## Abstract

We read search theory’s equilibrium conditions for unemployment as an iso-unemployment curve. A country’s position along the curve reveals its preferences over the destruction–duration mix. Using a panel of 20 OECD countries over 1985–2009, we find that the employment protection legislation and collective bargaining coverage have opposing effects on the job destructions and unemployment durations, while the remaining key institutional factors affect one or another. Implementing the right reforms could reduce job destruction rates by about 0.05–1.3 % points and unemployment rates by up to 4 % points depending on the country considered.

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## Notes

- 1.
This assumption is needed to apply the methodology developed by Shimer (2012) to measure job creation and job destruction flows. This is consistent with the view that, compared with workers’ flows within the labor force, flows in and out of the labor force play a lesser role in explaining unemployment movements. Once this assumption is relaxed, one cannot use publicly available data to construct all possible flows between employment, unemployment, and inactivity. Micro-data on individuals’ employment status should be used instead. Data availability issues prevent us from taking this route.

- 2.
The time subscript \(t\) is dropped hereafter for the sake of simplicity.

- 3.
As the model allows for regulatory costs, the zero-profit condition implies that firms’ profits are dissipated by such costs.

- 4.
See “Appendix 2” for details on the theoretical model.

- 5.
We follow closely the analysis of the comparative statics of equilibrium in Pissarides (2000), in particular, Section 2.3 on page 47–56 and Section 2.5 on page 59–63.

- 6.
The cutoff date for the forecasts was July 2012.

- 7.
Here is to provide an example of implementing possible policy reforms, and we focus on the policy implications regarding unemployment inflows, but one can easily conduct a similar exercise for unemployment durations.

- 8.
The analysis below is closely following Pissarides (2000), in particular, Section 2.2 on page 40–44 in.

- 9.
The worker with productivity lower than \(R\) can not be matched to a job.

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## Appendices

### Appendix 1

This appendix presents the methodology used to estimate annual time series of flow hazard rates into and out of unemployment. It also discusses how to infer the average duration of unemployment spells consistent with such flows. The procedure builds on Shimer (2012). However, this approach cannot be directly applied to European countries as unemployment duration is not available at monthly frequencies in the European Labor Force Survey. To overcome this limitation, we follow the methodology proposed by Elsby et al. (2013). This methodology exploits annual and quarterly data to measure annual averages of monthly unemployment flows.

Let us denote by \(F_{t}^{<12}\) the probability that an unemployed worker exits unemployment within 1 year. The annual change in the unemployment stock can be expressed as

Here, \(u_{t+1}^{<12}\) represents the stock of unemployed workers with duration less than 1 year (i.e., the yearly flow into unemployment), and \(F_{t}^{<12}u_{t}\) represents the flows out of unemployment. Solving for the annual outflow probability \(F_{t}^{<12}\), one obtains

where the factor \(A\) represents the fraction of unemployment with duration longer than 1 year and the ratio \(B\) is the annual gross growth rate of unemployment. Assuming that the monthly outflow hazard rate for workers unemployed less than 1 year \(f_{\mathrm{out},t}^{<12}\) is constant within years, the annual outflow probability \(F_{t}^{<12}\) is related to \(f_{\mathrm{out},t}^{<12}\) through

so that \(F_{t}^{<12}\) can be mapped into \(f_{\mathrm{out},t}^{<12}\) in the following manner

where \(f_{\mathrm{out},t}^{<12}\) is the hazard rate for unemployed workers of duration lower than 1 year, which is related to the probability that an unemployed worker at time \(t\) completes her spell within the subsequent 12 months.

In order to obtain estimates of the corresponding inflow hazard rates \(f_{\mathrm{in},t}^{<12},\) let us reformulate the evolution of the monthly unemployment rate over time as

Assuming that the flow hazards are constant within years and solving Eq. (17) forward 1 year, we can relate the variation in the unemployment stock \(u_{t}\) over the course of the year to the variation in the underlying hazard rates \(f_{\mathrm{in},t}^{<12}\) and \(f_{\mathrm{out},t}^{<12}\):

where the steady-state unemployment rate \(u_{t}^{*}\) is given by:

and the annual rate of convergence to the steady state \(\lambda _{t}\) is found to be:

To operationalize the methodology described above, we use OECD annual data on unemployment rates and unemployment rates by duration to compute Eq. (14). Given \(F_{t}^{<12},\) we use Eq. (16) to estimate \(f_{\mathrm{in},t}^{<12},\) which together with \(u_{t}\) allows us to obtain \(f_{\mathrm{out},t}^{<12}\) through equations (18), (19) and (20).

