Introduction What are these models about? Reforming Future work

Overlapping generations modeland within cohort heterogeneity

Jan Woznica

Beethoven Project meeting, November 2016

1 / 13

Introduction What are these models about? Reforming Future work

Where we are and want to be

Starting idea from the policy angle:

Plenty of countries have instruments aiming to foster voluntary pension savingsSo far in the literature NOBODY analyzed if these instruments make sense

Starting idea from the academic angle:

Within cohort heterogeneity is rare, also because it is conceptually difficultThere are no models, where agents within cohort would differ on decision rules

Combining the two together can make a valuable contribution (JPub?)This kind of question cannot be answered with tools other than OLG (low dataavailability, difficulties to identify, etc.)

2 / 13

Introduction What are these models about? Reforming Future work

Where we are and want to be

Starting idea from the policy angle:Plenty of countries have instruments aiming to foster voluntary pension savings

So far in the literature NOBODY analyzed if these instruments make senseStarting idea from the academic angle:

Within cohort heterogeneity is rare, also because it is conceptually difficultThere are no models, where agents within cohort would differ on decision rules

Combining the two together can make a valuable contribution (JPub?)This kind of question cannot be answered with tools other than OLG (low dataavailability, difficulties to identify, etc.)

2 / 13

Introduction What are these models about? Reforming Future work

Where we are and want to be

Starting idea from the policy angle:Plenty of countries have instruments aiming to foster voluntary pension savingsSo far in the literature NOBODY analyzed if these instruments make sense

Starting idea from the academic angle:

Within cohort heterogeneity is rare, also because it is conceptually difficultThere are no models, where agents within cohort would differ on decision rules

Combining the two together can make a valuable contribution (JPub?)This kind of question cannot be answered with tools other than OLG (low dataavailability, difficulties to identify, etc.)

2 / 13

Introduction What are these models about? Reforming Future work

Where we are and want to be

Starting idea from the policy angle:Plenty of countries have instruments aiming to foster voluntary pension savingsSo far in the literature NOBODY analyzed if these instruments make sense

Starting idea from the academic angle:

Within cohort heterogeneity is rare, also because it is conceptually difficultThere are no models, where agents within cohort would differ on decision rules

Combining the two together can make a valuable contribution (JPub?)This kind of question cannot be answered with tools other than OLG (low dataavailability, difficulties to identify, etc.)

2 / 13

Introduction What are these models about? Reforming Future work

Where we are and want to be

Starting idea from the policy angle:Plenty of countries have instruments aiming to foster voluntary pension savingsSo far in the literature NOBODY analyzed if these instruments make sense

Starting idea from the academic angle:Within cohort heterogeneity is rare, also because it is conceptually difficult

There are no models, where agents within cohort would differ on decision rules

Combining the two together can make a valuable contribution (JPub?)This kind of question cannot be answered with tools other than OLG (low dataavailability, difficulties to identify, etc.)

2 / 13

Introduction What are these models about? Reforming Future work

Where we are and want to be

Starting idea from the policy angle:Plenty of countries have instruments aiming to foster voluntary pension savingsSo far in the literature NOBODY analyzed if these instruments make sense

Starting idea from the academic angle:Within cohort heterogeneity is rare, also because it is conceptually difficultThere are no models, where agents within cohort would differ on decision rules

Combining the two together can make a valuable contribution (JPub?)This kind of question cannot be answered with tools other than OLG (low dataavailability, difficulties to identify, etc.)

2 / 13

Introduction What are these models about? Reforming Future work

Where we are and want to be

Starting idea from the policy angle:Plenty of countries have instruments aiming to foster voluntary pension savingsSo far in the literature NOBODY analyzed if these instruments make sense

Starting idea from the academic angle:Within cohort heterogeneity is rare, also because it is conceptually difficultThere are no models, where agents within cohort would differ on decision rules

Combining the two together can make a valuable contribution (JPub?)

This kind of question cannot be answered with tools other than OLG (low dataavailability, difficulties to identify, etc.)

