* This post will be occasionally updated.
Here are some Recently Asked Questions about TeX, entirely by myself, and some answers I found on the web.
Graphics & Tables/Floatings
Q: How do I place pictures inside a table?
A: Tips from LaTeX Matters
(This is useful for arranging pictures in neat format, as well as importing tables with nice formatting into LaTeX as pictures.)
In short, you can pretty much use \includegraphic within a \table environment.
Q: How to place wide tables in landscape?
A: Use lscape and pdflscape packages. See this.
Q: How to put all tables and figures at the end of the documents (as asked by many journals)?
A: Use endfloat package. See also these general tips.
Q: How to use table in landscape mode with endfloat?
A: 1.) Copy the file: efxmpl.cfg (which is located in the package
location: ...\latex\endfloat on my hard drive) to where the tex document is and leave it in that directory.
2.) rename the file: efxmpl.cfg to endfloat.cfg.
3.) Compile.
*** I haven't managed to do this successfully.
Q: How to vertically align numbers in different cells of the table?
A: Lots of suggestions on this, but I find the most flexible and simplest method is to use \phantom{}. E.g. to align 4.56 with (0.02)***, with 4.56 aligned with 0.02, we centre both cells, and use \phantom{***}(0.02)***.
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).
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).
EE432: Reading pack for topic 3
The lecture note and the reading pack for topic 3 is now available for download.
Let me know if you have problems unzipping the file.
By the way, we will have to reschedule the class for February 25th to some other date. More update coming up.
Let me know if you have problems unzipping the file.
By the way, we will have to reschedule the class for February 25th to some other date. More update coming up.
EE432: Q&As for topic 1 and reading pack for topic 2
This is the first post for this semester, welcome to EE432!
Here are some questions I get for topic 1, which are based on Blanchard and Fischer textbook.
The rate of return on money is simply the change in the 'value' of money over time. In this model, money is valued relative to only one good available in the economy. The price level P_t tells us how much that good is worth relative to money, or equivalently how much money is valued relative to good. Rate of return on money is then simply P_t/P_t+1, the deflation rate! If you hold money, and it buys more goods over time, money is effectively paying a rate of return.
Also, there is a statement "we can rule out non-steady-state paths in which the price level is falling at a rate greater than n".
The last sentence of your argument is wrong. Suppose that there is a non-steady-state equilibrium where g>n. You're right that the real balance per person will keep growing over time, because money pays a higher return than population growth. As real balance per person keeps growing, it will eventually exceeds 1. That implies that each young person will have to save more than 1 unit of good. That is impossible since he is only endowed with 1 unit of good. So our assumption that there is a non-steady-state equilibrium must be false. (This is called proof by contradiction)
Not quite. In Blanchard and Fischer, a monetary equilibrium is an equilibrium in which money is used. This is in contrast to a barter equilibrium, in which everyone ignores money and use storage technology if available. (In this model, since trade cannot take place anyway, a barter equilibrium is really the same as an autarky equilibrium, that is you are on your own and never trade with anybody)
Thanks for the questions and keep them coming.
*********************
Here's the reading pack for topic 2.
Happy reading!
Here are some questions I get for topic 1, which are based on Blanchard and Fischer textbook.
In the text book on page 161, What is the rate of return on money? Is it n or ((the money demand @t+1) - (the money demand @t))/(the money demand@t)?
The rate of return on money is simply the change in the 'value' of money over time. In this model, money is valued relative to only one good available in the economy. The price level P_t tells us how much that good is worth relative to money, or equivalently how much money is valued relative to good. Rate of return on money is then simply P_t/P_t+1, the deflation rate! If you hold money, and it buys more goods over time, money is effectively paying a rate of return.
Also, there is a statement "we can rule out non-steady-state paths in which the price level is falling at a rate greater than n".
Does this mean that if g is greater than n, the non-steady-state is impossible?
If this is the case, why the non-steady-state is impossible.
With g greater than n, the real balance @t+1 divided by the real balance @t is greater than 1. Since this is possible, that g is greater than n should be possible, isn't it?
The last sentence of your argument is wrong. Suppose that there is a non-steady-state equilibrium where g>n. You're right that the real balance per person will keep growing over time, because money pays a higher return than population growth. As real balance per person keeps growing, it will eventually exceeds 1. That implies that each young person will have to save more than 1 unit of good. That is impossible since he is only endowed with 1 unit of good. So our assumption that there is a non-steady-state equilibrium must be false. (This is called proof by contradiction)
On the same page, does the word " a monetary equilibrium" mean the equilibrium in the money market?
Not quite. In Blanchard and Fischer, a monetary equilibrium is an equilibrium in which money is used. This is in contrast to a barter equilibrium, in which everyone ignores money and use storage technology if available. (In this model, since trade cannot take place anyway, a barter equilibrium is really the same as an autarky equilibrium, that is you are on your own and never trade with anybody)
Thanks for the questions and keep them coming.
*********************
Here's the reading pack for topic 2.
Happy reading!
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