In praise of General Equilibrium Models

Q1. What happens if they built robots that could do my job as well as I could, and those robots got cheaper and cheaper over time? My wages would have to fall so I could compete with the robots, and I would be worse off.

Q2. What happens if they built robots that could do everyone's job as well as they could, and those robots got cheaper and cheaper over time? Everyone's wages would have to fall so they could compete with the robots, and everyone would be worse off.

Q1 is a partial equilibrium question and answer.

Q2 is a general equilibrium question and answer.

If you say "Therefore" between my Q1 and Q2, you are committing a Fallacy of Composition. The Fallacy of Composition is when you assume that what is true for each of the parts must be true of the whole. (The classic example is "If any individual stands up at the theatre that individual can see the stage better; therefore if every individual stands up every individual can see the stage better.")

The very fact that we bother to put names on some logical fallacies seems to suggest that people have a tendency to commit those fallacies. I don't think there's a name for the following logical fallacy: "1+1=2; therefore Mazdas are better than Hondas". We don't have a name for that particular logical fallacy because even the most crazed Mazda fanboy is unlikely to argue like that. Named fallacies are named fallacies because they are not just fallacies; they are seductive fallacies that we really want to commit.

It is very easy to understand that if I stand up I can see the stage better. It is less easy, but still easy to understand, that if I stand up I will make some other people see the stage worse. It is much harder to figure out whether the losses to some other people's vision are bigger or smaller than the gains to my vision. It depends. On a lot of things. And adding up those gains and losses when each individual stands up in turn is extremely hard. Instead we have to jump to the general equilibrium experiment, where everyone stands up at once. And even then we need to make some assumptions about the distributions of people's heights, and the locations of seats in the theatre, to figure out who can see better or worse when everyone stands up.

Trying to add up all the partial equilibrium effects in the case of robots is almost impossibly hard. Let's see. If a robot could replace me, and my wages fell, what would that do to the cost of a university education? And how would that affect prices and other people's wages? And how would the Bank of Canada react if it pushed down prices across the economy? And what about investment in robots, and the jobs created there? What would I do instead? And what would happen to profits of robot manufacturers? And the owners of robots?

There is no way that anyone, economist or not, could trace through all the effects of cheap robots competing to do my job. And there is absolutely no way whatsoever that anyone could do that for my job, and then repeat it for all the jobs in the economy, and then add up all the effects.

But that's what we so often try to do. And we fail miserably.

Instead we should build a general equilibrium model, like I did in my last post.

My model's answer might be right, or it might be wrong. But at least it doesn't commit the fallacy of composition. You can check the assumptions, check the conclusions, and you can check that things add up.

It was a very simple model (rather, three simple models, so I could explore the effects of different assumptions). But some of the results were surprising. Surprising even to me, the builder of those models. What is true of the whole is sometimes very different from what is true of the parts.

And to figure out what some of those results were I had to do some math. Yep, even a mathophobe like me, who likes to try to figure things out intuitively. And when I got some of the math wrong, commenter Kathleen could see it was wrong and told me it was wrong, so I fixed it.

That's why we do, and sometimes need to do, general equilibrium models.

PS. When I say "general equilibrium models" I mean as opposed to partial equilibrium. For example, MMT economists are equally general equilibrium in this sense when they insist that stuff must add up across sectors.

PPS. And I want to give kudos to those (mostly non-economist) commenters who made a serious effort to really figure out what was going on in my models.

Comments

[nemi]

An alternative title could have been “ A critique against current “micro founded models” “

[CBBB]

But the fact remains that what happens in the general equilibrium is not really relevant to the discussion of robots replacing workers as most people see it. Your statement that people are concerned that "everyone's wages will fall" is a red haring, it's pretty obvious owners of robots will benefit and people involved in designing robots will benefit.

The problem with a lot of these general equilibrium models is that economists usually assume people can easily move between sectors and jobs. So professors get replaced by robots, university tuition falls to rock bottom prices freeing up consumer money to go elsewhere and hence jobs shift to some other sector. Except in the real world retraining time is often extremely long and in fact the majority of workers might not even have the capacity to retrain if the growth sector is something very high-end like astrophysics.

When people talk about the harm to workers done by automation they are talking about the partial equilibrium because the workers lives are destroyed in the partial equilibrium and by the time some long-run general equilibrium is reached everyone is dead so why care?

