Automatic adjustment mechanisms and budget balancing · PDF fileAutomatic adjustment...

Automatic adjustment mechanisms and budgetbalancing of pension schemes

Frédéric Gannon (U. Le Havre)Florence Legros (U. Dauphine, Paris)

Vincent Touzé (OFCE - Sciences Po, Paris)

November 2013

Gannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 1 / 36

IntroductionPreliminary remarks (1)

In general, governments are reluctant to reform pension systems,fearing that the reforms might induce too high political costs. As aconsequence, they tend to procrastinate and to postpone theadoption of measures that would guarantee solvency.

Of course, faced with the emergency of the insolvency of theirpension systems, all governments have conducted reforms - some ofthem very substantial - but without setting restoring forces. Theproblem with ad hoc reforms is that, quoting Turner (2009), "(they)have a high degree of political risk because their timing andmagnitude are unknown".



In general, governments are reluctant to reform pension systems,fearing that the reforms might induce too high political costs. As aconsequence, they tend to procrastinate and to postpone theadoption of measures that would guarantee solvency.

Of course, faced with the emergency of the insolvency of theirpension systems, all governments have conducted reforms - some ofthem very substantial - but without setting restoring forces. Theproblem with ad hoc reforms is that, quoting Turner (2009), "(they)have a high degree of political risk because their timing andmagnitude are unknown".



To avoid that the future states of the pension system depend onchoices that politicians would not take willingly, two types ofstrategies are used by governments:

Delegate the management of the pension systems to competentindependent authorities.Introduce new rules to allow for Automatic AdjustmentMechanisms (AAM). =) guarantee the solvency of the system atany date without needing political intervention and eliminating the"need for large program changes made in crisis mode" (Turner, 2009).




Delegate the management of the pension systems to competentindependent authorities.

Introduce new rules to allow for Automatic AdjustmentMechanisms (AAM). =) guarantee the solvency of the system atany date without needing political intervention and eliminating the"need for large program changes made in crisis mode" (Turner, 2009).




Delegate the management of the pension systems to competentindependent authorities.Introduce new rules to allow for Automatic AdjustmentMechanisms (AAM). =) guarantee the solvency of the system atany date without needing political intervention and eliminating the"need for large program changes made in crisis mode" (Turner, 2009).



This means straightforward and clear choices about transfers betweengenerations + strong underlying social acceptance. To avoid regularand politically costly ad hoc reforms, Sweden was the �rst to designNotional De�ned Contributions (NDC) plans in 1994.

To reinforce the robustness of the system, it has launched anAutomatic Balance Mechanism (ABM) that relies on the key rulethat every year, the solvency of the pension system must be checked,permitted by the �exibility of the present and future pension bene�ts(Settergren, 2001). The return of the "savings" invested in the NDCcrucially depends on this indexation.



This means straightforward and clear choices about transfers betweengenerations + strong underlying social acceptance. To avoid regularand politically costly ad hoc reforms, Sweden was the �rst to designNotional De�ned Contributions (NDC) plans in 1994.To reinforce the robustness of the system, it has launched anAutomatic Balance Mechanism (ABM) that relies on the key rulethat every year, the solvency of the pension system must be checked,permitted by the �exibility of the present and future pension bene�ts(Settergren, 2001). The return of the "savings" invested in the NDCcrucially depends on this indexation.


IntroductionAims of the paper

)Characterizing the properties of the Automatic AdjustmentMechanisms (AAMs) and proposing a general form of AutomaticBalance Mechanism (ABM) based on dynamic programming and theminimization of a loss function.


IntroductionOrganization of the presentation

1 De�nition of the intertemporal pension budget constraint.

2 Addressing the issue of AAM: what are their roles in adjusting,stabilizing and balancing?

3 Building a "smooth" ABM (S-ABM), assuming a trade-o¤ betweenpresent and future receipts and expenditures.

4 Application of our S-ABM to the U.S. Social Security.



1 De�nition of the intertemporal pension budget constraint.2 Addressing the issue of AAM: what are their roles in adjusting,stabilizing and balancing?














