Optimal Unemployment Benefit Scheme

This section turns to the evaluation of the optimal unemployment benefit scheme. I assume that the government implements a change in policy, and offers a different UI schedule than the baseline. The government takes private behavior as given and therefore it does not exert direct control over the risk sharing arrangement between workers and firms. To characterize the optimal policy I focus on the steady steady outcome. Therefore the evaluation of the optimal policy is made, assuming that the economy has settled to

9Note that this corresponds to the current policy in most states in the US, assuming that benefits are not extended as usual in periods of ”high unemployment”. Since my target rate of unemployment is 6.2% the baseline benefit scheme is realistic.

the new steady state distribution.

Moreover, I consider a restricted class of UI schemes here, and in particular schemes that give out different levels of unemployment benefits over two time intervals: the gov-ernment pays out b≤m for any duration smaller that m, and it pays b>m for durations exceeding m. One example of such a policy, is the current UI benefit schedule in the US that pays a constant replacement ratio for up to two quarters, and no benefits subse-quently (hence b≤1 = b and b>1 = 0). I maximize welfare over b≤m and b>m considering cases where where m is either 0 or 1 that is benefits are given for either one or two quarters. ¹⁰ I restrict the analysis along these lines for two reasons: First, because it is computationally very difficult to consider policies that optimize benefits over many dif-ferent time intervals. Second, because in the model most unemployment spells end after two quarters. Therefore extending to consider a more complex benefit scheme would not affect my conclusions.

In table1I report the results from various UI schemes. ”Zero benefits” sets the levels of bothb≤m andb>m equal to zero. ”Optimal Timing” shows the outcome from maximiz-ing welfare over b≤m and b>m. The welfare effects reported in the second column of the table, are shown relative to the baseline scheme and are stated in terms of the compensat-ing variation (hereafter CV): Practically this measures how much more consumption (in percentage terms) individuals require in the original steady state to be as well off as under the new UI scheme. ¹¹ For each of the policies considered columns three and four report percentage changes in the unemployment rate and the required tax revenue to balance the budget.

10As previously them denotes the number of periods in unemployment prior to the current quarter.

Therefore,m= 0 corresponds to a newly unemployed individual.

11To evaluate the welfare effects of different policies I assume that the social planner assigns equal weight to all agents in the economy. The welfare criterion is of the form:

Θ =

I convert the welfare numbers in terms of percentage consumption using the following calculation:

Θ1= Θ0+ 1

1−βlog(1 +ǫ)

Where Θ0is the expected utility in the baseline regime and Θ1is the analogous object under a different policy regime. The fraction ǫis therefore the standard measure of compensated variation.

Within the class of UI policies considered, the optimal scheme is one that pays for the first quarter of unemployment, benefits equal to 1.165 and subsequently (for all durations greater than a quarter) it pays 0.40. According to the results in the table under this policy there is a welfare gain of 0.75% in terms of CV. Other policies considered may also improve considerably on the baseline UI scheme, however, the welfare gains are smaller.

For instance an ”Optimal Timing” which sets m= 1 (i.e. chooses benefits optimally for two quarters and separately for longer durations) gives a gain of 0.50%. Moreover, setting optimal benefits for the firstmquarters, but subsequently restricting benefits to zero (last two rows of the table) also does better than the baseline and delivers similar gains for m = 0,1.

4.2.1 Understanding the result

These patterns can be explained using the results of previous sections. An important implication of the analysis, was that the scope of insurance is maximized when the firms participation constraint binds. It was in that region that assets were beyond the desired stationary point (the buffer stock level) and consumption declined over time. If the worker lost her job, the drop in consumption relative to employment was less, because savings were effective in mitigating the risk of unemployment. Moreover, these properties were common with the model of heterogeneous agents; in fact the optimal allocation was to offer a wage equal to y (flat contract) in that region.

Given these remarks we anticipate that the government would have an implicit in-centive to maximize the frequency with which the firms’ participation constraints bind over the stationary distribution. Figure 4shows on the left panel the wage profile under the optimal UI scheme, and on the right, the stationary wealth distribution of employed individuals. Notice that the optimal contract is effectively a flat wage contract: the entire distribution falls in the region where a wage equal to y is offered to the worker in all periods. Therefore, under the optimal policy the firms participation constraint is tight independent of the initial wealth endowment of the worker.

Frontloading UI payments accomplishes to tighten the firm’s constraint for two rea-sons: First, benefits that exceedy in the first period of unemployment but fall rapidly for

the remaining periods of a spell, induce individuals to save. This effectively means that a considerable fraction of workers who manage to find jobs after one quarter, will start their matches with wealth above the stationary point. This effect operates through the ergodic distribution.

To further explain this point, assume that unemployment benefits were equal to zero at all horizons. In the simulations such as scheme implies that over the entire ergodic distribution the optimal contract is one that offers a frontloaded wage and a constant consumption path over time (i.e. the constraint is slack everywhere). Workers accumulate assets when the match formulates, through the wage schedule properties, but when the unemployment shock arrives they run them down. Over the stationary distribution there is no one with wealth at or above the buffer stock level. The opposite holds under the suggested UI scheme. Individuals save in unemployment and a large fraction find new jobs with high wealth.

The second reason for why the frontloaded UI scheme is most effective in tightening the firms constraint is that in the model, wealth is the vehicle via which firms can contract on the worker’s value in unemployment, and control their consumption in that state.

However, since the agent is effectively beyond the reach of the firm when she becomes unemployed, it is only consumption in the first period that may be influenced, or the payoff U(a,0). Frontloading benefits reduces the value of wealth in U(a,0) but not in U(a,1), U(a,2) and so on. Therefore the optimal investment in wealth is less under this policy.

The combined effect of these channels, is important to get the results in figure4. To illustrate this point in figure 5 I show the wage profile and the stationary distribution in the case where UI payments are received only in the first quarter of unemployment and subsequently they are set to zero (second to last column in table 1). Notice that in this case in the stationary distribution there is still a considerable mass of individuals whose wealth level is below the buffer stock level. This is so because individuals reduce their savings very rapidly, if their spell lasts for longer than one quarter. The welfare gains implied are smaller than under the optimal policy, as unemployment benefits extended to longer durations are particularly useful in mitigating the risk from prolonged spells.

Finally, note that policies setting benefits optimally for the first two quarters (i.e.

m = 1 in the table) do not induce individuals to save sufficiently in quarter one. In effect these schemes produce very few individuals with sufficient wealth to reach the point where the firm’s participation constraint is binding. This also reduces the welfare gains from UI.