[Becky Hargrove]

I often struggle to understand logic in fallacies of composition. Not only did you make this one clear, but also gave me a better feel for the General Equilibrium model. Thanks!

[Marc]

Nick,

I am a fan of our posts (which I read regularly). And I agree with your point about the fallacy of composition and that one should not simply sum up partial equilibrium effects to get to general equilibrium. However, I do have one question. In an earlier post on the welfare cost of business cycles (which built on a post by Steve Williamson) didn't you (and Steve Williamson) essentially fall into the same trap? Or perhaps there is a subtletly I'm missing...

[Nick Rowe]

Marc: Thanks!

And well-spotted! I remember thinking about that very same question when I drew that trapezoid picture for macro. Was I committing a fallacy of composition? And after a fair bit of thought I decided that my picture worked at the macro level too.

Think about the representative agent's utility in a New Keynesian macro model. Imagine the representative agent as a yeoman farmer, who owns and works on his farm (Larry Ball's old model). Assume a simple production function where Y=L. The MB curve shows diminishing marginal utility of consumption, and the MC curve shows increasing marginal disutility of labour. Because of monopolistic competition (each farmer produces a unique variety), MB > MC in equilibrium. It works.

[Nick Rowe]

nemi: I don't get that. Microfounded general equilibrium models are still general equilibrium models.

CBBB: What you are talking about is a long run general equilibrium model with sector-specific shocks and search frictions (or similar) with a constantly-rotating pool of unemployed. It's still general equilibrium. Just a more complicated model than mine.

Becky: thanks!

[Marc]

Thanks, Nick. I can see how it works in that context. Cheers!

[Sandwichman]

Well, yes, moving from a partial equilibrium result to a general equilibrium conclusion would indeed be a fallacy of composition. But affirming the consequent is ALSO a logical fallacy. That's what you do when you assume that general equilibrium model is a realistic representation of the real world (and the only admissible model) and that therefore people must be committing a fallacy when they conclude things that don't agree with your general equilibrium assumption.

That's why we (& Marx & Keynes) do, and sometimes need to do, critiques of general equilibrium models.

http://ecologicalheadstand.blogspot.ca/2012/12/production-of-robots-by-means-of-rowe.html

[Nick Rowe]

I wrote down three general equilibrium models. They had different predictions. They can't all be right. I can't be affirming the consequent. I rejected two of them, because they predicted rising real interest rates, which doesn't work empirically. Maybe the third is right? Or maybe someone else has a better general equilibrium model. nemi is working on one right now, in comments on my other post. He seems to be maybe getting somewhere. Maybe his will be better.

Keynes was thinking General Equilibrium too. So was Marx (but Marx had a problem getting things to add up right, with the Transformation Problem).

[CBBB]

"What you are talking about is a long run general equilibrium model with sector-specific shocks and search frictions (or similar) with a constantly-rotating pool of unemployed. It's still general equilibrium. Just a more complicated model than mine."

But also would get more to the heart of the matter. If you're trying to model what would happen if we had robot competition for all jobs it really ignores the entire point if you assume full employment, or assume there are no barriers to entry between professions, etc. I would argue that given the increasing scrutiny employers put on potential candidates these days, it's becoming very difficult to switch professions or jobs and any economic model trying to describe labour markets must take these frictions into account - this includes the Ricardian trade model which assumes countries can shift resources from one sector to another.

[Nick Rowe]

CBBB: C + I/a = (1-g)(L + K)

There's a first cut at just such a model. The higher the growth rate of technology, g, the higher the proportion of humans and robot workers that are unemployed.

[Sandwichman]

Is the economic system self-adjusting?

[Anon]

The 1/a & (1-g) model you outlined is close to the 1/a & a model I suggested in the other thread.

(A simpler one would be 1/a & (1-1/a): an increasing rate of robotic productivity evolution excludes workers and shrinks their pool of work.)

Most of these models result in a catastrophic outcome both intuitively and quantitatively, starving everyone to death except the owners of robots, do you agree?

[Anon]

Nick:

In your models what is the justification for treating robots and humans interchangeable, I.e. making them only compete on price?

In the real world robots are often replacing human workers permanently, because robots offer things humans physically cannot do: very low time to market latencies, very low retraining latencies and very high precision of work.

