Germany (Post-Reform)

The modeling of post-reform Germany will incorporate:

a) Employment without UI entitlement: working but not entitled to UI benefits.

b) UI minimum qualification criteria: those who are working without UI entitlement for a certain duration, on average, will quality for minimum UI entitlement.

c) UI maximum qualification criteria: those who are working for a certain duration with minimum UI entitlement, on average, will quality for maximum UI entitlement (max benefit duration).

d) Unemployment Insurance: while unemployed receive UI benefits that last, on average, for a predetermined benefit duration. UI benefit amount and duration is dependent on EI entitlement status.

e) Unemployment Assistance/Social Assistance: is paid to the unemployed who exhaust their UI benefits or those who failed to qualify for UI and is paid until re-employment occurs.

This system will be modeled with three different states of employment and three different states of unemployment. The value state equations for Germany (post-reform) are stated in

Equations (4.34) to (4.39) where 𝑊_!"#$ is the state of working without UI entitlement, 𝑊_!"#$#

is the state of working with minimum UI entitlement, 𝑊_!"#$% is the state of working with maximum UI entitlement, 𝑈_!"#$%  /  𝑈_!"#$% is the state of receiving UI benefits, and 𝑈!"/!" is the state of receiving unemployment assistance/social assistance benefits.

𝑊_!"#$= 𝑢 𝑐_!(1 − 𝜏) + 𝛽  𝜆𝑈!"/!"+ 1 − 𝜆 {𝑡_!"#$  ^!"#$𝑊_!"#$+ 𝑡_!"#$  ^!"#$#𝑊_!"#$#} (4.34)

𝑊_!"#$#= 𝑢 𝑐_! 1 − 𝜏 + 𝛽  𝜆𝑈_!"#$%+ 1 − 𝜆 𝑡!"#$#  !"#$#𝑊_!"#$#+ 𝑡!"#$#  !"#$%𝑊_!"#$% (4.35)

𝑊_!"#$%= 𝑢 𝑐_! 1 − 𝜏 + 𝛽  𝜆𝑈_!"#$%+ 1 − 𝜆 𝑊_!"#$% (4.36)

𝑈_!"#$%= max

!_!"#$%  {𝑢 𝑐_!"#$%(1 − 𝜏 − 𝜑 𝑝_!"#$%

+ 𝛽  𝑝_!"#$%𝑊_!"#$+ 1 − 𝑝_!"#$% 𝑡!"#$%  !"#$%𝑈_!"#$%+ 𝑡!"#$%  

!"/!"𝑈!"/!"   }

(4.37)

𝑈_!"#$%= max

!_!"#$%  {𝑢 𝑐_!"#$%(1 − 𝜏 − 𝜑 𝑝_!"#$%

+ 𝛽  𝑝_!"#$%𝑊_!"#$+ 1 − 𝑝_!"#$% 𝑡!"#$%  !"#$%𝑈_!"#$%+ 𝑡!"#$%  

!"/!"𝑈!"/!"   }

(4.38)

𝑈!"/!"= max

!!"/!"  {𝑢 𝑐!"/!"− 𝜏 − 𝜑 𝑝!"/!" + 𝛽[  𝑝!"/!"𝑊_!"#$+ 1 − 𝑝!"/!" 𝑈!"/!"  ]} (4.39) Depending on the state, an agent receives a predetermined level of income 𝑐!"#"$ with utility of 𝑢 𝑐!"#"$ , and exerts an optimal level of search intensity 𝑝!"#"$while unemployed. If the agent is in an unemployed state, the agent receives a disutility of 𝜑 𝑝!"#"$ from job search.

Additionally, a proportional tax rate 𝜏 is applied to all wages and benefits that fully fund the social insurance system (UI and UA/SA).

The agent chooses the job search intensity 𝑝!"#"$such that it maximizes the value of their current (unemployment) value state. The optimal set of search intensities satisfies Equations (4.40- 4.42).

−𝜑′ 𝑝_!"#$% + 𝛽[  𝑊_!"#$− 𝑡!"#$%  !"#$%𝑈_!"#$%+ 𝑡!"#$%  

!"/!"𝑈!"/!"  ] (4.40)

−𝜑′ 𝑝_!"#$% + 𝛽[  𝑊_!"#$− 𝑡!"#$%  !"#$%𝑈_!"#$%+ 𝑡!"#$%  !"/!"𝑈!"/!"  ] (4.41)

−𝜑′ 𝑝!"/!" + 𝛽  𝑊_!"#$− 𝑈!"/!"   (4.42)

The optimal search intensities for each value state is chosen such that the marginal cost of job search equates to the discounted marginal benefit.