1. The intertemporal pension budget balanceBudget constraint

The budget constraint of the pension system writes at time t:

Ft�1|{z} +Reserve fund

interest ratez}|{rt � Ft�1 +

contrib. ratez}|{τt � ∑

a

aver. wagez}|{wa,t �

employ. ratez}|{ea,t �

populationz}|{Na,t| {z }

Total revenues=

∑a

aver. pensionz}|{pa,t �

% of retired peoplez}|{λa,t �

populationz}|{Na,t| {z }

Total expenses

+ Ft|{z}Reserve fund


1. The intertemporal pension budget constraintWhat about solvency (Boado-Penas, Vidal-Meliá and Sakamoto, 2010)?

Accountancy point of view: di¤erent methods to estimate the implicitliabilities and the solvency of unfunded pension systems.In practice, two measures of solvency are used:

Assessing the discounted sum of revenues and expenditures: used inthe United States to estimate the present value of the underfundingof the system.

Another method is adopted by Sweden (Settergren, 2001). It de�nesits pension plan is solvent when:Present value of contributions payable by workers alive today+ Value of the reserve fund=Value of pension commitments towards generations alive today.


1. The intertemporal pension budget constraintWhat about solvency (Boado-Penas, Vidal-Meliá and Sakamoto, 2010)?

Accountancy point of view: di¤erent methods to estimate the implicitliabilities and the solvency of unfunded pension systems.In practice, two measures of solvency are used:

Assessing the discounted sum of revenues and expenditures: used inthe United States to estimate the present value of the underfundingof the system.

Another method is adopted by Sweden (Settergren, 2001). It de�nesits pension plan is solvent when:Present value of contributions payable by workers alive today+ Value of the reserve fund=Value of pension commitments towards generations alive today.


2. Automatic rules: adjusting, stabilizing and balancingDe�nition

With the AAM, the institutional parameters are adjusted according to theprede�ned rules. Otherwise, the changes are considered as discretionarydecisions. They are therefore subject to the hazards of political choice.



Choosing a speci�c Automatic Adjustment Mechanism requires to de�neseveral elements (see Bosworth and Weaver, 2011):

1 Legitimating the rules according to the example "one objective, onetool." We need to identify objectives and tools (parameters). Mainobjectives concern equity, social justice and solvency.

2 De�ning the frequency of reviewing/updating.3 Choosing the elements underlying the adjustment.4 Setting adjustments as ex ante based on expectations(prediction-based) or ex post based on the states of nature.

5 Fixing the degree of automaticity (no questioning): the adjustmentsare mandatory, which guarantees credibility of the process.





2 De�ning the frequency of reviewing/updating.

3 Choosing the elements underlying the adjustment.4 Setting adjustments as ex ante based on expectations(prediction-based) or ex post based on the states of nature.






2 De�ning the frequency of reviewing/updating.3 Choosing the elements underlying the adjustment.

4 Setting adjustments as ex ante based on expectations(prediction-based) or ex post based on the states of nature.















2. Automatic rules: adjusting, stabilizing and balancingHow the Automatic Adjustment Mechanisms (AAM) contribute to stabilize pensionschemes

Bene�ts index: For each retiree i , the pension bene�t evolves eachyear as follows: pi = I � p�i where I is an indexing factor. The mainobjective of the indexing factor is to preserve the level of quality oflife. In general, I corrects the increase in the cost of living andpermits to maintain the purchase power of the pension.


2. Automatic rules: adjusting, stabilizing and balancingHow the Automatic Adjustment Mechanisms (AAM) contribute to stabilize pensionschemes

Contributory period: To obtain a full pension requires to validate asu¢ cient number of quarters. The duration of the assessment periodcan be connected to life expectancy.

Retirement age ("normal" or minimum): In many countries, thereforms have modi�ed the law relative to the legal retirement ages.The minimum age is the age at which workers can liquidate theirpensions (for example, 61 y.o in Sweden).

Pension-earnings links: In Sweden, the coe¢ cient of conversion ofcapital into an annuity depends on the age and the birth year. Thiscoe¢ cient is revised to re�ect the evolution of generation mortalitytables.


2. Automatic rules: adjusting, stabilizing and balancingTowards Automatic Balance Mechanisms (ABM)

What happens if AAM are not su¢ ciently stabilizing?In 2001, Sweden opted for a type of ABM. The choice of an ABM raisesfour major issues:

1 How is de�ned the pension budget balance?

2 What are the criteria for choosing changes in current law?3 What room is left for optimization?4 What planning time horizon for full balancing?




