Livin’ in a Shapiro-Stiglitz World

I have been wondering why so many seem to be indifferent to the plight of the unemployed. Sometimes, the attitude is not so much indifference, but rather irritation that the poor are exempted from the burdens of society (see e.g., [0]).


Here is a plot of the unemployment rate and the alternative unemployment rate including marginally attached and part-time workers.


Figure 1: Unemployment rate (blue), and unemployment rate plus marginally attached and part-time for economic reasons rate (U6RATE, red), all seasonally adjusted, in percentage points. Source: BLS via FREDII.

I think some insights can be gleaned from an interesting model, from Shapiro and Stiglitz (1984) (Autor lecture notes, which I follow below).


Suppose that there are N identical, risk neutral workers, whose instantaneous utility is a function of wages (w) and effort (e), such that u(w, e) = w − e. e is either 0 or a constant, e > 0. The unemployed workers receive w ≥ 0 and e = 0. There is an exogenous separation rate per unit time (b). Finally, r is the intertemporal discount rate (the workers solve a dynamic problem).


The workers maximize the present discounted value of the utility, and either decide to work (and expend effort) or not work. There is an exogenous probability of being caught shirking, q. This parameter q is a function of the monitoring technology. If caught shirking, the worker is fired.


What one wants to do is to find the conditions under which a worker will be exactly indifferent between shirking and not shirking (taking the value of being unemployed as given). Once one finds the situation in which the worker is indifferent, one obtains the “No Shirking Condition” or NSC.


The NSC is such that the critical wage rate is higher when effort is more expensive, the utility of being unemployed is higher, the lower the probability of being caught shirking, the higher the interest rate, and the higher the exogenous quit rate; see equation 11.

Where the unemployment rate u = (N-L)/N.


What about firms and the demand for labor? This is standard. There are M identical firms, with production functions Qi = f (Li). Hence, the aggregate production is Q = F (L).


Each worker contributes one until of labor unless she shirks. Assume the marginal product of labor exceeds the disutility of effort, so F’(N) > e; consequently, full employment is efficient. The monitoring technology q is exogenous. Finally, the only way to punish shirkers is therefore to fire them.


The two schedules are shown in the following figure.

Figure 2 from Shapiro and Stiglitz (1984).

The aggregate NSC is upward sloping in w-L space because as employment rises, the pool of unemployed workers declines, reducing the expected value of the cost of shirking; hence a higher wage is required to prevent shirking, for a given unemployment benefit (w-bar) and a given disutility of effort. The aggregate NSC asymptotes to N because when L=N, then the pool of unemployed is zero, and the probability of finding a job if fired is infinity.

The aggregate labor demand curve is downward sloping for the usual reason — namely the declining marginal product of labor. Notice that equilibrium employment is below N, i.e., below full employment. Hence, there is involuntary unemployment, which exists to prevent shirking.


The unemployment is involuntary, and firms will not raise wages since it gets the needed workers it needs at that wage, and it won’t decrease wages as this induces shirking. Another way of thinking about this is a wage higher than a neoclassically determined wage makes the cost of shirking higher by raising the expected discounted value of being employed, and raises the expected costs of shirking (since a large pool of unemployed increases the probability of staying unemployed for a longer time). Hence the title of the paper,
“Equilibrium unemployment as a worker discipline device.” Alternatively, there is an externality in the economy; the private cost of an additional worker is w, while the social cost is e (w > e). From a social perspective, employment is too low.


Clearly, unemployment benefits have a pernicious effect from one perspective, as it shifts up the aggregate NSC curve, raising unemployment. Figure 3 shows what a raise in w-bar would do (also consistent with a decrease in q or an increase in b).

Figure 3 from Shapiro and Stiglitz (1984).

Reducing unemployment benefits has the happy outcome (at least from some people’s perspective) of lowering unemployment. In fact, an infinite tax on unemployment would shift down the NSC curve, and could then nearly eliminate unemployment (That’s a way of getting those shiftless workers working! Debtor’s prison would serve an analogous purpose, I think). So, in some sense I am unsurprised by the view by many commentators that unemployment insurance should be done away with, as a halfway step.