We are seeing this in the auto and smartphone industries: wherever industrial robots take over, humans cannot compete for those jobs anymore, at any price, in most cases. Even if the manufacturers had human slaves, they'd still use robots, because minimum acceptable product quality constraints.

Humans can generally re-train themselves only to non-robotic jobs - competing with other humans in that field and decreasing wages there. For 200 years (healthy) humans squeezed out by machines could quickly retrain in the same industry, at a higher, non-automated level. Humans are good general purpose industrial robots, and for 200 years that saved them from being replaced by machines.

But this dynamic has changed about 10 years ago: human workers are being replaced permanently by better general purpose industrial robots, and this is happening in a number of high growth industries.

So the Luddites were right after all, just off by 200 years.

[Anon]

Nick:

I suspect you will ask for a model.

The model that would describe it well is a GE model but with a twist: instead of having an equilibrium in a single system described by economic parameters, we'd have two systems, coupled via the parameter "a" (rate of robotic evolution).

The first system is the output of human workers:

C_h = L / a

The second system is that of robotic production:

C_r = R * (1 - 1/a)

If R=L (robot population = human labor population) then total production is 1.

As "a" increases, so do robots produce more output - and humans produce less.

Initial value of "a" is 1: zero production by robots, only human output.

At a value of "2" we get 50% - 50% share of production. At a value of 4 - and still at the same population - 75% of production is done by robots, 25% by humans.

In this model, robot population is not determined by pricing, but by an exogenous "quality threshold" mechanism: if robots are cheap and good enough then they permanently replace human workers from that point on, in that industry and won't switch back to humans.

The model could be further simplified if we expressed "a" not as a time dependent exogenous parameter, but as a ratio of human versus human population:

a = R/L + 1

Where robotic population R continues to be exogenous, mainly dictated by technology thresholds, not price.

The equilibrium simplifies to:

C_h = L / (1+R/L)
C_r = R * (1 - 1/(1+R/L))

C_h is interesting: for large values of R it converges to 1/R: output by humans depends on the number of robots and dwindles, together with labor wages.

C_r converges to "R" at high values of R: robots produce almost everything.

[Vladimir]

Nick,

My last comment in the previous thread didn't make much sense -- it was late, and I was too tired to think clearly, so I misread the definitions of some of your variables. I'll continue my comments here, though.

We seem to be largely in agreement about the Malthusian scenario resulting from abundant robot labor combined with scarce land. However, what I'm interested in, and somewhat confused about, is the implication of your second model ("labor and robots plus other capital"), namely that robots could cause wages to fall even assuming no scarcity of land. (The context of my interest here is primarily in futuristic speculation, not analysis of current economic trends.)

So, after thinking carefully about it, here's what I still don't understand. Assume that a is constant, so that g is zero. Then the price of a robot (1/a) is also constant. Wouldn't a then put a floor on the interest rate? Whatever this constant price of robots might be, you can always buy N robots today and sell (1+a)N robots next year. So how can then R_c be less than a? (Your formula asymptotically approaches R_c = sqrt(a) for a>>1. Such a huge a doesn't sound unrealistic if we imagine that multiplying robots is more like copying computer files than traditional mechanical assembly.)

I've been trying to feed concrete numbers into your model to see how it would map to concrete scenarios from my hypothetical infitite-land world, but I keep stumbling into this problem. I'm probably just being dense here, but I'd appreciate if you could clarify this point.

[JP Koning]

Ok, I cheated by reading this post before reading the one on robots, but it is still very useful. For some reason I prefer reading about how economists think rather than getting into the nitty gritty of their actual models. Will mosy over to your robot piece now.

[Nick Rowe]

Vladimir: "So, after thinking carefully about it, here's what I still don't understand. Assume that a is constant, so that g is zero. Then the price of a robot (1/a) is also constant. Wouldn't a then put a floor on the interest rate? Whatever this constant price of robots might be, you can always buy N robots today and sell (1+a)N robots next year."

First model: that would be exactly what happens. Not just a floor, but a ceiling too (provided robots are actually being produced in equilibrium, which means if saving(=investment) is positive.

Second model: Not quite, because baby robots have a 1 year gestation period, so you have to wait 2 years until you get (1+a)N robots. (I think that works, but my model is continuous time and you are thinking discrete time).

