Does Unemployment Insurance Necessarily Raise the Unemployment Rate and Decrease Employment?

Some analysts (e.g., most recently Professor Mulligan) have stressed the disincentive effects of unemployment insurance on the unemployment rate and the level of employment. I think it useful to consider the offsetting effects arising from various effects, and hence distinguishing between the two variables. In my view, the impact of UI is more complicated than it would seem at first glance, with UI potentially increasing employment while concurrently increasing the unemployment rate. In addition, according to newer research, even if UI extends unemployment duration, it still might be welfare-enhancing. In other words, some researchers appear to have had their worldview frozen in 1990.

A Decomposition, and a Little Structure

Let’s first consider the definition of the unemployment rate (and the corresponding log approximation):

(1) U ≡ (L-N)/L ≈ u ≡ l – n

Where L is the labor force, N is employment, and lowercase letters the log counterparts. One can then express the change in the unemployment rate into constituent parts:

(2) Δ u ≡ Δ l – Δ n

It is important to recall that an increase in unemployment insurance has two effects. First is the disincentive effects stressed by a number of economists [0] and noneconomists [1]. The second is the aggregate demand effect, as discussed by CBO/Elmendorf.

One can see how this breaks down in the following fashion. Suppose employment supply and employment demand (ns and nd, respectively) are given by:

(3) ns = α0 + α1 UI + α2 w

(4) nd = β0 + β1UI + β2w

Where UI is a measure of unemployment insurance payments, and w is the wage rate. α1 < 0, α2 > 0; β1 > 0; β2 < 0 . (Note the system can't be estimated since there's only one exogenous variable and two endogenous variables -- fortunately, this set-up is just for expositional purposes.) Hence, we are assuming some disincentive effects from UI, but stimulative effects from UI increasing consumption and hence demand for labor.

Solving for the reduced form solution for n, one finds:

(5) n = (β2/(β2– α2)) × [constant + (α1 – (α2 β12))×UI ]

Take the total differential:

(6) Δn = (β2/(β2– α2)) × [(α1 – (α2 β12))× ΔUI ]

Offsetting Effects

The coefficient in front of the square bracket can be signed as less than zero. However, the composite coefficient inside the square bracket cannot be signed; essentially it depends on whether the disincentive effect summarized by the coefficient α1 is sufficiently large in absolute value to overwhelm the second term.

In addition, UI probably keeps some people in the labor force, l, that would otherwise have become discouraged, and have not been counted. In this sense, UI increases the measured labor force, thereby pushing up the measured unemployment rate.

Expanding equation (2), substituting in the various expressions, one obtains:

(7) Δ u = Δ l – (φ1Δ UI + φ2ΔUI )

Where φ1 ≡ (α1β2)/(β22) < 0 and φ2 ≡ – (α2 β1)/(β22) > 0 .

While Δl > 0, the net effect on Δn is ambiguous.

Partial Equilibrium, and Empirical Estimates

What is interesting is that Professor Mulligan emphasizes the effect coming through φ1, dismissing φ2 effects (I grant that Professor Mulligan is consistent in his views, but this view flies in the face of CBO’s assessment of the impact of aid to unemployed, as shown here, and discussed in this post). He cites Bruce Meyer’s 1990 Econometrica paper, “Unemployment Insurance and Unemployment Spells”. This is an extremely well cited paper, and deservedly so. It was a state of the art micro based econometric modeling of the impact of unemployment insurance a couple decades ago.

It is important to recall that this is a partial equilibrium analysis. There is no feedback effect from UI payments to aggregate demand and hence demand for labor. Once one realizes this point, one sees that the impact on overall employment is ambiguous (as is, technically, the effect on the unemployment rate, although this is more easily signed as having a positive impact).

In addition, even if unemployment duration rises, this might be welfare enhancing. The approach favored by Professor Mulligan assumes that agents are not liquidity constrained. However, I believe we know that there are a good number of liquidity constrained agents in the economy. Professor Raj Chetty at Harvard has shown that for the liquidity constrained individuals, UI can be overall welfare enhancing as it allows liquidity constrained households to smooth consumption (he calls this the liquidity effect, to differentiate it from the moral hazard effect that some have obsessed upon). A nontechnical summary is here. The working paper version of Chetty’s Journal of Political Economy paper is here.

By the way, Professor Mulligan castigates the CBO for not incorporating the disincentive effects of UI in its analysis of the ARRA. However, as CBO notes, this effect might be quite small in current circumstances:

The availability and size of UI benefits may, however,
somewhat discourage recipients from searching for work
and from accepting less desirable jobs. Extending the
duration of benefits or increasing their size means that at
least some recipients may remain unemployed longer
than they would have without that aid.31 The effect is
probably most pronounced when jobless rates are relatively
low; when joblessness is high and work is especially
hard to find, extensions of UI benefits appear to lengthen
spells of unemployment by a smaller amount.