Shapiro and Stiglitz suggest taxing away the profits of the firms and providing a wage subsidy to drive w closer to e (i.e., internalizing the externality). Interestingly, this is not a pareto improving measure, since firms will be worse off.


The optimality conditions are derived assuming risk neutrality. Once risk aversion is assumed, the socially optimal unemployment benefit is greater than zero, but firms will still opt to pay zero benefits.


Long Term Unemployment, Again


One relevant question is whether the pool of long term unemployed has the same effect on disciplining workers as those short term unemployed. I don’t know the answer to this question, but we do know long term unemployment is at all time highs.

Figure 2: [CORRECTED 8/5 1:15pm] Unemployment rate (blue), and unemployment rate for workers unemployed 27 weeks and over (UNEMP27OV divided by CNP16OV CLF16OV, dark red), all seasonally adjusted, in percentage points. Source: BLS via FREDII.

[Update, 8/5 1:15pm Pacific: Thanks to Chad Stone for catching my error on the long term unemployed rate. I get by with the help of my friends.]


My intuition is that, with risk aversion (perhaps of first order), the possibility of dropping into a pool of workers from which it is particularly difficult to exit from into a job will disproportionately push down the NSC. In other words, a pool of long term unemployed might be particularly effective in driving down the equilibrium wage.


Given the likely contractionary impacts of the recently agreed to debt ceiling agreement [1], it seems unlikely we will have a rapid decrease in either of these series. This is unfortunate, since high levels of long term unemployment can eventually transform into heightened levels of structural unemployment, as discussed in this April conference on Long Term Unemployment in Industrial Countries. (Discussed in this post and this post).


By the way, the morning panel video presentations by Rob Valletta (SF Fed), Prakash Loungani (IMF), Phill Swagel (U. MD, formerly Treasury), and Ken Scheve (Yale), are now online.


The worries outlined in April seem ever more salient. For now, it seems that the political process has resulted in a situation where unemployment, both total and long term, will persist.

34 thoughts on “Livin’ in a Shapiro-Stiglitz World

  1. Robert

    Raise tax rates on small business owners, increase regulations on corporations, pander to unions, and extend the Democrat welfare state. This will make Menzie happy and I’m sure he can come up with some explanation for why it would lower unemployment.
    Speaking of unemployed, how many undergraduate classes are you teaching during the 2011-12 academic year Menzie? 0 or 1 or 2? Me thinks Scott Walker should go after some of you UW shirkers……

  2. Gus Satkowski

    Menzie Chinn: “Given the likely contractionary impacts of the recently agreed to debt ceiling agreement [1], it seems unlikely we will have a rapid decrease in either of these series.”

    …or without the debt ceiling agreement, for that matter. There was little imposed austerity in the debt ceiling agreement for this year and next, but there was no rapid decrease in unemployment the last 2 years either. So no legitimate inference should be made here.

    Still, getting the unemployed back to work should be a national priority.

  3. Ricardo

    I can tell you have never run a company. Your “No Shirking Condition” or NSC is a total joke not ready for prime time. I hire because I have a need for someone to do a job. If that person falls below your NSC point they will be fired but I will immediately hire a replacement because my reason for employment is not “shirk or no shirk.” Employment is fulfilling the requirements of the job. An employer is a fool to hire a person when there is no work, and is also a fool to not hire a worker when there is work. If the person wants the job then they will work.
    Your NSC is typical of an economist enamored with sudoku, but oblivious to actual commerce.