Third model: No, because you would also need to rent some land before your N robots could produce (1+a)N robots next year. [typo fixed NR]

[Nick Rowe]

Anon: "The first system is the output of human workers:

C_h = L / a"

Suppose there's an improvement in technology for robot hairdressers ("a" increases). Why would that mean human hairdressers can cut less hair per hour?

[Richard]

"The very fact that we bother to put names on some logical fallacies seems to suggest that people have a tendency to commit those fallacies. I don't think there's a name for the following logical fallacy: "1+1=2; therefore Mazdas are better than Hondas". We don't have a name for that particular logical fallacy because even the most crazed Mazda fanboy is unlikely to argue like that. Named fallacies are named fallacies because they are not just fallacies; they are seductive fallacies that we really want to commit".

Yes we do--non sequitor (http://en.wikipedia.org/wiki/Non_sequitor).

[Nick Rowe]

Richard: Hmmm. But isn't "non sequitur" just another name for *all* failures in logic?

[A H]

I think you are redefining the term "general equilibrium" away from the way economists usually use it. It usually is taken to refer to Arrow-Debreu type models which have specific assumptions.

It certainly does not mean that "you can check that things add up", there are lots of models that are internally consistent that don't tend toward any equilibrium.

[John Hulls]

At a certain point of robotic reduction of costs of goods (disregarding resource and ecological issues) it will be necessary for economic growth to force satiated consumers to consume. (advertising and public relations) One of the huge problems in studying these issues is the quality of economic data, which Krugman described in a recent interview as resembling very boring science fiction, or words to that effect. If one had accurate sectional data, there are many natural experiments that economists could examine. As an example of foggy data, look at the difficulties of measuring the impact of information technology and the personal computer.

Here are some further comments I posted on deLong's website.

" And the computers, (robots) who are obviously reading Shakespeare, decided to kill the lawyers, as in this NY Times piece, 'Armies of Expensive Lawyers, Replaced by Cheaper Software' at
http://www.nytimes.com/2011/03/05/science/05legal.html?pagewanted=all&_r=0 One wonders how this reduction of billable hours is reflected in the pay to senior partners, but I'd be willing to bet their incomes have not suffered greatly. Also, does this mean that complex litigation is now cheaper so that corporations can pay attorneys to file ever more convoluted lawsuits, such as in the current massive IP battles over cell phones and software?

It looks like the legal profession might be a wonderful natural experiment as to the incursion of robots into what was previously considered intellectual areas.

For a great story on computerization of literature that somewhat parallels the situation, try Roald Dahl's 1954 short story of the Great Automatic Grammatizator, full text on line at http://lengish.com/texts/text-89.html After completing a massive computer for the government, a young engineer at the company proposes a machine to write stories,and finally novels. The computer company sets up a literary agency where the business model is one where famed authors are paid a guaranteed annual stipend to stop writing and put their names on novels produced by the machine. Older writers, at the end of their creativity, sign up in droves, while younger writers are more resistant. The ending of the story, from the narrator, a writer who refuses to sign (spoiler alert):

"But on the whole, it was a satisfactory beginning. This last year — the first full year of the machine's operation — it was estimated that at least one half of all the novels and stories published in the English language were produced by Adolph Knipe upon the Great Automatic Grammatizator.
Does this surprise you?
I doubt it.
And worse is yet to come. Today, as the secret spreads, many more are hurrying to tie up with Mr. Knipe. And all the time things get worse for those who hesitate to sign their names.
This very moment, as I sit here listening to the crying of my nine starving children in the other room, I can feel my own hand creeping closer and closer to that golden contract that lies over on the other side of the desk.
Give us strength, Oh Lord, to let our children starve."

[Nick Rowe]

A H: I agree with your first paragraph. I am doing that. But I think it would be a good thing if we did redefine "general equilibrium" that way, so that we could talk about non-Arrow-Debreu-type general equilibrium models (which, I think, some economists do, like for example some search-theoretic macro models, which are GE, but are not A-D).

On your second paragraph, it again depends on what we mean by "equilibrium". If we restrict "equilibrium" to mean "market-clearing equilibrium where things don't change over time", then you are right. But we could instead use it in the more general sense of "a time path for the endogenous variables that is a solution to the equations of the model".

[Nick Rowe]

John: "At a certain point of robotic reduction of costs of goods (disregarding resource and ecological issues) it will be necessary for economic growth to force satiated consumers to consume."