The inflow rates estimated above are combined with annual data for the unemployment rates to estimate through equation (16) the average duration of unemployment spells for the four decades ranging from the 1970s throughout the 2000s.^{Footnote 8}

### Appendix 2

There are two more assumptions on depreciation rate and interest rate needed to derive equations (7) and (8). \(\delta \) is supposed to be the depreciation rate. The interest rate, \(r\), is determined by \(r=\frac{1-\delta }{\delta }\). Before a certain job match happens, the firm holds a vacant position, and the worker is unemployed enjoying unemployment income. The asset value of a vacant job to the firm satisfies

And the present-discounted valued of the expected unemployment income stream of an unemployed worker is

After a job match happens, the vacant job is occupied by the worker with productivity \(x\) drawn from the distribution \(G(x)\). In order to form the job match, the firm has to give up the asset value of the vacant job, \(V\), for the asset value of an occupied job \(J(x)\), and the worker has to give up the expected unemployment income, \(U\), for the occupied job’s value to a worker, \(W\). Therefore, \(V\) and \(W\) function as the threat points for job matching decision of the firm and the worker. Furthermore, the asset value of an occupied job \(J(x)\) with productivity \(x\in [R,1]\)
^{Footnote 9} satisfies

The above equation can be rewritten as

And an occupied job’s value to an employed worker with productivity \(x\), \(W(x)\), satisfies

It follows that

Equation (24) describes that when a productivity shock arrives and the productivity of the worker changes from \(x\) to \(s\), the firm has to give up the previous value of the occupied job \(J(x)\) for a new value \(J(s)\) if \(R\le s\le 1\). Or, the firm destroys the job if \(s<R\). Equation (26) shows that before a productivity shock arrives, an employed worker has enjoyed the expected return of an occupied job, \(W(x)\). After the shock arrives and the productivity of the worker changes from \(x\) to \(s\), there are two possibilities. Either the worker remains employed, and \(W(x)\) doesn’t change, if the new productivity \(R\le s\le 1\). Or the job is destructed, and the worker becomes unemployed for an unemployment income \(U\), if the new productivity \(s\le R\).

Furthermore, to identify the wage rate \(w\) follows the Nash bargaining, that is, \(w\) maximizes the weighted product of the worker’s and the firm’s net return of the job match.

The first-order condition follows that

The following job creation condition is derived by Eqs. (26) and (28)

And the job destruction condition is derived from Eqs. (24) and (28)

The job creation condition (29) determines the vacancies on the labor market, that is, the labor market tightness \(\theta \), and then influences the duration of unemployment spells. The job destruction condition, Eq. (30), describes the dynamics of \(R\), and the job destruction rates on the labor market.

Equation (29) describes the job creation process, when unemployment inflows are constant. That is, it show how job creation reacts to the changes of labor market institutions and aggregate economic conditions. Hence, we can generate first-order derivatives of Eq. (29) with respect to \(\theta \), when fixing \(R\), i.e., the expression (9). Equation (30) displays the job destruction process, when unemployment durations are constant. That is, how job destruction reacts to the changes of labor market institutions and other economic conditions. Hence, we can derive the first-order derivatives of Eq. (30) with respect to \(R\), when fixing \(\theta \), i.e., the expression (10).

Equation (29) gives us that \(\theta \) responds to the changes in \(c\), \(r\), \(\lambda \), \(\mu \), and \(\beta \), while Eq. (30) describes how \(\theta \) responds to \(z\), \(p\), \(\beta \), \(c\), \(r\), \(\lambda \), and \(s\) given \(R\). Equation (29) gives us that \(R\) responds to the changes in \(c\), \(r\), \(\lambda \), \(\mu \), and \(\beta \), while Eq. (30) describes how \(R\) responds to \(z\), \(p\), \(\beta \), \(c\), \(r\), \(\lambda \), and \(s\) given \(\theta \). The directions of \(\theta \) and \(R\)’s responses are summarized in the Eqs. (9) and (10). Therefore, the job destruction rate increased by higher \(R\) and expected unemployment durations decreased by higher \(\theta \) responses are summarized in the Eqs. (9) and (10).

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Pérez, E., Yao, Y. Can institutional reform reduce job destruction and unemployment duration? Yes it can.
*Empir Econ* **49, **961–983 (2015). https://doi.org/10.1007/s00181-014-0898-3

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### Keywords

- Search model
- Labor market institutions
- Unemployment inflows
- Unemployment duration