  4. Buzzcut

    Responding to Menzie’s above-the-fold rant, the unemployed (including the long term unemployed), and the poor, are not necessarily the same people. We have a class of people in this country that have NEVER been employed.
    It doesn’t change your model, but it just seems that you’re not talking about what you think you are talking about.
    I hesitate to link to my famous “analysis” of household income data, since 2slugs says that it makes every undergraduate statistics mistake in the book…
    …so let me just speculate and ask, IF household income is strongly correlated with hours worked, education achieved, and the number of people in the household who are employed, are the poor responsible for their plight? Should we expect them to work more, get more education, and get their lazy, no good boyfriends off the couch and into a job?
    And if the real issue is globalization, and that firms can substitute Chinese and Indian labor for US labor and save boatloads of money… what is the solution to that problem?

  5. jonathan

    A big part of the answer, Professor, is that white men are still employed at a much higher rate. Actually, white women have been doing better than white men, but the basic point is that unemployment is much, much higher for non-whites. That has a couple of effects on the mindset. One is essentially selfish: I’m working, must their fault they’re not. That’s easier to believe when the guy not working is different skinned than you – and particularly when you’ve been misled into believing it’s all illegals taking jobs. Another effect is relative: others are doing the same or worse and there’s a lot more of them who are doing worse. I’m not saying it’s racism but that difference makes it easier to draw lines.
    Consider one effect. We hear all the time that the way to grow is cut unions, cut restrictions, etc. Those arguments come from states which are poor. So for example, you have the odd circumstance that the South is a model and yet these states are net recipients of federal dollars – transferred from the North – because these states have a lot of poverty. How can it be that this is a model? These states have been growing for about 4 decades, since the New South started to be talking about in the early 1970’s. Back then, the USSR was powerful and China didn’t even allow private property and India was having famines while S. Korea had roughly the same income as N. Korea. Entire nations have lifted themselves out of poverty but the American South is still poor, still net receivers of money to prop up incomes and provide for basics. Why? Relative differences. White Southerners have been doing pretty well. Not all that well overall but certainly better than non-white Southerners. That seems to be the real test. Someone from outside would say Southern priorities have been wrong, that they should have invested in education and healthcare and technical infrastructure, but that ignores the actual truth that relatively speaking things have been going well for white Southerners.
    The problem is relative is relative. Here in MA, our personal income just rose again. It’s substantially more than in the South. We pay a significant portion in taxes to prop up those states. We are richer. We have more money. No one wants to emulate what we do. Wisconsin is emulating Alabama, where a significant percentage of the population is on food stamps – it went up to over 1/3 recently, partly because of the tornadoes but also because Alabama remains poor despite 40 years of those great policies Wisconsin wants to put in place.

  6. A.West

    It doesn’t requre emperical tools much beyond eyes and ears to conclude that there are major cultural factors that explain which ethnic/regional groups choose to avail themselves to the structurally unemployed/welfare/relief system and which do not.
    For some groups, becoming unemployed is traumatic and stressful. For other groups, it’s a cultural norm. A study of this would be so politically incorrect (concluding that some cultures lead to bad results in life) that the author would probably endure death threats and widespread ostracism.
    Government employed economists are probably the group least capable of comprehending/fixing this problem.

  7. Jeff

    This whole post seems a little schizophrenic to me. First you open with a quick Republican jab–ok, annoying but expected. Then you summarize the Shaprio-Stiglitz model–Ok, fine. Then you pose the question that maybe the long-term unemployed will actually increase employment for some–interesting question, but you kind of leave it hanging. Then you close with a comment that you think the debt ceiling deal will be contractionary. So help me connect the dots, what does the debt ceiling deal, or Republican comments about tax burdens have to do with the Shapiro-Stiglitz model?

