Toy Stories

toysPaul Krugman is at it again, casting aspersions on everyone who opposes extended unemployment benefits while offering absolutely no positive argument for those benefits. Let me explain what would count, to an economist, as a positive argument.

There’s no question that extending benefits would be good for the currently unemployed, and no question that it would be bad for those who are called on to foot the bill. Economists usually deal with that kind of conflict by asking what policy you’d prefer if you had amnesia, and and didn’t know your own employment status. (You can read a lot more about this approach to policy analysis in Chapter 16 of The Big Questions.) The amnesiac is an impartial judge who is forced to care about everyone, because he/she might be anyone.

To translate this philosophical position into concrete policy choices, we have to figure out what the amnesiac wants. Fortunately, we have a lot of experience observing amnesiacs, or at least their equivalents. When you buy health insurance, you don’t know how much medical care you’re going to need; when you accept a sales job, you don’t know how you’ll perform; when you buy a share of stock, you don’t know whether it will go up or down. So you’re making choices in the dark, much like an amnesiac who doesn’t know his own health status, or his own salesmanship skills, or how his own portfolio is doing. By observing those choices, we can estimate how real amnesiacs are likely to behave.

By the industry standards of economics, to justify further unemployment benefits, you’ve got to at least to attempt to argue that an amnesiac would favor them. And you do this not by posturing a la Krugman, but by computing.

Now that’s not an easy business. You need to make educated guesses about a lot of things an amnesiac might care about, like: What’s the chance of becoming unemployed? How costly is unemployment? What utility function do people maximize? How much do people discount the future? How much deadweight loss (i.e. lost production due to disincentive effects) is caused by taxation? Different economists might make different guesses, and so get different answers. But at that point we can at least pinpoint the locus of our disagreements and try to get better estimates in the areas where we differ.

To show you how that kind of thing might work, I’ve just written down a (warning: technical!) toy model where I invented answers to the key questions, did some computations, and concluded that our amnesiac would oppose further benefits. (Honest, I didn’t know in advance what answer I would get.) These computations prove nothing, because at least some of my invented answers surely have nothing to do with reality. But my point is that if you’re claiming as an economist to support further benefits, then it’s your job to do the hard work of writing down a more realistic model and show me how the numbers work out. As far as I’ve seen, neither Krugman nor any of his ilk have even tried to do that.

Edited to add: Joe Walsh of the University of Alabama writes to tell me there are arithmetic mistakes in my account of the toy model. For those who want to understand the model, a very good exercise would be to work through it, correcting all the arithmetic mistakes.

Edited further: It was an overstatement to say that my pdf file contains arithmetic errors. In fact all it contains is a typo. In the first displayed equation, c-50 should be just c. After making that correction, all of the follow-up math is right. Thanks to reader A.J. Lenze for checking this.


33 Responses to “Toy Stories”

  1. 1 1 Henry

    I think you’re expecting too much of opinion columns for laymen. Should Krugman be expected to produce detailed explanations for how his policy proposals would be preferred under a veil of ignorance in every column he writes? This would be a tad complex for his audience (you even implicitly admit this by warning about how your own model is technical).

    His arguments (such that unemployment benefits are unlikely to have much of an effect on employment rates when the economy is doing poorly) could form part of a social welfare argument. It’s a little much to expect him to fully explain his social welfare function in every post, though.

  2. 2 2 Stephan

    That’s indeed very good news! There’s no such thing as the fallacy of composition in economics anymore. I also like your realistic assumptions.

  3. 3 3 Sergei

    Wow! Does your 50% chance of being unemployed this year also apply to members of Congress and all econ PhD, in particular paid by the Fed?

  4. 4 4 John Faben

    Steve, the last sentence of your ‘toy model’ says:

    Therefore, because 16.87 is less than 16.84, the amnesiac
    rejects the unemployment benefit.

    I think that the amnesiac might also have rejected arithmetic… (the conclusion is actually the one the model predicts, the wording is just backwards).

  5. 5 5 Steve Reilly

    But Krugman’s arguments are based, at least in part, on unemployment benefits affecting aggregate demand.

    He writes, “One main reason there aren’t enough jobs right now is weak consumer demand. Helping the unemployed, by putting money in the pockets of people who badly need it, helps support consumer spending. That’s why the Congressional Budget Office rates aid to the unemployed as a highly cost-effective form of economic stimulus. And unlike, say, large infrastructure projects, aid to the unemployed creates jobs quickly — while allowing that aid to lapse, which is what is happening right now, is a recipe for even weaker job growth, not in the distant future but over the next few months.”