1 How is de�ned the pension budget balance?2 What are the criteria for choosing changes in current law?

3 What room is left for optimization?4 What planning time horizon for full balancing?




1 How is de�ned the pension budget balance?2 What are the criteria for choosing changes in current law?3 What room is left for optimization?

4 What planning time horizon for full balancing?




1 How is de�ned the pension budget balance?2 What are the criteria for choosing changes in current law?3 What room is left for optimization?4 What planning time horizon for full balancing?



Main choices: de�ning a reference horizon and the frequency of theautomatic adjustments.

What about the forecasts?

As the other AAM, the Automatic Balance Mechanisms can bedetermined:- ex ante: shocks are anticipated and changes in law are planned.- ex post: the law evolves w.r.t to the knowledge of the states of nature.

AAM ) Changes of the pension formula parameters and thecontribution rate.

It can be interesting to plan the budget balance on a large number ofperiods. But the thorniest question is:

How to plan a sequence of changes in pension parameters?

That requires to identify an objective function.Gannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 14 / 36

3. In search of a smoth ABM (S-ABM)

We develop a "simple" model.

The objective function is de�ned as a quadratic loss function.Quadratic cost functions are commonly used in the analysis ofmonetary policy (Svensson, 2003).

A similar approach applied to retirement has been developed byBerger and Lavigne (2007). But their adjustment relates solely to thecontribution rate, and the social cost is measured by the square of thechange in each period. Moreover, they do not introduce intertemporaldiscount, which leaves no possibility of procrastination. Here theapproach is improved because it leaves two possible adjustmentmodes: by costs and/or by revenues.



With ABM, the adjustment should result in incremental changes.Indeed, it is hoped that the AAM lead to su¢ cient adjustments andthey contribute to a better �nancial balance. The ABM is an ultimatesetting that should be expected to be marginal. At each period, the"ideal" timing ought to be:

First step: the public planner sets the values of the pension parameters;Second step: she checks the solvency of the pension schemes;Third step: she uses ABM to recalibrate the parameters.

Of course, it would be naive to think that minimizing a quadratic lossfunction could be su¢ cient to capture all the problems related to theadjustment of the pension system. However, the quadratic loss is away to catch the public will to change smoothly the currentlegislation.



The value of the loss associated to each period is measured by:

LFt = α � (At � 1)2 + (1� α) � (Bt � 1)2 . (1)

where At and Bt are two deformation coe¢ cients which modifyrespectively the present and future payroll taxes and pension expendituresrelatively to those established by the current law. This loss functioncaptures the fact that changing parameters is costly (both socially andpolitically) and that minimizing it means the social planner hopes to limitchanges.



The social planner sets a time horizon T to balance the sum of discountedreceipts and the sum of discounted expenditures.The optimizing program is:8<: min

fAt ,Btg∑Tt=1 βt�1 � LFt

s.t. ∑Tt=1

At �τt �wt �et �LtΠti=2Ri

+ R1 � F0 = ∑Tt=1

Bt �ρt �wt �dt �LtΠti=2Ri

. (2)



The F.O.C gives:(At : βt�1 � 2 � α � (At � 1) = ψ � τt �wt �et �Lt

Πti=2Ri

Bt : βt�1 � 2 � (1� α) � (Bt � 1) = �ψ � ρt �wt �dt �LtΠti=2Ri

. (3)

where ψ is the Lagrange multiplier.



We identify A1 and B1 :8>>>>><>>>>>:A1 = 1�

FTΠTi=1Ri

∑Tt=1

1

βt�1 �(Πti=1Ri )2 ��(τt �wt �et �Lt )2+ α

1�α �(ρt �wt �dt �Lt )2

τ1 �w1 �e1 �L1

�

B1 = 1+FT

ΠTi=1Ri

∑Tt=1

1

βt�1 �(Πti=1Ri )2 ��1�α

α �(τt �wt �et �Lt )2+(ρt �wt �dt �Lt )2ρ1 �w1 �d1 �L1

�(4)



and deduce the dynamics of coe¢ cients adjustment:8<: At = 1+ τt �wt �et �Ltτ1 �w1 �e1 �L1 �

1βt�1 �Πt

i=2Ri� (A1 � 1)

Bt = 1+ρt �wt �dt �Ltρ1 �w1 �d1 �L1

� 1βt�1 �Πt

i=2Ri� (B1 � 1)

(5)



This maximizing problem can be completed by adding constraints on thelevel of the reserve fund (FT > 0 or Ft � 0 8t without debt constraint) orthe adjustment parameters.