  8. Buzzcut

    “Here in MA, our personal income just rose again. It’s substantially more than in the South. We pay a significant portion in taxes to prop up those states. We are richer. We have more money. No one wants to emulate what we do.”
    Because it can’t be emulated. It is built on the backs of an educated populace, one that values education.
    If you are, say, Indiana, Taxachussets can’t be a model, because we don’t have your educated population. Our population is not educated, and in fact does not value education. Without the educated population, you can’t move up the global value chain.
    And I am not talking race here, stricly whites vs. whites. Whites in Taxachussets value education, whites in Indiana do not. Thus, the policies to cut, cut, cut. We were this close to getting Right-to-work in Indiana this year, for example. Only a walkout by Democrat legislators stopped it.
    Mike Pence is running for governor, and is talking about income tax cuts. If we get RTW and eliminate our income tax, we will be emulating the Texas model (a good thing in my opinion, I am sure not a good thing in yours and Menzie’s)
    Also, keep in mind that while Taxachussets might have income growth, perhaps even strong income growth, that doesn’t make it a great place for the unskilled to live. It could just lead to increased cost of living, as well as a net outflow to cheaper areas in the South. I don’t know the specifics of Taxachussets, but that is certainly what is happening in New York State, and New York City in particular. And the outflow is strongest among African Americans, who ironically are moving back to the South, the place their ancestors left because of legalized discrimination.
    Finally, I really don’t take arguments like, “Taxachussets is taxed and the money is sent to the South” seriously. It is legislators like Barney Frank who are responsible for the tax and spending policies that tax money from high income states and send it to low income ones. You have no one to blame but yourselves.

  9. Steven Kopits

    Obama has not come out and said that government spending as a share of GDP is aimed for a particular level. (He is no Clinton.) As such, many believe that the administration would like as high a level of spending as the taxpayer is willing to bear.
    As a consequence, all spending is viewed with suspicion. It’s a ratchet up–feed the beast–no matter what the purpose. Right now, the average family–including those with jobs–are finding themselves pressed due to high oil and food costs, plus the impacts of reduced government spending in many cases (increased health care contributions, increased public transport costs, etc.). There is, as a consequence, little appetite for increased taxation for whatever cause, worthy or not.

  10. Steven Kopits

    I was watching Bill Maher last night, and it was truly astounding. He had on three guests, Traditional Democrat (Eliot Spitzer), Traditional Republican, and a Tea Party representative. He had three points of view on, two of them conservative by some measure. That’s truly remarkable.
    So where is the median voter boundary? Clearly, it’s not between the traditional Republicans and the Democrats. Rather, it would appear to be between the Republicans and the Tea Party. This is as I have maintained for some time.
    Since Obama has conceded the fiscally conservative left (ie, the legacy of Clinton), he has allowed the Tea Party to slip into the middle (structurally, that’s where the Tea Party should be). As a result, the Democrats are all but irrelevant. Some Senate Democrats may yet save themselves, but I suspect Obama is cooked.

  11. Anonymous

    I can tell Ricardo has never run a thought experiment. As far as I can tell, Ricardo has said nothing that contradicts Menzie’s “shirking” analysis, but thinks he has. Menzie was offering an analysis of worker behavior. Ricardo’s argument in response had entirely to do with managerial behavior. How does Ricardo try to make a complete mistake stick? By offering 5 denigrations of Menzie or Menzie’s thinking, without offering a single telling objection to that thinking.
    As to A. West’s comment, I am in whole-hearted agreement — with the beginning premise. There are parts of our society for which loss of employment is less of a surprise, and perhaps less likely to be a shock, than for others. The conclusion of the argument, however, doesn’t follow from the premise. Yes, some parts of our culture attach far greater shame to unemployment than do others. However, there is more downside to unemployment than just shame. If college-educated white guys feel a greater shock from job loss initially, they are also less likely to suffer the other costs of job loss than non-white, non-college-educated, non-guys. The fact that unemployment is normal (not, by the way, to be confused with a “norm”) makes it a bigger problem to lose a job, not a smaller one. In a part of society in which having a job is abnormal, the loss of opportunity upon loss of a job is greater than for those for whom having a job is the norm.

  12. Chris

    Of course as Summers pointed out recently, simply dropping the Bush tax cuts, plus some minor adjustments to entitlements could put the deficit controversy to rest. (I found it odd that Summers didn’t also mention cutting Pentagon funding since that would probably make entitlement cuts unnecessary). But how can we do that when the anti-tax fanatics rule the roost?

