring is their progeny, and its hard to tell what that progeny will do. In the U.S., we admitted many poor immigrants with low human capital and their children went on to do amazing things. On the other hand, I would argue that the 2005 era wave of muslim immigration in Europe now has been really harmful. Will it remain harmful in 100 years? It's a tough call, and a big risk to take, especially when you absorb a lot of illiberal immigrants. Maybe the biggest asset is actually values that can be passed on to children.

Basically, this problem is so hard, there is a dearth of data, and you can take this discussion in pretty much any direction.

[Devin Lavelle]

The discussion of infrastructure focused capital is interesting, but I'd argue the current state of affairs highlights realities that could draw us to the opposite conclusion.

In most of the developed world, we have inadequate, aging infrastructure that is already inadequate to fully meet our needs. This is the nature of the beast with major fixed capital of these sorts, because they cannot be built, replaced or even really maintained incrementally. In the US the bulk of our infastructure was largely paid for during a time of dramatic growth in the economy and the workforce driven by post WWII circumstances (diminished foreign competition, soldiers returning to the workforce, desegregation, new technologies). As that boom has faded into an increasingly distant memory, we have failed to replace the revenue with a stagnant and aging domestic population. While we can hope for technology and favorable trade situations to drive future largess, the only reliable source of a growing economy, and associated surplus revenues for investment, is a growing workforce -- and the only source of that (that does not require 20+ years of investment and infrastructure to prepare for the market) is immigration.

[Nick Rowe]

Devin: OK, but lots of people still want to emigrate to the US, despite its ageing infrastructure. So it must have some assets (whether tangible or intangible) that have been created over the years. A thought-experiment: suppose immigrants were charged a fee for entry, and that fee were earmarked for infrastructure. Many would be willing to pay. What Open Borders people are implicitly saying is that that fee must be set at $0. Which seems strange. It's very rare that the optimal market price of any valuable asset should be $0.

[Devin Lavelle]

That's a true statement, but not really a response to what I'm saying.

It's true that many would be willing to pay, the US government could certainly turn to new immigrants as more of a profit center. I'm not sure it would be fair (neither you nor I were asked to reimburse the government for infrastructure built before we became taxpayers), I'm also not sure that it would be profitable in the long run, since it would disincentivize many from coming, thus slowing economic growth and associated future tax revenues.

[SqueekyWheel]

Nick - off topic - when I moved to my neighbourhood, there was one hair salon. In the last year 4 more have opened. I feel like my neighbourhood is turning into one of your thought experiments.

[rsj]

Devin,

I think you are confusing per-capita assets and GDP versus total assets and GDP. Yes, increasing the population will increase total GDP, but that doesn't benefit anyone. You want to increase per-capita GDP. It's not obvious why you think that per-capital GDP will go up. In Europe, for example, the vast number of immigrants are simply unable to find employment and must live off of social benefits. Per capita GDP went down, not up. But suppose they are able to find employment, why would per-capita GDP go up?

You seem to also think that we need more immigrants to build infrastructure, as if a shortage of labor is why we don't have better infrastructure. But again, more population creates the need for more infrastructure, so why do you think that infrastructure per capita would go up? There just no evidence of this happening. As you point out, the U.S. had an infrastructure boom in the post war period when immigration was at a historic role.

You seem to really think that we can't afford things until an influx of immigration gives us the resources to afford it. It's just a really weird thing to believe.

The one case where a large economy increase per-capita GDP is with increasing scale industries or other agglomeration effects. However if we are to look at this carefully, we'll see that in those industries with flat or declining marginal costs, the binding constraint is not shortage of labor but market size. Indeed, a small proportion of the economy is employed in these types of industries, simply because each worker can produce so much. Most of the labor force is along for the ride with Baumol cost effects while a small -- even shrinking -- proportion is engaged in industries subject to these agglomeration effects. In that case, it's certainly true that increasing the market size will increase income, which is the big case for trade. It seems to me that importing consumers is a fairly expensive proposition, relative to the costs of trade. Especially today, when trade tarriffs are so low. I don't think the infrastructure costs of adding an additional consumer are lower than the trade frictions. Is that really the argument you are making? It seems implausible.

