# Econstudentlog

## Work Blogging 3

I’ve gotten behind on this stuff, but I hope to post a few posts this week – we’ll see.

In my last post on this subject I said that the next paper I’d be covering was Pissarides Short-Run Equilibrium Dynamics of Unemployment, Vacancies, and Real Wages, but it turns out that I got the course reading order mixed up and that the Pissarides paper actually came before the Andersen & Svarer paper I covered in my second post. Basically the Pissarides paper was used to introduce us to the DMP-model [Diamond Mortensen Pissarides-] framework, whereas Andersen and Svarer was meant to tell us how that model setup is applied in research today. It would have been very hard to read and understand the A&S paper without implicitly also ending up having a pretty good idea what is going on in Pissarides, which means that there isn’t much point in covering this paper here. Though there are a few technical differences between the models applied it’s the same model framework the papers make use of. Pissarides is also a rather short paper, so there isn’t that much new stuff to talk about which I’ve not already touched upon to some extent when covering A&S.

Maybe a few general aspects should however be touched upon here briefly before I move on, if only so that I can remember this stuff later. One thing to note is the accumulation of rents which are associated with the labour market friction in these models; the free entry assumption means that the expected value from creating a vacancy by a firm is driven to zero in equilibrium, but the value of a filled job is greater than zero (for reasonable parameter values). Another thing to note is that whereas there are search costs introduced into the labour markets in these models (realism: +1 compared to the alternatives), they still make use of some key simplifying assumptions (realism: -(?)) – assumptions which may be driving some of the results of the models. Some normal structural assumptions that are used in these models are: i. additively separable utility functions + ii. Cobb–Douglas matching functions – we need these assumptions to solve the models, but they might be problematic. Perhaps it’s also worth noting here that we tend to think of the labour market as uncoordinated in these models; basically firms and jobs are pretty much the same thing. So free entry of firms means that a new job vacancy will get opened if the expected value of that vacancy is positive, but we don’t care if that vacancy is made by a firm with 500 employees or one with two employees. In the real world, stuff like labour market centralization, unionization and similar stuff impact search costs/matching dynamics of both workers and firms.

So anyway, I’ve decided below to cover Boone, Fredriksson, Holmlund and Ours’ Optimal unemployment insurance with monitoring and sanctions. That paper also applies a DMP model framework. It briefly covers/contrasts its results with Becker’s 1968 paper on crime, because it’s sort of the starting point for this literature. The very short version is that Becker argues in his paper that by raising the sanction in a model with risk-neutral agents, monitoring costs can be reduced without affecting the incentives for crime. So when monitoring is costly and punishment is free (which it arguably is in the case of fines, which impose no cost as such to society as they’re just a transfer payment from one group to another), the optimal level of monitoring will go toward zero and the optimal punishment will increase rapidly. However the (Boone) paper points out that when risk aversion is introduced into the model, Becker’s result no longer holds, and if the monitoring technology is plagued by type II errors so that some complying individuals are sanctioned, the welfare losses from these errors may be severe. They conclude that “a system with monitoring and sanctions represents a welfare improvement relative to other alternatives for reasonable estimates of the monitoring costs. In particular, the monitoring and sanction system leads to higher welfare than a system with time limits.”

As in A&S, there are three groups of interest; employed, unemployed and activated/sanctioned. A key difference between Boone et al. and A&S is that in the latter activation was a random sanction, whereas in the former the sanction rate is now dependent on the search intensity of an individual (the variable s in the paper is the search intensity). In order to make the sanction rate dependent on search intensity, it is of course necessary to add (costly) monitoring to the model. Like in A&S, the utility level of sanctioned/activated individuals (receiving a benefit UA = Z = zw) is lower than the utility level of an unemployed worker (receiving a benefit UI = B = bw). However the precise way this utility differential comes about is another of the key differences between their setup and the A&S setup; in this paper, sanctions hits income directly, not leisure; when people are sanctioned, rather than obtaining a lower utility level through an implicit tax on leisure, they simply suffer a direct negative income shock – i.e. Z < B.

