经济代写|宏观经济学代写Macroeconomics代考|ECON6002

Doug I. Jones

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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
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经济代写|宏观经济学代写Macroeconomics代考|A simple extension

But how come we have no dynamic inefficiency in this model? Just switching to continuous time does away with this crucial result? Not really. The actual reason is that the model so far is not quite like what we had before, in another aspect: there is no retirement! In contrast to the standard OLG model, individuals have a smooth stream of labour income throughout their lives, and hence do not need to save a great deal in order to provide for consumption later in life.

Introducing retirement (i.e. a stretch of time with no income, late in life) is analytically cumbersome, but as Blanchard (1985) demonstrates, there is an alternative that is easily modelled, has the same flavour, and delivers the same effects: assuming labour income declines gradually as long as an individual is alive.

Let’s take a look. Blanchard (1985) assumes that each individual starts out with one unit of effective labour and thereafter his available labour declines at the rate $\gamma>0$. At time $t$, the labour earnings of a person in the cohort born at $\tau$ is given by $w_t e^{-\gamma(t-\tau)}$, where $w_t$ is the market wage per unit of effective labour at time $t$. It follows that individual human wealth for a member of the $\tau$ generation is
$$h_{t, \tau}=\int_t^{\infty} w_s e^{-\gamma(s-\tau)} e^{-\int_t^{\prime \prime}\left(r_r+p\right) d v} d s .$$
Using the same derivation as in the baseline model, we arrive at a modified Euler equation
$$\dot{c}_t=\left(\alpha k_t^{\alpha-1}+\gamma-\rho\right) c_t-(n+\gamma)(p+\rho) k_t,$$
which now includes the parameter $\gamma$.
The steady state per-capita capital stock is now again pinned down by the expression
$$k^{* \alpha-1}=(n-p)+\frac{(n+\gamma)(p+\rho)}{\alpha+\gamma-\rho},$$
which can be rewritten as
$$\alpha k^{* a-1}-\rho=\frac{(n+\gamma)(p+\rho)}{k^{* \alpha-1}-(n-p)}-\gamma .$$
So if $\gamma$ is sufficiently large, then the steady-state per capita capital stock can be larger than the golden rule level, which is the one that solves the equation $\alpha k^{a-1}=\rho$. This would imply over-accumulation of capital. The intuition is that the declining path of labour income forces people to save more, too much in fact. Again, intergenerational transfers would have been a more efficient way to pay for retirement, but they cannot happen in the decentralized equilibrium, in the absence of intergenerational altruism.

In this case, dynamics are given by Figure 8.6, with the steady state to the right of the modified golden-rule level of capital:

经济代写|宏观经济学代写Macroeconomics代考|Revisiting the current account in the open economy

We can also revisit the small open economy as a special case of interest. For that, let’s go back to the case in which $\gamma=0$, and consider what happens when the economy is open, and instead of being capital, the asset is a foreign bond $f_t$ that pays the fixed world interest rate $r$. In turn, labour income is now, for simplicity, an exogenous endowment $y_{t, \tau}=y$ for all moments $t$ and for all cohorts $\tau$.
The two key differential equations now become
\begin{aligned} &\dot{c}_t=(r-\rho) c_t-n(p+\rho) f_t, \ &\dot{f}_t=[r-(n-p)] f_t+y-c_t, \end{aligned}
$$[r-(n-p)] f^+y=c^,$$
$$(r-\rho) c^=n(p+\rho) f^,$$
which together pin down the levels of consumption and foreign assets. The first equation reveals that in steady state the current account must be balanced, with consumption equal to endowment income plus interest earnings from foreign assets. As the second equation reveals, the steady-state stock of foreign assets can be positive or negative, depending on whether $r$ is larger or smaller than $\rho$.

If $r>\rho$, individual consumption is always increasing, agents are accumulating over their lifetimes, and the steady-state level of foreign assets is positive. If $r=\rho$, individual consumption is flat and they neither save nor dissave; steady-state foreign assets are zero. Finally, if $r<\rho$, individual consumption is always falling, agents are decumulating over their lifetimes, and in the steady state the economy is a net debtor.

Equilibrium dynamics are given by Figure 8.7, drawn for the case $r>\rho$. It is easy to show that the system is saddle-path stable if $r<\rho+p$. So the diagram below corresponds to the case $\rho<r<\rho+p$. Along the saddle-path, the variables $c_t$ and $f_t$ move together until reaching the steady state.

In this model the economy does not jump to the steady state (as the open-economy model in Chapter 4 did). The difference is that new generations are constantly being born without any foreign assets and they need to accumulate them. The steady state is reached when the accumulation of the young offsets the decumulation of the older generation.

统计推断代考

经济代写|宏观经济学代写宏观经济学代考|一个简单的扩展

$$h_{t, \tau}=\int_t^{\infty} w_s e^{-\gamma(s-\tau)} e^{-\int_t^{\prime \prime}\left(r_r+p\right) d v} d s .$$使用与基线模型相同的推导，我们得到一个修正的欧拉方程
$$\dot{c}_t=\left(\alpha k_t^{\alpha-1}+\gamma-\rho\right) c_t-(n+\gamma)(p+\rho) k_t,$$
，它现在包含了参数 $\gamma$稳定状态下的人均资本存量现在再次由表达式

$$\alpha k^{* a-1}-\rho=\frac{(n+\gamma)(p+\rho)}{k^{* \alpha-1}-(n-p)}-\gamma .$$

经济代写|宏观经济学代写宏观经济学代考|在开放经济中重新审视经常账户

\begin{aligned} &\dot{c}_t=(r-\rho) c_t-n(p+\rho) f_t, \ &\dot{f}_t=[r-(n-p)] f_t+y-c_t, \end{aligned}

$$[r-(n-p)] f^+y=c^,$$
$$(r-\rho) c^=n(p+\rho) f^,$$
，它们共同确定了消费和外国资产的水平。第一个方程表明，在稳定状态下，经常账户必须达到平衡，消费等于禀赋收入加上来自外国资产的利息收益。正如第二个等式所示，外国资产的稳态存量可以是正的也可以是负的，取决于$r$比$\rho$大还是小。

有限元方法代写

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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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