Silviase/jgov_v1.4_full_ann huggingface dataset:
we also include government; (iv) we analyze the effects of policy changes on international capital flow.

The rest of this paper is organized as follows. Section 2 depicts the model. Section 3 presents the values of the parameters and the scenarios, and the results are given. Finally, Section 4 concludes the paper.

### 2. The Model Structure and Parameterization of the Model

#### 2.1. The Model

In this section, we present the model we use in this paper, and then we describe the choice of demographic, preference and technology parameters used in the baseline simulations. The model used here is a computable two-country multi-period overlapping generations model with perfect foresight agents developed by Sadahiro and Shimasawa (1999). Since our purpose is to estimate the effects of differences in age structure and the effects of policy changes on international capital flow, the countries we consider (country A and country B) are assumed to be exactly the same in every aspect except for the population growth rate, n, after the transition starts. Each of the countries is populated by 60-period living generations. And each country has a household sector, firm sector, government sector, and public pension sector. But before we move on to the main subject, it is necessary to pay attention to some features of the economy from which we abstract. First, our model is entirely real. It has no money, only real debt. Second, uncertainty does not exist, i.e. we consider a non-stochastic world. Finally, we assume an inelastic labor supply. In addition, we do not believe the results gained from following analysis will be changed greatly by introducing these omitted factors into our model. Below, we briefly review the outline of each sector $ ^{2} $ .

## (1) Household Behavior

There is a representative individual for each generation in the household
sector. Each individual lives for a fixed number of periods (60 periods) and maximizes his/her intertemporal utility function with consumption. They are also assumed to be rational, to have perfect foresight. Each generation enters the labor market at age 21 ( $ 1^{st} $ period), retires at age 64 ( $ 44^{th} $ period), is granted a pension at 65 ( $ 45^{th} $ period), and dies at age 80 ( $ 60^{th} $ period). In addition, each supplies labor inelastically. His/her utility functions are specified as

$$ U_{i}=\sum_{j=l}^{60}\left(\frac{1}{1+\rho}\right)^{j-l}\frac{\left[c_{i,j}\right]^{I-\gamma}}{1-\gamma} $$

where i refers to the i th generation, j refers to the j th period of life, $ \rho $ is the pure rate of time preference, and $ \gamma $ is the reverse of the elasticity of intertemporal substitution. The arguments of the utility function are the consumption per period $ (c_{i,j}) $ .

His/her intertemporal budget equation may be described as follows:

$$ \sum_{j=I}^{44}PDV_{i,j}(I-\tau w_{t}-\tau p_{t})w_{t}(I+\lambda)^{t}e_{j}+\sum_{j=45}^{60}PDV_{i,j}p_{i,j}=\sum_{j=I}^{60}PDV_{i,j}(I+\tau c_{t})c_{i,j} $$

where PDV refers to the factor of the present discounted value, $ w_{t} $ is the wage rate at time t, $ e_{j} $ is the wage profile i at age j, $ \tau w_{t} $ is the labor income tax rate at time t, $ \tau p_{t} $ is the public pension contribution rate at time t, $ \lambda $ measures the rate of technical progress, $ \tau c_{t} $ is the consumption tax rate at time t, and $ p_{i,j} $ stands for pension benefit of generation i at age j. Each generation maximizes his/her utility function (Equation (1)) under the budget constraint (Equation (2)).

With the maximization procedure, the following Euler equations can be solved, concerning consumption per period.

$$ c_{i,j}=\left\{\frac{1+r_{t}\left(1-\tau r_{t}\right)}{1+\rho}\right\}^{\frac{l}{\gamma}}\left\{\frac{1+\tau c_{t-l}}{1+\tau c_{t}}\right\}^{\frac{l}{\gamma}}c_{i,j-l}\quad,\quad C_{t}=\sum_{j=l}^{60}N_{t,j}c_{i,j} $$

where $ N_{t,j} $ measures the number of the people of age j at period t, and $ C_{t} $ is the aggregated consumption at time t.