2 / 13

Introduction What are these models about? Reforming Future work

Where we are and want to be

Starting idea from the policy angle:Plenty of countries have instruments aiming to foster voluntary pension savingsSo far in the literature NOBODY analyzed if these instruments make sense

Starting idea from the academic angle:Within cohort heterogeneity is rare, also because it is conceptually difficultThere are no models, where agents within cohort would differ on decision rules

Combining the two together can make a valuable contribution (JPub?)This kind of question cannot be answered with tools other than OLG (low dataavailability, difficulties to identify, etc.)

2 / 13

Introduction What are these models about? Reforming Future work

OLG Model

Cohorts live for J periods

Simultaneously J cohorts aliveConsumers working and chose labor supply endogenouslyDuring work years they earn wage income (which may be consumed or saved)During retirement they obtain pension benefitsVoluntary savings used to smoothen consumption over lifetime, but preferencesmatter (e.g. really impatient and lazy agents will borrow all working life torepay from pension benefits)

⇒ OLG is a GE model, so there are partial equilibrium and general equilibriumeffects (may decompose!)⇒ We can see spillovers between cohorts (between-cohort redistribution)

3 / 13

Introduction What are these models about? Reforming Future work

OLG Model

Cohorts live for J periodsSimultaneously J cohorts alive

Consumers working and chose labor supply endogenouslyDuring work years they earn wage income (which may be consumed or saved)During retirement they obtain pension benefitsVoluntary savings used to smoothen consumption over lifetime, but preferencesmatter (e.g. really impatient and lazy agents will borrow all working life torepay from pension benefits)

⇒ OLG is a GE model, so there are partial equilibrium and general equilibriumeffects (may decompose!)⇒ We can see spillovers between cohorts (between-cohort redistribution)

3 / 13

Introduction What are these models about? Reforming Future work

OLG Model

Cohorts live for J periodsSimultaneously J cohorts aliveConsumers working and chose labor supply endogenously

During work years they earn wage income (which may be consumed or saved)During retirement they obtain pension benefitsVoluntary savings used to smoothen consumption over lifetime, but preferencesmatter (e.g. really impatient and lazy agents will borrow all working life torepay from pension benefits)

⇒ OLG is a GE model, so there are partial equilibrium and general equilibriumeffects (may decompose!)⇒ We can see spillovers between cohorts (between-cohort redistribution)

3 / 13

Introduction What are these models about? Reforming Future work

OLG Model

Cohorts live for J periodsSimultaneously J cohorts aliveConsumers working and chose labor supply endogenouslyDuring work years they earn wage income (which may be consumed or saved)

During retirement they obtain pension benefitsVoluntary savings used to smoothen consumption over lifetime, but preferencesmatter (e.g. really impatient and lazy agents will borrow all working life torepay from pension benefits)

⇒ OLG is a GE model, so there are partial equilibrium and general equilibriumeffects (may decompose!)⇒ We can see spillovers between cohorts (between-cohort redistribution)

3 / 13

Introduction What are these models about? Reforming Future work

OLG Model

Cohorts live for J periodsSimultaneously J cohorts aliveConsumers working and chose labor supply endogenouslyDuring work years they earn wage income (which may be consumed or saved)During retirement they obtain pension benefits

Voluntary savings used to smoothen consumption over lifetime, but preferencesmatter (e.g. really impatient and lazy agents will borrow all working life torepay from pension benefits)

⇒ OLG is a GE model, so there are partial equilibrium and general equilibriumeffects (may decompose!)⇒ We can see spillovers between cohorts (between-cohort redistribution)

3 / 13

Introduction What are these models about? Reforming Future work

OLG Model

Cohorts live for J periodsSimultaneously J cohorts aliveConsumers working and chose labor supply endogenouslyDuring work years they earn wage income (which may be consumed or saved)During retirement they obtain pension benefitsVoluntary savings used to smoothen consumption over lifetime, but preferencesmatter (e.g. really impatient and lazy agents will borrow all working life torepay from pension benefits)

⇒ OLG is a GE model, so there are partial equilibrium and general equilibriumeffects (may decompose!)⇒ We can see spillovers between cohorts (between-cohort redistribution)

