Q1: Phillips curve...is it a tradeoff between (1) inflation and unemployment, or (2) inflation and output? Does it mater?
Unemployment and output are both measures of the economic activity, so they are tightly correlated. The empirical relationship between the two is called the Okun's law. No surprise the correlation is negative, as in an economic expansion you'd expect unemployment to be low and output high, while in a recession the opposite happens. You can think of it in terms of production function - output is a function of labour input, so the correlation must be there.
So for me it is almost semantic whether we use unemployment or output in the Phillips curve...the choice doesn't really matter conceptually. What we're essentially doing is tracing a relationship between inflation and economic activity.
Q2: I don't understand abt the third solution in the term of Reputation Equilibrium and Subgame Perfect.
We say in the lecture that the Nash equilibrium in output and inflation is inefficient, as the Phillips curve allow the inflation to be closer to desired level while the output gap needs not change. Of course the problem is, the central bank cannot credibly commit to that desired inflation. We calculate this Nash equilibrium assuming that the game is played only once, or in the game theory term, it is a static game.
If we allow the game to be played many many times (i.e. we have a 'repeated game'), so that each player maximises the discounted sum of utility instead of just one single utility, then we can get all sorts of interesting Nash equilibria and a good Nash equilibrium may be achievable. The central idea is, cheating may only earn you a welfare gain in the short run, but cheating destroys the trust (or your reputation), and hence it can be bad for you in the long run. If the long-run loss is greater than the short-term gain, you will decide not to cheat. And we get a good equilibrium.
Let me sketch 2 examples.
Suppose the game is played for infinite number of times. The public may decide to adopt the following strategy: Expect low inflation to begin with, and continue to expect low inflation as long as the central bank implements low inflation. But as soon as the central bank chooses a high inflation even for one period, expect a high inflation forever. This is called a 'trigger strategy', i.e. I choose to be well-behaved as long as my opponent cooperates, and retaliate forever if my opponent cheats even only once. Under this strategy, the central bank may find that cheating only earns him one period gain (when he surprises the public), and loss of welfare in every period after that. Cheating to get short-term gain may not be worth it for the central bank, in which case, we can observe a low inflation every period. Good equilibrium rules.
In the 2nd example, suppose the game is played twice, and there are 2 types of central bank, one that is like in our lecture (i.e. wants to cheat), and the other who cares only about low inflation. The public doesn't know which type the central bank is. In this case, the outcome of the game in the 1st period tells the public something about the type of the central bank. If the central bank misbehaves in the 1st period, he gives away his type, and the public may expect a high inflation in the 2nd period, which is bad for him. Anticipating this, the central bank may implement a low inflation in the 1st period, to build a 'reputation' and pretends to be the 2nd type. This pretense allows the central bank to earn trust and manipulate the inflation expectation, and get a better inflation-output tradeoff in the 2nd period. You may find this line of reasoning and the model in Romer's book.
Q3: In solution 1, Can we derive other L preference to solve Time inconsistency Problem??
You certainly can. There is an infinite number of loss functions you can write down that will solve the problem just as well. Can you think of some?
Q4: In Policymaker Reaction function,if a=0 then this mean policymaker don't care inflation that made L=0 ?? I don't understand the economic intuitions behind this??
Yes, if a=0, that means the policy maker only cares about the output deviation from y_star. The loss then takes a parabola shape, with minimun point at y=y_star, at which point L=0 as you said. The exact value of L is of no importance...we're operating in ordinal utility world (and not cardinal), so we care only about the relative loss. When a=0, the minimum loss is L=0, which is the best that the central bank can hope for.
Q5: Policy maker must be let independent or discretion or commit the rule?? In my thought, CB should be independent to solve explosive inflation,but when CB commit the rule yield better solution than discretion.
When CB has no independence, the monetary policy is dictated by the elected government. In that case, you can safely assume the loss function will include the targeted output y_star term, as short-term growth brings votes. When CB has independence and retains discretion, you must ask what is the loss function. With the right loss function, efficient outcome may be achievable. Otherwise, committing to a rule (i.e. specifying a credible pre-commitment, which can take the form of legal commitment like a binding inflation-targeting regime), can improve the welfare.
Q6: In Journal, I found content is not the same in your lecture? I don;t understand so much so Need I understand this outside your lecture? Is Romer 9.4 is the same as we learn from you??
The Kydland-Prescott paper is a little hard, but the Barro one is easier. Romer's is the easiest one. The central idea is identical, whichever reading you consult.
To be continued.
Q7: We assume y*= natural rate output>th e reason is because Incentive Distortion- I don't understand this word. and its process and why CB must target y* > naturate output not eq output. Pleae example in term of income tax?
When you impose income tax, this distorts the people's incentives to work. They work less hard, and produce less. The resulted neutral rate of output is y-bar, the natural rate. But in an ideal world, give the technology and preferences for consumption/leisure etc, it is socially desirable for this economy to produce more output (optimal, without tax distortions, to sleep less and work m0re) at y_star. This is what the CB is after...the first-best solution.
Q8: I know that because y*> natural rate output that drive inflation bias (constant term right? May be I don't clear this word) this made CB to cheat but how?
Is there other factors that driving this inflaton bias?
The central bank wants to raise output up beyond the natural rate, but the Phillips curve forbids it from doing it for free...the CB must sacrifice some inflation. So to get a higher output, they must allow inflation to rise. But the public catches up with the CB, and hence the CB ends up getting a higher inflation with no gain in output. The Nash equilibrium is inefficient, and is a consequence of the CB's incentive to raise output up at bit at the margin. Please make sure you understand the mechanics of the model well...this is the key point of this topic.
The central bank wants to raise output up beyond the natural rate, but the Phillips curve forbids it from doing it for free...the CB must sacrifice some inflation. So to get a higher output, they must allow inflation to rise. But the public catches up with the CB, and hence the CB ends up getting a higher inflation with no gain in output. The Nash equilibrium is inefficient, and is a consequence of the CB's incentive to raise output up at bit at the margin. Please make sure you understand the mechanics of the model well...this is the key point of this topic.
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