Figure 4.5 shows the Markov process of the Germany post-reform model. To qualify for minimum UI entitlement (𝑊_!"#$#) an agent will have to work an average duration 1/𝑡_!"#$  ^!"

without UI entitlement (𝑊_!"#$) and work an additional average duration of 1/𝑡!"#$#  !"#$% to qualify for maximum UI entitlement (𝑊_!"#$%). Only those with UI coverage will receive UI benefits  (𝑈!"#"$%&') when unemployment occurs; maximum duration of UI benefits depend on UI entitlement status. Those who exhausted UI benefits or failed to have UI entitlement (𝑊_!"#$) will receive unemployment assistance/social assistance (𝑈!"/!") until re-employment occurs. All those who are re-employed must re-qualify for benefits and thus enter the 𝑊_!"#$ state.

Figure 4.5 Germany (Post-Reform) Model Markov Process

4.3.5. France

The modeling of France will incorporate:

a) Employment without UI entitlement: working but not entitled to UI benefits.

b) UI minimum qualification criteria: those who are working without UI entitlement for a certain duration, on average, will quality for minimum UI entitlement.

c) UI maximum qualification criteria: those who are working for a certain duration with minimum UI entitlement, on average, will quality for maximum UI entitlement (max benefit duration).

d) Employment with UI entitlement: working and entitled to UI benefits.

e) A waiting period: a standard waiting period before receiving UI benefits.

f) Unemployment Insurance: while unemployed receive UI benefits that last, on average, for a predetermined benefit duration. UI benefit amount and duration is dependent on EI entitlement status.

g) Social Assistance¹⁸: is paid to the unemployed who exhaust their UI benefits or those who failed to qualify for UI and is paid until re-employment occurs.

This system will be modeled with three different states of employment and five different states of unemployment. The value state equations for France are stated in Equations (4.43) to (4.50) where 𝑊_!"#$ is the state of working without UI entitlement, 𝑊_!"#$# is the state of working with minimum EI entitlement, 𝑊_!"#$% is the state of working with maximum UI entitlement, 𝑈!"#$%"& /  𝑈!"#$"%& is the waiting period state before receiving UI benefits,  𝑈_!"#$%

/ 𝑈_!"#$% is the state of receiving EI benefits, and 𝑈_!" is the state of receiving social assistance

benefits.

𝑊_!"#$= 𝑢 𝑐_!(1 − 𝜏) + 𝛽  𝜆𝑈_!"+ 1 − 𝜆 {𝑡_!"#$  ^!"#$𝑊_!"#$+ 𝑡_!"#$  ^!"#$#𝑊_!"#$#} (4.43)

𝑊_!"#$#= 𝑢 𝑐_! 1 − 𝜏 + 𝛽  𝜆𝑈!"#$%"&+ 1 − 𝜆 𝑡!"#$#  !"#$#𝑊_!"#$#+ 𝑡!"#$#  !"#$%𝑊_!"#$% (4.44)

𝑊_!"#$%= 𝑢 𝑐_! 1 − 𝜏 + 𝛽  𝜆𝑈!"#$"%&+ 1 − 𝜆 𝑊_!"#$% (4.45)

𝑈!"#$%"&= max

!!"#$%"&

   𝑢 𝑐!"#$%"&(1 − 𝜏 − 𝜑 𝑝!"#$%"&

+ 𝛽  𝑝!"#$%"&𝑊_!"#$+ 1 − 𝑝!"#$%"& 𝑡!"#$%"&  !"#!"#$𝑈!"#$%"&+ 𝑡!"#$%"&  !"#$% 𝑈_!"#$% }

(4.46)

𝑈!"#$"%&= max

!!"#$"%&

   𝑢 𝑐!"#$"%&(1 − 𝜏 − 𝜑 𝑝!"#$"%&

+ 𝛽  𝑝!"#$"%&𝑊_!"#$+ 1 − 𝑝!"#$"%& 𝑡!"#$"%&  !"#$"%&𝑈!"#$"%&+ 𝑡!"#$"%&  !"#$% 𝑈_!"#$% }

(4.47)

