In the Long Run, We’re All Earthlings
In a recent post on the economics of immigration, Nick Rowe engages in the most astonishing example of “use the Cobb-Douglas model to assume away the very problem under discussion and don’t even realize you did it” that I’ve ever seen. Here’s Nick:
When economists disagree with public opinion, I normally agree with the economists. But we ought to think twice when this happens. Maybe, just maybe, public opinion is based not on ignorance but on something that our models leave out. When it comes to immigration policy, I think it is correct to say that elite opinion (which includes economists) in rich countries that are attractive to immigrants is generally more favourable to immigration than is public opinion. The elite finds public opinion a bit embarrassing, and tries to ignore it. They remind me of parents trying to get their kids to eat broccoli: “It’s good for you, and you will like it once you get used to it”.
The basic economics of immigration are quite simple. If we assume constant returns to scale, with output a function of labour and capital, and realise that increased labour creates increased capital (either immediately through capital inflows or slowly through immigrants’ saving), everything expands in proportion. Both supply and demand for labour expand, leaving real wages, per capita income, and the unemployment rate, all unchanged. [Bold added.]
Do you see that?! Marvel at its beauty. If people show up in a capital-rich country with nothing but their bare hands and work ethic, we can treat it the same as if they showed up with 8 tractors.
Later on, Nick starts relaxing assumptions, but he never says, “Oh yeah, it might take a generation or two for people from Africa to reach the level of per capita wealth that the US currently has, so that could depress wages and enrich capitalists only for 60 years tops. Maybe some people who work for wages don’t want to see a drop in their standard of living for 60 years–but they watch ‘Matlock’ too, the rubes.”
Also, I don’t think Nick even uses this approach consistently. Later in his post he writes: “So immigration probably doesn’t matter much for natives; but for immigrants it can sometimes matter a lot.”
But why would it? Wherever the home country of the immigrant is, they have the same Y=F(K,L) CRS production function. And Nick has told us that in the long run, K/L is mean-reverting. So real wages, per capita income, and the unemployment rate should be basically the same all over Earth, give or take. Why would any worker want to move to the US or Canada?
Bob: I posted this comment on WCI:
Ah Bob! I’m so glad that someone finally picked up that assumption of the “standard model” and questioned it.
Assume “perfect capital mobility”. What the heck do we mean by that? We can’t just mean that foreign and domestic IOUs are perfect substitutes. There must be some real goods flowing into the country in exchange for those IOUs that flow out. Now what are those goods? Machines? Or consumption goods that the workers consume while they build more machines? And are foreign and domestic machines or consumption goods perfect substitutes? And can they be imported at zero transportation costs? Well, maybe not.
Plus, if the “standard model” were true, and were equally true everywhere, and there were “perfect capital mobility”, why would some countries be richer or poorer than others, and why would anyone ever want to emigrate anyway, unless it’s for the weather or scenery?
Eh, I dunno Nick, you started listing all sorts of things we could relax in your post, but you never brought up your quick line about labour and capital moving in tandem. To me, it sure looked like you were saying: “People trained in economics know that your standard of living in material terms won’t be affected by open borders, so why are people scared of open borders? Maybe because we rightly don’t like their culture, or maybe because they will invade us.”
That didn’t sound like you were really thinking, “I wonder who will notice my long-run capital accumulation Easter egg! Heh heh I’m so naughty, hiding it in plain sight.”
Rowe’s post seems to boil down to something important that you have omitted from your synopsis. Here it is:
“Maybe the standard model leaves something out? Starting with Arthur wanting to continue to live in Britain, and not England. People’s preferences can be a bit conservative like that. Foreign holidays are OK for a bit of novelty, but it’s nice to come home afterwards. Most people don’t want to be forced to live in a “foreign” country.
“What else might it leave out?“
Rowe’s point seems to be that the standard model leaves important stuff out. Your point seems to be that Rowe’s invocation of the standard model leaves important stuff out. As far as I can tell, you two are in perfect alignment here.
Maybe I misread Rowe’s post?
RPLong if you read my first five sentences in this post (not counting Nick’s quote) your question would be devastating. But in the 6th sentence I explain…
Haha, oops. I’m going to mea culpa this one. When you say, “but he never says…” I misread that and took you to mean the opposite of what you mean.