We can also obtain the following physical wealth accumulation equation with the maximization procedure:

$$ a_{i,j}=a_{i,j-l}\left\{I+r_{t}\left(I-\tau r_{t}\right)\right\}+(I-\tau w_{t}-\tau p_{t})w_{t}(I+\lambda)^{t}e_{i,j}-(I+\tau c_{t})c_{i,j}\\ ,P A_{t}=\sum_{j=l}^{60}N_{t,j}a_{i,j}(\equiv K_{t}^{S}) $$

where $ a_{i,j} $ is physical wealth asset of generation i at age j, $ r_{t} $ is the interest rate
at time t, $ \tau r_{t} $ is the tax rate on interest income at time t, and $ PA_{t} $ is the aggregated private asset at period t.

## (2) Firm Behavior

The input/output structure is represented by the Cobb-Douglas production function with constant return to scale. The firm decides the demand for physical capital $ (K^{D}) $ and effective labor $ (L^{D}) $ to maximize its profit with the given factor prices of wage and rent, which are determined in the perfect competitive markets.

$$ Y_{t}=A K_{t}^{\alpha}L_{e,t}^{I-\alpha}\quad,\quad K_{t}=K_{t}^{D}\quad,\quad L_{e,t}=L_{e,t}^{D} $$

$$ K_{t}=I_{t}+\big(1-\delta\big)K_{t-I} $$

$$ r_{t}=\alpha A K_{t}^{\alpha-l}L_{e,t}^{l-\alpha}\mathrm{-}\delta\mathrm{~,~}w_{t}=\left(l\mathrm{-}\alpha\right)A K_{t}^{\alpha}L_{e,t}^{-\alpha} $$

where Y is output, a stands for capital income share, A is a scale parameter, $ \delta $ is the depreciation of physical capital, K is the physical capital stock, and $ L_{e} $ is the effective labor.

## (3) The Government

The government sector has three types of taxes: wage tax, consumption tax, and capital tax. It also has the public debt issue income as its revenue, and pays the consumption, investment, and interest payments as expenditures. As the government decides the tax rate according to intertemporal budget constraints, the budget does not have to balance for each period. Here, the wage tax rate is endogenously determined according to the difference of government revenues and government expenditures.

Budget constraint in each period:

$$ D_{t+1}-D_{t}=G_{t}-T_{t}+r_{t}D_{t} $$

Intertemporal budget constraint:

$$ D_{t}+\sum_{i=0}^{T}G_{t+i}\left/\prod_{j=0}^{T}R_{t+j}\right.=\sum_{i=0}^{T}T_{t+i}\left/\prod_{j=0}^{T}R_{t+j}\right. $$
where $ G_{t} $ stands for government expenditure at time t, $ T_{t} $ denotes tax revenue at time t, $ D_{t} $ denotes public debt at time t, and $ R \equiv 1/1 + r_{t} $ .

## (4) Public Pension

The pension sector grants a pension to the retirement generations while pension contributions are collected from the working generations.

$$ B_{t}=\sum_{j=I}^{r e t}N_{i,j}\tau p_{t}w_{t}(I+\lambda)^{t}e_{i,j} $$

where B stands for the aggregated pension contribution. The aggregated pension at time t is given by the product of the population of retirement age, replacement rate, and wage.

$$ P_{t}=\sum_{j=r e t+l}^{60}N_{i,j}\beta\Bigg(\frac{1}{r e t}\sum_{j=l}^{r e t}w_{t}(I+\lambda)^{t}e_{i,j}\Bigg) $$

where p is the pension, $ \beta $ denotes replacement rate, ret stands for retirement age, and P is the aggregated pension benefit.

The pension contribution rate is endogenously determined to keep the budget constraint.

## (5) Abroad

A part of domestic savings, e.g. capital, can move freely to outside countries according to the difference of rate of return on capital. To satisfy the following constraint, capital is distributed to the two countries through interest rate arbitrage:

$$ \begin{aligned}&\left(I-\tau r_{t}^{A}\right)r_{t}^{A}=\left(I-\tau r_{t}^{B}\right)r_{t}^{B}\\&s.t.P A_{t}^{A}+P A_{t}^{B}=K_{t}^{A}+K_{t}^{B}\\ \end{aligned} $$

This shows that world capital supply equals world capital demand. Moreover, we assume the existing capital stock is removable with no cost, and moves freely.