Footnote 31 reads:

A rough rule of thumb is that making benefits available to all regular
UI recipients for an additional 13 weeks increases their average
duration of unemployment by about two weeks and that
increasing UI benefit levels by 10 percent increases the average
duration of unemployment by about one week. Those estimates
are based on surveys of the relevant literature, reported in Stephen
A. Woodbury and Murray A. Rubin, “The Duration of Benefits,”
and Paul T. Decker, “Work Incentives and Disincentives,” in
Christopher J. O’Leary and Stephen A. Wandner, eds., Unemployment
Insurance in the United States: Analysis of Policy Issues
(Kalamazoo, Mich.: W.E. Upjohn Institute for Employment
Research, 1997), pp. 211-320.

Professor Mulligan cites Jurajda and Tannery (2003) as evidence that the sensitivity to UI is not dependent upon the degree of slack in the labor market. I’m not enough of an expert on the data and methodology to critique the analysis. However, the point estimates on the sensitivity of duration to an extension are even smaller in Jurajda and Tannery than what the CBO cited in its analysis. Hence, while I agree there are disincentive effects on employment from UI extensions, I think they are pretty small in these circumstances, with arguably the largest output gap in the past 50 odd years.

Parsing Estimates of the Impact of Extended UI on Current Unemployment Rates

Finally, I have tried to figure out what is being done in the various estimates being cited about the impact on current unemployment rates, including those cited by Professor Mulligan in this post. For instance, JP Morgan mentions both the φ1 and φ2, but only includes a numerical figure for φ1. Robert Shimer’s estimate is 1.5 percentage points, but there is no explanation of how it was obtained. It too would appear to incorporate only the φ1 effect. A side point: Professor Mulligan mentioned the FOMC minutes as supportive of his incentives view. But if one actually reads the minutes, one finds that the emphasis is on how UI keeps people in the measured labor force, inducing an extra percentage point of unemployment. Hence, the cited impact is not on φ1, but rather on the induced increase in l. To quote from the FOMC minutes:

The several extensions of emergency unemployment insurance benefits appeared to have raised the measured unemployment rate, relative to levels recorded in past downturns, by encouraging some who have lost their jobs to remain in the labor force. [emphasis added — MDC]

Summing Up

Bottom line: Decompositions can be useful in highlighting where ceteris paribus is being invoked.

Bottom line II: Read what’s linked to, to see if the document truly validates the point asserted.

By the way, none of the foregoing analysis should be construed as an argument for keeping the unemployment insurance system as it is. See e.g., CBPP, Urban Institute/Rosen, Brookings/Burtless.

21 thoughts on “Does Unemployment Insurance Necessarily Raise the Unemployment Rate and Decrease Employment?

  1. Steven Kopits

    I think you need to consider the comparative relevance of benefits to understand their behavioral impact.
    For example, I had lunch with a friend yesterday who has been unemployed for two years. He used to structure SIV’s for a large insurance company. For him, the $405 weekly max UI payment in New York is not motivational, as his normal wage would probably approach twenty times as much. Rather, he is motivated primarily by his savings and his credit line in taking work materially outside his expertise and sense of social standing (eg, he would probably perceive flipping burgers at McDonalds to be inconsistent with his social standing).
    On the other hand, for low-skilled labor, UI payments could be quite motivational. If we assume that McDonald’s would pay $8/hour, then a 40 hour week is worth $320, possibly not far off unemployment benefits for that person. It might make sense, all things considered, for a low wage earner to choose unemployment over employment.
    Context matters.

  2. Mark A. Sadowski

    Menzie wrote:
    “Bottom line II: Read what’s linked to, to see if the document truly validates the point asserted.”
    I can’t tell you how often I’ve seen research papers mentioned by articles in Real Clear Markets that upon reading turned out not to support the original article’s claims at all. Very good advice.
    I’m also curious (off the top of my head) if similar analysis has been performed in Europe. GDP will be, according to IMF forecasts, down 9% and 14% below trend in Germany and Spain respectively this year (my calculations) but unemployment has dropped by over a point in Germany (work sharing has played a role) and more than doubled to nearly 20% in Spain (where short term contracts are common and unemployment insurance is reportedly generous). The divergence in unemployment rate performance in the EU is rather striking.

  3. AnnS

    “On the other hand, for low-skilled labor, UI payments could be quite motivational. If we assume that McDonald’s would pay $8/hour, then a 40 hour week is worth $320, possibly not far off unemployment benefits for that person. It might make sense, all things considered, for a low wage earner to choose unemployment over employment.
    Context matters.
    You are right about context – and your context as to the UE benefit of an $8 an hour wroker is WRONG.
    $300-320 is the ‘average’ UNE. It is NOT THE MINIMUM. Nearly every states caps UNE at a % of the state median wage. UNE is calculated as a % of the higest earnings of a quarter in the past year or so.
    FOr an $8 an hour worker, UNE is NOT $320. It is about $175. And that is 46% cut in an already meager income.

