The efficiency of job separations: A revealed-preference test of the Coase theorem in the labour market

Simon Jäger, Benjamin Schoefer, Josef Zweimüller 04 October 2019

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Labour market quantities adjust largely along the employment (extensive) margin, rather than the hours (intensive) margin. At the micro level, extensive-margin adjustments become discrete choices of individual workers and firms within employment relationships that are destroyed, maintained or formed. These job-level adjustments have a fundamental condition: each party must be better off inside the job than with the respective outside option, and so there is worker and firm surplus from the job. By this theory, the distribution of job surplus determines the level of employment, and its adjustment (Mortensen and Pissarides 1994, Bils et al. 2012, Mui and Schoefer 2019).

Theories of job formation and separation

Coasean theories argue that the employer and the worker exploit all gains from trade. They reach efficient outcomes through flexible bargaining and unrestricted contracting. Importantly, in Coase's theory, all job separations are mutually preferable and efficient, because no bargain could have been struck, however complex, to prevent the separation and preserve the employment relationship. 

Conversely, frictional ('non-Coasean') models put limits on this bilateral contracting, for example from wage rigidity or institutional constraints. Inefficient separations can emerge, which are costly to the firm or the worker.

The answer to which would provide a better description of real-world job dynamics helps determine the welfare properties of employment adjustment, and hence the potential for policy interventions, such as short-term work (Giupponi and Landais 2018), unemployment insurance (Chetty 2006), minimum wages (Lee and Saez 2012, Cengiz et al. 2019), payroll taxes (Saez et al. 2019), seniority layoff rules (Sorensen 2018), retirement policies (Lazear 1979), and monetary policy (Berger et al. 2015).

Yet, an empirical test of the Coasean benchmark is challenging exactly because of the abstract allocative concepts underlying its strong efficiency properties. Identifying a set of separations and their observable attributes does not tell us whether they are efficient. Measured flow wages, despite the substantial evidence suggesting rigidity, can be viewed as consistent with bilaterally efficient bargaining outcomes (Barro 1977, Hall 2005, Shimer 2004, Hall and Milgrom 2008). Similarly, a 'quit' and a 'layoff' may both be efficient separations (McLaughlin 1991). 

Revealed preference

To overcome this, we conducted a revealed-preference test of whether Coasean theory can account for separation behaviour in the data (Jäger, Schoefer and Zweimüller 2019). We studied a transitory policy that, while active, reduced job surplus. This was a programme in Austria, in 1988, that raised the duration of unemployment insurance benefits from one to four years. Eligibility was determined by age cutoffs (age 50 and up) and was restricted to specific regions, so we could implement a sharp difference-in-difference design comparing age groups and regions, based on Austrian social security data. 

In Figure 1, we plot the potential duration of UI benefits for workers 50 and older (potentially eligible if in the treatment regions), and 40-49 years old (ineligible no matter the region), and by region (treatment regions, where the policy was active, and control regions, where it was not).

Figure 1 Duration of UI benefits in Austria following 1988 policy reform

Source: Jäger et al. (2019)

The programme triggered a dramatic increase in separations of 10.9 percentage points (27%) over the five-year horizon the programme was active: 51.4% of jobs in the treatment group separated, compared to a counterfactual separation rate of 40.5% in the absence of the reform. 

Figure 2, shows these separations in raw administrative population-level data in form of birth-month-cohort gradients of job separations, defined as whether a given worker employed at the onset of the reform in 1988 is no longer in that same job (establishment) by then end of the policy in 1993. The red dashed and blue solid lines of Figure 2a show the share of workers in the treatment and control regions who had separated from their 1988 employer by 1993. Figure 2b shows the difference between the share of separators in the treatment and in the control regions. 

Figure 2a Treatment effect on separations in Austria following 1988 policy reform

Figure 2b Difference in separations (treatment – control) in Austria following 1988 policy reform

Source: Jäger et al. (2019)

Younger cohorts born after 1943 turned 50 after the policy was abolished in 1993, and therefore could never claim extended benefits under the program, while their slightly older peers were eligible for extended benefits. Empirically, the untreated younger cohorts had similar separation behaviour in both regions. In contrast, there were sharp increases in separations among slightly older cohorts who were eligible for the surplus-reducing extended benefits in treatment regions. At its peak, the difference in separations was about 20 percentage points higher in the treatment regions relative to a control region share of about 50%. Most of these separations were into long-term nonemployment.

The efficiency benchmark predicts that these program-induced separations should have extracted jobs with low joint surplus, which even efficient rebargaining could not have saved. Studying these initial separations themselves, for example by counting, or by their observable characteristics, would not be informative about their efficiency properties (as we explained above).