Current account is shown as a difference of net foreign assets:

$$ CA_{_{t}}=FA_{_{t}}-FA_{_{t-l}} $$

where CA presents current account, and FA measures net foreign assets. Consequently, current account converges to zero in the long run. And the total of the current balance of the two countries at time t is zero:

$$ CA_{t}^{A}+CA_{t}^{B}=0 $$
In addition, trade balance is defined by deducting the net factor income from abroad from the current balance.

$$ TB_{t}=CA_{t}-r_{t}FA_{t} $$

where TB stands for trade balance.

We find that trade balance equal to net factor income in the steady state.

## (6) Model Closure

To close the model structure, the following condition must be held:

$$ Y_{t}=C_{t}+I_{t}+G_{t}+CA_{t}-r_{t}FA_{t} $$

#### 2.2. Parameterization

First, we present the values of the main parameters of the model in Table1. In both countries the elasticity of intertemporal substitution $ \gamma $ is set at 4.0. The pure rate of time preference $ \rho $ is set to 0.0017, as documented in Auerbach and Kotlikoff (1987). The earnings profile is calculated by the actual Japanese data. Concretely, it is similar to the one in Sadahiro and Shimasawa (2001):

$$ e_{j}=88.3+7.08j-0.146j^{2}\ (j:age) $$

The replacement rate $ \beta $ is 60 percent which equals the value of the Japanese public pension program. The share of capital $ \alpha $ is set at 0.30. The technological progress $ \lambda $ is set to 2.0 percent, which is similar to the value of the long run average annual growth rate in Japan. The depreciation rate of capital $ \delta $ is set to 5 percent. The sources of the parameter values are: Auerbach and Kotlikoff (1987) for household preferences, Sadahiro and Shimasawa (2001) for production and the Cabinet Office (2003) for macroeconomic variables. As both countries have common parameters and model structures, there are no differences between their economic situations before fertility transition starts. Thus country A and country B have the same initial steady states.

Second, we assume that both countries have different population growth rates between generations. Country A has negative growth rate, and country B has positive growth rate. Then we can show the transitional equation of generation growth rate to be:

$$ \begin{cases}n_{t}^{A}=-0.0001t\quad,\quad n_{t}^{B}=0.0001t\quad\left(1\leq t\leq100\right)\\n_{t}^{A}=-0.01\quad,\quad n_{t}^{B}=0.01\quad\left(100
period t in country A/B. Both start from 0 percent in the original steady state, and converge to -1 percent (country A) and to +1 percent (country B) in the new steady state after a 100-period transition. Thus the population decreases (increases), and the elderly dependency ratio increases (decreases) in country A (country B). We plot the population growth rate in Figure 3, and the old-age dependency ratio in Figure 4. Moreover, as we compute forward for 500 periods, we consider a sufficient period for a steady-state to be achieved.

### 3. Simulation Analysis

In this section, we present estimates of the macroeconomic effects of ageing as well as the potential impacts on international capital flow, based on the two-country OLG model described in the previous section. First, we present the baseline simulation results on the main economic variables. Second, we compare the results with those of a simulation in which international capital flow is not admitted at all, e.g. a closed economy OLG model. Finally, we provide the results of the two alternative scenarios.

We now present the results of our baseline simulation. For tractability, we report on the variables of country A. The simulation results describing the macroeconomic impacts of ageing are summarized in Figures 5 to 8.

## (1) Baseline Simulation

First, we see the baseline simulation results. Figure 5 presents results. In our analysis, the demographic shock is generated through changes in the fertility rate. In country A, birthrate decreases by following the equation (p), and converges to a -1.0 percent growth rates in the steady state. Thus, ageing of the demographic structure will progress in this country. According to Figure 5, ageing leads to a decline in savings. As mentioned earlier, the life-cycle theory of savings behavior is a key assumption of the model and one which explains the reduction in the savings rate. According to our results, the national savings rate falls by 4.8 percent points between initial steady state and the new one. Moreover, as capital flows from the ageing country to the population-growing country for a higher rate of return, the capital labor ratio decreases; this puts upward pressure on the rate of return, and downward pressure on wages. And ageing also leads to a rise in the tax and pension contribution.
rates. As a result, though the lifetime utility exceeds that of the initial steady state generations, the deviation decreases gradually. As capital moves to country B, country A has positive net foreign assets in the long run. Thus, the ageing country records a positive rate of return on foreign assets from country B in the long run.