Okay, now having re-read this a couple of times, I think I’m on board. Sorry Nick. I think Bob’s got this one.
OK thanks RPLong. If you go to Nick’s post you’ll see notsneaky is lecturing me on growth theory now. Keeps me humble.
Your error is in the sentence “they have the same Y=F(K,L) CRS production function”
That is NOT what is being assumed. What is being assumed is that “they all have a CRS production function”. The word “same” or even the equation “Y=F(K,L)” aren’t being assumed.
Great, so I’ve got Nick congratulating me on pointing out his hidden assumption that has all sorts of implications, and I’ve got notsneaky criticizing me for thinking it was a hidden assumption.
“… “they all have a CRS production function” …”
LOL
😉
And actually it is only being assumed that the host country has a CRS production function, who knows what happens in the source country.
Nick was right the first time but then he backtracked.
Maybe he’s thinking about land again (Nick?), in which case you wouldn’t have constant returns to scale and capital would not fully accumulate to offset the increase in labor. But even there (going by a quick and dirty calculation) it would still accumulate to offset something like 91% of the increase (I’m assuming that physical + human capital’s share is 2/3 and land’s share is 6%)
“Immigration probably doesn’t matter much for natives”.
I think I have found something that needs to be double checked.
In economic terms it probably doesn’t. Perception-wise, it’s a different story.
If immigration boosts the specialization of labor that is otherwise not feasible cross-borders due to political barriers, then that in itself boosts productivity, i.e. real wages.
This is why “mere” labor movements from Europe over to the US during the 17th to 19th centuries increased labor productivity worldwide as such. Economic freedom is necessary for a stable evolution in the division of labor.
The real core problem is not open borders. It is the system of Democracy. It accepts Sharia law if the majority are Muslims who vote for it.
I am happy that by the time Democracy naturally evolves into Dictatorship the world over, just like it did in ancient Greece, I’ll likely be old or dead and not have to live through it. Democracy is a cancer, slowly rotting and eating away at civilization, totally apart from “productivity”.
So maybe I don’t get how this trick is done. We have a hypothetical island where amongst the island population are 100 plumbers and the going rate for a plumber in those parts (give or take depending on reputation) is $50 per hour.
A boat pulls up to that island and and extra 200 trained plumbers step off the boat, but none of the original island inhabitants want to leave. Seems like the going rate for a plumber is going to go down, given that supply has tripled. That’s short term at any rate.
How long would this imbalance last? Well I don’t see how savings and capital investment will fix it… unless you consider time spent retraining as “savings” which it sort of is, but not the way most people think.
Of course for the people in the market to BUY some plumbing service, it’s excellent… they will probably buy more as the price has fallen.
“Seems like the going rate for a plumber is going to go down, given that supply has tripled. That’s short term at any rate.
“How long would this imbalance last?”
It depends on how long the old plumbers wanted to go on losing money.
And, apparently, the new plumbers are able to profit off of the lower price, so 200 are doing better than they were without those jobs.
And now that people have more money left over, they will increase demand for other businesses – whose employees can now be underbid by the unemployed plumbers.
And so on, until people find their new niche.
You got 100 plumbers and 100 plumbing machines. Every period the population saves a fraction of its income and invests in new plumbing machines. Plumbing machines depreciate over time. So initially the island’s population is saving just enough to keep the number of plumbing machines at 100 and the plumber/plumbing machine ratio at 1.
Boat drops off 200 plumbers. Initially plumber/machine ratio goes up and as a result wages of plumbers go down. But total output of the economy goes up (since there’s more labor). So with the fraction of income that is saved, the total investment in new plumbing machines goes up and now exceeds the depreciation. So over time the number of plumbing machines goes up, until you get to 200, when once again any new investment just offsets depreciation. And you’re back to the 1 machine per plumber situation which means that plumbers’ wages have come back to where they were.
It’s a world with more than one factor. Capital and labor, not just labor. And returns to factors depend on the ratio of a non-labor factor (capital) to labor (this is the constant returns to scale assumption).