I disagree. Why should we force "growth" if nobody wants it? People who approach satiation will stop saving and investing in robots (why save and invest for the future if you will be satiated in future?). And if they find they accidentally saved and invested too much, and have more than they need, they won't worry about giving their excess goods or robots to charity, if anybody is still not satiated.

I will wander over to Brad's blog.

[Nick Rowe]

And why would anyone want to work, if they were satiated? Labour supply falls as we approach satiation. Unless we want to work to fight off existential ennui. That's where canoeing, or fox-hunting, or video games, or competing to be the best-read human (even if you are reading books written by Roald Dahl's robot), or some such daft activity, takes over our ambitions.

[Anon]

Nick Rowe:

The cutting of hair is partly social activity, which is not automated yet to the level car construction has been automated in the auto industry or smartphone assembly has been automated in the smartphone industry.

The model I outlined captures technological advances that replace workers permanently. Do you contest that those kinds of advances exist?

A fuller model would be:

C_h = L_r/a + L_h

Where L_h is the labor force not threatened by robotic workers and L_r are automatable workers.

The outcome does not change much, as long as L_r is a significant portion of the labor force.

[Sandwichman]

"And why would anyone want to work, if they were satiated?"

Intrinsic rewards of the work.

[Jacques René Giguère]

Provided you get the right work...
If only Peter Cook had his wish and became a judge instead of a coal miner...

http://www.youtube.com/watch?v=ofUZNynYXzM

[John Hulls]

Nick

Perhaps your models should include a ‘satiation’ equilibrium condition, in which case the only thing that could bring about change, would be new or improved technology, such as in health care, or perhaps development of a drug that makes everyone feel good, such as Soma, the drug in 'Brave New World' Imagine a model in which there is a universal robot, capable of fulfilling all of an individual's physical needs. (disregarding resource and other limitations to keep the model simple) To keep the rentier economy going, these robots would have to be rented out to the general populous to gain a return on investment in developing and manufacturing the units, but what would happen if everyone could afford such a robot? In such a simple model, the circular flow of cash in the economy would cease, but I suspect that in the real world, the value of material resources would rise, but that brings us to the problem as to how the robot owners would purchase the raw materials to enable the robots to serve them, absent the payments for the labor to create products.

From a practical point of view it is also important to note the rise of public relations. The founder of modern P.R. was Edward Bernays, Freud’s nephew. Freud convinced him that existing advertising informed consumers as to the utility of the product, whereas the markets would be far larger if advertising were directed at creating an emotional desire for a given product. Just before the Depression, Hoover held a meeting with Bernays and the heads of the consumer goods advertisers and members in America, and told them, “"You have taken over the job of creating desire and have transformed people into constantly moving happiness machines. Machines which have become the key to economic progress."
(from: http://pialogue.info/books/Century-of-the-Self.php)

I suspect that Keynes was correct when he noted that there would not be many endeavors undertaken where mere financial gain is the only profit, and there are always those people fascinated with engineering and the sciences and the arts for their own sake. Forgive my harping on science fiction, but it is useful to explore society at the limits. For instance, even the term ‘robot’ comes from Karal Capek’s 1920 novel RUR (Rossom’s Universal Robots), derived from the Czech word ‘robota’ meaning slave labor. You can check out the plot line for RUR on wiki and see how much it mirrors the current ‘robot’ economic debates on which Brad DeLong and Paul Krugman have commented. Funnily enough RUR was made into the first televised science fiction drama by the BBC in 1938

[John Hulls]

Sorry about the garble from 'cut and paste' editing in the second paragraph..should read ...heads of consumer goods advertisers and members of America's rapidly growing PR industry....
If you read the link to Century of Self, you'll find out how Bernays used a very clever PR stunt to induce women to smoke, causing a near doubling of the cigarette market for his client, presaging a far more recent campaign to sell cigarettes to women...'You've come along way, baby...

[Sandwichman]

Evil Effects of Robot

From Hungary and Transylvania: with remarks on their condition, social, political and economical, Volume 1 by John Paget (1839):

"The system of rent by robot or forced labour,—that is, so many days' labour without any specification of the quantity of work to be performed,—is a direct premium on idleness. A landlord wishes a field of corn to be cut; his steward sends out, by means of his Haiduks, information to the peasants to meet at such a field at such an hour with their sickles. Some time after the hour appointed a great part of them arrive, the rest finding some excuse by which they hope to escape a day's work; while others send their children or their wives, declaring some reason for their own absence. After much arranging they at last get to work; a Haiduk stands over them to see that they do not go to sleep, and between talking, laughing, and resting, they do get something done. Where horses are employed, they are still less inclined to hurry; lest they should tire them for the next day, when they use them for their own purposes.