We next compare the closed economy scenario. Figure 6 shows the results. Ageing also leads to a reduction in savings. However, since the labor force is more negatively affected by the demographic shock than is the capital stock, the capital-labor ratio increases; this puts downward pressure on the rate of return on capital, and upward pressure on real wages. As a result, the lifetime utility worsens compared with the open-economy case. Thus we conclude that these simulation results show the possibility that the effect given to the utility at retirement age by the increase in interest rates overwhelms that of the decrease of wages given to the utility at working time caused by the international capital movements in the ageing country.

## (2) Alternative Scenarios

Our figures represent the effect on savings rate, international capital flow, capital-labor ratio, rate of return, wage rate, lifetime utility, foreign assets, and trade balance in terms of deviations from the baseline simulation results. To evaluate the importance of the policy changes on international capital flow, we examine two alternative scenarios.

In the first alternative scenario, we assume that the public pension system is reformed in one or both countries; Case $ P_{A} $ is the case that a pay-as-you-go pension system is abolished only in country A under perfect international capital mobility. This simulation models a crude transition from a pay-as-you-go pension system to a fully funded private system. Case $ P_{B} $ is the case that pension reform is implemented only in country B. Case $ P_{AB} $ is the case that pension reform is conducted in both countries.

The second alternative policy change is a cut in government expenditure. In this scenario, we suppose that the government expenditure to output ratio is cut by 5 percentage points. Case $ F_{A} $ is the case that fiscal reconstruction is executed only in country A in an open economy. Case $ F_{B} $ is the case that the same fiscal reform is implemented only in country B. Case $ F_{AB} $ is the case that fiscal consolidation is conducted in both countries. Thus we have two policy change scenarios: public pension reform, and government expenditure cuts.
We can see the cases in detail in Table 2. The results in Figure 7 to 8 show the deviation from the baseline case.

## (3) Public Pension Reform

The first effect of pension reform is to raise the savings rate in all simulations except Case $ P_{B} $ . The rise of the savings rate leads to increased international capital flow. However, in Case $ P_{B} $ , where pension reform is performed only in country B, the direction of international capital flow is opposed compared with the baseline case and other simulation cases. As the capital labor ratio increases in Case $ P_{B} $ and Case $ P_{AB} $ , the rate of return decreases and wages increase in the long run. Though it has negative effects on lifetime utility in the transitional path, the public pension reform improves utility in the long run because of the net income increase caused by the reduction of the pension contribution rate and the wage tax rate. In Case $ P_{A} $ and Case $ P_{AB} $ , as country A begins to have positive net foreign assets in the long run, it receives a positive income gain from country B. However, the level of income gain falls in Case $ P_{AB} $ because of a great reduction in the rate of return. On the contrary, country A is to have net negative foreign assets in the long run in Case $ P_{B} $ where pension reform isn't implemented in country A. We can see the results in Figure 7.

## (4) Fiscal Consolidation

First, government expenditure cuts lead to an increase in savings and the aggregated consumption rate in Case $ F_{A} $ and Case $ F_{AB} $ . The increase of aggregated consumption rate corresponds to the decrease in government spending. Though the rise in savings also increases international capital flow, the capital-labor ratio increases compared to the baseline scenario. The increase of capital-labor ratio makes the rate of return fall and the wage rate rise. And since the cut in government expenditures reduces the tax rate substantially, net income increases. Consequently, lifetime utility increases because of the increase in consumption levels. Also in this case, as long as the ageing country implements the policy change regardless of whether the young population country changes policy, the ageing country might improve its economic situation and economic welfare in the long run. We present the results in Figure 8.
### 4. Conclusion

In this paper, we have used a computable two-country multi-period OLG model developed by Sadahiro and Shimasawa (1999) and calibrated for assumed population data to estimate the potential effects of differential ageing processes across countries and policy changes on international capital flow. We have thus computed the response of the model to three large shocks: a population ageing (baseline scenario), a switch to a fully funded pension scheme (scenario 2), and a government expenditure cut by 5 percentage points to output (scenario 3). Our main conclusions are as follows.

