EE432 2009: Revision series - Misc

Here are some questions from some of you.

1) Can u explain more in details on " Impulse responses in the Inflation-Unemployment-Interest rate Recursive VAR"(details on each graph) ie. Inflation shock to unemployment- how inflation causes higher unemployment, Unemployment shock to unemployment- why it go up and down(below 0) then up again ?

Remember that VAR gives you a statistical fact...so it doesn't have to agree with any theory necessarily (in the case of disagreement, you could either blame the theory, or VAR itself). The job of interpreting the result and checking if it makes sense lies with us, the economists. I encourage you to try and interpret these, using what you know from the course and elsewhere. In this example, why should inflation raise unemployment? We learn from various topics that inflation shock is an AS (or Phillips curve shock). What happens when there is a positive inflation shock? The equilibrium output will be reduced! (Revise topic 5 again if you don't follow this step.) So it's no surprise that unemployment rises. As for unemployment on itself, you may interpret it as a 'pendulum effect'...the economy is trying to settle to a new equilibrium after the shock, and the adjustment process involves overshooting in unemployment in the medium term.

2) For the supply of bank reserves (last lecture page10) I dont understand the graphes
and what is the shape for supply of bank reserves(horizontal,vertical or upward sloping?)

The supplier of bank reserves in this case is not motivated by profit, so there's no reason for the supply curve to have any slope. The supply is motivated by the central bank's objective of meeting it's operating target - the overnight interest rate, as set by the monetary policy committee. In this case, you may think the idealised supply should be perfectly elastic at the targeted overnight rate...i.e. the central bank stands ready to supply whatever reserves to meet its target. This would in principle be correct. In practice, it is more complicated, because the central bank is only one among many participants in the market for reserves. The central bank in practice calculates how the supply of reserves is changing in quantity in the absence of its action (i.e. conduct liquidity forecasting), and then decides on the amount of open market operation needed to bring reserves supply in line with te reserves demand. In view of this practical implementation, it would be closer to the truth that the supply for reserves is vertical, i.e. just in line with the demand. But then the central bank quickly communicates to the market it's intention to meet the target interest rate. The vertical supply collapses to a point...on which the interest rate is as announced, and the quantity equals reserves demand.

3)In topic 5 what would be the optimal rule for commitment?
What whould be the level of pi that CB should commit to? Is it the same as problem set's answer: plug in y=y_star and pi=pi_star in AS function and find expected pi?
do we have to saperate into cheat case(y_star>y_bar) and no cheat case(y_star=y_bar)?

The upshot of this model is, if the public holds rational expectations, there is never any gain in terms of output that the central bank can enjoy. Output will always equal the natural rate in the rational expectations equilibrium (check the maths to see that you agree with me in this). So the best that the central bank can achieve is in meeting its inflation target. Committing to this particular inflation is the optimal strategy.

In topic 6, from the journal "The Science of Monetary Policy:..." by Richard Clarida, Gali, Gertler,
On Page 1680, on the right hand side paragraph
"... As the future comes to pass, the central bank has the incentive to renege on its planned toughness and, instead, promise again to undertake contractionary policy down the road. To see this, ......If the central bank is free to deviate from the rule, it will always choose the optimal policy under discretion,...."
So under this paragraph, does it mean that the central bank will choose to cheat from its commitment to fix the shock? which means it will fall into the case of time inconsistency? Would taking the limit to infinity into the model prove this statement?

At last, someone asks questions related to papers!
Yes, this is very similar to time inconsistency issue, as the problem arises because of the inability of the central bank to achieve an outcome that it deems optimal ex ante, but wishes to deviate ex post. Clarida et al mentions down the paragraph that they think this is different from the traditional time inconsistency however, because the incentive to cheat has nothing to do with the desire to push output beyond the natural rate (note that Clarida et al associates the concept of time inconsistency with k>0). Instead, the incentive to cheat here arises because the 'tough' act, which has a long-term benefit in taming inflation expectations but painful for output in the short-run, is not carried out under discretion. Hence the benefit in terms of low inflation expectations is never realised, because the people expect that the touch act is not optimal ex post. This leaves room for the commitment regime to add value.

EE432 2009: Solution to Problem Set 4

Solution guide for the last problem set.

Download here.

For people having questions during their revisions, I encourage you to post them using the chat, so that your friends may read them and interact etc. If the space limit gets on your nerve, let me know, and I'll open up a new post, and we can use the comment space there instead.