(btw, it doesn’t actually doesn’t matter if the new arrivals don’t save. Per capita income on the island will be lower but per capita income of the original natives will come back to where it was)
“Of course for the people in the market to BUY some plumbing service, it’s excellent… they will probably buy more as the price has fallen.”
Yes, and since they’re willing to buy more wouldn’t that pull the price back up? This sort of illustrates that you need to analyze this in terms of general equilibrium not partial equilibrium.
notsneaky,
A lot of times common sense can help in being a guide to the right answer.
If in your deductions you come to the conclusion that a world with one person alive will have the same real income per person as a world with 7 billion people, then you should really have the courage to critique your own beliefs and not worry so much about opposing arguments.
What you are totally overlooking in your deduction is the crucial fact that additional capital is in itself a means by which even more additional capital can be produced. This is in addition to the 200 additional plumbers.
With more plumbing capital in existence, that in itself allows for newer, previously impossible capital to come into existence.
Think of a group of 100 workers building a skyscraper, which is capital. They can build more skyscrspers with the use of cranes and jackhammers than with bamboo and shovels.
As an analogy, saving to productivity is akin to force to acceleration, not force to motion (in the world of physics).
Capital begets more capital. Even if everyone never increases their ratio of savings, provided they save a sufficiently high ratio out of their incomes, the economy can keep growing in real terms and real incomes will keep increasing.
Again, saving is as force to acceleration.
If there are an additional 200 plumbers who save more than they consume, thus bringing about 200 additional plumbing machines, the story does not stop there. With 200 additional machines in existence, that additional capital is in itself a means to physically help in the production of yet even more capital, which raises everyone’s real incomes.
The only plumbing machines I can think of are spanners and wrenches, those don’t depreciate very quickly. Maybe someone could invent a robot plumber but that might happen any time and in any trade, so I don’t accept there’s a predictable curve for that type of technical advance.
How did you measure total output of the economy? Not by using GDP obviously, because although more hours are spent doing plumbing, the hourly rate is lower. Total money spent on plumbers has gone down, and perhaps people are spending the residual on something else, but quite likely at least some professionals might increase their fees (like Chiropractors for example are now highly in demand with so many plumbers doing their back in as they try to turn a buck in the cut throat plumbing market).
Why would anyone invest in building more plumbing equipment? I mean plumbers are poor now, they are barely making minimum wage (some work cash in hand for less than minimum wage, shhhh don’t tell). Not like plumbers will be able to buy all the best equipment or anything. If I were investing I’d invest in Chiropractic couches, because that’s where the money is.
Besides, not as if it’s difficult to get a plumber these days, I mean you can find them sleeping in every park around town. Why try to produce capital equipment to *INCREASE* the supply of plumbing when there’s a massive glut? Who does that?
I’m pretty sure supply and demand doesn’t work that way. All the plumbing jobs that really needed doing (i.e. high importance stuff) have already been done by now. People are buying more because it’s cheap, because there’s a supply glut… and you seem to think investors are going to dump their life savings creating more of this product where the price has already collapsed.
major.Freedom,
Well, yes, I guess if we had a world with just one person in it then constant returns to scale probably wouldn’t be a good assumption. But we don’t live in a world with just one person in it. We live in a world a few more folks than that. And in that world it turns out constant returns to scale is a pretty good assumption (if anything, it’d be increasing returns to scale, which would mean that capital expands MORE than proportionately with population)
So… I’m having trouble seeing how talking about a world we DON’T live in to criticize the world we DO live in is “common sense”
And no, I am not overlooking the fact that new capital is produced with old capital. I just didn’t state it explicitly because I thought it was understood.
I’m also not sure how the idea that one can grow an economy indefinitely by accumulating more capital (one can’t, but that’s a separate issue) supports the notion that an increase in population lowers wages in the long run. That doesn’t make sense, common or otherwise.
Tel,
The rate at which depreciation takes place is not really important here. Slow or fast, either way it works and it doesn’t change the point of the story. This is a red herring.
