### 经济代写|宏观经济学代写Macroeconomics代考|ECON6002

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|宏观经济学代写Macroeconomics代考|Productivity shocks and the current account

Suppose the economy initially has total factor productivity $A^H$, with corresponding optimal stock of capital $\left(k^\right)^H$ and consumption level $\left(c^\right)^H$. At time 0 there is an unanticipated and permanent fall in productivity from $A^H$ to $A^L$, where $A^L<A^H$ (maybe because this economy produced oil, guano, or diamonds and its price has come down). This means, from (4.28), that $z(A)$ falls from $z\left(A^H\right)$ to $z\left(A^L\right)$. Capital holdings are reduced: residents sell capital in exchange for bonds, so after the shock they have $\left(k^\right)^L<\left(k^\right)^H$, where $\left(k^\right)^H$ was the optimal stock of capital before the shock. Assets $a_0$ are unchanged on impact. From (4.29) it follows that consumption adjusts instantaneously to its new (and lower) value: $$\left(c^\right)^L=r a_0-(1-\alpha) z\left(A^L\right)<r a_0-(1-\alpha) z\left(A^H\right)=\left(c^*\right)^H \text {, for all } t \geq 0 .$$
What happens to the current account? After the instantaneous shock, assets remain unchanged, and $\dot{b}_t$ is zero. The economy immediately converges to the new BGP, where the current account is in balance.

At this point, you must be really disappointed: don’t we ever get any interesting current account dynamics from this model? Actually, we do! Consider a transitory fall in productivity at time 0 , from $A^H$ to $A^L$, with productivity eventually returning to $A^H$ after some time $T$. Well, it should be clear that consumption will fall, but not as much as in the permanent case. You want to smooth consumption, and you understand that things will get back to normal in the future, so you don’t have to bring it down so much now. At the same time, the capital stock does adjust down fully, otherwise its return would be below what the domestic household could get from bonds. If current output falls just as in the permanent case, but consumption falls by less, where is the difference? A simple inspection of (4.9) reveals that $\dot{b}$ has to fall below zero: it’s a current-account deficit! Quite simply, residents can smooth consumption, in spite of the negative shock, by borrowing resources from abroad. Once the shock reverts, the current account returns to zero, while consumption remains unchanged. In the new BGP, consumption will remain lower relative to its initial level, and the difference will pay for the interest incurred on the debt accumulated over the duration of the shock – or more generally, the reduction in net foreign asset income.
‘This example underscores the role of the current account as a mechanism through which an economy can adjust to shocks. It also highlights one feature that we will see over and over again: the optimal response and resulting dynamics can be very different depending on whether a shock is permanent or transitory.

## 经济代写|宏观经济学代写Macroeconomics代考|Sovereign wealth funds

This stylised model actually allows us to think of other simple policy responses. Imagine a country that has a finite stock of resources, like copper. ${ }^4$ Furthermore let’s imagine that this stock of copper is being extracted in a way that it will disappear in a finite amount of time. The optimal program is to consume the net present value of the copper over the infinite future. So, as the stock of copper declines the economy should use those resources to accumulate other assets. This is the fiscal surplus rule implemented by Chile to compensate for the depletion of their resources. In fact, Chile also has a rule to identify transitory from permanent shocks, with the implication that all transitory increases (decreases) in the price level have to be saved (spent).

Does this provide a rationale for some other sovereign wealth funds? The discussion above suggests that a country should consume:
$$r \int_{-\infty}^{\infty} R_t e^{-r t} d t,$$
where $R$ is the value of the resources extracted in period $t$. This equation says that a country should value its intertemporal resources (which are the equivalent of the $a_0$ above, an initial stock of assets), and consume the real return on it.

Is that how actual sovereign funds work? Well, the Norwegian sovereign fund rule, for instance, does not do this. Their rule is to spend at time $t$ the real return of the assets accumulated until then:
$$r \int_{-\infty}^t R_t e^{-r(s-t)} d s$$
This rule san only be rationalised if you expest no further dissoveries and reat sach uew dissovery as a surprise. Alternatively, one could assume that the future is very uncertain, so one does not want to commit debt ahead of time. (We will come back to this precautionary savings idea in our study of consumption in Chapter 11.) In any event, the key lesson is that studying our stylised models can help clarify the logic of existing policies, and where and why they depart from our basic assumptions.

## 经济代写|宏观经济学代写Macroeconomics代考|Productivity shocks and the current account

‘这个例子强调了经常账户作为经济体可以调整中击的机制的作用。它还强调了我们将一遍又一遍地看到的一个特 征：最佳响应和产生的动态可能会因冲击是永久性的还是暂时的而有很大不同。

## 经济代写|宏观经济学代写Macroeconomics代考|Sovereign wealth funds

$$r \int_{-\infty}^{\infty} R_t e^{-r t} d t$$

$$r \int_{-\infty}^t R_t e^{-r(s-t)} d s$$

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## MATLAB代写

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