Pension Reform, Factor Mobility and Trade with Country-Specific Goods

Abstract

This paper studies the effects of pension reform in a two-country model with country-specific goods. It shows that in the case of dynamic efficiency, a switch from a pay-as-you-go to a more-funded pension scheme leads to an inflow of labour to the reforming country. Reallocation of capital depends on the degree of substitutability between goods produced in the countries. If the goods produced in the countries are substitutes (complements), capital stock grows (declines) in the reformed country relative to the neighbouring country. Social security reform makes goods produced in the reformed country cheaper; this has an additional negative effect on the old generation in the reformed country, but compensates the old generation in the neighbouring country with cheaper imports due to a reduction in the tax base arising from emigration.

Appendix

1.1 Derivation of Equation (5)

As mentioned in the text, if an agent chooses to exchange one unit of goods produced in the Home country for composite goods, her optimal inputs to composite goods are $X_{t}= 1/\big (1+p_{t}^{1-\theta }\big ((1-\gamma )/\gamma \big )^\theta \big )$ and $X_{t}^{'}=1/\big (p_{t}+\big (p_{t}\gamma /(1-\gamma )\big )^\theta \big )$. Inserting these values into Eq. (3) we find, that she can buy

$$\begin{aligned} \pi _{t}&= \bigg [ \gamma \bigg ( \frac{1}{1+p_{t}^{1-\theta } \big (\frac{1-\gamma }{\gamma }\big )^\theta } \bigg )^{1-1/\theta } +(1-\gamma ) \bigg ( \frac{1}{p_{t}+\big (\frac{p_{t} \gamma }{1-\gamma } \big )^\theta } \bigg )^{1-1/\theta } \bigg ]^\frac{\theta }{\theta -1}\\&= \frac{\gamma ^\frac{\theta }{\theta -1}}{1+p_{t}^{1-\theta }\big (\frac{1-\gamma }{\gamma } \big )^\theta } \bigg [1+ \frac{1-\gamma }{\gamma } \bigg ( \frac{1+p_{t}^{1-\theta } \big (\frac{1-\gamma }{\gamma }\big )^\theta }{p_{t}+\big (\frac{p_{t} \gamma }{1-\gamma } \big )^\theta } \bigg )^{1-1/\theta } \bigg ]^\frac{\theta }{\theta -1} \end{aligned}$$

composite goods. Note that

$$\begin{aligned} \frac{1+p_{t}^{1-\theta } \big (\frac{1-\gamma }{\gamma }\big )^\theta }{p_{t}+\big (\frac{p_{t} \gamma }{1-\gamma } \big )^\theta } =\bigg (\frac{1-\gamma }{\gamma }\bigg )^\theta p_{t}^{-\theta }, \end{aligned}$$

then

$$\begin{aligned} \pi _{t}&= \frac{\gamma ^\frac{\theta }{\theta -1}}{1+p_{t}^{1-\theta }\big (\frac{1-\gamma }{\gamma } \big )^\theta } \bigg [1+p_{t}^{1-\theta } \bigg (\frac{1-\gamma }{\gamma } \bigg )^\theta \bigg ]^\frac{\theta }{\theta -1} \\&= \gamma ^{\frac{\theta }{\theta -1}} \bigg [1+p_{t}^{1-\theta }\bigg (\frac{1-\gamma }{\gamma } \bigg )^\theta \bigg ]^\frac{1}{\theta -1}. \end{aligned}$$

1.2 Derivation of Equation (17)

Inserting $C_{t}^{y}=\Psi _{t}^{y}/\big (1+p_{t}^{1-\theta }((1-\gamma )/\gamma )^\theta \big )$, $C_{t}^{'y}= \Psi _{t}^{y}\big (p_{t}+(p_{t} \gamma /(1-\gamma ))^\theta \big )$ and so forth to Eqs. (15–16), we get

$$\begin{aligned} Y_{t}&= \frac{L_{t} s_{t}+\tilde{L}_{t}\tilde{s}_{t} +L_{t} \Psi _{t}^{y}+ \tilde{L}_{t}\tilde{\Psi }_{t}^{y}+L_{t-1} \Psi _{t}^o +\tilde{L}_{t-1} \tilde{\Psi }_{t}^{o}}{1+p_{t}^{1-\theta }\big ((1-\gamma )/\gamma \big )^\theta },\\ \tilde{Y}_{t}&= \frac{L_{t} s_{t}+\tilde{L}_{t}\tilde{s}_{t} + L_{t} \Psi _{t}^{'y}+\tilde{L}_{t}\tilde{\Psi }_{t}^{'y} +L_{t-1} \Psi _{t}^{'o} +\tilde{L}_{t-1} \tilde{\Psi }_{t}^{'o}}{p_{t}+\big (p_{t} \gamma /(1-\gamma )\big )^\theta }. \end{aligned}$$

Dividing one equation by another we get Eq. (17).