"Now how much does the reader suppose such workmen perform in one day ? Count S-- says, just one-third of what the same men can do easily when working by the piece; and he has accordingly compounded his peasants' one hundred and four days' robot for a certain amount of labour, which they generally get through in about thirty-four days.

"Another evil of the robot is the ill-will it begets between the masters and the workmen : their whole lives seem to be a constant effort, on the one hand, to see how much can be pressed out of the reluctant peasant; and, on the other, how little can be done to satisfy the terms of agreement, and escape punishment. Mutual injury becomes a mutual profit; suspicion and ill-will are the natural results."

[Nick Rowe]

Jacques Rene: Now I have just wasted 2 hours watching old Pete and Dud youtubes! (I was afraid you had posted a link to some of their later Derek and Clive work - not safe for a family blog!)

John: "Perhaps your models should include a ‘satiation’ equilibrium condition,.."

I didn't include preferences in my models. I rigged the technology so i could solve for W and R without specifying tastes. Tastes would matter for: saving/investment, and for labour supply.

I can't help but remember though, some economist (can't remember who) saying that schools and universities try to create tastes we never knew we had, for art, literature, music, history, knowledge, etc.

Anon: I think you have missed my point @07.18.

[Dan Kervick]

Nick, how are your models affected if instead of using human workers and robots, you just consider two different classes of robots, with robots in the first class replaced by robots in the second class? What happens to the robots in the first class after the replacement? They could be re-purposed I suppose. But isn't it also possible that they are simply junked?

One way to view the comparison of humans to robots is to think of the replacement robots as being leased by new companies that own them, and then to think of a human worker as something like a robot-leasing firm whose entire capital consists of a single robot. When the replacement robots come along, the first generation of firms are put out of business. The owners of those firms might be able to go into another business if they have been able to transform income into capital during the time they were in business. But if they weren't, then they own nothing to invest or exchange, and are thus ejected from the economy entirely.

Many workers can be thought of as small firms that have small capital to start with, and whose mouth-to-mouth existence and limited resources precludes the accumulation of additional capital while they are working.

[Nick Rowe]

Dan: I could change my model so that every vintage of robot became (1+a) times as productive as the earlier vintage, so that every new vintage earned (1+a) higher wages than the previous vintage. The production function would become:

C(t) + I(t) = L(t) + I(t).a^t + I(t-1).a^(t-1) + I(t-2).a^(t-2) etc.

But I think I could just do the math (OK, someone could do the math) showing that this model is at root the same as my model. Just redefine one new robot as really 1+a of last years robots, etc.

E.g. if one new robot is twice as productive as one old robot, just say that one new robot is really two old robots.

[Dan Kervick]

mouth-to-mouth existence

Eew...bad trope. I meant "hand to mouth".

[Steve Roth]

@Nick: I haven't had time to read the whole thread (or preceding posts'), so excuse me if this has been broached already.

I think much of this discussion ignores the limits of human capabilities. The median human IQ (by definition) is 100. I think those of in this discussion have trouble remembering that half the people have an IQ below that, or to even comprehend how hard it would be to make a go of things, provide for a family, in a modern society with an IQ at that level. Even finishing high school.

Some horses can pull and carry more than others. The weak ones were driven below subsistence sooner. But hey: they shoot horses, don't they?

The range of human capabilities is far wider, but it's not infinite on the upside. And while the median on the IQ scale is jiggered every so often to account for apparently increasing intelligence, that shift is glacial compared to technological progress, and to the rise in the skills level necessary to claim a >subsistence share of the pie.

What if we're the horses this time?

[Peter N]

In any model with exponentially increasing numbers/abilities of robots the price of a robot in terms of the inputs needed to manufacture it will go to 0, though prestige goods and goods in inherently limited supply (land, collectibles) will still command a premium.