3 / 13

Introduction What are these models about? Reforming Future work

Standard model: households

“Born” at age 20 (j = 1) and live up to 100 years (J = 80)

Subject to time and cohort dependent survival probability πj,tChoose labor supply lj endogenouslyMaximize remaining lifetime utility derived from consumption c and leisure 1− l:

Uj,t =J−j∑s=0

[δsπj+s,t+sπj,t

[cφj+s,t+s (1− lj+s,t+s)1−φ − 1

]]Subject to the budget constraint

(1 + τ ct )cj,t + sj,t = (1− τ lt )(1− τ)wtlj,t ← labor income

+ (1 + (1− τkt )rt)sj−1,t−1 ← capital income

+ (1− τ lt )bj,t ← pension income+ beqj,t ← bequests−Υt ← lump-sum tax

There exists a closed-form solution to this problem

4 / 13

Introduction What are these models about? Reforming Future work

Standard model: households

“Born” at age 20 (j = 1) and live up to 100 years (J = 80)Subject to time and cohort dependent survival probability πj,t

Choose labor supply lj endogenouslyMaximize remaining lifetime utility derived from consumption c and leisure 1− l:

Uj,t =J−j∑s=0

[δsπj+s,t+sπj,t

[cφj+s,t+s (1− lj+s,t+s)1−φ − 1

]]Subject to the budget constraint

(1 + τ ct )cj,t + sj,t = (1− τ lt )(1− τ)wtlj,t ← labor income

+ (1 + (1− τkt )rt)sj−1,t−1 ← capital income

+ (1− τ lt )bj,t ← pension income+ beqj,t ← bequests−Υt ← lump-sum tax

There exists a closed-form solution to this problem

4 / 13

Introduction What are these models about? Reforming Future work

Standard model: households

“Born” at age 20 (j = 1) and live up to 100 years (J = 80)Subject to time and cohort dependent survival probability πj,tChoose labor supply lj endogenously

Maximize remaining lifetime utility derived from consumption c and leisure 1− l:

Uj,t =J−j∑s=0

[δsπj+s,t+sπj,t

[cφj+s,t+s (1− lj+s,t+s)1−φ − 1

]]Subject to the budget constraint

(1 + τ ct )cj,t + sj,t = (1− τ lt )(1− τ)wtlj,t ← labor income

+ (1 + (1− τkt )rt)sj−1,t−1 ← capital income

+ (1− τ lt )bj,t ← pension income+ beqj,t ← bequests−Υt ← lump-sum tax

There exists a closed-form solution to this problem

4 / 13

Introduction What are these models about? Reforming Future work

Standard model: households

“Born” at age 20 (j = 1) and live up to 100 years (J = 80)Subject to time and cohort dependent survival probability πj,tChoose labor supply lj endogenouslyMaximize remaining lifetime utility derived from consumption c and leisure 1− l:

Uj,t =J−j∑s=0

[δsπj+s,t+sπj,t

[cφj+s,t+s (1− lj+s,t+s)1−φ − 1

]]

Subject to the budget constraint

(1 + τ ct )cj,t + sj,t = (1− τ lt )(1− τ)wtlj,t ← labor income

+ (1 + (1− τkt )rt)sj−1,t−1 ← capital income

+ (1− τ lt )bj,t ← pension income+ beqj,t ← bequests−Υt ← lump-sum tax

There exists a closed-form solution to this problem

4 / 13

Introduction What are these models about? Reforming Future work

Standard model: households

“Born” at age 20 (j = 1) and live up to 100 years (J = 80)Subject to time and cohort dependent survival probability πj,tChoose labor supply lj endogenouslyMaximize remaining lifetime utility derived from consumption c and leisure 1− l:

