Abstract
This study employs a two-country overlapping generations (OLG) model to examine how the pay-as-you-go (PAYG) pension system affects national welfare through changes in capital accumulation. In a closed economy, increase in per capita pension reduces individual savings, and the decrease in capital weakens welfare under dynamic efficiency. However, when a two-country model with capital mobility is considered, the increase in pension plan in a country may increase the welfare of the capital-exporting country. Employing a two-country model in which capital accumulates and moves between two countries, we present the marginal effect of pension plans on countries’ welfare for the steady-state generations and initial and transitional generations. We demonstrate that a paradoxical result occurs when the increase in pension plans in a country improves the country’s welfare because a higher interest rate improves the capital-exporting country’s intertemporal terms of trade. However, we show that the marginal change in a country’s PAYG pension plan cannot simultaneously improve both countries’ welfare in the steady state.
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Notes
The PAYG pension system is common in developed countries, such as Japan, the UK, Germany, and Canada, and even in emerging countries such as China, where the PAYG pension system was adopted in cities. For example, in Japan, pension benefits are about 0.5 trillion US dollars and exceeds 10% of GDP. However, in recent decades, the continuous decline in the total fertility rate has raised significant concerns regarding the sustainability of the PAYG pension system. For an ideal pension system, refer to The World Bank (1994) and Orszag and Stiglitz (2001).
The issues examined by Casarico (2001) relate closely to the ones we examine because both studies focus on the international effect of pension systems on welfare through capital markets. However, there are three differences. First, Casarico (2001) focuses only on the transition from a closed economy to an open one and qualitatively compares the different economic situations, whereas this study examines how the marginal increase in pension benefit affects the welfare of both countries. Second, Casarico (2001) assumes that when a country adopts the PAYG pension system, it becomes a net borrower on the capital market. However, we consider a general situation wherein a country is a capital borrower or lender. Third, although not an essential difference, in Casarico’s (2001) analysis, one country adopts the PAYG pension system, whereas another adopts the funded pension system. In our study, both countries adopt PAYG pension systems.
Notably, in the log-linear utility function setting, savings do not depend on the interest rate. However, in our setting, where the PAYG pension system is considered, savings depend on the interest rate even if the utility function is log-linear. To avoid the complexity of analysis, we limit the argument to the log-linear utility function. Hamada et al. (2017) deal with the PAYG pension system when utility is a general functional form.
The first-order partial derivatives of \(\widetilde{w}_{t}^{i}\) are as follows: \(\partial \widetilde{w}_{t}^{i}/\partial p_{t}^{i} =-1\), \(\partial \widetilde{w}_{t}^{i}/\partial p_{t+1}^{i} =(1+n)/(1+r_{t+1})\), and \(\partial \widetilde{w}_{t}^{i}/\partial r_{t+1} =-(1+n)p_{t+1}^{i}/(1+r_{t+1})^{2}<0\).
Haaparanta (1989) considers a general setting on utility function and assumes that savings increase with the interest rate, that is, \(s_{r}\ge 0\). Although the study focuses on a log-linear utility function, savings increase with the interest rate when the PAYG pension system is considered.
Although the substitution effect and the income effect cancel each other out when the utility function is log-linear, a substantial decrease in pension benefits due to an increase in the interest rate increases the savings.
Since \(\Gamma =\Delta +(s_{w}^{A}+s_{w}^{B})k\), an additional assumption is required to guarantee the dynamic stability in addition to Walrasian stability.
In the steady state, we omit the time variable.
Note that this result is obtained even under the assumption that the utility function is log-linear because the PAYG pension system exists.
For a similar analysis on the impact of pension on welfare in a transitional process, refer to Hu (2019).
However, the opposite result does not necessarily hold. If capital exports are sufficiently large even when the country is a net capital exporter, curve \(UU'\) exhibits a gentler slope than curve \(FF'\).
A substantial increase in pension contributions reduces utility under dynamic efficiency for any combination of r and w. However, in this subsection, because we consider a marginal increase in the pension contributions from no pension policy, we focus only on the transitional processes caused by the changes in capital accumulation while ignoring the income effect of pension contributions.
Broadly, using an OLG model to examine two countries with different population growth rates has complicated the analysis considerably. However, a few exceptions, such as Hamada et al. (2019), examine the impact of international transfer in an OLG model when population growth rates contrast between two countries.
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Acknowledgements
We thank Tsuyoshi Shinozaki and Hideya Kato for their valuable suggestions. The authors are solely responsible for any remaining errors.
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This study was supported by JSPS KAKENHI (grant numbers 19K01679 (Hamada, Kaneko, and Yanagihara); 20K01629 (Hamada); 17K03762, 19H01505 (Yanagihara)).
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Hamada, K., Kaneko, A. & Yanagihara, M. Impact of PAYG pensions on country welfare through capital accumulation. Int Econ Econ Policy 21, 207–226 (2024). https://doi.org/10.1007/s10368-024-00585-0
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DOI: https://doi.org/10.1007/s10368-024-00585-0