International Welfare Spillovers of National Pension Schemes

James Staveley-O’Carroll; Olena M. Staveley-O’Carroll

doi:10.1515/bejm-2019-0207

Published by De Gruyter July 13, 2020

International Welfare Spillovers of National Pension Schemes

James Staveley-O’Carroll and Olena M. Staveley-O’Carroll

From the journal The B.E. Journal of Macroeconomics

https://doi.org/10.1515/bejm-2019-0207

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Abstract

We employ a two-country overlapping-generations model to explore the international dimension of household portfolio choices induced by the asymmetric provision of government-run pensions. We study the resulting patterns of risk-sharing and the corresponding welfare effects on both home and foreign agents. Introducing the defined benefits pay-as-you-go system at home increases the welfare of all other agents at the expense of the home workers and improves the degree of intergenerational risk sharing abroad. Conversely, a defined contributions system leads to welfare losses of both home cohorts accompanied by gains abroad, but does increase the extent of intergenerational risk sharing at home.

Keywords: welfare; pay-as-you-go system; international portfolio choice; OLG model

JEL Classification: D52; F21; F41; G11; H55

Corresponding author: James Staveley-O’Carroll, Economics Division, Babson College, 231 Forest Street, Babson Park, MA02457, USA, E-mail: jstaveleyocarroll1@babson.edu

Acknowledgments

We would like to thank conference participants at the 2018 Infiniti Conference on International Finance, Southern Economic Association 2018 Annual Meeting, and the 14th Annual Conference of Macroeconomists from Liberal Arts Colleges for valuable comments and suggestions. All remaining mistakes are our own.

Appendix

The Social Planner’s Problem

The social planner maximizes the Lagrangian (21) by choosing the optimal home and foreign consumption levels of each cohort, where (5) and (6) can be monotonically transformed by

vti,j=11−γ(υti,j)1−γ for i={h, f} and j={t, t−1}

into

vth,t=11−γ{(cth,t)1−γ+βE[(ct+1h,t)1−α]1−γ1−α}vth,t−1=11−γ(cth,t−1)1−γvtf,t=11−γ{(ctf,t)1−γ+βE[(ct+1f,t)1−α]1−γ1−α}vtf,t−1=11−γ(ctf,t−1)1−γ

and consumption baskets are defined in (1).

This optimization gives the following first order conditions:

(25)λh,t=ϕh,t1−σ(ch,th,t)σ−1[ϕh,t1−σ(ch,th,t)σ+(1−ϕh,t)1−σ(cf,th,t)σ]1−γ−σσλf,t=(1−ϕh,t)1−σ(cf,th,t)σ−1[ϕh,t1−σ(ch,th,t)σ+(1−ϕh,t)1−σ(cf,th,t)σ]1−γ−σσλh,t=ϕh,t1−σ(ch,th,t−1)σ−1[ϕh,t1−σ(ch,th,t−1)σ+(1−ϕh,t)1−σ(cf,th,t−1)σ]1−γ−σσλf,t=(1−ϕh,t)1−σ(cf,th,t−1)σ−1[ϕh,t1−σ(ch,th,t−1)σ+(1−ϕh,t)1−σ(cf,th,t−1)σ]1−γ−σσλh,t=(1−ϕf,t)1−σ(ch,tf,t)σ−1[ϕf,t1−σ(cf,tf,t)σ+(1−ϕf,t)1−σ(ch,tf,t)σ]1−γ−σσλf,t=ϕf,t1−σ(cf,tf,t)σ−1[ϕf,t1−σ(cf,tf,t)σ+(1−ϕf,t)1−σ(ch,tf,t)σ]1−γ−σσλh,t=(1−ϕf,t)1−σ(ch,tf,t−1)σ−1[ϕf,t1−σ(cf,tf,t−1)σ+(1−ϕf,t)1−σ(ch,tf,t−1)σ]1−γ−σσλf,t=ϕf,t1−σ(cf,tf,t−1)σ−1[ϕf,t1−σ(cf,tf,t−1)σ+(1−ϕf,t)1−σ(ch,tf,t−1)σ]1−γ−σσ

Note that the equations for the young and old cohorts are the same for each country, which implies that cth,t=cth,t−1 and ctf,t=ctf,t−1. Next, combine the Euler equations (25) of the young cohorts to get the optimal ratio of home and foreign consumption for the young cohorts:

(26)cf,th,tch,th,t=(1−ϕh,t)ϕh,t(λh,tλf,t)11−σch,tf,tcf,tf,t=(1−ϕf,t)ϕf,t(λf,tλh,t)11−σ.

Plug the optimal consumption ratios (26) into the definitions of the consumption baskets (1) to get optimal bundles in terms of only home or foreign consumption:

(27)cth,t=1ϕh,t[ϕh,t+(1−ϕh,t)(λh,tλf,t)σ1−σ]1σch,th,tctf,t=1ϕf,t[ϕf,t+(1−ϕf,t)(λf,tλh,t)σ1−σ]1σcf,tf,t

Recombine the Euler equations (25) with optimal ratios (26) to solve for consumption of home goods by the young home cohort and consumption of foreign goods by the young foreign cohort:

(28)ch,th,t=ϕh,t(λh,t)−1γ[ϕh,t+(1−ϕh,t)(λh,tλf,t)σ1−σ]1−γ−σγσcf,tf,t=ϕf,t(λf,t)−1γ[ϕf,t+(1−ϕf,t)(λf,tλh,t)σ1−σ]1−γ−σγσ

Solve for the optimal consumption bundles in terms of the Lagrangian multipliers using (27) and (28):

(29)cth,t={[ϕh,t(λh,t)σσ−1+(1−ϕh,t)(λf,t)σσ−1]1−σσ}1γctf,t={[ϕf,t(λf,t)σσ−1+(1−ϕf,t)(λh,t)σσ−1]1−σσ}1γ

Equation (29) imply the following:

(30)cth,tctf,t={[ϕh,t(λh,t)σσ−1+(1−ϕh,t)(λf,t)σσ−1]1−σσ[ϕf,t(λf,t)σσ−1+(1−ϕf,t)(λh,t)σσ−1]1−σσ}1γ

Observe that λh,t=Ph,t and λf,t=StPf,t, as these are the shadow prices of home and foreign goods from the social planner’s problem, then employ (3) to find that

Pth=[ϕh,t(λh,t)σσ−1+(1−ϕh,t)(λf,t)σσ−1]σ−1σStPtf=[ϕf,t(λf,t)σσ−1+(1−ϕf,t)(λh,t)σσ−1]σ−1σ

represents the CPIs of the home and foreign consumption baskets, respectively. Recall the definition the RER as

qt=StPtfPth

Then equation (30) implies that

Cth,tCtf,t=qt1γ.

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Received: 2019-10-08

Accepted: 2020-05-31

Published Online: 2020-07-13

International Welfare Spillovers of National Pension Schemes

Abstract

Acknowledgments

The Social Planner’s Problem

References

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