Empirically adjudicating between models

Instead we exploited the sudden abolition of the programme in 1993. Our revealed-preference test assumes that after the programme abolition, the group of formerly treated job survivors, whom we track in population-level administrative panel data, should be more resilient – have fewer separations – in response to any future shocks, compared to the former control group. This is because after the treatment is sharply deactivated, the group of surviving jobs then lacks a mass of marginal (low-surplus) matches, whereas these low-surplus jobs are still present in the former control group. By the Coasean model, this resilience is predicted for any kind of surplus-relevant shock. 

At a broad level, our revealed-preference test relates to a dynamic known as 'harvesting effects' in demography and epidemiology (see for example Schwartz 2000, Basu 2009). In these fields, analogous ideas apply to transitory negative health shocks (like heat waves) that induce deaths among low-health individuals and reduce the subsequent average mortality rate of the survivors.

As a basic test of this prediction, Figure 3 shows post-abolition separation rate among 'job survivors' in the two regions. 

Figure 3a Post-abolition separations among programme survivors in Austria

Figure 3b Difference in post-abolition separations (former treatment – former control)

Source: Jäger et al. (2019)

Strikingly, the relevant older cohorts in the former treatment and control regions exhibit identical post-abolition separation behaviour. This is despite the massive depletion of the former treatment group, which is around 18% smaller than the control group due to the treatment. 

This lack of resilience in separations holds unconditionally as well as in response to negative labour demand shocks, for example, sharp establishment shrinkage events and negative industry growth. For example, in Figure 4 we generate 'hockey stick' graphs in the spirit of Davis et al. (2013), relating separation rates to establishment net employment growth, separately for treated and untreated cohorts. Even in shrinking establishments, the treated cohorts are not shielded from separations compared to their less-selected peers.

Figure 4 Exposure to negative labour demand shocks: 'Hockey sticks' of post-abolition separations against net employment growth at the establishment level

Source: Jäger et al. (2019)

The large separations effect and subsequent absence of resilience are hard to reconcile with the Coasean view of jobs. We developed a basic model to plot the predicted post-abolition separations following a Coasean benchmark in the former treatment group as a function of the initial treatment effect and post-abolition separations in the control group, and plot this benchmark. It is the yellow dashed line in Figure 3. The data clearly reject this Coasean benchmark. 

We were able to show that the Coasean view can only rationalise the perfect comovement of separation rates under narrow conditions: if idiosyncratic job-level surplus exhibits no persistence whatsoever, so that the post-abolition surplus distributions reconverges in the first year after the abolition. Our structural model estimates that the entire Austrian labour market would need to have this implausible property.

The nature of frictions

Our alternative interpretation is that the separations were non-Coasean. Yet, while all efficient separations are fundamentally alike, each frictional setting is inefficient in its own way. One specific parsimonious and plausible non-Coasean mechanism builds on wage rigidity, which would be consistent with our findings. By preventing the flexible re-bargaining underlying the Coasean result, such frictions complicate the 'positive surplus' test from single-dimensional Coasean joint surplus, to two unilateral surplus concepts: separations may occur because either worker-specific or firm-specific surplus turns negative. 

As a result, jobs can inefficiently separate even though one party’s surplus remains large enough to, in principle, bribe the other party into continuation (if only the requisite trade were implementable). In this non-Coasean setting, the original UI extension that boosted worker’s outside options would have destroyed matches with initially low worker surplus. After the abolition, the non-Coasean model would therefore predict resilience in response to worker-surplus shocks – but need not have selected jobs with low firm surplus. Consequently, if firm-surplus shocks account for most post-abolition separation, then the non-Coasean model can easily rationalise the absence of resilience.

Our specific case study naturally leaves an important question for future research: whether, and which, other institutional or demographic contexts come closer to the Coasean benchmark of efficient separations.

References

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Hall, R E and P R Milgrom (2008), "The Limited Influence of Unemployment on the Wage Bargain", The American Economic Review 98(4): 1653–74.

Jäger, S, B Schoefer, and J Zweimüller (2019), "Marginal Jobs and Job Surplus: A Test of the Efficiency of Separations", NBER working paper 25492.

Jäger, S, B Schoefer, S Young, and J Zweimüller (2019), "Wages and the Value of Nonemployment", NBER working paper 25230.


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Assistant Professor of Economics, Massachusetts Institute of Technology (MIT)

Assistant Professor of Economics, University of California, Berkeley

Professor at the Department of Economics, University of Zurich and CEPR Research Fellow

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