The reason why we haven't kept our infrastructure per capita up is that, politically, we didn't want to. Maybe that was a bad decision, but that's democracy. Those politics reflect a decline in solidarity and faith in collective public works. It's not that we need more immigrants in order to "afford" to build more infrastructure per capita -- rather would increasing immigration increase solidarity or not? And perhaps the decline in solidarity also plays a role in the decline in support for immigration.

[rsj]

^^some spelling errors there. per-capital should be "per-capita" and "historic role" should be "historic low". sorry.

[Eric Crampton]

Thanks for this.

On the public capital per capita point, is this necessarily the case? I'm imagining a model where infrastructure is fully debt-financed, where the repayment period of the debt matches the life-span of the capital, and where the asset needs replacing when the debt expires. I can see cases where surprise population increases from net migration flows cause problems - you need to find a way of then funding an expansion to the infrastructure before it's fully depreciated. But even in that case, the cost would be either the losses from bringing forward an infrastructure refresh before the asset were fully depreciated, or the cost of a bolt-on to let the depreciating asset carry a higher capacity for its remaining lifespan net of the tax contributions towards that debt servicing borne by the surprise population.

At least here in NZ, it looks like some cities have nearly fully depreciated infrastructure, are close to having to replace that infrastructure regardless of population size, are having to bring forward replacement by a few years to deal with population growth, and are trying to blame the total cost of the infrastructure refresh on population growth. But population growth should only really take the blame for the (relatively minor) marginal increase in cost from having larger water pipes than otherwise be needed (digging up the streets is a fixed cost) - and the cost of bringing forward investment that had been planned for later.

[rsj]

Eric,

The time schedule is a distraction. The issue is who pays for the extra capital.

For example, the following are all equivalent:

1. Immigrants pay lump sum upon entry
2. immigrants take out a loan to pay lump sum and pay for the capital and then make the payments on the loan.
3. Government takes out a loan and keeps track of the immigrants, sending them regular pays to make payments.

The following are also all equivalent:

1. Government pays for extra infrastructure in a lump sum, funded by taxes paid by everyone
2. Government takes out a loan and payments are paid by everyone.

The only question is whether, in the first case, the immigrants pay to raise A/P back to what it was, or if in the second case, everyone pays to raise A/P back to what it was.

[Nick Rowe]

rsj on Devin: yes, unless the public infrastructure is non-rival goods, where the tax revenue increases with population, but the costs don't. Which might be what Devin was implicitly assuming. Like improving a bridge that is not at capacity, vs needing to build a second bridge because the first is at capacity.

[Nick Rowe]

Eric: yes, I think 100% debt-financing can, in principle, solve the problem. Because it means that net public assets (assets minus public debt) are zero.

But a 100% debt/equity ratio sounds a bit worrying if the investment is risky?

And if you think about public assets very broadly, to include everything that makes one country more attractive to migrants than another, having a national debt equal to the value of those assets......is gonna lead us somewhere weird!

[EricCrampton]

Thanks Nick. Let's split public assets into two broad categories.

In the first one, there's the ephemeral stuff that's nonrivalrous - rule of law and the like. That's part of what makes a country lovely. Since the value of that isn't diminished by population, it seems odd to worry about per capita values. You could rather say that where there's a per capita value for it and the capitas have increased, the total value of it has just increased. I'd put parks in here too. The total value of parkland owned by the government doesn't change (except to the extent that a proper valuation would be derived from use or opportunity cost, which should increase anyway with population), and it would similarly seem odd to charge people for the per capita change in value in that stuff. It's not like it costs any more to maintain or run it. And if it did, it's better solved with user fees, right?

In the second camp, there's the stuff that costs more to maintain or that needs upgrading with population growth. The three waters for councils; roads; schools; hospitals. All the horizontal infrastructure stuff plus those potentially congested public buildings. I don't have any particular reason to think that the net value of those public assets should be positive. You can easily imagine PPP arrangements where they're privately provided and funded out of an annual charge to government, or you run 100% debt financing on them and time the debt to the life cycle of the building so the debt goes away at the same pace as the capital depreciates and then you just build a new one when the debt's finished, again debt-financed on similar terms. There'll be some capital value to the land under the buildings, but that seems neither here nor there except where you have to buy more land for expansions - but so long as you time the expansion for the next debt round, it's all good.