    So when you write that paying such benefits is bad for those who foot the bill, he seems to be disagreeing. They’re paying some money in order to lessen their own chances of being unemployed. Whether he’s right or wrong about that is another question, but a model that fails to take that argument into account doesn’t really seem relevent to the column.

  6. 6 6 Stephan

    @Steve Reilly
    Aggregate Demand? There’s no such thing in the toy story world. Once you start with a model of the representative consumer maximizing his utility living in a Ricardian Equivalence paradise you are done with macroeconomics. Microeconomics is King! Always the same bullshit ;-)

  7. 7 7 Jacob Williams

    Krugman seems to have reverted back to a static, 80 year old model in which individuals don’t attempt to maximize lifetime utility or anything similar. In fact, in almost every article I read he does things that no self-respecting macro theorist (saltwater or fresh) would do. 1st year students in my Ph.D. program can see that he is no longer an “Economists” but rather a pundit who uses his former life and achievements as an economist to slander and belittle other economists for his own political agenda.
    It is quite sad, really.

  8. 8 8 Alan Wexelblat

    I have a tangential, but serious, question: why would you use a model of anyone ‘maximizing a utility function’ when in fact peoples’ actual behavior, preferences, and choices do not resemble such functions at all? Utility functions, at least insofar as I can determine traditional economists use them, are patent falsehoods.

    In physics one uses patently false models (such as frictionless vacuums) in two cases – one is where you don’t know the actual values and are forced to use known-false models, or situations where the values are sufficiently close to the model as to be acceptable approximations. Insofar as I understand behavioral economics and such, neither applies in this case. (But perhaps I’m wrong about that?)

  9. 9 9 Steve Landsburg

    Alan Wexelblat: The statement that people maximize expected utility is not an assumption; it’s a conclusion that follows from more fundamental assumptions about behavior. This, of course, only pushes your question back one step: Why do we make *those* assumptions, when we know they are sometimes violated?

    The answer is that our models seem to predict behavior quite well in a broad variety of contexts (though we also know of violations, e.g. the Allais paradox—which I really should blog about). Of course it would be better to have better models, and plenty of economists are working on that.

  10. 10 10 TjD

    “Therefore, because 16.87 is less than 16.84, the amnesiac
    rejects the unemployment bene fit.”

    16.87 > 16.84

    Also, if with a 100% chance of employment chance, the difference is 0.03 ( assuming no further mistakes were made ), then with the same model even 99% percent of employment chance will have amnesiacs go for unemployment benefits.


  11. 11 11 Jonathan Kariv

    I’m wondering how sensitive your toy model is to parameter changes?
    (i.e. if we changed our assumptions of how much more employed people earn than unemployed ones,how many are unemployed this year and next year and how much we discount future utility etc)?

    Admittedly I’m a bit too lazy to actually do the calculation with letters in place of the numbers (and it might get very messy if I tried). But I’d be interested to know exactly how sensitive this model is to that. 16.87 and 18.64 seem close enough that we should be concerned about this (in so far as we are concerned about the model)?

  12. 12 12 John Scott

    You might try an appeal to authority in order to counter Krugman. The idea that unemployment benefits increase unemployment under some circumstances is noted by at least one Nobel Prize winning economist–Paul Krugman, in his principles text.

  13. 13 13 Bob

    Steve Reilly:

    I’m puzzled. By this reasoning, shouldn’t tax cuts (perhaps temporary, perhaps concentrated in the lower tax brackets) be more cost-effective than, say, large infrastructure projects? And yet, I don’t seem to remember this policy being heavily pushed by one Paul Krugman…

  14. 14 14 Steve Reilly

    @Bob, my point wasn’t so much to defend Krugman’s piece, and in all honesty I don’t know enough about these matters to know the best forms any sort of stimulus should take. My point was much simpler; if we’re going to disagree wtih Krugman, then we have to do so with models that deal with what he’s talking about. His argument was, in part at least, about boosting aggregate demand, so a model that fails to take AD into account doesn’t answer his arguments.

    I haven’t read the CBO piece he mentions that pushes unemploymnet benefits as a useful stimulus. I have no idea if it answers your questions or not.

  15. 15 15 PaulRoscelli

    Expecting too much from a columnist? He won the Nobel prize in a discipline on which he writes.

  16. 16 16 Bob

    Steve Reilly:

    I don’t claim any expertise, nor even much of an opinion, regarding the extension of unemployment benefits. My point too was simple: if Krugman wants me to take him seriously (as a columnist), I expect a minimum of consistency, as befits someone with his professional standing. Instead, he has over the years proved to be a partisan advocate. One Bob Herbert is too much, thank you.

    (None of which is meant to invalidate your point.)


    If Krugman were to write his opinion columns under a pseudonym, nobody would believe that their author was a Nobel-winning economist. In fact, attributing them to him would seem like slander.