𝑈_!"#$% = max

!_!"#$%  {𝑢 𝑐_!"#$% 1 − 𝜏 − 𝜑 𝑝_!"#$% + 𝛽[  𝑝_!"#$%𝑊_!"#$

+ 1 − 𝑝_!"#$% 𝑡!"#$%  !"#$%𝑈_!"#$%+ 𝑡!"#$%  !" 𝑈_!"  ]}

(4.48)

18 Unemployment Assistance has been removed since Social Assistance pays out the same benefit

𝑈_!"#$%= max

!_!"#$%  {𝑢 𝑐_!"#$% 1 − 𝜏 − 𝜑 𝑝_!"#$% + 𝛽[  𝑝_!"#$%𝑊_!"#$

+ 1 − 𝑝_!"#$% 𝑡!"#$%  !"#$%𝑈_!"#$%+ 𝑡!"#$%  !" 𝑈_!"  ]}

(4.49)

𝑈_!"= max

!_!"   𝑢 𝑐_!"(1 − 𝜏) − 𝜑 𝑝_!" + 𝛽  𝑝_!"  𝑊_!"#$+ 1 − 𝑝_!" 𝑈_!"   (4.50)

Depending on the state, an agent receives a predetermined level of income 𝑐!"#"$ with utility of 𝑢 𝑐!"#"$ , and exerts an optimal level of search intensity 𝑝!"#"$while unemployed. If the agent is in an unemployed state, the agent receives a disutility of 𝜑 𝑝!"#"$ from job search.

Additionally, a proportional tax rate 𝜏 is applied to all wages and benefits that fully fund the social insurance system (UI, UA, and SA).

The agent chooses the job search intensity 𝑝!"#"$such that it maximizes the value of their current (unemployment) value state. The optimal set of search intensities satisfies Equations (4.51- 4.55).

−𝜑′ 𝑝!"#$%"& + 𝛽  𝑊_!"#$− 𝑡!"#$%"&  !"#$%"&𝑈!"#$%"&+ 𝑡!"#$%"&  !"#!" 𝑈_!"#$% = 0 (4.51)

−𝜑′ 𝑝!"#$"%& + 𝛽  𝑊_!"#$− 𝑡!"#$"%&  !"#$"%&𝑈!"#$"%&+ 𝑡!"#$"%&  !"#$% 𝑈_!"#$% = 0 (4.52)

−𝜑′ 𝑝_!"#$% + 𝛽  𝑊_!"#$− 𝑡!"#$%  !"#$%𝑈_!"#$%+ 𝑡!"#$%  !" 𝑈_!"   = 0 (4.53)

−𝜑′ 𝑝_!"#$% + 𝛽  𝑊_!"#$− 𝑡!"#$%  !"#$%𝑈_!"#$%+ 𝑡!"#$%  !" 𝑈_!"   = 0 (4.54)

−𝜑′ 𝑝_!" + 𝛽    𝑊_!"#$− 𝑈_!"   = 0 (4.55)

The optimal search intensities for each value state is chosen such that the marginal cost of job search equates to the discounted marginal benefit.

Figure 4.6 shows the Markov process for the France model. To qualify for minimum UI entitlement, and move to state 𝑊_!"#$#, an agent must work for an average duration of 1/𝑡_!"#$  ^!"#$#

without UI coverage (𝑊_!"#$) and an additional average duration of 1/𝑡_!"#$#^!"#$% for maximum UI entitlement (𝑊_!"#$%). If unemployment occurs while the agent is not entitled to UI benefits, they move to social assistance (𝑈_!") next period and will remain in that state until re-employment occurs. If unemployment occurs while the agent is entitled to UI benefits, the agent moves to a mandatory waiting period (𝑈!"#"$%&#'")  before UI benefits begin  (𝑈!"#"$%&'); the duration of UI benefits depends on UI entitlement status. When the agent exhausts UI benefits the agents moves

to social assistance (𝑈_!") until re-employment occurs. While the agent is unemployed in state 𝑈!"#"$%&#'", 𝑈!"#"$%&',  or 𝑈_!" the probability of re-employment is 𝑝!"#"$%&#'",𝑝!"#"$%&', and 𝑝_!", respectively. All those who are re-employed must re-qualify for benefits and thus enter the 𝑊_!"#$ state.

Figure 4.6 France Model Markov Process

5. MEASUREMENT STRATEGY