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

#### Doug I. Jones

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## 经济代写|宏观经济学代写Macroeconomics代考|Macroeconomics and finance

We’ve come a long way in understanding consumption. Now it is time to see if what we have learnt can be used to help us understand what asset prices should be in equilibrium.

To understand this relationship, we can use Lucas’s (1978) metaphor: imagine a tree that provides the economy with a unique exogenous income source. What is this tree worth? Optimal consumption theory can be used to think about this question, except that we turn the analysis upside down. Typically, we would have the price of an asset and have the consumer choose how much to hold of it. But in the economy the amount held and the returns of those assets are given because they are what the economy produces. So here we will use the FOCs to derive what price makes those exogenous holdings optimal. By looking at the FOCs at a given equilibrium point as an asset pricing equation allows us to go from actual consumption levels to asset pricing. Let’s see an example.
Start with the first order condition for an asset that pays a random return $r_{t+1}^j$ :
$$u^{\prime}\left(c_t\right)=\frac{1}{1+\rho} E_t\left[\left(1+r_{t+1}^i\right) u^{\prime}\left(c_{t+1}\right)\right] \quad \forall i .$$
Remember that
$$\operatorname{cov}(x, y)=E(x y)-E(x) E(y),$$
so, applying this equation to (12.51), we have that
$$u^{\prime}\left(c_t\right)=\frac{1}{1+\rho}\left{E_t\left(1+r_{t+1}^i\right) E_t\left(u^{\prime}\left(c_{t+1}\right)\right)+\operatorname{cov}\left(1+r_{t+1}^i, u^{\prime}\left(c_{t+1}\right)\right)\right} .$$
This is a remarkable equation. It says that you really don’t care about the variance of the return of the asset, but about the covariance of this asset with marginal utility. The variance may be very large, but, if it is not correlated with marginal utility, the consumer will only care about expected values. The more positive the correlation between marginal utility and return means a higher right-hand side, and, therefore, a higher value (more utility). Notice that a positive correlation between marginal utility and return means that the return is high when your future consumption is low. Returns, in short, are better if they are negatively correlated with your income; and if they are, volatility is welcomed!
As simple as it is, this equation has a lot to say, for example, as to whether you should own your house, or whether you should own stocks of the company you work for. Take the example of your house. The return on the house are capital gains and the rental value of your house. Imagine the economy booms. Most likely, prices of property and the corresponding rental value goes up. In these cases your marginal utility is going down (since the boom means your income is going up), so the correlation between returns and marginal utility is negative. This means that you should expect housing to deliver a very high return (because it’s hedging properties are not that good). Well, that’s right on the dot. Remember our mention to Kaplan et al. (2014) in Chapter 8, who show that housing has an amazingly high return.

## 经济代写|宏观经济学代写Macroeconomics代考|What next?

Perfect or not, the idea of consumption smoothing has become pervasive in modern macroeconomics. Many of you may have been taught with an undergraduate textbook using a consumption function $C=a+b Y$, with a so-called marginal propensity to consume from income equal to $b$. Modern macroeconomics, both in the version with and without uncertainty, basically states that this equation does not make much sense. Consumption is not a function of current income, but of intertemporal wealth. The distinction is important because it affects how we think of the response of consumption to shocks or taxes. A permanent tax increase will imply a one to one reduction in consumption with no effect on aggregate spending, while transitory taxes have a more muted effect on consumption. These intertemporal differences are indistinguishable in the traditional setup but essential when thinking about policy.

The theory of consumption has a great tradition. The permanent income hypothesis was initially stated by Milton Friedman who thought understanding consumption was essential to modern macroeconomics. Most of his thinking on this issue is summarised in his 1957 book A Theory of the Consumption Function (Friedman (1957), though this text, today, would be only of historical interest. The life cycle hypothesis was presented by Modigliani and Brumberg (1954), again, a historical reference.

Perhaps a better starting point for those interested in consumption and savings is Angus Deaton’s (1992) Understanding Consumption.

For those interested in exploring value function estimations you can start easy be reviewing Chiang’s (1992) Elements of Dynamic Optimization, before diving into Ljungqvist and Sargent (2018) Recursive Macroeconomic Theory. Miranda and Fackler (2004) Applied Computational Economics and Finance is another useful reference. Eventually, you may want to check out Sargent and Stachurski (2014) Quantitative Economics, which is graciously available online at url:http://lectures. quantecon.org/.

There are also several computer programs available for solving dynamic programming models. The CompEcon toolbox (a MATLAB toolbox accompanying Miranda and Fackler (2004) textbook), and the quant-econ website by Sargent and Stachurski with Python and Julia scripts.

If interested in macrofinance, the obvious reference is Cochrane’s Asset Pricing (2009) of which there have been several editions. Sargent and Ljungqvist provide two nice chapters on asset pricing theory and asset pricing empirics that would be a wonderful next step to the issues discussed in this chapter. If you want a historical reference, the original Mehra and Prescott (1985) article is still worth reading.

# 宏观经济学代考

## 经济代写|宏观经济学代写宏观经济代考|宏观经济与金融

$$u^{\prime}\left(c_t\right)=\frac{1}{1+\rho} E_t\left[\left(1+r_{t+1}^i\right) u^{\prime}\left(c_{t+1}\right)\right] \quad \forall i .$$

$$\operatorname{cov}(x, y)=E(x y)-E(x) E(y),$$

$$u^{\prime}\left(c_t\right)=\frac{1}{1+\rho}\left{E_t\left(1+r_{t+1}^i\right) E_t\left(u^{\prime}\left(c_{t+1}\right)\right)+\operatorname{cov}\left(1+r_{t+1}^i, u^{\prime}\left(c_{t+1}\right)\right)\right} .$$

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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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