These results can be interpreted in three ways:

At and Bt can induce practical implications in terms of pensionreforms. They de�ne distances to a �xed target in terms of payrolltaxes (receipts) and pension bene�ts (expenditures).

Measuring At and Bt would show how the pension schemes arestrongly unbalanced in the long run;

Revealed preferences: reforms imply changes in legislation. The levelsof expenditures and receipts are modi�ed w.r.t a previous scenariowithout reform. Assuming At and Bt to be measured with accuracywould associate public decisions with an implicit function of publicpreferences.














4. Applications of the S-ABM o the U.S. Social SecuritySensitivity analysis

Fig. 1. Sensitivity to the social weighting (α)Gannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 24 / 36

4. Applications of the S-ABM to the U.S. Social SecuritySensitivity analysis

Fig. 2a. Sensitivity to the time preference (δ)Gannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 25 / 36


Fig. 2b. δ : Time lag before a signi�cant adjustment (At)Gannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 26 / 36


Fig. 2c. δ : Time lag before a signi�cant adjustment (Bt)Gannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 27 / 36


Fig. 3. Sensitivity to the time horizon (T )Gannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 28 / 36

4. Applications of the S-ABM to the U.S. Social SecurityGlobal analysis of a benchmark S-ABM

For the following set of parameters, α = 0.5, β = 0.975 and T = 75, wecompute the evolution of the adjustment coe¢ cients. Note that wecompute the "mixed" tax gap with a 50%/50% weighting: A = 1.085 andB = 0.915.



Fig. 4. Adjustment coe¢ cients



Fig. 5. Generational impactGannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 31 / 36


Fig. 6. Adjustment Primary balanceGannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 32 / 36


Fig. 7. AssetGannon-Legros-Touzé (PBSS-IA) Automatic Adjustment Mechanisms November 2013 33 / 36

Conclusion

This article has identi�ed di¤erent types of AAM that can beimplemented and has shown how they contribute to a better solvency.

Similarly as in the Swedish pension, we propose to build an ABM in adynamic programming setting. For a given planning horizon, weobtain formulas that determine how at each period revenues andexpenses must be adjusted. That allows to consider the ABM chosenby Sweden as a special case.


Conclusion

This article has identi�ed di¤erent types of AAM that can beimplemented and has shown how they contribute to a better solvency.

Similarly as in the Swedish pension, we propose to build an ABM in adynamic programming setting. For a given planning horizon, weobtain formulas that determine how at each period revenues andexpenses must be adjusted. That allows to consider the ABM chosenby Sweden as a special case.


Conclusion

Sweden is the only country that strengthens its AAM with an ABMthat ensures �nancial stability. Indeed, the Swedish ABM can beobtained by assuming very high adjustment costs on revenue andchoosing a particular concept of measure of solvency.

We apply these formulas to the �nancial balances of the Americansystem. Using dynamic programming avoids brutal adjustments andthus moderates or smooths the marginal adjustments necessary for�nancial stability.


Conclusion

Sweden is the only country that strengthens its AAM with an ABMthat ensures �nancial stability. Indeed, the Swedish ABM can beobtained by assuming very high adjustment costs on revenue andchoosing a particular concept of measure of solvency.

We apply these formulas to the �nancial balances of the Americansystem. Using dynamic programming avoids brutal adjustments andthus moderates or smooths the marginal adjustments necessary for�nancial stability.


Conclusion

However, this exercise of dynamic programming presents a majorlimit. In e¤ect, the ABM is evaluated in a context where economicvariables are assumed to be exogenous. A study of the relationshipbetween the �tting parameters and the evolution of the economy canbe a natural extension of this article. From a macroeconomic point ofview, OLG-CGE models have been developed to estimate the impactof Social Security reforms in an intertemporal and intergenerationalgeneral equilibrium framework. Such models are used to "optimize"Social Security reforms. Furthermore, dynamic microsimulationmodels give a lot of details on the microeconomic impacts of SocialSecurity reforms.


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