First, we have shown that capital basically flows from the ageing country to the population-growth country. Second, the ageing country will have foreign assets, and the population-growth country becomes indebted in the long run. Third, our results suggest the possibility that lifetime utility gets worse due to the drop of rate of return on capital if the policy reforms are performed to increase savings in case international capital flow is hindered for whatever reason. As a result, the possibility can be pointed out that the effects of policy changes to macroeconomic variables, along with the welfare of generations, are overestimated when we analyze the impacts of ageing by using a closed economy OLG model. Fourth, the direction of the international capital movement might reverse if the ageing country doesn't adopt policies that raise the savings rate while the population-increase country does. Finally, when a labor-abundant country exists, the country with an ageing population can improve its economic welfare by implementing the policy reforms that raise the savings rate with or without the policy changes of the labor-abundant countries.

Thus we deliver the policy implication that the advanced ageing-population countries should reduce the barriers of international capital movement, and execute the policy of increasing savings—regardless of whether the population-growing countries implement such policy reforms—for the sake of improvement of their own macroeconomic situations and lifetime utility.

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Table 1 Values of Key Parameters and Exogenous Variables

Capital income share	a	0.30
Intertemporal elast. of subst.	1/γ	4.0
Pure rate of time preference	ρ	0.0017
Replacement ratio	β	0.60
Physical capital depreciation	δ	0.05
Gov. exp. to GDP ratio	g	23.4
Consumption tax rate	τc	0.05
Interest tax rate	τr	0.20
Rate of technical progress	λ	0.02

Table 2 Simulation Cases

Capital mobility	Pension reform	Fiscal reform
Baseline case	F	✗	✗
Case $ P_{A} $	F	▲ (county A)	✗
Case $ P_{B} $	F	▲ (country B)	✗
Case $ P_{AB} $	F	●	✗
Closed case	N	✗	✗
Case $ F_{A} $	F	✗	▲ (county A)
Case $ F_{B} $	F	✗	▲ (country B)
Case $ F_{AB} $	F	✗	●

Notices:

1. F indicates there is perfect capital mobility.

2. N indicates there is no international capital flow.

3. × means no policy reform.

4. ● means policy reform is performed in both countries.

5. ▲ (A/B) indicates policy reform is performed in only country A or country B.
Figure 1 Elderly Dependency Ratio

Source: United Nations “World Population Prospects: The 2002 Revision” 2003.

Figure 2 Population Growth Rate

Source: United Nations “World Population Prospects: The 2002 Revision” 2003.
Figure 3 Population Growth Rate in Country A/B

Source: Authors' calculation.

Figure 4 Old-age Dependency Ratio in Country A/B

Source: Authors' calculation.
Figure 5 Simulation Results (Baseline case)

(1)Saving rate

(6) Lifetime utility

(2) International capital flow to GNI

(3) Capital-labor ratio

(7) Net foreign assets to GNI

(8) Trade balance to GNI

(4)Rate of return

(9) Pension contribution rate

(5) Wage rate

(10) Wage tax rate
(1)Saving rate

(2) Capital-labor ratio

(5)Lifetime utility

(6) Pension contribution rate

(3)Rate of return

(7) Wage tax rate

(4) Wage rate

(8) Aggregated consumption rate
Figure 7 Pension Reform (deviation from baseline case)

(1)Saving rate

(6) Lifetime utility

(2) International capital flow to GNI

(7) Net foreign assets to GNI

(3) Capital-labor ratio

(8) Trade balance to GNI

(4)Rate of return

(9) Pension contribution rate

(5) Wage rate

(10) Wage tax rate
Figure 8 Fiscal Reform (deviation from baseline case)

(1) Savings rate

(6) Lifetime utility

(2) International capital flow to GNI

(3) Capital-labor ratio

(7) Net foreign assets to GNI

(8) Trade balance to GNI

(4)Rate of return

(9) Wage tax rate

(5) Wage rate

(10) Aggregated consumption rate