# The Long-Term Unemployed

I think a lot about long-term unemployment as a social and economic ill -- and perhaps for that reason, I find it hard to judge the attention and effort paid to it through public policy as anything but shamefully inadequate.

As of this July, 74.2 percent of the unemployed no longer have unemployment insurance; it's likely this is the highest fraction since the very establishment of federal unemployment insurance during the Great Depression. The fraction of the unemployed who do not have insurance continues to rise rapidly.

5.2 million Americans have been out of work for half a year or more. That is 40.7 percent of all unemployed persons -- and as a fraction of the labor force, the long-term unemployment rate is 3.3 percent. Before the recession, it was under 1 percent. Even as the economy teeters at something we'd like to call a returning normal, this will produce a significant increase in structural unemployment and natural rate of unemployment.

Many states max out benefits at 99 weeks, and I worry that extending benefits further has severe effects on incentives over the long term. Strong evidence for this comes from a study which found that the duration of unemployment benefits and their generosity relative to private wages are the best predictors of high unemployment rates in developed nations. It is also well known that recipients, by and large, do not find work until just after their benefits expire -- see this study for one example.

And yet, I support unemployment benefits for the simple reason that they are humane -- aggregate monetary stimulus is essential and primary, but unemployment benefits are an automatic (i.e. rule-based) fiscal stabilizer which block the hardest blows recessions deal to individual workers.

I want to put forward, then, a modest proposal which would seek to align the incentives of the insured unemployed with aggregate utility. Whenever I propose a policy, I try to find "free lunches" through inefficiencies, pushing out the possibilities frontier of public policy rather than participating in normative disagreements about which side of trade-offs governments should take.

What I think we should do is, in essence, provide a lump-sum bonus to the insured unemployed when they accept a job offer. As a brilliant article in *The New York Times* testifies, the unemployed are often unwilling to "trade down" to regain employment when they are on benefits. That may make sense for them as individuals under the current incentives structure, but it's bad policy in aggregate for federal and state governments, and for the economy.

Since the long-term unemployed are highly liquidity-constrained and have marginal access to lending, they will have effectively high discount rates on future cash flows. The lump-sum payment the government pays, then, should approximately equal the net present value to them of the remainder of their unemployment benefits, adjusted for the likelihood they would otherwise find a job in any particular week. This would mean that the "buyout offer," so to speak, would necessarily decrease as the unemployed approach the end of their benefits. That would provide loss-averse individuals an incentive to quickly find employment. While the unemployed "break even," this is an excellent deal for governments, whose discount rate is far lower than the unemployed -- their obligations would drop substantially in net present value terms.

We can look at payday lending to estimate the discount rates of the insured unemployed and the magnitude of the lump-sum bonus under consideration. It is not uncommon for the effective interest rate on a 12-month $100 loan to be roughly 100 percent. That implies an internal rate of return of 92 percent per annum for the payday lender. It follows that the insured unemployed have a discount rate on the order of 90 percent -- otherwise, the net present value of the loan would be negative to payday borrowers.

Let's assume that I live in the average U.S. state, which provides $300 in weekly benefits and that, given the recession, the benefits last 99 weeks. As long as I estimate a discount rate in the ballpark of the prior thought experiment, my calculations show that a lump-sum payment of approximately $15000 on Week 0 would replace the entire net present value of 99 weeks of benefits. Assuming a per-annum discount rate of 4 percent for government, the gain in net present value for government is roughly $13000.

These calculations do not assume that workers have any expectation they will find work over the 99 weeks. Therefore, $15000 represents the upper bound on lump-sum payments.

Now I want to adjust that number for the expectation these individuals will find work over 99 weeks. Because I don't know of a granular data source for this sort of thing, this is an exercise in back-of-the-envelope estimation.

The inverse of the median duration of unemployment is the percentage chance that the median unemployed individual will find work in any given week. From this, I can estimate the cumulative probability that an individual does not find work over 99 weeks. Since not finding work in Week 1 implies an increased probability of not finding work in Week 2, I need to adjust downward the percentage chance of finding work in any given week. A generous assumption, in my opinion, is to assume that the average chance of finding work in any week over 99 weeks is reduced to one third of the chance of the median unemployed person in any week. From those assumptions, I found that during the recession, the cumulative probability an unemployed person found work over 99 weeks of benefits was 80 percent. I would need a week-by-week percent chance of finding work to adjust the expected value of benefits, but since such numbers do not exist, we will assume that adjusting the total net present value downward will roughly approximate the sum of adjusting downward every particular week. (This is akin to treating 99 weeks as a single Riemann sum.)

If we know that 80 percent of the insured unemployed would expect to otherwise find a job within 99 weeks -- and thus stop drawing benefits sometime during that interval -- a lower bound on the lump-sum payment would be $3000.

It's the lower bound because workers would be giving up the chance to find (presumably) a higher-paying job during the interim, and thus the net present value of the expected difference in pay over time. Since I have no hope of guessing what that would be for the average unemployed American, I find it sufficiently convincing to average the upper and lower bounds. This implies that a reasonable first-pass estimate of the lump-sum payment conditional on taking a job in Week 0 would be $8000, scaled down week by week thereafter. (Ideally, the unemployment office would customize the payout according to the difference in old-job and new-job salaries. On average, that cut is roughly 20 percent of annual salary.)

Most importantly, these numbers pass my "gut check." That is, it's intuitive for me to suppose that the average person, after a year of unemployment, would be indifferent between a lump sum of $4000 to accept a low-pay, low-status job and waiting 99 weeks in hope of finding something better.

I'm curious to hear what others think of this proposal.