Uj,t =J−j∑s=0

[δsπj+s,t+sπj,t

[cφj+s,t+s (1− lj+s,t+s)1−φ − 1

]]Subject to the budget constraint

(1 + τ ct )cj,t + sj,t = (1− τ lt )(1− τ)wtlj,t ← labor income

+ (1 + (1− τkt )rt)sj−1,t−1 ← capital income

+ (1− τ lt )bj,t ← pension income+ beqj,t ← bequests−Υt ← lump-sum tax

There exists a closed-form solution to this problem

4 / 13

Introduction What are these models about? Reforming Future work

Standard model: households

“Born” at age 20 (j = 1) and live up to 100 years (J = 80)Subject to time and cohort dependent survival probability πj,tChoose labor supply lj endogenouslyMaximize remaining lifetime utility derived from consumption c and leisure 1− l:

Uj,t =J−j∑s=0

[δsπj+s,t+sπj,t

[cφj+s,t+s (1− lj+s,t+s)1−φ − 1

]]Subject to the budget constraint

(1 + τ ct )cj,t + sj,t = (1− τ lt )(1− τ)wtlj,t ← labor income

+ (1 + (1− τkt )rt)sj−1,t−1 ← capital income

+ (1− τ lt )bj,t ← pension income+ beqj,t ← bequests−Υt ← lump-sum tax

There exists a closed-form solution to this problem

4 / 13

Introduction What are these models about? Reforming Future work

Extension: within cohort heterogeneity I

1 Each cohort consists of M subcohorts that can differ in preferences:

Uj,m,t =J−j∑s=0

βm

[δsm

πj+s,t+sπj,t

[cφmj+s,m,t+s (1− lj+s,m,t+s)1−φm

]]

2 Within each cohort there is ex ante productivity heterogeneity ω

(1 + τ ct )cj,m,t + sj,m,t = (1− τ lt )(1− τ)ωmwtlj,m,t ← labor income

+ (1 + (1− τkt )rt)sj−1,m,t−1 ← capital income

+ (1− τ lt )bj,m,t ← pension income+ beqj,t ← bequests−Υt ← lump-sum tax

5 / 13

Introduction What are these models about? Reforming Future work

Extension: within cohort heterogeneity II

3 Hands-to-mouth consumers (e.g. financially illiterate population whichconsumes all available income): same utility function but different budgetconstraint

(1 + τ ct )cj,m,t = (1− τ lt )(1− τ)wtlj,m,t ← labor income

+ (1− τ lt )bj,m,t ← pension income+ beqj,m,t ← bequests−Υt ← lump-sum tax

4 Differences in financial literacy to form expectations about net present value ofthe future stream of income

5 Differences in “pension system” literacy to form expectations about futurepension benefits (δb/δl)

6 Other possible ideas (related to Konrad’s work)

6 / 13

Introduction What are these models about? Reforming Future work

Producers

Perfectly competitive representative firm, with Cobb-Douglas (or otherproduction) function

Yt = Kαt (γtLt)1−α

Profit maximization

max(Yt,Kt,Lt)

Yt − wtLt − (rt + d)Kt

Results in

wt = γt(1− α)k̂αtrt = αk̂α−1

t − d

where d is the capital depreciation rateand k̂ is capital per effective unit of labor

7 / 13

Introduction What are these models about? Reforming Future work

Producers

Perfectly competitive representative firm, with Cobb-Douglas (or otherproduction) function

Yt = Kαt (γtLt)1−α

Profit maximization

max(Yt,Kt,Lt)

Yt − wtLt − (rt + d)Kt

Results in

wt = γt(1− α)k̂αtrt = αk̂α−1

t − d

where d is the capital depreciation rateand k̂ is capital per effective unit of labor

7 / 13

Introduction What are these models about? Reforming Future work

Producers

Perfectly competitive representative firm, with Cobb-Douglas (or otherproduction) function

Yt = Kαt (γtLt)1−α

Profit maximization

max(Yt,Kt,Lt)

Yt − wtLt − (rt + d)Kt

Results in

wt = γt(1− α)k̂αtrt = αk̂α−1

t − d

where d is the capital depreciation rateand k̂ is capital per effective unit of labor

7 / 13

Introduction What are these models about? Reforming Future work

Government

Spends a fixed share of GDP g on government consumption

Collects taxes T

Tt =J∑j=1

M∑m=1

{Nj,m,t ·

[τ ct · cj,m,t + τkt · rt · sj−1,m,t−1

+τ lt ((1− τ)wtlj,m,t + bj,m,t)]}

Closes the gap between pension system contributions and benefits (subsidyt)Can take on debt D