  13. Steve

    Solution: Open up the oil fields. Cut all exisiting mortgages by 10% and refinance them at 3.00%. This would create 3,000,000 jobs, reduce gasoline prices by 50% and increase consumer spending by 10%. Next, place a tariff on all consumer goods made offshore. Between the job growth, the increased consumption and the import tariffs, the deficit would be wiped out. Finally, let’s have a national telethon once every year on April 15th to paydown the national debt. Those folks that always say they would love to givew more of their income to the govt. could pledge and pay it every year.

  14. tj

    The model misses the impact on worker spending. An increase in long term unemployment not only serves as a worker discipline device, but also as a device to convert workers from borrowers to savers.
    The debt driven (gov’t, mortgage, margin) consumption based society cannot be restored through keynesian stimulus. The solution is to stimulate the supply side with payroll incentives to get firms hiring. Only then will workers be convinced their job is secure and engage in a sustainable level of spending.
    In terms of the model, if w = marginal product of labor (MPL) and we add a payroll subsidy,s, and w’ is defined as w*-s then w’

  15. David Penwell

    I think it was one of the late nite guys who said things are so bad even Kenya says Obama was born in America.

  16. Mark A. Sadowski

    I believe Chris is thinking of this:
    “Soon, relief will give way to alarm about the United States’ economic future. Among all the machinations ahead, two issues stand out: First, the single largest and easiest method of deficit reduction available is the non-extension of the Bush tax cuts for upper incomes. President Obama should make clear that he will not accept their extension on any terms. Clarity on that trillion-dollar point, along with very modest entitlement reform, will be sufficient to hit current targets for deficit reduction. Second, it is essential that the payroll tax cut be extended and that further measures, such as infrastructure maintenance and extension of unemployment insurance, be taken to spur demand. There is still time to confirm Churchill’s maxim that the United States always does the right thing after exhausting all the alternatives.”
    Of course, Summers did not go far enough. From long term debt perspective, he should have suggested that we simply do nothing:

  17. W.C. Varones

    Taxachussetts benefits from Fed easy money. They have a huge investment and banking industry in Boston.
    Take away Fed asset bubbles and see how long they can keep the lights on in Taxachussetts.

  18. MarkS

    Unemployment is high and the REAL economy is contracting because our banking system is over-leveraged… Want to reduce unemployment? Then let the bad credit and over-leveraged banks go belly up. When the dust settles, there will be plenty of credit and opportunities for business expansion.

  19. Bryce

    Anyone truly interested in the plight of the unemployed would be interested in honest relative prices. After all, it was the massive distortion of relative prices, primarily by the central banks of the world, that led to the over-production of housing, autos, & hundreds of other goods for which an honest interest rate is critical.
    It is a little late to be concerned about a hangover once you have it, but you should learn that drinking more booze is not the way to avoid another one.

  20. Charles

    Buzzcut says, “We have a class of people in this country that have NEVER been employed.”
    Yes. They’re called the idle rich, and they’ve been living off of trust funds and government handouts that they acquire by bribing elected officials. Many times, they do makework jobs created by their families to improve their self-esteem.
    These shiftless people should be forced off their government handouts and into real jobs.

