ECO4217 Monetary Policy Making
2024 Fall
MONETARY POLICY MAKING — Project Report Instruction
December 2, 2024
1 Logistics
Congratulations! You have finished two midterm tests and all the quizzes,i.e., most of the coursework. This project report is the last piece for your evaluation. You have one week to finish the report. The deadline for submission is Dec 11, at 14:30 exactly. Be sure to submit your report on time. As we have agreed, late submissions will be penalized.
This report’s format is problem-solving. In class, we focused on the operation and impact of monetary policies. We did not talk much about the design of monetary policies, i.e., how the central bank should do monetary policy-making. This report aims to complete this missing piece. Through this exercise, we will see why good monetary policy-making is hard at some fundamental level.
Think about this problem using the concepts and methodologies you learned in class, and present your work as much as you can. Discussions between students are encouraged, but individual report writing is required. Copy-and-paste work will be assigned zero points!
2 Motivation
Think about this. A professor cares about students learning something and, in addition, about them being happy. To motivate students to learn, at the beginning of the semester, the professor may announce that the class content is difficult and that students can pass only by studying very hard. However, when the professor has to give grades at the end of the semester, should the professor enforce his rules and standards strictly? Probably not. Because how much the students have learned is fixed and will no longer be affected by grades. But, you can always make students happier by inflating the evaluation. Taking this into consideration, however, students may not take the professor’s announcement (threat) very seriously at the very beginning.
Monetary policy-making shares this logic. Suppose low inflation is desirable for society in the long run, and so the Fed announces that it intends to achieve such a target. Observing this announcement, wage contracts are made in the private sector. Now, does the Fed want to carry out the low inflation policy after wage contracts have been signed? No! By increasing the inflation rate (expansionary monetary policy), the Fed can reduce the real wage and stimulate the economy. Considering this, the private sector would not believe the low inflation target in the first place.
This is actually the contribution of Kydland and Prescott (1977), and helped them earn the Nobel Prize in 2004 “for their contributions to dynamic macroeconomics: the time consistency of economic policy and the driving forces behind business cycles” . Digest the idea a bit, and solve the following exercise step by step. This exercise is a simplified version of Kydland and Prescott (1977).
3 Exercise
The starting point is the supply curve we introduced in class
π = πe + λ(Y − YP)
where YP is the potential output, π e is the expected inflation of the private sector (or the public), and λ is the responsiveness of inflation to the output gap. Note that we omit the supply shock here. In the lecture, we emphasize the interpretation of the supply curve ashow the output gap shapes inflation. In this exercise, it is useful to think the other way around. Note that we can write the supply curve as follows.
Y - Y P = λ/1(π − π
e
) (1-1)
where λ
1
can be thought of as the responsiveness of the output gap to inflation surprises. Therefore, there will be a positive output gap if inflation is higher than expected.
Suppose that the Fed has the following loss function, which can be thought of as the negative of the social welfare function
L(π, Y ) = (π - πO )2 + η(Y - YO )2 (1-2)
where YO is the output target, π O is the inflation target, and η reflects the Fed’s relative weights on output stabilization. A higher η means the Fed puts more weight on output stabilization over inflation stabilization. π O and YO are what the Fed thinks is the best for the economy. The Fed tries to minimize the loss function. Without loss of generality, we assume π O = 0, i.e., the Fed has a zero inflation target.
The structure of the game, including the value of YP and YO , are all public information. For simplicity, we think that the Fed can directly choose the level of inflation. The game between the Fed and the private sector (the public) is as follows.
1. The Fed announces an inflation target π F .
2. The private sector, after observing π F , forms an inflation expectation π e.
3. The Fed chooses π to minimize the loss function.
4. Production and social welfare realize.
To complete the description of the environment, we must specify how the private sector’s inflation expec- tations are formed. Here, we adopt the notion of perfect foresight that we introduced in the first class, that the private sector’s inflation expectation must turn out to be exactly correct. Therefore, unless otherwise specified, we have assumption I as follows.
Assumption I: π
e
= π (1-3)
A second assumption we will always maintain is that the target output YO is higher than the potential output YP . A defense to this assumption could be that the potential output is too low for various distortions and frictions in the economy.
Assumption II: Y
O > Y
P (1-4)
Make sure you fully understand the environment, and answer the following questions. (Suggestive answers for questions 1-3 are given to you. I recommend you think about them by yourself first and still show your work in your own words.)
1. What is the unconstrained social optimal inflation and output? Note here that “unconstrained” means you can specify inflation and output directly and not be constrained by the supply curve.
2. Suppose the Fed has a commitment technology, i.e., it can creditably promise that it will enforce the announced level of inflation. Find out the equilibrium π F , π , π e , Y , and L.
3. Now, suppose the Fed does not have any commitment technologies. If the Fed still announces the π F you found in the previous question, does it have an incentive to deviate later? Find out L in the case that the Fed announces π F you found in the previous question and the private sector believes the Fed, but the Fed deviates in the end. Note here you need to abandon the perfect foresight assumption.
4. Solve for the equilibrium π F , π , π e , Y , and L when there are no commitment technologies and perfect foresight holds.
5. Redo 1-4 with π O > 0. Feel free to make necessary assumptions if needed.
6. Read this Vox article on Paul Volcker’s fight against inflation (click here). Use what you have learned from this exercise, analyze (verbally) why Volcker could successfully curb the inflation in the 1980s.
7. (optional, try this one only if you are interested) Note that the Fed’s attitude η is important. In the above analysis, we assume η is fixed and publicly known. However, in reality, the public may not know whether the Fed is weak (with a high η) or strong (with a low η) in fighting inflation, i.e., η can be private information. Therefore, the Fed may care about its reputation in a repeated game (think about Paul Volcker in the 1980s). In other words, a weak Fed may have the incentive to pretend to be a strong one if it sufficiently cares about the future. Try extending the above model to illustrate this idea.
4 Suggestive Answers
1. Unconstrained social optimum means π = 0 and Y = YO . Therefore, L = 0.
2. Under commitment, π = πF , and π e = π F . The game is reduced to a one-shot game. The loss function
L = π2 + η(YP - YO )2
To minimize it, the Fed will choose π = 0 = π F = π e. Output Y = YP and L = η(YP - YO )2 . Note the social loss here is higher than the unconstrained optimum.
3. Without commitment technologies, the game is dynamic. A common routine for thinking about dynamic problems is to use backward induction. According to the question, the public naively believes the Fed, i.e., π e = 0, and therefore, Y = Y P + π . Use backward induction, the loss function will be
L = π2 + η(Y - YO )2
= π2 + η(YP + λ/1π − YO)2
Now we see the Fed’s motive to deviate: by increasing inflation, there is a gain in production. As- sumption II is important here: only when the potential output is too low for the Fed can the deviation be justified. To find the optimal π, it’s convenient to use some calculus. If you are unfamiliar with calculus, the high school method for quadratic functions can also do the job. Either way, we end up getting π = η+λ2/ηλ (YO - YP ) > 0. Note that the deviated inflation is higher than zero, and output is higher than YP.