  4. Will

    Prof. Chinn, Mulligan is making the plausible assumption that beta_1 is very small relative to a_1. Do you have reason to think this is a bad assumption? I mean do you have estimates that suggest otherwise?
    Not to mention that you could spend the money on other AD boosting programs which don’t have the bad incentive effects.

  5. Will

    The problem with Chetty’s paper is that getting a job (even if its not a perfect match) relaxes the liquidity constraint as much as UI would. But he implicitly assumes there’s no job search while employed (his model has perpetual jobs). As an aside, as Chetty mentions there’s better ways than UI to relax the liquidity constraint.

  6. Menzie Chinn

    Will: On the β1 issue, well, yes I do have information on that count, and have mentioned it numerous times on Econbrowser, but for your benefit, let me provide the links to the relevant posts which in turn contain the relevant hyperlinks: [a] [b] [c]. See also various posts under the multipliers category.

    I do think there are less distortionary AD-boosting programs, although I’m not sure the multipliers are larger (once again, I refer you to the various posts under the “multiplier category”). And while I am sympathetic to the concerns about distortions, on a less technical note, I am reminded of the question: “Are there no poorhouses?”.

  7. Menzie Chinn

    Will: Regarding your second comment on the assumptions in the model, point well taken. But, for me, the basic intuition that once one relaxes the no-liquidity constraint assumption, the benefit-cost ratio changes remain. And I’ve been impressed with liquidity constraints ever since graduate school (hey, you’ve got ’em implicitly in every policy DSGE that tries to fit the real world data…).

  8. Will

    Well, I meant do you have the estimates in a form that allow us to compare a_1 and beta_1 (e.g. employment elasticities)? My intuition is that when the multipliers you cite are put in this form, they’ll still be very small relative to a_1.
    I guess here’s one way to estimate b_1 using multipliers: UI extensions from last year’s stimulus were about $30-40B for the last calendar year or so (if I read the CBO’s analysis correctly). Let’s take a generous multiplier of 2. This means GDP increased by about 0.5% due to UI extensions. From Okun’s law, then, unemployment is about 1/4% lower because of the AD effects of UI extensions.
    This generous estimate (high multiplier and high estimate of benefits spent) is much smaller than the estimates Mulligan is citing for disincentive effects. Where did I go wrong?

  9. Menzie Chinn

    Will: Oh, I see. Apologies for misunderstanding. Well, I think your math is fine. Didn’t see the exact amount of the UI anywhere (CEA reports about $60 billion total in aid to impacted individuals from June-December, so I’d say $30 billion over the past calender year might be low). But really, as Mulligan concedes here, he doesn’t have an estimate of α1 — so I don’t know really what the actual net outcome is. As he says, the impact on employment could be 8 million, 2 million, or something else. I do agree that measured unemployment probably rises, exactly because of the Δl term, but for me, the impact on Δ n remains ambiguous.

  10. Anonymous

    annS, “FOr an $8 an hour worker, UNE is NOT $320. It is about $175. And that is 46% cut in an already meager income.”
    Remove this and all a family has to live on is savings, family and welfare. There maybe problems in the current system but what is to replace it?

  11. Ted K

    Does anyone know what Senator Tom Coburn of Oklahoma thinks of this academic research and data presented by Professor Chinn???
    I’ll try to put this in an equation. Here X denotes total money (contributions) for Coburn’s Campaign committee. L defines money contributed by middle to low income labor. ∆ denotes how much Coburn cares about the unemployed.
    L=$0.00 (in reality this number is larger, but we keep it zero for simplicity’s sake, but this number is so low in actuality it doesn’t make a statistical difference in the results)
    X-L=X so this proves the theorem Coburn doesn’t care about unemployed labor therefore:
    All those who didn’t appreciate this deep and complex research and it’s scientific methods are free to offer some Socratic Method below.

  12. Kaleberg

    I don’t see where you take into account one of the major drivers. Unemployment insurance enables employment by seasonal businesses like logging, construction, tourism, agriculture, retail and dozens of others. If a seasonal business has to carry employees through the off-season it would have much higher costs, so there would be far fewer such businesses reducing the total number of employment hours available.
    In Washington State, unemployment insurance is still a big employment driver and recognized as valuable by many businesses which is why there is so much fighting over rates. The state would like to make each sector pay its way, but such a capitalist approach doesn’t work with businesses which by their nature require a cross subsidy.

  13. sgt_doom

    The problem with fundamentally idiotic and moronic drivel such as this is that it conveniently ignores the negative jobs output in a neoliberal/neocon Ponzi economy which has offshored almost as many jobs as can possibly be offshored.
    It is those debt-financed billionaires who are deserving of unemployment – and removal of their ill-gotten gains.