  21. jonathan

    WC Varones, you post nonsense so I’m wasting my time but you are so out of touch with reality that I have to say something.
    First, MA is not highly taxed. Our sales tax burden, because of exemptions, is near the bottom of all states with sales taxes. Our overall tax burden without taking average income into account is average. Taking income into account, our tax burden is in the lower tier of states. We have more money so the average level of taxes we pay is less of a burden. Our houses are worth more – my assessment is over $1.3M – so our real estate taxes are somewhat higher on average. If we adjust for home values, which I don’t do, but just to make the point, then our tax burden is near the very bottom.
    As for employment, we do not have a large banking industry. We have no large banks headquartered here at all anymore. We have mutual funds and related retail fund businesses together with some private banks. We have some large insurers. These companies mostly sell to retail customers: Fidelity, MassMutual, Prudential, John Hancock, etc. are not big Wall Street firms but are retail sellers of insurance, managers of 401(k)’s, etc. Not one of them was bailed out.
    We were an industrial economy. We took the money from that and invested it in education – our schools are ranked at the top – and in services. We transitioned from an industrial economy to a service economy that has higher income – 2nd in the nation to Connecticut. We export a lot of services.
    Two parts of our economy relate to the government. One is healthcare: Boston is the 2nd largest medical cluster. This is a positive for us in terms of employment but a negative in terms of cost: it costs more for us for healthcare because so much of our local system is high-cost nationally and internationally known institutions. Another government connection is defense. Much of what remains of our industry is defense related and much of that is because military hardware requires software and we do a lot of that.
    Four decades ago, there was nothing but empty land in east Cambridge. It is now filled with tech companies. This land was cleared for development by the government and then made available for development. This is similar to what was done in Raleigh, NC.
    I have no idea what state you live in, other than one of irrationality, but my state is wealthy, has universal healthcare – with almost all children covered* – and high property values and good schools.
    *The people who aren’t covered are those who feel it’s cheaper to pay the penalty. We expected more would opt out. We’ve been surprised we aren’t making as much in penalties. We literally have universal coverage; 98% have insurance and 2% opt out. We expected closer to 95% with a 5% opt out. People who say we don’t cover people are liars: those people choose not to buy insurance.

  22. beezer

    Time for the stick because the carrot isn’t working. Tax cuts serially since what, 2001? Not working at all.
    Raise marginal tax rates. Use it or lose it. Take the money and hire people directly building infrastructure.
    Not pretty, but I’ll wager very effective.

  23. Young Economist

    Federal Reserve must use all monetary tools to ensure that employment moves back into full employment with price stability. I think Bernanke act too little to use monetary tool to meet dual mandate. He should use QE with unlimited supply and should set one year employment target as monetary objective. If I were him, I am not going to let 9% unemployment rate without any action. Currently, we see deflation risk is prominent with sharp drop on producer and consumer inflation expectation (ISM price paid drop nearly ten points in one month and could see deflation for next month). For QE#1, he brought unemployment rate from 10% to 9.8% and QE#2 brought unemployment rate to 9.1%. I think he acted too little. He must set concrete objective to use any QE to bring unemployment rate to less than 8% in one year rather than setting the size of QE that is difficult to calibrate because it can change expectation immediately for every part of economy. For producers, if they know unemployment rate below 8% next year, they will start to spend and expand businesses. They start to invest and borrow. For consumers, they start to consume because now they think they can be unemployed one day, so they choose to spend less than normal level. This action can use less asset size than the last QE from the change expectation of economic units once announcement. People do not understand that 600bnQE can affect economy. But if Fed change new target of QE to what people understand, they will action first before Fed action. I think expectation is more important than action.
    Furthermore, he should be aggressive to act because the longer high unemployment rate, the more difficult to reduce it. Social problems will be another key issue. I think three years to bring near full employment would be the challenging objectives for all policy makers. Bernanke should be flexible to expand asset purchases to ensure that banks will start to lend again. He should consider mortgage securities or any other assets.
    At end, now the inflation change quickly from inflation to deflation expectation, he should use this opportunity of no inflation threats to act aggressively to change producers and consumers behaviors to expect stronger growth and see target employment rather than size of QE that is difficult to be calibrated by ordinary people.

  24. Mark A. Sadowski

    I’m glad you responded because although I’ve been to MA as a tourist (one of it’s biggest industries) I’m clearly not an expert.
    Just looking at the latest BEA report on GSP I observed that over half of MA’s incredibly steller GSP growth (number 4 in the nation) in the past year was due to two sectors: *durable* manufacturing and the information sector. (i.e. it had nothing to do with FIRE.)

  25. Menzie Chinn

    Jeff: Actually, my point was that capital might be happy with a reserve army of unemployed, to drive down wages. A contractionary fiscal policy that raised the pool of unemployed would be just dandy in that context. Further, efforts to increase the cost to being unemployed would be a plus to capital. Sorry my explication was unclear to you.

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