Introduction What are these models about? Reforming Future work Overlapping generations model and within cohort heterogeneity Jan Woznica Beethoven Project meeting, November 2016 1 / 13
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