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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
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• 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|Are actual economies dynamically inefficient

Recall that in the decentralised equilibrium we had
$$r_{\mathrm{SS}}=f^{\prime}\left(k_{\mathrm{SS}}\right),$$
so the rental rate is equal to the marginal product of capital. Notice also that the rate of growth of the economy is $n$ (income per-capita is constant, and the number of people is growing at the rate $n$ ). Therefore, the condition for dynamic inefficiency is simply that $r_{S S}$ be lower than the rate of growth of the economy, or, taking depreciation into account (which we have ignored here), that the rate of interest minus depreciation be lower than the rate of growth of the economy.

Abel et al. (1989) extend the model to a context with uncertainty (meaning that there is more than one observed interest rate, since you have to adjust for risk), and show that in this case a sufficient condition for dynamic efficiency is that net capital income exceeds investment. To understand why, notice that the condition for dynamic efficiency is that the marginal product of capital $(r)$ exceeds the growth rate of population $(n)$, which happens to be the growth rate of the economy $g$. So, $r K$ is the total return to capital and $n K$ is total investment, so the condition $r>g$ can be tested by comparing the return on capital vs new investment: the net flow out of firms. Their evidence from seven industrialised countries suggests that this condition seems to be comfortably satisfied in practice.

However, a more recent appraisal, by Geerolf (2013), suggests that this picture may have actually changed or never been quite as sanguine. He updates the Abel et al. data, and provides a different treatment to mixed income and land rents. ${ }^4$ With these adjustments, he finds that, in general, countries are in dynamically efficient positions, though some countries such as Japan and South Korea are definitely in a dynamically inefficient state! (And Australia joins the pack more recently…) In other words, it seems at the very least that we cannot so promptly dismiss dynamic inefficiency as a theoretical curiosity.

## 经济代写|宏观经济学代写Macroeconomics代考|Why is this important

At this point you may be scratching your head asking why we seem to be spending so much time with the question of dynamic efficiency. The reason is that it is actually very relevant for a number of issues. For example, a dynamically inefficient economy is one in which fiscal policy has more leeway. Any debt level will eventually be wiped out by growth. Blanchard (2019) (p. 1197) takes this point seriously and argues

… the current U.S. situation, in which safe interest rates are expected to remain below growth rates for a long time, is more the historical norm than the exception. If the future is like the past, this implies that debt rollovers, that is the issuance of debt without a later increase in taxes, may well be feasible. Put bluntly, public debt may have no fiscal cost.
Not surprisingly, during 2020/2021, in response to the Covid-19 pandemic, many countries behaved as if they could tap unlimited resources through debt issuing. Dynamic inefficiency, if present and expected to remain in the future, would say that was feasible. If, on the contrary, economies are dynamically efficient, the increases in debt will required more taxes down the road.

The second issue has to do with the possibility of bubbles, that is, assets with no intrinsic value. By arbitrage, the asset price of a bubble will need to follow a typical pricing equation
$$(1+r) P_t=P_{t+1} \text {, }$$
assuming for simplification a constant interest rate. The solution to this equation is
$$P_t=P_0(1+r)^t,$$
(simply replace to check it is a solution). The price of the asset needs to grow at the rate of interest rate (you may hold a dividend-less asset, but you need to get your return!). In an NGM where $r>g$, this asset cannot exist, because it will eventually grow to become larger than the economy. But if $r<g$ this is not the case, and the bubble can exist. We will come back to this later. What are examples of such assets? Well, you may have heard about Bitcoins and cryptocurrency. In fact, money itself is really a bubble!

Finally, notice that the OLG model can deliver very low interest rates. So, it is an appropriate setup to explain the current world of low interest rates. We will come back to this in our chapters on fiscal and monetary policy.

Before this, however, we need to provide a continuous-time version of the OLG model, to provide continuity with the framework we have been using so far, and because it will be useful later on.

# 宏观经济学代考

## 经济代写|宏观经济学代写宏观经济代考|实际经济是动态低效的吗

$$r_{\mathrm{SS}}=f^{\prime}\left(k_{\mathrm{SS}}\right),$$
，所以租金率等于资本的边际产量。还要注意，经济增长率为$n$(人均收入不变，人口数量以$n$的速度增长)。因此，动态无效率的条件很简单，$r_{S S}$低于经济增长率，或者，考虑到折旧(这里我们已经忽略了)，利率减去折旧的比率低于经济增长率

Abel et al.(1989)将模型扩展到具有不确定性的背景下(意味着存在不止一个可观测利率，因为你必须对风险进行调整)，并表明在这种情况下，动态效率的充分条件是净资本收入超过投资。要理解其中的原因，请注意动态效率的条件是，资本的边际产量$(r)$超过人口增长率$(n)$，而人口增长率恰好是经济增长率$g$。因此，$r K$是总资本回报率，$n K$是总投资，因此条件$r>g$可以通过比较资本回报率和新投资(企业净流出)来检验。来自7个工业化国家的证据表明，这一条件在实践中似乎得到了很好的满足

## 经济代写|宏观经济学代写宏观经济代考|为什么这很重要

$$(1+r) P_t=P_{t+1} \text {, }$$
，假设简化利率恒定。这个方程的解是
$$P_t=P_0(1+r)^t,$$
(只需替换以检查它是一个解)。资产的价格需要按利率增长(你可能持有一个无股息的资产，但你需要得到你的回报!)在一个$r>g$的NGM中，这个资产不可能存在，因为它最终会增长到超过经济的规模。但如果$r<g$不是这样，泡沫就可能存在。我们稍后再讨论这个问题。这类资产的例子有哪些?你可能听说过比特币和加密货币。其实，金钱本身就是一个泡沫!

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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