  17. 17 17 dave

    in your model, jill borrows from jack instead of jack paying jill unemployment benefits via taxation.

    why would jack lend a dime to jill if she is unemployed? is it the future assumption that there will be 100% employment?

    hasnt jill paid her own unemployment benefit from previous taxation?

  18. 18 18 Seth

    “There’s no question that extending benefits would be good for the currently unemployed, and no question that it would be bad for those who are called on to foot the bill.”

    My Grandma may not agree with that first part. She’d say it may be good for people to get creative now and for the future. Then she may tell me the story of the Ant and Grasshopper.

  19. 19 19 John Scott

    Though I have concocted complex microeconomic models (on terrorism and the media, ecommerce, etc.) my heart is seldom in it. After all, basic principles do so much. Unemployment imposes a cost on the individual. Unemployment insurance lowers the cost of unemployment and that, other things equal, results in more unemployment.

    With regard to macroeconomic effects of unemployment insurance, I am a fan of Bastiat. Since the payments do not descend from the moon, we take from one to give to another. An employed person buys fewer books so that an unemployed person can buy more light bulbs–no net effect. However, when we depart from a market system in which the person who buys books is able to do so by merit of their productivity and allow another person to buy light bulbs by merit of their non-productivity, we are sure to encourage non-productivity and discourage productivity; hence, we make ourselves poorer as a nation.

  20. 20 20 Alan Wexelblat

    Steve: so the statement about maximized utility may be a conclusion but if your conclusion is contradicted by data (e.g. the work on behavioral economics – Ariely et al) then doesn’t that suggest there’s a problem with the assumptions?

    Or take the various studies on parenting (most recent one I noticed here: they all seem to conclude that having children is not a decision that people make based on utility functions because – at least in modern Western countries with advanced medicine – the utility of more than one child is clearly negative. People with > 1 child are less happy, less well off, etc. By any measure of utility parenting is an irrational choice.

    So then we have to either say that every parent with more than one child is irrational – billions of people – or we have to question what the usefulness is of idealized models of utility. Or have I got it wrong again?

  21. 21 21 Steve Landsburg

    Alan Wexelblat:

    the utility of more than one child is clearly negative. People with > 1 child are less happy, less well off, etc. By any measure of utility parenting is an irrational choice

    You are confusing the word “utility” as it used as a term of art in economics with the word “utility” in its everyday sense. This is on the order of saying that earth’s gravity cannot possibly attract objects, because we all know that attraction always has some sexual component and the earth is sexless.

    Utility is not meant to bbe a measure of happiness or any other psychological state.

    By any measure of utility parenting is an irrational choice.

    Obviously this is false. If, for example, the measure of utility was “number of children” then the only rational choice would be to have as many children as possible. The fact that people don’t (generally) do this tells us that “number of children” is the wrong measure of utility. So, quite probably, is happiness.

  22. 22 22 jpd

    “a very good exercise would be to work through it, correcting all the arithmetic mistakes”

    thats funny

  23. 23 23 jre

    May I paraphrase?

    My critique ignores Krugman’s central argument regarding demand, and it also contains arithmetic errors that I’m too lazy to correct, so I’ll leave them as an exercise for the student.
    Except for those minor flaws, it’s perfect.

    Does the Bank of Sweden award a prize for chutzpah?

  24. 24 24 Steve Landsburg

    jre: Krugman’s central argument regarding demand says that unemployment benefits will increase aggregate demand and therefore reduce unemployment. It would not be difficult to incorporate that effect into a model.

    But you are missing the central point, which is that “reducing unemployment” is not the goal. Reducing unemployment is costly, and it might or might not be worth the cost. To address this problem usefully, you need a model that is capable of addressing the “is it worth the cost?” question; my toy model is meant to illustrate the bare bones of how such a model might look.

    My point is that you’ve got to ask the right question. I am not claiming that this toy model comes close to *answering* the question, but it does illustrate what the right question is. Krugman is asking the wrong question. (More specifically, Krugman is asking “how best can we alleviate the problem of unemployment?” without asking “given the costs, is the problem worth alleviating?”.)

  25. 25 25 Harold

    Been away for a few days, so a bit late in with this one. Still, maybe someone is watching. Your calculation takes away 1/3 of the tax as deadweight loss – this will surely make the total utility less in the tax case – there is simply less to go around.

    Krugman seems to be talking about the wonderful “multiplier” we have seen before. If we assume that each dollar invested in unemployment benefit generates 1/3 more, this will exactly cancel out the 1/3 deadweight loss.

    The best position in any scenario is for Jack to lend to Jill, and get paid back next year. This will procuce the beneficial “multiplier” effect, but not cost the deadweight loss. Trebles all round!

