EE432: Questions for Midterm Exams

Here are some questions I got from the mailbox. Check back for more.

In Fischer's staggered wage model, why do we set m = -v(-1)?

The objective here is to make output as stable as possible. With constant money supply, we found that output is given by 0.5(0.33(u-E(u|-1)) + 0.67(u-E(u|-2)). We know that the first part (u-E(u|-1))=v which the policy maker cannot do anything about. The current-period surprise v cannot be predicted by anyone. But the second part (u-E(u|-2))=v+v(-1) contains past shock v(-1) which has been observed by everyone. Therefore v(-1) is adding to the fluctuations of output unnecessarily.

How should we set m to eliminate this extra shock v(-1)? Because m and u enter the output in exactly the same way and we know (u-E(u|-2))=v+v(-1), it makes sense to set m such that (m-E(m|-2))=-v(-1) so that to cancel out v(-1). Setting m=-v(-1) accomplishes this goal precisely

Could you briefly summarize (in words) why money works in Staggered wage setting introduced by Fischer, Taylor and Calvo and why it does not work in Lucas'?

In Lucas (as well as Friedman), the starting point is the natural rate hypothesis which is the idea is that any change in monetary policy will translate into higher inflation, simply because nothing real or fundamental has changed in the economy. Any change in the quantity of money is a change in nominal quantity, that should not affect real quantities like employment or output. The exception is when people confuse these nominal changes with real changes, as in Lucas where agents sometimes interpret aggregate demand shock (which is nominal shock) wrongly as a relative price shock (which is real shock). When they make this kind of mistake, they may respond by producing more or less, which is why monetary policy is effective. But people only make mistakes when the change in monetary policy manages to surprise them (i.e. there is unanticipated demand change). Money does not work in this setting, in the sense that monetary policy cannot always surprise people, unless it is implemented randomly (and even so, we show in Lucas model that this will soon become ineffective too).

In (new) Keynesian models, we don't have an immediate pass-through from nominal changes to price adjustments, because these models assume price (or nominal) rigidity. Because prices do not fully adjust, real quantities such as output or employment must adjust instead to any aggregate demand changes. For example, after a negative demand shock (e.g. a monetary contraction), if the prices do not fall, lower demand will necessarily lead to lower equilibrium output. This holds true even with rational expectations (as we see in Fischer's model). Since a change in monetary policy is a demand or nominal change, this means that monetary policy is effective.

Questions from readings:
Lucas' Nobel Lecture, p.675, how does it follow from U'(n)=x that the equilibrium level of employment n will be a decreasing function of the rate of money growth.

The rate of money growth in this model is x. That n is decreasing in x follows from the fact that the marginal utility function U'(n) is decreasing in n (because of diminishing marginal utility assumption).