Do Matching Frictions Cause Unemployment? Not in Bad Times

Unemployment spikes frequently across the U.S. and Europe, most recently from 2007 to the present day, and remains a major concern for policymakers. To determine optimal policy responses, it is critical to identify the main sources of unemployment. In recent work CEP Macro program member Pascal Michaillat draws on the search and matching framework, extending it to allow for what he calls "rationing unemployment".

The search and matching framework explains unemployment using matching frictions: the heterogeneity between workers and jobs can create unemployment in equilibrium as individual workers are temporarily unemployed whilst searching for jobs. Pascal argues that in recessions the more acute problem in creating unemployment is the shortage of jobs caused by the business cycle. He thus forms a model to distinguish between these two kinds of unemployment, frictional and rationing unemployment, and quantify their relative importance at different points in the business cycle.

Calibrating his model against US data, Pascal finds that the cyclical variations in the composition of unemployment are large. His model predicts that when unemployment is below 5 per cent all unemployment is frictional, but when unemployment reaches 8 per cent only 2 percentage points of this are frictional, with the other 6 percentage points being caused by shortfalls in the demand for labour. Paradoxically, he finds that frictional unemployment falls during recessions.

The key to his results is the combination of rigidity in real wages and diminishing marginal product of labour. Previous work in the matching framework assumes rigidity in wages, but keeps the assumption of a constant marginal product of labour. The implication of this is that in these models, if matching frictions are removed, there is not actually any possibility of further unemployment. Thus all unemployment in such models is frictional. This happens because with a constant MPL even if wages are rigid you always want to increase employment as long as they are lower than marginal product - each unit of labour yields the same net benefit. So without frictions we get full employment. On the other hand, if we allow the MPL to fall, for a given wage there is a maximum level of workers that firms will want to hire. Once employment is too high the MPL falls below the wage and the net benefit of hiring becomes negative. Hence, with diminishing MPL and rigidity in wages we have rationing unemployment, to which we can add frictional unemployment. Pascal's work thus represents a synthesis between matching methods and unemployment as understood by insider outsider models, social norm models, or efficiency wage models.

Pascal combines this framework with technology shocks to study the effect of changes in productivity on unemployment composition. Using this model the intuition behind the fall of the importance of frictional unemployment during recessions becomes clearer. Following a negative technology shock the marginal product of labour falls. Since wages do not adjust fully wages remain above productivity, so there is an increase in rationing unemployment since firms do not want to hire enough at the going wage. This increase in unemployment reduces matching frictions, since it becomes easier for firms and workers to match given the larger pool of available labour. This effect is captured in the canonical matching function, in which the number of matches is increasing in both the number of vacancies and the number of unemployed workers. The resulting reduction in matching frictions reduces the scale of frictional unemployment.

Pascal's model has very important policy implications, since the optimal policy response to unemployment depends on its source. During good times unemployment is mostly frictional, so policy should be directed towards reducing matching frictions. However, during recessions matching becomes less important, and rationing of jobs more important. This implies that fears that generous unemployment insurance during recessions extends unemployment may be overstated - the chief concern is a lack of jobs, and policy should instead be directed at job creation. One possible policy response is thus countercyclical unemployment insurance, which is extended during recessions and shortened during expansions.

Optimal Unemployment Insurance Over the Business Cycle

In further work with Camille Landais and Emmanuel Saez, Pascal goes on to explore this idea of countercyclical unemployment insurance. They characterise optimal unemployment insurance (UI) in the model setting described above, and find that countercyclical unemployment insurance is indeed optimal. They derive a simple optimal UI formula, which features a “macro elasticity” capturing the elasticity of unemployment to a change in the generosity of UI. This is in addition to the usual statistics that appear in such Baily-Chetty formulas, such as risk aversion and the micro-elasticity of unemployment with respect to UI. This formula is not model dependent, and can be adapted to a broader class of models, such as the Pissarides (2000) model with Nash Bargaining.

The government faces a trade-off when setting UI optimally. On the one hand, with risk averse consumers, providing insurance increases welfare by reducing uncertainty. On the other hand it causes inefficiency by reducing search effort and hence reduces welfare.

In the setting above with job rationing the formula implies that optimal UI is countercyclical. There are two reasons for this. Firstly, in a recession there is high employment due to job rationing regardless of matching. Since the aggregate matching function is increasing in unemployment this means that workers would be very easily matched to jobs, were it not for rationing. This means the standard criticism of UI – that it reduces search effect and thus increases unemployment – is much less relevant, because search (and hence search effort) are themselves not relevant when there is a large pool of unemployed workers who could be easily matched. Thus the macro-elasticity is smaller, and the “cost” of UI (i.e. increased unemployment) is lower. Hence a larger amount is optimal.

Secondly, the authors show that individual search effort creates a negative externality by reducing other workers’ probability of finding a job. This externality is not taken into account by individual workers, and hence individual search effort will be too high in equilibrium. In fact, UI can correct for this externality by reducing search effort since the cost of unemployment is lowered. The authors show that over the cycle this externality is more pronounced in a recession and thus the government would want to optimally increase UI in a recession.

The authors calibrate their model to US data and find that it predicts quantitatively important variation in UI over the cycle. The baseline model, in which the government runs a balanced budget and UI never expires, has an optimal replacement ratio of 67% when unemployment is low at 4%, and a higher replacement ratio of 85% when unemployment increases to 9%. The effects are very robust to different modelling assumptions, including allowing the government to run budget deficits. Finally, they make the model more realistic by allowing the government to choose the length of UI payments. Calibrating the model so that the optimal length is 26 weeks when unemployment is 5.9%, as observed in the US, they find that it is optimal for the government to raise the length of UI to over 100 weeks when unemployment rises to 8%.

Given the persistence of the high unemployment associated with the current economic climate, this research is essential in forming optimal policy responses. The research also lends support to the response of the US state and federal governments, who systematically increase the maximum length of UI benefit during downturns. US states extend the maximum length by 13 to 20 weeks when state unemployment rises above a trigger level. The federal government gives additional extra weeks of UI, which it has also raised by 53 weeks during the current recession. Combining these two extensions, the maximum length of UI in the US has risen from 26 weeks before the recession to 99 weeks, which is very similar to the policy prescriptions of the current authors.

For further reading please see:

• "Do Matching Frictions Explain Unemployment? Not in Bad Times" [Full document in Adobe PDF] (Pascal Michaillat), CEP Discussion Paper 1024, November 2010
• "Optimal Unemployment Insurance Over the Business Cycle"[ Full document in Adobe PDF] (Camille Landais, Pascal Michaillat, Emmanuel Saez) CEP Discussion Paper 1078, September 2011