RSJ: The timing question I think enters in more as a matter of political perception on the debt versus lump-sum question, but as a real issue on asset lifespan. If the infrastructure's paid off over time on the bonds, then it's obvious that the new people are paying taxes towards those annual payments. If the infrastructure was paid as a lump sum 20 years ago and new people show up, people get mad about how the new people are using infrastructure that the existing people's parents paid for and whatnot.

In either case, the only real issue is whether the arrival of new people increases maintenance costs in ways that are difficult to apportion to new people, or requires bringing forward of infrastructure refresh that was only going to happen down the track - and how to apportion the costs of that bringing forward.

[Nick Rowe]

Eric: yep, the rival vs non-rival distinction is important. Even for the non-rival capital though, there's a problem in that countries will underinvest, relative to the efficient quantity, in a public choice setting where twice as many people benefit from the good than the original population that votes and pays for it.

Strange thing I can't get my head around yet: it does not seem obvious to me that large countries are better at providing these club goods (or provide more club goods) than small countries.

[rsj]

Eric,

Yes, I see your point. I'm thinking about why it strikes me as wrong, though, and I think I have to revisit this issue and change some of my definitions. In other words, I need to change my thinking to keep you wrong :)

To keep things simple, say we are talking about toll roads. All roads are toll roads operated by the government. The price of a toll is exactly set so that the profit == 0, and the government doesn't need to levy any additional taxes or float any more bonds other than the payment of the toll. Your interest payments are equivalent to this, because it's not enough to pay for an asset as it depreciates, but you'd also need to make sure that if Group A uses the asset more over its lifetime, that Group A pays exactly in proportion of its usage. And since you want to avoid things like special fees or payments by new entrants versus incumbents, the payment might as well occur right when the road is used.

In that environment, who cares how many new people there are, because everyone pays for their own individual use. But I would say that in that environment, there really isn't a lot of solidarity or commonly held assets. It's kinda of a libertarian nation. So clearly there are problems in my definition of A, because I want to say that in this case A = 0, so A/P doesn't matter.

In most nations, we don't have an individual pay per use situation for every conceivable public asset like that, but rather we think in terms of solidarity. E.g. "canadians" pay for the road so that "canadians" can use the road. We are not so selfless as to value other canadians as strongly as we do our own family but we do value them. And here, we include future generations, because we have a stake in the future of the country as a whole and want the future to do better than we are doing, maybe not with the same concern as we have for our own children, but there is such a concern. Now there are big welfare and efficiency gains from doing this because you can't write contracts and monitor every conceivable usage to ensure that those who use something exactly pay for it. There are huge Coasian problems. In that environment, you wouldn't be able to build a lot of roads, and you'd spend a lot of money putting fences around every road, and the country would be filled with suspicion and resentment. People hate privatizing infrastructure because immediately the fees are hiked and everyone starts trying to rip each other off. They want a non-transactional sphere of life, in which solidarity replaces monitoring and accounting, micro payments. But at the same time that's exactly where you run into problems about letting anyone else become "canadian" whenever they want -- basically the gates are pushed out from being around every individual road to being on the border, so it makes sense to push the tolls out there, too.

Look for example, at Switzerland, which has some of the most restrictive immigration policies on the planet. In switzerland, the local community votes on granting you citizenship and you have to be there for decades. There are literally people who have lived in Switzerland for three generations and aren't citizens yet -- citizenship is purely on the basis of blood, not soil. Only recently they passed a law so that marrying a non-swiss doesn't cause you to lose your citizenship. Here's a woman who's been living in Switzerland for more than 30 years and her citizenship application was denied because she's a vegan and the local community thought her vegan activism was annoying, so they voted against giving her citizenship.

http://www.cnn.com/2017/01/12/health/switzerland-citizenship-vegan-trnd/index.html

It's no accident that Switzerland has the best infrastructure in the world, and almost no corruption. People feel a sense of strong obligation to each other. There is enormous solidarity and national pride and it has a reputation of being a very well run country. I'm not saying that we all need to become Switzerland, but you can't get those types of roads built on the basis of pay as you go.