How do we measure output of the economy? Well, that’s a question you should answer since you’re the one who started it off with the plumbers. If this is a world of only plumbers then we measure it in terms of quantity of plumbing services. If it’s plumbers and something else then we construct some index – but that’s also exactly when we need to do general equilibrium, not plumber (partial) equilibrium. We could measure it in money but then we’d have to worry about changes in prices vs quantities and so on. But again, this isn’t really relevant to the point being made. You can make it more complicated and the end result is the same.
Why would anyone invest? Well, maybe everyone invest less now but we have more people so total investment is higher. Also since now plumbing machines are scarce the return to a new plumbing machine is high so that induces investment. And again, you’re talking about general equilibrium effects (which account for interaction between plumbers and chiropractors) but want to have partial equilibrium results (using only plumbers wages as a measure of what happens to income).
“I’m pretty sure supply and demand doesn’t work that way.” – well, no, at the aggregate level it works exactly like that.
“I’m also not sure how the idea that one can grow an economy indefinitely by accumulating more capital (one can’t, but that’s a separate issue) supports the notion that an increase in population lowers wages in the long run. That doesn’t make sense, common or otherwise.”
Try not to focus on only the lower wages aspect of population increases. At some point a wage becomes lower than what someone can earn with their own bare hands – which is the lower bound of all wage-labor, so it will never be zero, and yet it will always be more than one can earn on their own (from the individual laborer’s perspective), otherwise there’d be no reason to be employed by someone else.
The only other reason, then, that someone would have for opposing the lower wages that come with increased population is that it makes current producers poorer in their current occupation.
But it’s a mistake to view economic growth as “producers making money”, since you always need consumers for production to make sense.
Economic growth, therefore, is about the consumer, not the producer. Producers should not expect to make a profit producing what consumers don’t want at an opportunity cost that is greater than what it would cost them, elsewhere.
If consumers want cheaper goods, and some new guy is able to supply that, then it’s the consumers that are putting the old guy out of work, not the new guy.
Sorry, still doesn’t make any sense to me.
Hmm … think, think.
Maybe it helps to say that it has to be the “right” capital – that is, capital that can be used to satisfy consumer demand.
Any other kind of capital is a malinvestment from the Austrian point of view.
So, it’s definitely not just adding productive capacity. It’s adding the capacity to produce more of what consumers want.
Of course, the producer will consume, too, so he should only invest in productive capacity that also lowers his costs.
There’s a limit to the amount of productive capacity that is economically beneficial, and that limit is set by consumer demand (even from consumers who are also producers).
Not sure I get: “But we don’t live in a world with just one person in it. We live in a world a few more folks than that. And in that world it turns out constant returns to scale is a pretty good assumption”
Wikipedia says ‘The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant (“ceteris paribus”), will at some point yield lower incremental per-unit returns.’.
Do you disagree with the definition, which seems watertight ?
It’s a bit sloppy and imprecise. Not sure what that “in all productive processes” is doing there. Or the “at some point”. But regardless constant returns to scale and diminishing returns are two different things.
OK, so when you talk of “constant returns to scale” you are looking at what happens when you increase all factors by the same proportion, while the diminishing returns that Wikipedia talks about is for “more of one factor of production, while holding all others constant”?
Yes. So if you have more than one productive, then constant returns to scale IMPLY diminishing returns.
“more than one productive factor”
““in all productive processes” = the law applies to all productive processes
““at some point”’ = Initially you may get increased returns to scale but eventually (“at some point”) diminishing returns will kick in.
notsneaky:
In my example above I was certainly not thinking of an economy where everyone is a plumber… firstly it’s ridiculous, secondly the whole idea of having an economy is division of labor so if everyone was a plumber it would be pointless hiring someone to do the work you can easily do yourself.
Most of your confusion seems to stem from that single, rather peculiar, assumption. No I never made a statement about total economic output, nor did I at any point attempt to pretend that hourly rate for a plumber represents wages in general.
I don’t think I’m the one who’s confused. Or I guess I am but I don’t think it’s because of anything I said.
We were discussing the impact of immigration on wages, no? You want more than one good? Ok then you have to tell me about demand. About substitution between the goods. About factor intensity in each sector. If you don’t provide these details then neither I nor you can draw any general conclusions.
But roughly, the same story as above still holds. Capital adjusts to keep the capital labor ratio constant and wages return to where they’re at.