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  and noneconomists . 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 β1/β2))×UI ]
Take the total differential:
(6) Δn = (β2/(β2– α2)) × [(α1 – (α2 β1/β2))× ΔUI ]
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)/(β2-α2) < 0 and φ2 ≡ – (α2 β1)/(β2-α2) > 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]
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.