[Nick Rowe]

rsj: without necessarily disagreeing with what you are saying, another reason is simply that user tolls are costly to collect.

[Nick Rowe]

rsj: on second reading, I notice you already said that. Never mind.

[Scott Sumner]

I can't find it now, but I did a post where I argued that future Americans would be better off if there was lots of immigration, relative to the alternative of little immigration. I also argued that future Americans would be better off if there was relatively little immigration, relative to the alternative of high immigration. This sounds like a logical contradiction, but it is not. The trick is that "future Americans" are two very different groups in those two cases. Which is the point you also make at the end of your post.

[EricCrampton]

RSJ: Where bond/tax financing achieves a similar objective to tolling (albeit not quite as nicely), but tolling proves too difficult, can revert to bond/tax. I can see problems in that world if population growth means you have to bring forward needed infrastructure refreshes and that comes at real cost (because the infrastructure was planned for a smaller population than obtained), but I'm not seeing a capital per capita problem.

Am familiar with the Swiss example - I liked that one.

Nick: I take your public choice point. But that depends on when the spending must obtain for the nonrival stuff. Like, does a country expecting larger population growth have to invest substantially more *prior to that growth* in setting strong institutions? Or can it simply bolster its investment as population grows? I think all of this is suggesting that the capital per capita point is likely minor. But it's one that's been bugging me a lot, because it gets a lot of traction in NZ. Here, the argument goes that expanding the capital stock to accommodate migrants crowds out other productive investment. And while I could see that if NZ were a closed economy, we're a tiny drop in a global sea of capital. I just don't buy the posited mechanism here that it can substantially bid up interest rates.

[Nick Rowe]

Scott: yes, that's a good way of putting it. I hope you are happily settled in in California!

Eric: I *think*, but I'm not 100% sure my head is straight, that you get the same public choice problem in a continuous time setting. It's sorta like the current population is discounting projects by their declining share of the future population.

I think you are right about no crowding out in the standard Small Open Economy model. (Though I'm always puzzled, like New Zealanders are puzzled, by NZ seeming to have so high real rates, and it makes me wonder if NZ faces an upward-sloping supply curve of loans from the ROW, unlike in the standard model.)

[Oliver]

Rsj, there are a bunch of factual inaccuracies in what you say about Switzerland. Only in couple of smaller communities is there a plebiscite like vote on granting (communal) citizenship. The procedure and the terms differ a lot from community to community. So a lot of foreigners traditionally choose to live in places with less restrictive laws. And, quite frankly, the community vote is an anachronism and a legal abomination. It is true that children born in Switzerland to parents with foreign passports do not automatically become Swiss until the fourth generation (which is a sad joke if you think about it - I mean, those children have no link whatsoever with the country their great grandparents came from. Trump would still be German... All it does is create double standards). But it is also true, for example, that many foreigners who are eligible for naturalisation choose not to become Swiss because they are too proud to undergo the humilitating procedure or just can't be bothered. Myself, for example. It's complete bollocks that Swiss must give up their passport if they marry foreigners. Germany has a law forbidding dual citizenship with certain countries, most notably Turkey (there is a very large Turkish population).
Also, with about 20%+ permanent foreign population, not counting naturalised citizens, I am at a loss about how you can call that 'restrictive immigration'. Apart from Luxembourg and maybe Monaco, no other European country has more immigrants per capita than Switzerland. Not that everybody is happy about that. There was a referendum on restricting immigration from the EU - a bit like Brexit - last year. And the 'leavers' won by a thin margin. Depending on how parliament interprets the result, implementing it could mean terminating existing contracts with the EU. Same muddle that Britain is in, but we have more experience in watering down referenda and finding compromises.

And what this all has to do with infrastructure and corruption, I really do not know. Also your muslim slur further up is completely off the mark, if you ask me.

[Tel]

All very interesting, but I'm worried that you might not be allowed to say these things in Canada any more.

If the politically correct police come knocking at your door after midnight then I can recommend you keep away from Australia where things are even worse.

Remember: truth is a social construct. Tootles!