Most people will be either unable or unwilling to compete with robots, so even though goods will be cheap, there remains a question of how people would earn enough to buy inputs. This is a social problem, not an economic one. There is no economically inevitable answer to the question of the distribution of claims on the necessary inputs. It is likely, however, that technology will have substitutes for inputs that are currently scarce like rare metals and energy, and, of course, robots can be applied to the extraction of inputs, driving down their cost. A dole would be perfectly reasonable.

I think the most likely outcome is a tiered society where everyone has the means to buy (or produce) ordinary goods beyond (today's)dreams of avarice, but there would still be a wealth distribution where wealth was used for prestige assets, but it's an open question how one would become/remain wealthy. Being grandfathered only gets you so far.
.

[Steve Roth]

@Peter N:

Based on recent trends, I'd suggest that absent intentional redistribution (rich>poor), the tiers would diverge rapidly. An emergent property of the system absent such redistribution.

[Steve Roth]

Suppose there's an obstruction in front of the audience, so they can't really see anything sitting down. If everyone stands up, the audience in aggregate can see better.

But some people are short.

A fallacy of decomposition?

[Nick Rowe]

Steve: "What if we're the horses this time?"

That's the question I'm exploring. And I say we need a general equilibrium model to explore it. And my (tentative) answer is: it all depends on putting land in the model. If horses had free land, we could always put them out to pasture, and let them feed themselves.

Peter N: you really need to distinguish between: the price of robots; wages of robots. If the rate of interest were fixed, there would be a very simple relation between those two variables. If the price of robots fell, the wages of robots will fall in proportion. But the rate of interest won't stay fixed. Which is why you need a GE model, to see how improving robot technology will affect the rate of interest.

[Steve Roth]

@Nick: "If horses had free land, we could always put them out to pasture, and let them feed themselves."

Yeah: if they had a chunk of technology that converts sunlight to sustenance. (Which would be a pretty good description of a productive economy, especially if you include burnable fuels, which are stored sunlight.)

But: "had free land" is confusing here. "Free" would mean they could *acquire* it at no cost, right, not that they "had" it. Like, if someone gave it to them.

Or add another word: "if *all* horses had land," we could just let them retire to their landed estates. But they don't. All the land's been claimed by the more capable horses.

So this kind of begs its own question: given their insufficient capability, should we give them some land? Whose? Will all the horses be better off if we do? (There's the general equilibrium question.) You know my answers (still tentative, but getting somewhat less so...).

[W. Peden]

Steve Roth,

"Suppose there's an obstruction in front of the audience, so they can't really see anything sitting down. If everyone stands up, the audience in aggregate can see better.

But some people are short.

A fallacy of decomposition?"

The fallacy of division.

"America is rich, John Doe is American, therefore John Doe is rich."

In syllogistic terminology, the fallacy is usually a result of interpreting a predicate (in this case, "rich") to the subject (in this case, "America/Americans") distributively when it should be interpreted collectively. So it's true of the Americans collectively that they are a rich nation, but it's not true of each and every American.

The fallacy of composition usually features a predicate being interpreted distributively when it should be interpreted distributively, e.g.

"Eating one apple a day is good for you, so eating 30 apples a day is 30 times as good for you."

[W. Peden]

* Interpreted collectively when it should be interpreted distributively.

[Nick Rowe]

Steve: i don't have any brilliant answers. Remember though, I was deliberately trying to rig things for a worst case scenario. As a history of the last 200 years, my model has been very wrong. Malthus was wrong. But will be still be wrong for the next 200 years?

[Dan Thorn]

Something strikes me as sort of classical econ/Say's Law type analysis regarding this robot model.

I suspect the 'sticky wages' of the robot problem have to do with land, this I gather is consistent with your models.

Classical analysis (simplistically as I understand it) made the assumption that economics is a self-adjusting system. Keynes observed that wages were not self-adjusting. (I think it also has been noted that money is cost-less to produce which breaks the virtuous cycle of self-correction.)

Is there a corollary with Robots? In your prior post the string of comments included someone who tried to address inequality. Let's set aside inequality as a social/moral issue and just ask the practical question; if land is either naturally limited, or in some way monopolistic-ally limited for say periods of monopolistic control greater than 5-10 years, won't the welcome outcome of your model fail to be realized in the short run? That is, a few people will monopolize the land inputs required for robots and create a virtuous world for a small subset of the population, with negative outcomes for a majority of the population.