  14. MikeR

    In the trade off between hours of leisure and hours of labor, it seems that paying for leisure would decrease the amount of labor supplied.
    The average weeks unemployed is the longest it has ever been and I suspect we have never had such generous extensions to UI. On top of that, the real minimum wage has never been this high.
    Employment growth has never been this slow. If the two fundamental inputs to the ecomomy are labor and captial, how can our economy achieve the growth we expect when labor growth is the slowest on record?

  15. Menzie Chinn

    MikeR: I agree that there is a disincentive effect when UI is provided; in fact I explicitly mention these effects. The question is the magnitude, and whether the disincentive effect is overwhelmed by the increase in demand for labor relative to the counterfactual.

    By the way, could the slow growth of employment be possibly due to the unprecedented duration and depth of the recession (in the post-War era)?

    Finally, yes, the minimum wage has never been so high in nominal terms — like movie theater tickets and so forth. If you examine the minimum wage series and deflate by the CPI-All, you would see that your statement in real terms is not true (unless you conveniently cut off the sample at about 1983…).

  16. mulp

    Am I correct in understanding that the primary issue is the size of L given UI benefits, not the actual number of people employed, N?
    I’m convinced based on the ignorance of the natural world demonstrated by every economist (other than Brad DeLong who clearly understands physics) that my love of physics and the other natural sciences disables me from understanding economic “theory”.
    In the natural world, we must conserve matter and energy, but in economics, “theory” assumes matter can appear from nothing and likewise vanish without consequence. Even using the “short run” and “long run” idea in physics requires conserving matter within limits.
    L is a subset of P, the population, so if we look to balance the equation, using the obvious mindset of economists who argue against UI, we must look at them as P=L+leeches, and substituting, we have P=N+leechesonUI+leeches.
    Or do economists think that ending UI would more rapidly reduce L, with L=P, and the reduction in L by x would result in P, the number of people, being reduced by x?
    What I find totally inconsistent is the argument that wages should respond to the market, but total opposition to debt contracts responding dynamically to the market. Why don’t economists call for all debt contracts to vary the principle based on market value, so that the mortgage payment responds dynamically to unemployment which drives down real estate prices? Of course, that is just one of the expenses faced by those who make up L, rent, food, auto payments and fuel, children, and many others are burdens each part of L must meet or else bad things happen.
    I would note that Federal taxes do respond more dynamically than anything else; if your wages are halved, taxes are almost always reduced by more than half.
    The exception is if the reduced income is from the tax preferred pump and dump activity classified as short term capital gains. Someone who made their living doing pump and dump, aka speculating aka “investing”, forced into working as bus boy sees his marginal tax rate increase. The tax laws promote unproductive economic activity which discouraging real productive work. Again, I note that those who seem to oppose UI are also in favor of promoting pump and dump “capital gains” unproductive income while punishing relatively speaking productive work, so criticizing UI is just more punishing of those who productively work.
    And those who criticize UI also seem to be those who claim taxes discourage hiring workers, thus calling for lower taxes. Well, we have the lowest Federal tax burden in six decades, less than 15% of GDP, down at least 25% from 2000 when employment was at record highs (remember think rates) and unemployment at near record lows when the tax burden was over 20%. According to the cut tax economist crowd, this means 5% of GDP “is being spend and invested more wisely than government.” Apparently, the free market is saying the US economy needs to creatively self-destruct, with UI being an impediment to the much wiser creation of homelessness, abandoned real estate, empty factories and shopping malls.
    In the economist ideal world, the wise investment from not having UI is a rapid reduction of L, a rapid rise in bankruptcy, abandoned properties, increased numbers of swatters who become self sufficient by mining those abandoned properties for valuable metals, etc, and engaging themselves in more productive ways like dealing drugs as self sufficient business people. Making the cities and towns the liberal bleeding hearts call crime ridden of Mexico and Somalia represent the perfect free market solution to an era of pump and dump tax preference asset bubbles.

  17. MikeR

    Thanks for the reply Menzie. I actualyl did not run the numbers on inflation adjusted minimum wage myself, I got it from a chart that was in the WSJ.
    I feel the slow employment growth that I mention is more of a demographic result from the aging baby boomers, stability in the pecentage of women in the workforce and slowing immigration. Those three factors, which lead to very strong employment growth over the past 50 years are no longer providing growth…

  18. Jim S

    My problem with the idea of UI as a disincentive is the fact that so many Americans are only a paycheck or two away from financial meltdown and UI is always only a fraction of what they are making. So if you’re barely getting by and UI is half of what your job paid where is the disincentive given the low savings rate of most Americans?

  19. M

    You missed the point. You are taking wealth away from the more productive to the less productive, and so you are reducing future wealth by slowing capital accumulation in key industries.

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