They mention early on (p.402) that they consider a system with four policy variables of interest: The level of unemployment benefits [B] and unemployment assistance [Z] (the difference between the two is the sanction), the rate of monitoring of people receiving UI benefits [μ] and the precision of the monitoring technology [σ]. Given that, you’d expect the policy variables to be Z, B, μ and σ. Guess again. b, p, μ and σ are the four instruments involved here. Using those variables amounts to the same thing though [ p = 1 – (z/b) – you can think of p as a ‘penalty’ – and B = b*w]. Incidentally, a level of σ = 0 implies an Andersen & Svarer-type model, where sanctioning is random; the higher σ is, the more precise is the monitoring technology. Also note that the monitoring costs per individual monitored is increasing in σ – i.e. the more precise the monitoring technology, the more expensive the monitoring system is per person monitored.

φ is the job separation rate, α is the exit rate from unemployment to employment, θ = v/S is the labour market tightness, π(s) [s(-e-upperbar) – this is part of why I hate to write this in wordpress)] is the probability of being sanctioned given search effort e… The probability of being sanctioned depends linearly on search. It’s standard search-matching stuff with a matching function depending on θ, workers that optimize value functions (log-utility, before 3.3.3. where they introduce a different risk aversion specification as well – see below..) over search effort, firm side similar to standard DMP and wage determination through Nash Bargaining with bargaining power β…). As mentioned earlier, monitoring is costly and this is another aspect where the paper is different from A&S’; here, the government uses a wage tax on the employed to finance benefits of unemployed and sanctioned, as well as the monitoring that is required. There’s an additively separable welfare function which depends on the utility levels of the three groups in the economy which can be optimized over the policy variables of interest subject to the budget constraint – I won’t go into details about this stuff but rather focus on the conclusions.

Two analytical results can be obtained from the model: The first one is that the optimal policy involves a p > 0. Recall that p satisfies z = ( 1 – p ) * b, which means that if p is equal to zero, there’s no difference in the benefit level of people who are sanctioned and people who are not. An optimal p > 0 means that it’s optimal for sanctioned individuals to have a lower income than non-sanctioned individuals. There are two key mechanisms driving the result: A taxation externality and an entitlement effect. It’s a combination of the fact that in the model, sanctioned individuals don’t take into account that if they increase search, the government will be able to finance the same level of insurance with a lower tax level; and the fact that if the government increases the penalty, it will increase the search effort of sanctioned individuals because increasing search effort will make them more likely to become entitled to UI benefits.

The second result relates to the question of whether introducing monitoring and sanctions into a model with time limits will be optimal. Here we have the usual problem with tradeoffs: The simple answer is that this is not always the case; it’s the case only when the benefits from introducing the scheme exceeds the costs. The benefits from the scheme relates to the search incentives of unemployed, the costs relate to the monitoring activities which need to be financed. In the simulations, they basically find that it’ll almost always be welfare improving to introduce monitoring and sanctions.

Introducing a different (CRRA-) specification of risk aversion where the degree of relative risk aversion is less than one [ 1 − ζ ] (see also here) doesn’t change the conclusions in the paper; stronger risk aversion strengthens the case for monitoring and sanctions. They introduce preference heterogeneities in the last part of the paper, by introducing random shocks to the value of leisure. Here there are four states instead of two; unemployed and sanctioned individuals in either state one or state two. State one is the default state we’ve previously operated with, whereas state two is a state where search effort becomes prohibitively costly for the affected individual. Individuals transition randomly across states, however the transition rate from state two to employment is zero. Unsurprisingly the welfare gains from introducing monitoring and sanctions in this model are smaller than in the baseline case.

The paper briefly mentions that sanctions are much more widespread in the US than in Europe; we’ve covered that in more detail in the lectures. US sanction rates are often in the order of 30 percent, whereas as an example the Danish sanction rate was around 0,3% from 2004-2006. Sanctions are relatively rare in Denmark, and most of them belong in the mild category (a few days’ income, rather than complete loss of income over an extended period of time). However it’s worth mentioning here that if you also think of the Danish activation requirements as (random) sanctions as well, the pattern looks different and the sanction rates differ less; as mentioned before, the Danish government spends a lot of money on activation measures compared to most other countries, and an unemployed Dane is far more likely to go into activation than is e.g. an unemployed person from the U.S.