Robots aren't categorically unique (I don't think, you haven't said?) but IF robots are simply a continuation of capital substituting for labor, we have a long history of industrial economies robotizing. It seems to me we also have a long history of capital monopolizing land inputs. I think you need Teddy Roosevelt in your model, or it will cause social discontinuity.

[Vladimir]

Nick,

Thanks for the clarification! I think I finally understand your second model fully, and the numbers check out.

What I'm now trying to do is to find a more concrete hypothetical scenario from the infinite-land world where a fall in wages occurs due to the second-model mechanism. It's still not clear to me if the falling wages in this model are a consequence of some artificial assumption, or if this effect could actually happen in some plausible future course of events (and have comparable significance to the Malthusian effect due to land scarcity).

[Steve Roth]

@Nick:

1. I think that the limits on human capacity have to be calculated into the general equilibrium somehow.

2. I don't think the general equilibrium can be properly calculated without some assumed utility function relative to income/wealth. IOW, $1 ≠ 1 util. (Yes: *cardinal* utility. Horrors.) Also some functions for the income and substitution effects relative to income/wealth. And a function for the surplus from production resulting from different investment/consumption spending mixes. Tall order, that.

I also don't have any brilliant answers to the theoretical/modeling problem(s). (I get why my redistribution model has problems since it doesn't include the interest rate [or inflation]. Thanks.) My intuition says: Santa Fe-style population simulation models with *very* heterogenous decision agents.

But to quote Jim Manzi, Mr. Causal Density himself, ultimately "any responsible critic must always answer the basic question: 'If not this, then what?'"

In the context of this discussion -- which I'll characterize as "optimizing well-being in an increasingly automated and productive economy in which humans have limited capacities and robots potentially (effectively) don't" -- the flawed and intuitive general-equilibrium model that's running in my head tells me that the brilliant answer for the U.S. is increased redistribution in the form of a greatly simplified earned income tax credit (indexed to unemployment), higher minimum wage (indexed to inflation), and (much more) publicly provided education, health care, research, and infrastructure spending. All (except the minimum wage) transferred/funded through government via a tax system (local, state, federal combined) that actually *is* progressive above about $60 or $80K in income, and that generates significantly more revenue than the current one.

Assumption behind that: the Fed can handle some bumps in the road, but long-term it has to stay inside the lines -- lines that are painted via policies such as those above. (The big monetary game changers -- '33, '44, and '71, plus 1791 and 1862 -- were presidential actions, not monetary authority. Think: trillion-dollar coin.)

You've got a much much more robust general equilibrium model in your head than I do. I'm always astounded to watch you working with it, learn immense amounts doing so. My impression is that its recommendations are quite different from mine. But I'm not really sure. You spend a lot of time working on the model, but I'd like to hear more about what recommendations your current mind-model suggests (besides NGDPLT).

[JR Hulls]

Nick,

Thanks for your reply, but I still feel it would add a lot if one were to include preferences and a satiation level. Perhaps you could model the demand for basic needs going to zero with ownership of the basic robot, (eliminating resource constraints) with a demand for luxuries by an ever smaller elite expanding on a per individual basis. Such luxuries should obviously to be manufactured by Delux Robots, which would also require investment and sufficient income from rents to pay for them. Shades of Adam Smith's silver buckle replacing the maintenance of a thousand men and $8000 Gucci handbags.

As a big fan of analog simulations, Phillips Moniac could be used as it essentially does Cambridge equation/Keynesian economics. Basically nearly all relationships between supply and demand and the financial sector can be defined by the shape of the slots in the graphs that operate the valves that control the relationship. You don't even need to define the math to do an experiment, just draw the shape of the curve, as the machine will do non-linear simulations based only on the shape of the operating slot in the graph.

I've mentioned it on Worthwhile' before but for a great demo, see the links to Cambridge's Allan McRobie's video in this article. http://oecdinsights.org/2012/06/27/going-with-the-flow-can-analog-simulations-make-economics-an-experimental-science/ I've been doing some work on this type of simulation, with some success, as alluded to in the article.

Incidentally, in some of his later work, Phillips speculated that construction of a sufficiently sophisticated electronically based true analog simulator, continuously tuned by econometric analysis of real world data, might be the best way to advance understanding of economic stability and employment and how to regulate them.

You really come up with good topics, and may I wish 'Worthwhile' and its contributors all the season's best.