### 经济代写|宏观经济学代写Macroeconomics代考|ECOS3007

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
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• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

Let us paint a simple model of the exchange rate. Suppose you have $\$ 10,000$that you wish to save, and you are deciding whether you should buy$\$10,000$ worth of U.S. Treasury bonds or $\$ 10,000$worth of British government bonds which you intend to hold for 1 year. What is the expected return on the U.S. bond? It is just the interest rate you will earn, call it$\mathrm{R}_{\mathrm{US}}$. What about the expected return on the British government bond? Well, here are the steps you would need to take: you first swap your dollars for pounds and then buy British government bonds. At the end of the year you earn the British interest rate on those bonds, and at that point you sell your British bonds for pounds and then swap those pounds back into dollars. Now, here is the tricky part: when you are calculating the expected foreign return in this example, we know the British interest rate, and we know the current dollarpound exchange rate. But we also need a forecast of the dollar-pound exchange rate for 1 year’s time, because that will be the relevant exchange rate for when we swap our pound earnings back into our home currency. Fortunately, we can write down a formula that encapsulates all of these steps succinctly – the expected foreign return, denominated in the domestic currency, is given by the expression$\mathrm{R}{\mathrm{UK}}+\left(\mathrm{X}^{\mathrm{e}}-\mathrm{X}\right) / \mathrm{X}$, where$\mathrm{R}{\mathrm{UK}}$is the British interest rate,$\mathrm{X}$is the current dollar-pound exchange rate, and$\mathrm{X}^{\mathrm{c}}$is the forecasted future dollar-pound exchange rate. In equilibrium, investors will be indifferent between dollars and pounds when the expected returns on the two are equal to each other: $$\mathrm{R}{\mathrm{US}}=\mathrm{R}{\mathrm{UK}}+\left(\mathrm{X}^{\mathrm{e}}-\mathrm{X}\right) / \mathrm{X}$$ This equation is referred to as the (uncovered) interest parity condition, and the value of$\mathrm{X}$that solves this equation is the equilibrium exchange rate. The really useful part of this equation is that we can turn it into graphical form. Let’s draw a diagram (Figure 6.1) that shows the expected return of the domestic bond (left-hand side of the interest parity condition) against the expected foreign return of the foreign bond (right-hand side of the interest parity condition). ## 经济代写|宏观经济学代写Macroeconomics代考|Purchasing power parity Economists and currency traders, as well as participants in international markets, keep abreast of certain market indicators in order to predict movement in foreign exchange rates. One such indicator is the measure of Purchasing Power Parity (PPP). Really a theory, it is the suggestion that exchange rates between currencies tend to push toward equilibrium, meaning that a basket of goods valued in one currency should cost the same in another currency, after adjustment for currency exchange. What does this mean? For simplicity, imagine that a pizza pan costs$\$100$ dollars in the United States. What would that same pizza pan cost in Mexico? Well, if the prevailing exchange rate indicates that one dollar is equivalent to 12 pesos, then you would expect the pan to cost 1,200 pesos, right? The formula that follows this is:
$$\mathrm{X}=\mathrm{P}{\mathrm{US}} / \mathrm{P}{\mathrm{M}}$$
where $\mathrm{X}$ is the dollar-peso exchange rate, and $\mathrm{P}{\mathrm{US}}$ and $\mathrm{P}{\mathrm{M}}$ are the price levels in the United States and Mexico, respectively. What if you find out that Mexican companies are selling identical pizza pans for 800 pesos? If you own a chain of pizza parlors, wouldn’t you be motivated to purchase the pans from Mexico? Assuming the products are equivalent, and shipping costs are not an issue, then of course you would take advantage of the savings opportunity. And if that is the case, then purchasing power between the dollar and peso is not at parity.

While it may seem like a great opportunity for someone who is in the market for pizza pans, we must consider the long-term effects of disequilibrium. Demand for pizza pans sold by U.S. companies would drop as those sales shift to Mexican companies, therefore the demand for pesos would increase. This would place upward pressure on the value of the peso relative to other currencies. The increase in demand would push prices for Mexican pizza pans up. At the same time, to compete with Mexican companies, American companies would have to begin reducing prices for pizza pans in an attempt to attract customers. As the prices for the pizza pans move up in Mexico and down in the United States, they will eventually reach equilibrium. This type of trading that has moved the market back into equilibrium where prices are equalized across economies is known as arbitrage.

## 经济代写|宏观经济学代写Macroeconomics代考|A simple model of the exchange rate

$$\mathrm{X}=\mathrm{PUS} / \mathrm{PM}$$

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## MATLAB代写

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