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经济代写|宏观经济学代写Macroeconomics代考|Moving out of a pay-as-you-go system

There are several transitions associated with the introduction or revamping of pensions systems, and that we may want to analyze. For example, you could move from no pension system and implement a full capitalisation system. As aggregate saving behaviour does not change, we do not expect anything really meaningful to happen from such change in terms of capital accumulation and growth. (That is, of course, to the extent that rational behaviour is a good enough assumption when it comes to individual savings behaviour. We will get back to this pretty soon when we talk about consumption.) Alternatively, as discussed above, if we implement a pay-as-you-go system, the initial old are happy, while the effect for future generations remains indeterminate and depends on the dynamic efficiency of the economy.

However, in recent years it has become fashionable to move away from pay-as-you-go systems to fully funded ones. The reasons for such change is different in each country, but usually can be traced back to deficit and sometimes insolvent systems (sometimes corruption-ridden) that need to be revamped. ${ }^3$ But one of the main reasons was to undo the capital depletion associated with pay-asyou-go systems. Thus, these countries hoped that going for a capitalisation system would increase the capital stock and income over time.

In what remains of this chapter we will show that what happens in such transitions from pay-asyou-go to fully funded systems depends very much on how the transition is financed. There are two options: either the transition is financed by taxing the current young, or it is financed by issuing debt. Both have quite different implications.

To make the analysis simple, in what follows we will keep $n=0$. (Note that this puts us in the region where $r>n$, i.e. that of dynamic efficiency.)
Aggregate savings without pensions or with a fully funded system are
$$
s_t^{a g g \rho}=\left(\frac{1}{2+\rho}\right) w_t .
$$
With a pay-as-you-go system, they are
$$
s_t^{a g g}=s_t=\left(\frac{1}{2+\rho}\right) w_t-\frac{\left(1+r_{t+1}\right) d+(1+\rho) d}{(2+\rho)\left(1+r_{t+1}\right),}
$$
which is trivially lower (we knew this already). So now the question is how savings move when going from a pay-as-you-go to a fully funded system. You may think they have to go up, but we need to be careful: we need to take care of the old, who naturally will not be part of the new system, and their retirement income has to be financed. This, in turn, may have effects of its own on capital accumulation.

经济代写|宏观经济学代写Macroeconomics代考|Financing the transition with taxes on the young

If the transition is financed out of taxes, the young have to use their wages for consumption $\left(c_{1 t}\right)$, private savings $\left(s_t\right.$ ), to pay for their contributions ( $d$ and also for taxes $\tau_t$ ):
$$
c_{1 t}+s_t+d+\tau_t=w_t .
$$
Future consumption is in turn given by
$$
c_{2 t+1}=\left(1+r_{t+1}\right) s_t+\left(1+r_{t+1}\right) d,
$$

as we are in a fully funded system. Because taxes here are charged to finance the old, we have $\tau_t=d$ (remember we have assumed population growth to be equal to zero). If you follow the logic above, it can be shown that in this case we have
$$
s_t^{a g g}=\frac{\left(w_t-\tau_t\right)}{(2+\rho)} .
$$
You may notice that this is lower than the steady-state savings rate (next period, i.e. in 30 years, there are no more taxes), but you can also show that it is higher than in the pay-as-you-go system. To do so, replace $\tau_t$ with $d$ in (9.25) and then compare the resulting expression with that of (9.22).

So savings goes up slowly, approaching its steady-state value. These dynamics are what supports World Bank recommendations that countries should move from pay-as-you-go to fully capitalised systems. Notice however that the reform hurts the current young that have to save for their own and for the current old generation. Then remember that one period here is actually one generation, so it’s something like 30 years. What do you think would be the political incentives, as far as reforming the system, along those lines?

经济代写|宏观经济学代写Macroeconomics代考|ECON305

经济代写|宏观经济学代写宏观经济学代考|走出现收现付的体系


养老金制度的引入或改革有几个相关的转变,我们可能想要分析一下。例如,你可以从没有养老金制度转变为一个完全资本化的制度。由于总储蓄行为没有改变,我们不指望这种资本积累和增长方面的变化会带来任何真正有意义的结果。(当然,也就是说,就个人储蓄行为而言,理性行为是一个足够好的假设。当我们谈论消费时,我们很快会回到这个问题上来。)或者,如上文所述,如果我们实行现收现付制度,最初的老年人很幸福,而对后代的影响仍不确定,并取决于经济的动态效率


然而,近年来,从现收现付系统转向全资金系统已成为一种时尚。每个国家发生这种变化的原因各不相同,但通常可以追溯到赤字和需要改革的有时资不抵债(有时腐败猖獗)的体系。${ }^3$但其中一个主要原因是消除与现收现付制度相关的资本损耗。因此,这些国家希望实行资本化制度将随着时间的推移增加资本存量和收入


在本章剩下的部分中,我们将说明在从现收现付到资金充足的系统的这种过渡中会发生什么,在很大程度上取决于如何为这种过渡提供资金。目前有两种选择:要么通过向当前的年轻人征税为转型提供资金,要么通过发行债券为转型提供资金。两者的含义截然不同

为了使分析简单,在下面我们将保留$n=0$。(注意,这使我们处于$r>n$的区域,即动态效率的区域。)在没有养老金或资金充足的体系下,总储蓄
$$
s_t^{a g g \rho}=\left(\frac{1}{2+\rho}\right) w_t .
$$
在现收现付体系下,总储蓄
$$
s_t^{a g g}=s_t=\left(\frac{1}{2+\rho}\right) w_t-\frac{\left(1+r_{t+1}\right) d+(1+\rho) d}{(2+\rho)\left(1+r_{t+1}\right),}
$$
,略低一些(我们已经知道了这一点)。所以现在的问题是,当储蓄从现收现付体系转变为资金充足的体系时,储蓄将如何变化。你可能认为他们必须提高,但我们需要小心:我们需要照顾老年人,他们自然不会是新体系的一部分,他们的退休收入必须得到资助。反过来,这也可能对资本积累产生影响

经济代写|宏观经济学代写宏观经济学代考|用对年轻人征税为过渡提供资金

如果过渡的资金来自税收,年轻人必须用他们的工资来消费$\left(c_{1 t}\right)$,私人储蓄$\left(s_t\right.$),来支付他们的贡献($d$和也支付税收$\tau_t$):
$$
c_{1 t}+s_t+d+\tau_t=w_t .
$$
未来的消费反过来由
$$
c_{2 t+1}=\left(1+r_{t+1}\right) s_t+\left(1+r_{t+1}\right) d,
$$

给出

,因为我们处于一个资金充足的系统中。因为这里的税收是用来资助老年人的,所以我们有$\tau_t=d$(记住,我们假设人口增长等于零)。如果你遵循上面的逻辑,在这种情况下我们可以看到
$$
s_t^{a g g}=\frac{\left(w_t-\tau_t\right)}{(2+\rho)} .
$$
你可能会注意到这低于稳定状态下的储蓄率(下一个时期,即30年后,不再有更多的税收),但你也可以表明它高于现收现付制度。为此,将$\tau_t$替换为(9.25)中的$d$,然后将结果表达式与(9.22)的表达式进行比较 因此,储蓄增长缓慢,接近其稳态值。这些动态支持了世界银行的建议,即各国应从现收现付转向完全资本化的体系。然而要注意的是,改革伤害了现在的年轻人,他们不得不为自己和现在的老一代人储蓄。记住这里的一个时期实际上是一代人,大概是30年。你认为政治动机是什么,就改革体制而言,沿着这条路线?

经济代写|宏观经济学代写Macroeconomics代考

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