Pension Reductions and Retirement Delays Author: Marie-Eve Lachance Discussant: Casey Rothschild, Middlebury College

Stripped-Down Model  Individuals choose retirement date τ and consumption c t to maximize lifetime utility:  Subject to a lifetime budget constraint: Depends on τ via disutility of effort/utility of leisure Pre-existing wealth Labor Income Pension Wealth

Stripped Down Model (2)  Solve for optimal c t, for each given τ. Simplified problem:  Solving gives lifetime utility V * and optimal retirement date τ *. PV of lifetime earnings PV of Pension Wealth Direct Dependence on τ from Disutility of Labor

What happens when A decreases?  Utility decreases from V * to V **.  Key Question: How much lower is V ** ? “Naïve” answer: Naïve because fails to recognize endogeneity of τ. More sophisticated: delaying retirement can help offset the utility shock from A’<A.  But by how much?

Stylized “gist” (2)  Earlier literature (loosely) Delay of a few years can completely offset financial consequences of a 10% fall in A. So perhaps V ** ≈V * >> V Naive.  Lachance’s Paper: NO. Utility cost of working longer essentially undermines the whole benefit of delay.

Conclusions  Lachance: V** ≈ V Naive << V *  Numerically: a 10% decrease in retirement benefits Decreases welfare by $23,897 (Wealth Equiv) if don ’ t adjust retirement date Decreases welfare by $23,582 if does. Only a $315 difference!  Intuition: Envelope theorem

Comment 1: the fly and the maul?  Lachance’s model is sophisticated: A riskless and a (Brownian) risky asset. An exogenously imposed and stochastic retirement date τ Exo.  Makes solving for lifetime utility an extremely challenging (technical appendix plus supplementary material).  Kudos for the technical prowess. Some insight on what it adds would help.

Comment (2): Exogenous Retirement  Paper’s policy recommendations focus on increasing the exogenous retirement age.  Is this orthogonal to the key issues? Relaxing the exogenous retirement age is a response to inefficiently early exogenous retirement dates, not reductions in pension generosity per se.  Perhaps a model of optimal exogenous retirement dates to make the connection? Potential concern: optimality -> envelope theorem again?

Comment (3): Symmetric treatment of pension and earned wealth  Pension income is treated as a riskless bond Single lifetime budget constraint implicitly allows borrowing against pension income at the market interest rate.  Advantage: Analytically solvable.  Disadvantage: realism? Typical assumption: no borrowing against pension income.