Tt +Dt = (1 + rt)Dt−1 + gYt + subsidyt

8 / 13

Introduction What are these models about? Reforming Future work

Government

Spends a fixed share of GDP g on government consumptionCollects taxes T

Tt =J∑j=1

M∑m=1

{Nj,m,t ·

[τ ct · cj,m,t + τkt · rt · sj−1,m,t−1

+τ lt ((1− τ)wtlj,m,t + bj,m,t)]}

Closes the gap between pension system contributions and benefits (subsidyt)Can take on debt D

Tt +Dt = (1 + rt)Dt−1 + gYt + subsidyt

8 / 13

Introduction What are these models about? Reforming Future work

Government

Spends a fixed share of GDP g on government consumptionCollects taxes T

Tt =J∑j=1

M∑m=1

{Nj,m,t ·

[τ ct · cj,m,t + τkt · rt · sj−1,m,t−1

+τ lt ((1− τ)wtlj,m,t + bj,m,t)]}

Closes the gap between pension system contributions and benefits (subsidyt)

Can take on debt D

Tt +Dt = (1 + rt)Dt−1 + gYt + subsidyt

8 / 13

Introduction What are these models about? Reforming Future work

Government

Spends a fixed share of GDP g on government consumptionCollects taxes T

Tt =J∑j=1

M∑m=1

{Nj,m,t ·

[τ ct · cj,m,t + τkt · rt · sj−1,m,t−1

+τ lt ((1− τ)wtlj,m,t + bj,m,t)]}

Closes the gap between pension system contributions and benefits (subsidyt)Can take on debt D

Tt +Dt = (1 + rt)Dt−1 + gYt + subsidyt

8 / 13

Introduction What are these models about? Reforming Future work

Pension system – we can have it any way we like, with multiple components

Pay As You Go Defined Benefit (PAYG DB)

bJ̄,k,t = ρ · gross wageJ̄−1,k,t−1

Pay As You Go Defined Contribution (PAYG DC) pension system

bJ̄,m,t =accumulated sum of contributionsJ̄,m,t

expected remaining lifetimeJ̄,t

Voluntary pension saving schemes

9 / 13

Introduction What are these models about? Reforming Future work

Pension system – we can have it any way we like, with multiple components

Pay As You Go Defined Benefit (PAYG DB)

bJ̄,k,t = ρ · gross wageJ̄−1,k,t−1

Pay As You Go Defined Contribution (PAYG DC) pension system

bJ̄,m,t =accumulated sum of contributionsJ̄,m,t

expected remaining lifetimeJ̄,t

Voluntary pension saving schemes

9 / 13

Introduction What are these models about? Reforming Future work

Pension system – we can have it any way we like, with multiple components

Pay As You Go Defined Benefit (PAYG DB)

bJ̄,k,t = ρ · gross wageJ̄−1,k,t−1

Pay As You Go Defined Contribution (PAYG DC) pension system

bJ̄,m,t =accumulated sum of contributionsJ̄,m,t

expected remaining lifetimeJ̄,t

Voluntary pension saving schemes

9 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first periodLet economy adjust ...... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of model

Calibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first periodLet economy adjust ...... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)

Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first periodLet economy adjust ...... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first periodLet economy adjust ...... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first periodLet economy adjust ...... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first periodLet economy adjust ...... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reform

Reform introduced unexpectedly in the first periodLet economy adjust ...... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first period

Let economy adjust ...... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first periodLet economy adjust ...

... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first periodLet economy adjust ...... compare final steady states ...

but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Reforming something

Initial solution

Stable solution of modelCalibrated to replicate what we know about the economy (e.g. depreciation anddiscount rate to match investment rate in the economy)Solution satisfies kt+1 = kt which implies stability of other variables – steadystate

Transition path

Path between two steady states: with and without reformReform introduced unexpectedly in the first periodLet economy adjust ...... compare final steady states ...but also observe the process of adjustment

10 / 13

Introduction What are these models about? Reforming Future work

Consumption equivalence

Compute transition paths: status quo and reform

Calculate welfare for each cohort in each period for both pathsFind for each cohort λj that satisfies

W basej (cbasej ) = W reform

j ((1− λj)creformj )

λj is a fraction of lifetime consumption that a given cohort is willing to give upin order to introduce the reform

11 / 13

Introduction What are these models about? Reforming Future work

Consumption equivalence

Compute transition paths: status quo and reformCalculate welfare for each cohort in each period for both paths

Find for each cohort λj that satisfies

W basej (cbasej ) = W reform

j ((1− λj)creformj )

λj is a fraction of lifetime consumption that a given cohort is willing to give upin order to introduce the reform

11 / 13

Introduction What are these models about? Reforming Future work

Consumption equivalence

Compute transition paths: status quo and reformCalculate welfare for each cohort in each period for both pathsFind for each cohort λj that satisfies

W basej (cbasej ) = W reform

j ((1− λj)creformj )

λj is a fraction of lifetime consumption that a given cohort is willing to give upin order to introduce the reform

11 / 13

Introduction What are these models about? Reforming Future work

Consumption equivalence

Compute transition paths: status quo and reformCalculate welfare for each cohort in each period for both pathsFind for each cohort λj that satisfies

W basej (cbasej ) = W reform

j ((1− λj)creformj )

λj is a fraction of lifetime consumption that a given cohort is willing to give upin order to introduce the reform

11 / 13

Introduction What are these models about? Reforming Future work

What should we discuss

Which dimensions of heterogeneity we want to introduce (relationship tobounded rationality promised in project)

Which policy instruments to analyze (voluntary pension saving schemespromised in project)Possible instrumentsTax exemption on private retirement savings (with and without limits)

Does not affect HtM consumersMandatory private savings???

12 / 13

Introduction What are these models about? Reforming Future work

What should we discuss

Which dimensions of heterogeneity we want to introduce (relationship tobounded rationality promised in project)Which policy instruments to analyze (voluntary pension saving schemespromised in project)

Possible instrumentsTax exemption on private retirement savings (with and without limits)

Does not affect HtM consumersMandatory private savings???

12 / 13

Introduction What are these models about? Reforming Future work

What should we discuss

Which dimensions of heterogeneity we want to introduce (relationship tobounded rationality promised in project)Which policy instruments to analyze (voluntary pension saving schemespromised in project)Possible instruments

Tax exemption on private retirement savings (with and without limits)

Does not affect HtM consumersMandatory private savings???

12 / 13

Introduction What are these models about? Reforming Future work

What should we discuss

Which dimensions of heterogeneity we want to introduce (relationship tobounded rationality promised in project)Which policy instruments to analyze (voluntary pension saving schemespromised in project)Possible instrumentsTax exemption on private retirement savings (with and without limits)

Does not affect HtM consumersMandatory private savings???

12 / 13

Introduction What are these models about? Reforming Future work

What should we discuss

Which dimensions of heterogeneity we want to introduce (relationship tobounded rationality promised in project)Which policy instruments to analyze (voluntary pension saving schemespromised in project)Possible instrumentsTax exemption on private retirement savings (with and without limits)

Does not affect HtM consumers

Mandatory private savings???

12 / 13

Introduction What are these models about? Reforming Future work

What should we discuss

Which dimensions of heterogeneity we want to introduce (relationship tobounded rationality promised in project)Which policy instruments to analyze (voluntary pension saving schemespromised in project)Possible instrumentsTax exemption on private retirement savings (with and without limits)

Does not affect HtM consumersMandatory private savings

???

12 / 13

Introduction What are these models about? Reforming Future work

What should we discuss

Which dimensions of heterogeneity we want to introduce (relationship tobounded rationality promised in project)Which policy instruments to analyze (voluntary pension saving schemespromised in project)Possible instrumentsTax exemption on private retirement savings (with and without limits)

Does not affect HtM consumersMandatory private savings???

12 / 13

Introduction What are these models about? Reforming Future work

Thank you for your attention

13 / 13