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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|Classical version of the IS-LM model

In the classical version of the model, all prices are flexible, and so are real wages. Thus the labour market clears fixing the amount of labour as in Figure 15.1.

With full employment of labor and capital, output is determined by the supply constraint and becomes an exogenous variable, which we will indicate with a bar:
$$\bar{Y}=F(K, \bar{L}) .$$
The IS, can then be used to determine $r$ so that savings equals investment ( $S=I$, thus the name of the curve). The nominal interest rate is just the real rate plus exogenous inflation expectations (equivalent to the expected growth rate of prices). With $Y$ and $i$ fixed, then the $L M$ determines the price level $P$ given a stock of nominal money:
$$P=\frac{\bar{M}}{L(i, \bar{Y})},$$
which is an alternative way of writing the quantity equation of money:
$$M V=P Y .$$
In short, the structure of the model is such that the labor market determines the real wage and output. The IS determines the real and nominal interest rate, and the money market determines the price level.

This is typically interpreted as a description of the long run, the situation to which the economy gravitates at any given moment. The idea is that prices eventually adjust so that supply ends up determining output. That is why we ignored aggregate demand fluctuations when discussing long-run growth. There we concentrated on the evolution of the supply capacity. In the classical version of the model (or in the long run) that supply capacity determines what is produced.

经济代写|宏观经济学代写Macroeconomics代考|An interpretation: The Fed

Is the model useful? Yes, because policy makers use it. For example, when the Fed talks about expanding or contracting the economy it clearly has a Keynesian framework in mind. It is true that the Fed does not typically operate on the money stock, but one way of thinking about how the Fed behaves is to think of it as determining the interest rate and then adjusting the money supply to the chosen rate (money becomes somewhat endogenous to the interest rate). In our model, $i$ becomes exogenous and $M$ endogenous as in Figure 15.3:
$$\begin{gathered} \frac{M}{\bar{P}}=L(\bar{i}, Y) \ Y=A\left(\bar{i}-\pi^e, \text { Fiscal, } \ldots\right) . \end{gathered}$$

We can represent this using the same $Y, i$ space, but the LM curve is now horizontal as the Fed sets the (nominal) interest rate. Alternatively, we can think about it in the $Y, M$ space, since $M$ is the new endogenous variable. Here we would have the same old $L M$ curve, but now the IS curve becomes vertical in the $Y, M$ space. Both represent the same idea: if the Fed wants to expand output, it reduces the interest rate, and this requires an expansion in the quantity of money.

As a side note, you may have heard of the possibility of a liquidity trap, or alternatively, that monetary policy may hit the zero interest lower bound. What does this mean? We can think about it as a situation in which interest rates are so low that the demand for money is infinitely elastic to the interest rate. In other words, because nominal interest rates cannot be negative (after all, the nominal return on cash is set at zero), when they reach a very low point an increase in the supply of money will be hoarded as cash, as opposed to leading to a greater demand for goods and services. In that case, the IS-LM framework tells us that (conventional) monetary policy is ineffective. Simply put, interest rates cannot be pushed below zero!

This opens up a series of policy debates. There are two big questions that are associated with this: 1) Is monetary policy really ineffective in such a point? It is true that interest rate policy has lost its effectiveness by hitting the zero boundary, but that doesn’t necessarily mean that the demand for money is infinitely elastic. The Fed can still pump money into the economy (what came to be known as quantitative easing) by purchasing government (and increasingly private) bonds, and this might still have an effect (maybe through expectations). 2) In this scenario, can fiscal policy be effective? These are debates we’ll come back to in full force in our discussions of fiscal and monetary policy.

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|Classical version of the IS-LM model

$$\bar{Y}=F(K, \bar{L}) .$$
IS，然后可用于确定 $r$ 所以储薑等于投资 $(S=I$ ，因此曲线的名称）。名义利率就是实际利率加上外生通胀预期（相当于物价的预期增长率）。和 $Y$ 和固定， 然后 $L M$ 决定价格水平 $P$ 给定名义货币存量:
$$P=\frac{\bar{M}}{L(i, \bar{Y})},$$

$$M V=P Y$$

经济代写|宏观经济学代写Macroeconomics代考|An interpretation: The Fed

$$\frac{M}{\bar{P}}=L(\bar{i}, Y) Y=A\left(\bar{i}-\pi^e, \text { Fiscal }, \ldots\right) .$$

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MATLAB代写

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