Questions on topic 4: Diamond-Dybvig model

The followings are the questions asked by one of your classmates. You can download my answers here. Or go to http://groups.google.com/group/economaru/files and find file Questions_DiamondDybvig.zip.

1. Under the Bank Run model, when we analyze the competitive equilibrium. Why the t=0 price of period 1 good is 1, period t=1 and t=0 price of period 2 good are 1/R? How can we figure out there numbers since the paper did not explain and show calculation on them? What method should I use (assume utility is equal with Autarky case??)?

2. For the social planner allocation, after we try to maximize the social utility function we will have U'(c1*) = RU'[......can't type here...]. So, what can we imply from this ugly equation? Since c1* is still being inside the utility function, so, how can we know the exact c1*? What are the conditions for c1* and c2*? (the paper use another equation so it does not really help)

3. On the Suspension of Convertibility model, why the fraction f^ for suspension must exceed 1/r1? (how could they get this number?) Also, to demonstrate the model, the paper say that let r1=c1* and let f^ is a set of [t, [(R-r1)/r1(R-1)]. Why the maximum boundary of f^ must be at [(R-r1)/r1(R-1)]? If this is a correct number, so can we put this in the V2 equation to show that V2 > V1?

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And here are some questions from Hedhood in the chatter...

First, I dont quite understand about the integral and the outcome about the relative risk aversion. What is the difference between the absolute risk and relative risk aversion. and Second, why C1 and C2 that are allocated by policy planner can't be equal?????

Let me recall briefly the steps involved when we establish the social planner's solutions. Equation (3) on page 7 of the lecture note gives us the social planner's optimal allocation, which is essentially u'(c1)=Ru'(c2), only that I have substituted in the budget constraint for c2.

The key question was, how are c1 and c2 under social planner's allocation different from those under Autarky? i.e. can c1=1, and c2=R? If yes, then we must have u'(1)=Ru'(R), as we must obey equation (3). If not, then perhaps the society wants people to be exposed to less risk, so their consumption is not too dependent on their type. In this case, we're interested in finding the conditions under which c1 is bigger than 1 and c2 is less than R, so that indeed people will be exposed to less risk.

If c1 is greater than 1 and c2 is less than R, then it must follow that Ru'(R) is less than u'(1) (using dimishing marginal utility). In other words, we have some risk sharing (or less exposure to risk), if Ru'(R)-u'(1)<0. Now Ru'(R)-u'(1) can be written as an integral as shown in the lectures...we just integrate 1 with respect to a variable ru'(r), and then evaluate the integral by the upper limit R and lower limit 1.

When you play with this integral, you find that it is negative whenever ru''(r)/u'(r)<-1 for all r. This expression ru''(r)/u'(r) turns out to be what microeconomists use as a measure of relative risk aversion. So as long as agents are risk averse according to the relative risk aversion definition, our social planner will find it optimal to do risk sharing.

Intuitively, greater relative risk aversion means agents are risk averse to percentage changes (rather than absolute changes) in their wealth. Namely agents prefer a certain percentage change in wealth to a lottery which gives the same expected change, but with uncertainty attached. Absolute risk aversion, as the name suggests, measures the degree of being risk averse to absolute changes in wealth. It is mathematically defined by u''(r)/u'(r), so it is not scaled by the consumption level r.

Lastly, we cannot have c1=c2 as the optimal social planner's outcome because this would imply from equation (3) that u'(c1)=Ru'(c1), which cannot be true because R>1.

Topic 7: The Science of Monetary Policy

Last of the series! Here's the reading pack.

The key readings are:
- Clarida, Gali and Gertler (1999) "The Science of Monetary Policy: A New Keynesian Perspective" JEL
- Blinder (1997) "What Central Bankers Could Learn from Academics--and Vice Versa" JEP
- Bernanke and Mishkin (1997) "Inflation Targeting: A New Framework for Monetary Policy?" JEP

The first paper should provide a comprehensive coverage of theoretical issues we will cover (and more). The next two papers will provide useful discussions in relation to the policy implications. I have also attached a few other papers which you may find useful.

Solutions to problem set 4: Time Inconsistency

...are available here.

You'd probably notice that I have not put anything up for problem set 3. It's unlikely that I will ever have the time to do anything about it, especially with a few stacks of homeworks I have accumulated so far, I guess we'd talk about it in class instead.

Fed's new tools, summarised

Fed new OMO tools as explained by Francisco Torralba, a blogger and grad student at Chicago. Very simple and easy-to-understand explanation...great for topic 6!

Topic 6 Part Deux: The Transmission Mechanism

Reading pack is now available at http://groups.google.com/group/economaru/files
or download here directly!

The key readings are:

- The symposium papers on Transmission Mechanism in Journal of Economic Perspectives (JEP) 1995 issue (The article authors include Mishkin, Bernanke&Gertler, Taylor, Obstfeld &Rogoff, and Meltzer)

Other readings included in the pack:
- Dr. Piti's paper
- More recent works using VAR

This Week Side Dish

I have mentioned in class that the following would be interesting to read...

• Fed's latest FOMC minutes which has recently been released
  
• The FOMC transcripts detailing everything Greenspan and others said in the FOMC meetings not too long ago
  
• Lastly, more of an add-on, a concise article on Thailand's new Bilateral Repo market

Ben Bernanke in the Joint Economic Committee hearing on April 2nd

This is an excerpt from Ben Bernanke's testimony, when he was explaining the Bear Stearn emergency rescue. For full text, see his Testimony on economic outlook and Testimony on Financial Markets Developments




In the next clip, we have a Q&A session where Bernanke discussed the sources of business cycles, and the Federal Reserve's influence on them. For real economic contents, just skip Ron Paul's ramblings and go straight to 4.46th minute in the video.

Topic 6: The Mechanics of Monetary Policy

We'll split this topic into 2 parts:
Part 1: The implementation of monetary policy
Part 2: The transmission mechanism

We've circled around issues related to the second part in the previous lectures, when we talked about the credit market (CC-LM analysis), and how the subprime crisis requires more innovative monetary policy measures (as I discussed in the latest lecture). We'll deal with the rest of the issues in the latter part of this topic.

Part 1: The implementation
There will be no lecture notes on this part. The key readings are

• Powerpoint slides
• Borio (1997) "The Implementation of Monetary Policy in Industrial Countries: A Survey" BIS Economic Papers

Reading pack ready at http://groups.google.com/group/economaru/files

The name of file is Topic6_Mechanics_Implementation.zip

Part 2: The Transmission Mechanism

Forthcoming. Check this space!

Problem set 4: Bank Runs and Time Inconsistency

Due date: Friday 11th April, 8.00am.

Downloadable from the usual place
http://groups.google.com/group/economaru/files

File name EE432_test4.zip

There are 2 questions, with 60% of marks allocated to the first and 40% to the second.

Topic 5: Time Inconsistency

Reading pack available at the usual place:
http://groups.google.com/group/economaru/files The lecture note on the topic has also been uploaded.
*Note that I have also uploaded Bernanke (1983) (file name Topic4_Creditextra.zip), the paper I mentioned will be useful for topic 4 but was not covered in the lectures.

The key readings for topic 5 is
David Romer "Advanced Macroeconomics", chapter "Inflation and Monetary Policy" (chapter 9 in the old edition), sections on dynamic inconsistency.
Barro and Gordon (1983) "Rules, Discretion and Reputation in a Model of Monetary Policy", JME
Kydland and Prescott (1977) "Rules Rather than Discretion: The Inconsistency of Optimal Plans", JPE
Readings are ordered in ascending order of difficulty, so read the first one first.