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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|The random walk hypothesis

Suppose utility is quadratic ${ }^2$, that is
$$u\left(c_t\right)=c_t-\frac{a}{2} c_t^2 .$$
Here things become a bit simpler as marginal utility is linear:
$$u^{\prime}\left(c_t\right)=1-a c_t .$$
This implies that
$$1-a c_t=\frac{(1+r)}{(1+\rho)} E_t\left[1-a c_{t+1}\right] .$$
If we keep assuming that $r=\rho$ as we’ve done before, it follows that
$$a c_t=E_t\left[a c_{t+1}\right] \text {, }$$
or, more simply, that
$$c_t=E_t\left[c_{t+1}\right] .$$
Equation (12.11) can be depicted as the following stochastic process for consumption:
$$c_{t+1}=c_t+\varepsilon_{t+1},$$
where $\varepsilon_t$ is a zero-mean random disturbance (also called white noise).
A stochastic process that looks like this is called a random walk, for this reason this description of consumption (due to Hall 1978) is called the random walk hypothesisof consumption. It is a very strong statement saying that only unexpected events can change the consumption profile – all information that is already known must have already been taken into consideration and therefore will not change consumption when it happens. This result, one of the early applications of the rational expectations assumption, is a powerful empirical implication that can easily be tested.

## 经济代写|宏观经济学代写Macroeconomics代考|Testing the random walk hypothesis

A large number of papers have tried to assess the random walk hypothesis. One classical contribution is the Shea (1995) test on whether predictable changes in income are or are not related to predictable changes in consumption. He looks into long-term union contracts which specified in advance changes in wages. He then runs the consumption growth on the income growth. The theory suggests the coefficient should be zero, but the number comes out to be 89 .

Of course it can very well be that this is because people have liquidity constraints. So Shea runs the test on people that have liquid assets and could thus borrow from themselves. These people cannot have a liquidity constraint. Yet he still finds the same result. Then he splits people into two groups: those that are facing declining incomes and those for which income is growing. Those facing a future fall in income should reduce their consumption and save, so you should not find an effect of liquidity constraints. Yet, it seems that, again, changes in current income help predict changes in consumption.

This type of exercises has been replicated in many other contexts. Ganong and Noel (2019) for example, find that household consumption falls 13 percent when households receiving unemployment benefits reach the (anticipated) end of their benefits. Food stamp recipients and social security beneficiaries also show monthly patterns of consumption that are related to the payment cycle.

While important, the quadratic case is a very special case that allows a simple characterisation of the consumption path. Can we solve for more general specifications? Here is where the value function approach comes in handy. There are several ways of using the value function to approximate the optimal path. If the problem is finite, one can work the problem backwards from the last period. But this is not very useful in problems with no terminal time, which is our typical specification. One way to approach the problem is to simply guess the value function. This can be done in simple cases, but is not typically available, particularly because no problem should rely on having a genius at hand that can figure out the solution beforehand. An alternative is to do an iteration process that finds the solution through a recursive estimation. This is easier, and may actually deliver a specific solution in some cases. However, this approach can also be implemented by a recursive estimation using computational devices. So that you get a sense of how these methods work, we will solve a very simple problem through the guess and replace solution, and then through the value function iteration method. It is a bit tedious but will allow you to get a feel of the methodology involved.

# 宏观经济学代考

## 经济代写|宏观经济学代写宏观经济学代考|随机游走假说

.

$$u\left(c_t\right)=c_t-\frac{a}{2} c_t^2 .$$这里事情变得简单了一点，因为边际效用是线性的:
$$u^{\prime}\left(c_t\right)=1-a c_t .$$

$$1-a c_t=\frac{(1+r)}{(1+\rho)} E_t\left[1-a c_{t+1}\right] .$$

$$a c_t=E_t\left[a c_{t+1}\right] \text {, }$$
，或者更简单地说，
$$c_t=E_t\left[c_{t+1}\right] .$$(12.11)式可以描述为以下消费的随机过程:
$$c_{t+1}=c_t+\varepsilon_{t+1},$$
where $\varepsilon_t$ 是零均值随机干扰(也称为白噪声)。像这样的一个随机过程被称为随机游走，因此这种消费的描述(由于Hall 1978)被称为消费的随机游走假设。这是一个非常有力的声明，它表明只有意外事件才能改变消费状况——所有已知的信息都必须已经被考虑在内，因此当它发生时，不会改变消费。这一结果是理性预期假设的早期应用之一，是一个很容易检验的强大的经验含义

.

## 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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