    However, if Jack cannot be persuaded to lend to Jill, then we have either
    1) no loan position, where there is no multiplier benefit, but also no deadweight loss.
    2) Enforced loan via taxation, which gives both multiplier benefit and deadweight cost.

    Krugman’s main point seems to be that tax spent in this way will generate more, so the model must contain this element.

  26. 26 26 Steve Landsburg


    Your calculation takes away 1/3 of the tax as deadweight loss – this will surely make the total utility less in the tax case – there is simply less to go around.

    Not true. Redistributing from the rich to the poor raises total utility; deadweight loss lowers it. To see which effect wins, you need to estimate some parameters.

    Krugman’s main point seems to be that tax spent in this way will generate more, so the model must contain this element.

    No, Krugman’s main point seems to be that in his model, a tax spent this way will decrease unemployment. My whole point is that this is the wrong goal. We don’t want to blindly decrease unemployment; we want to figure out whether decreasing unemployment is worth the cost.

  27. 27 27 jre

    That was a more measured and gracious response than my smartmouth comment deserved, so I won’t complain. And we do owe you the courtesy of indicating that we understand your argument (or think we understand it):

    Society’s welfare, as mapped to some goodness function, is not necessarily optimized when unemployment is minimized; hence, the policy that does the most good for the most people may not be the best for lowering unemployment. In fact, that policy may not lower unemployment at all.


    Now, that’s a fine argument to have, and much good may come of it, but it is still arguing past Krugman. He was not trying the case against someone like you, who challenges the whole notion that minimizing unemployment coincides with maximizing good; he was trying it against people like John Kyl and Sharron Angle, who appear to share that notion. Kyl and Angle simply profess to think that extending unemployment benefits will actually make unemployment worse. If only they would explain that they want to do the most good for everybody, but don’t necessarily want to lower unemployment in the process, then Krugman could write another column, you and he could argue directly at one another, and the voters could indicate by revealed preference to which school they belong.

  28. 28 28 Steve Landsburg

    JRE: Your italicized paraphrase is exactly right. Thanks for taking the trouble to put it so clearly.

    As for the rest, Krugman has characterized all opposition to extended benefits as coming from a coalition of “the heartless, the clueless and the confused”. I’m suggesting that maybe there’s also a little room in that coalition for thoughtful policy analysts. I’m suggesting also that Krugman could be a fruitful contributor to a far more thoughtful discussion than we’re getting from Sharron Angle, et. al., and that it’s too bad he’s opted out of that.

  29. 29 29 Harold

    Steve, I had started to work out some examples, but life got in the way, so thanks for the clarification. Nice to see that utility can be potentially increased even with less to go around. I hope to paly around with the figures a bit more. By the way, I spotted that one “error” (at least as it is written) seemed to be use of natural logs, but that should not affect the argument.

    His main point does seem to be that paying more unemployment benefit will increase employment, even though the incentive to work is reduced. Perhaps he could have chosen the more complicted objective of “is it worth it”, but first he has chosen to get across the simpler point that more unemployment benefit may increasae employment. Perhaps he will persue the “is it worth it” later? You say it is the wrong goal, but perhaps it is a very important one.

  30. 30 30 A.J. Lenze

    As an economics grad student, I LOVE to find professors’ mistakes. But when I did the analysis myself, I was disappointed to find out that Professor Landsburg’s math/arithmetic was fine.

    But all you have to do is change the amount of deadweight loss from 5 to 3 (so that the employed person is taxed 13 instead of 15), and the scenario leads to the opposite conclusion. So maybe Krugman did the analysis but just used different numbers? Obviously the given numbers are unrealistic since unemployment is set at 50%.

  31. 31 31 A.J. Lenze

    By the way, if anyone wants to see my verification of Professor Landsburg’s math, email me at ajlenze at clarkhome dot org, and I’ll send it to you. I used variables for all of the given numbers, then created a spreadsheet, so you can plug in different numbers and see how the results change.

  32. 32 32 Neil

    Actually, it is Steve’s coefficient of risk aversion which is most suspect. He assumes a coefficient of one (log utility), but most estimates exceed four (much more risk aversion.) The greater the degree of risk aversion, the greater the demand for insurance.

  33. 33 33 Steve Landsburg

    Neil: You are absolutely right about this of course. I used a risk aversion coefficient of 1 because anything else would have made the calculations far uglier, and because accuracy wasn’t the point. If you were doing this kind of thing carefully, there would be lots more work to do, and you’d probably want to report results for a range of risk aversion coefficients ranging roughly from 1 to 10.

  1. 1 Some Links
  2. 2 A Pencil in the Eye at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics
  3. 3 Weekend Roundup at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics
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