Flexibility in hours: the role of short time compensation policies

João B. Sousa

European University Institute

31 October 2017

Short time compensation policy

Workers' compensation for a temporary reduction in hours of work

• $\Delta$: reduction in hours worked
• $r$: replacement rate
• $W$: usual (full time) salary

$\rightarrow$ worker gets a $\Delta r W$ compensation from STC program, plus $(1-\Delta) W$ from employer.

Exists in several countries: Germany, Belgium, Italy, Japan, some US states, ...

Widely used during the last recession

STC in Germany

Source: Brenke, Rinne and Zimmermann (2011)

STC in Germany

Source: Brenke, Rinne and Zimmermann (2011)

STC program during the recession in Germany

- 4% of workers and 4% of firms at the peak of crisis.

- among unemployed and ST workers, 1 out of 3 persons were ST workers.

Contribution

- describe and quantify effects of STC policy on labour market and welfare.

Motivation

Source: U.S. Bureau of Economic Analysis

Motivation

Source: U.S. Bureau of Labor Statistics.

Motivation

Source: BEA and Eurostat

Motivation

Source: U.S.: U.S. Bureau of Labor Statistics; DE: German Federal Statistical Office.

Motivation

Source: U.S.: U.S. Bureau of Labor Statistics; DE: German Federal Statistical Office.

Short time compensation (STC)

Government compensation for a reduction in working hours: $b\cdot\Delta h$

- $b$: unemployment benefits

- $\Delta h$: fraction of hours cut, relative to usual hours.

STC program didn't exist in most of U.S. States in the last recession

- only around 1% of STC beneficiaries, as % of regular UB beneficiaries.

- Job Creation Act (2012) clarified definition of STC program, that can be enacted by the States.

- Provided incentives for States to modify or adopt STC programs.

- Currently 30 states run a STC program.

Policy relevant mechanisms:

- allocation of workers across firms and sectors

R. Cooper et al (2017)

- allocation of workers within firms

Balleer et al (2016)

- depreciation of workers skills through unemployment

- consumption insurance

Policy relevant mechanisms:

- allocation of workers across firms and sectors

- allocation of workers within firms

- depreciation of workers skills through nonemployment

- consumption insurance

Today: simplest model to illustrate policy tradeoff

Contribution of this paper:

1. Thoretical model to describe policy tradeoff

2. Take model to the data and quantity effect of policy

Economy lasts 2 periods: $t=1,2$

• depreciation of workers' skills during unemployment

Populated by a measure of workers indexed by $z_t$: worker's skill

Two types of firms (sectors) indexed by $A^i_t$, $i=1,2$.

• allocation of workers across firms

workers supply hours of work, $h$ if the have a job

utility cost of $h$ hours: $\alpha(h)$

$\alpha(h)>0$, strickly convex.

out of the job, they receive $b(z)$ as nonemployment compensation

Technology

labour supply: $h$ hours supplied by worker $z_t$ $\rightarrow$ $z_th$ units of labour services.

production in sector $A^i_t$: $z_thn$ labour services $\rightarrow$ $A^i_t(z_thn)^{\alpha}$ units of output.

$n$: measure of workers employed; $\alpha\in(0,1)$.

Technology

- $\log(z_2)=\log(\bar{z})+\epsilon$ if employed in $t=1$, $\epsilon$ normal r.v.

- $\log(z_2)=\log(\underline{z})+\epsilon$ if nonemployed in $t=1$

- $\underline{z}<\bar{z}$ : skill loss through nonemployment.

Labour markets, indexed by $z$, open at begining of each period

- Firms post vacancies $v^i(z)$ at a cost $\kappa>0$

- $u(z)$ measure of nonemployed searching for jobs

- $v(z)$ measure of vacancies posted

- $m(z)$ matches between worker and firm: $m(z)=\mu u(z)^{\eta}v(z)^{1-\eta}$

Decentralized Equilibrium

a match lasts for 1 period.

when a firm and a worker match, they bargain over the match surplus.

Assume (to simplify) firms have all bargaining power:

- $( w h-\alpha(h)=b)\quad[z]$: $\quad w(z)$ reservation wage in market $z$

Comparative statics exercise

Characterise policy tradeoff as function of :

1. $\Delta A=A^2-A^1$: decreased in productivity of one sector, in period $t=1$.

2. $\Delta z= (\bar{z}-\underline{z})$: skill loss due to nonemployment in $t=1$.

Comparative statics exercise

First without STC policy

Second with STC: $b(H-h)/h$, with $H$ steady state hours in submarket z when $\Delta A=0$

Reservation wage: $(w h + b(H-h)/h -\alpha(h) = b )\quad [z]$.

1. No STC policy, $\Delta A=0$

1. No STC policy, $\Delta A>0$

1. No STC policy, $\Delta A>0$

2. With STC policy, $\Delta A>0$

2. With STC policy, $\Delta A>0$

2. With STC policy, $\Delta A>0$

2. With STC policy, $\Delta A>0$

Period 1, under STC policy:

- Aggregate employment is higher

- Hours per worker fall more in the low productivity sector

- Employment falls less in the low productivity sector

- Employment grows less in the high productivity sector

- Output is lower

2. With STC policy, $\Delta A>0$

Skill depreciation: $\Delta z>0$

Period 2, under STC policy

- Employment is higher is both sectors

- Hours per worker are higher in both sectors

- Output is higher in both sectors

- The larger is $(\bar{z}-\underline{z})$, the stronger the effect of STC policy.

Conclusions & next steps

1. STC policy affects the allocation of workers-time across firms;

1. STC policy affects the allocation of workers' human capital over time;

1. The two mechanisms have opposing effects on Output.

Next steps:

• Data (hours, productivity)

• Dynamic model