Week 10 - Macroeconomic Policy and Extreme Shocks

Exercises

Macroeconomics, ISCTE-IUL

Vivaldo Mendes, Ricardo Gouveia-Mendes, Luís Clemente-Casinhas

May 2025

Packages used in this notebook

Exercise 1. The Fed's Dual Mandate (again)

One of the Fed branches—the Federal Reserve Bank of Chicago—published an image that explains the Fed's double mandate in a very simple way. The figure can be found below, taken from here.

👉 a) In your own words, what are the two fundamental goals of the Fed over time?

👉 b) Given what you have studied in this course, suppose the natural unemployment $(U_n)$ rate is $4\mathrm{\%}$, and the current level of unemployment is $U=6\mathrm{\%}$. What would we expect the Fed's reaction would be?

👉 c) Given what you have studied in this course, suppose the rate of inflation $(\pi )$ is $5\mathrm{\%}$, while the target rate of inflation is $({\pi }^{{}_T})$ is $2\mathrm{\%}$. What would we expect the Fed's reaction would be?

👉 d) Suppose that the two cases above co-exist simultaneously. What should the Fed do in this case? Give up one of them, give up both, or balance both in some way?

Exercise 2. Unemployment and recessions

The following figure presents the evolution of the unemployment rate (UR) and the Fed Funds Rate (FFR) for the US economy from the mid 1960s to 2024.

👉 a) What happens to the unemployment rate in every single recession in this period? Why?

👉 b) What happens to the Fed Funds Rate in every single recession in this period? Why?

👉 c) The following figure presents a cross-plot between the US's unemployment and Fed Funds rates between 1955 and 2024, and the correlation coefficient between these two variables is close to zero $(0.063)$. Given this evidence and the theory that we have studied, in your opinion, what is the correct remark: (i) there is no causality between these two macroeconomic variables; (ii) if the Fed reduces the FFR, the unemployment rate goes up; (iii) if unemployment is very high, it has to come down, and the Fed is forced to reduce the FFR.

👉 d) Are there other major macroeconomic variables that directly affect the decision of the Fed regarding the FFR? If yes, what are they?

Exercise 3. Inflation targeting

On 8 July 2021, the European Central Bank (ECB) announced a revision of its monetary policy strategy for the first time since its creation in 1998. From the article above in the Financial Times, one can read:

"The central bank said its new target of 2 per cent was symmetric, “meaning negative and positive deviations of inflation from the target are equally undesirable”. The new target is a medium-term objective with flexibility to fluctuate in either direction in the short term [and] said it could tolerate temporary moves beyond that point, in a shift that gives policymakers flexibility to keep interest rates at historic lows for longer”.

👉 a) Figure 1 plots the data about inflation in the EuroZone (EZ) and Portugal since 1998. Why do you think the ECB stresses "the symmetric deviations of inflation from the target"?

👉 b) Why do you think the article stresses "...in a shift that gives policymakers flexibility to keep interest rates at historic lows for longer”?

👉 c) Figure 2 below shows the inflation deviations from its target, according to the old strategy (we will call it "Loss1"), while Figure 3 displays the deviations according to the new strategy ("Loss2").

👉 d) If you had responsibilities as a watchdog of the European Central Bank (for example, as a member of the European Parliament), and the ECB President argued that they had been doing a good job because the Loss to society was very small according to the old strategy, what would your position be?

Exercise 4. The Textbook Rule (MP curve)

In week 5 we introduced the MP curve into our framework:

$$\begin{array}{}\text{(1)}& r=\bar{r}+\lambda \pi \end{array}$$

where $r$ stands for the real interest rate, $\pi$ for the inflation rate, $\bar{r}$ as the natural real interest rate, and $\lambda$ is a parameter that shows how much central banks dislike inflation. This curve was supposed to express the way the central bank sets the nominal interest rate by using this curve in connection with the Fisher equation that we studied in week 3:

$$\begin{array}{}\text{(2)}& i=r+\pi \end{array}$$

where $i$ is the nominal interest rate. By inserting eq. (1) into eq. (2), we get the nominal interest rate that the central bank should set:

$$\begin{array}{}\text{(3)}& i=\bar{r}+(1+\lambda )\pi \end{array}$$

Interestingly, we can easily check whether a central bank (like the Fed) followed such a rule (MP curve) to set its nominal interest rates. We can collect data on $i$, on $\pi$, give reasonable values for $\bar{r}$ and $\lambda$, and see if the Fed followed this rule. Let us assume that $\bar{r}=2\mathrm{\%}$ and $\lambda =0.5$. The data is in the file "Taylor.csv" and can be found in the table below.

👉 a) In the figures below, we plot the Federal Funds Rate (the FFR, our $i$ in the equations above) and its value according to the rule presented by the textbook. Do you think the textbook rule does an excellent job of explaining the decisions of the Fed regarding interest rates?

👉 b) Given what we discussed in Exercise 1, in your opinion, why does the textbook rule perform so poorly in the case of the Fed?

Exercise 5. The Taylor rule

In 1993, John Taylor from Stanford University presented a monetary policy rule that became very famous. He conjectured that the Fed, according to its dual mandate, should set nominal interest rates according to the equation:

$$\begin{array}{}\text{(Taylor Rule)}& i=\overline{r}+\pi +{\lambda }_{\pi }\cdot {\pi }^{gap}+{\lambda }_y\cdot Y^{gap}\end{array}$$

where ${\pi }^{gap}=\pi -{\pi }^{{}_T}$ is the inflation gap between the actual rate of inflation and the target inflation rate, while $Y^{gap}=\frac{Y-Y^P}{Y^P}$ is the output gap in percentage units. Taylor suggested that the weights for the inflation gap and the output gap should be similar $({\lambda }_{\pi }={\lambda }_y=0.5)$, and the natural real interest rate should be $\bar{r}=2\mathrm{\%}$.

We will apply the same procedure as in the previous exercise. Let us insert the data into the notebook:

👉 a) In the figure below, we compare what the Taylor Rule predicts against the nominal interest rate that the Fed actually sets (the FFR). Does this rule better explain the Fed's decisions concerning the Fed Funds Rate than the textbook rule?