代考宏观计量经济学-Macroeconometrics代写
代考宏观计量经济学

代考宏观计量经济学-Macroeconometrics代写

Macroeconometrics 8:

Final Exam

代考宏观计量经济学 This exam is worth 100 points total and has four questions. For your submission, put all your answers in a .zip file called FINAL_LastnameFirstname

1 Instructions

  •  This exam is worth 100 points total and has four questions. For your submission, put all your answers in a .zip file called FINAL_LastnameFirstname. Analytical questions,as usual, should be handed in with all answers in a single .pdf file. There is one Stataproblem, and for this you need to submit a .do file.
  • In solving the exam, you are allowed to use all of the materials posted on Blackboard as well as the Becketti textbook. However, you are not allowed to use any other resources,including consulting the internet, seeking help from others, and whatnot. If there is the slightest suspicion that in solving your exam you have used references that are not allowed, then your exam grade is subject to automatically being a zero. Please note as well that any late exams whose tardiness is not justified by a legitimate and documented excuse, such as a health issue, will automatically earn a grade of zero as well.
  • All students must first encounter this exam and/or know of its contents when they first access it. Therefore, it is strictly prohibited for any student who downloads the exam to send a copy of this exam to any other students who have not yet accessed the exam themselves or discuss the contents of the exam with any other students who have not yet accessed the exam themselves. If there is the slightest suspicion that you have violated this policy, then your exam grade is subject to automatically being a zero.

2 Questioms  代考宏观计量经济学

Problem  1  (43  poimts  total).  Consider  the  following  ARMA(1,1)  process  (NB:  just  to ease any potential concerns, there is no typo here: the coefficient on yt—1 is the same as the coefficient on εt—1), where o is white noise.

yt = ∅yt—1 + εt — ∅εt—1.

Part  1.a  (6  poimts).   Find  the  pure  MA  representation.   Please  show  your  work  in detail.

  • HINT: This involves brute force iterative backwards Use theequation above to solve for 4t—fi, then plug into the equation above, etc. Later in this problem you will be asked to establish conditions on $ for stationarity. To get at this, two or three substitutions should be enough for you to get at a pattern that helps you get at these conditions.

Part 1.b (6 poimts).  Find the pure AR representation.  Please show your work in detail.

  • HINT: This involves brute force iterative backwards Use theequation above to solve for ot, then plug into the equation above, etc. Later in this problem you will be asked to establish conditions on $ for stationarity. To get at this, two or three substitutions should be enough for you to get at a pattern that helps you get at these conditions.

Part 1.c (Y poimts).  What conditions must the parameter $ satisfy for this process to be stationary? Please explain in detail. Your argument must be convincing in a disciplined way. In terms of being convincing, more is not necessarily better, but you should be as thorough as needed to make your point including, of course, showing any math work you deem necessary to include in as much detail as you judge necessary.  代考宏观计量经济学

  • HINT: This involves the same thought process as in the homeworks and the notes on stationarity. In essence, at the core of this question is: how does $ matter for us to be able to have process for 4 that has: a constant, time independent, and finite expected value¡ a constant, time independent, and finite variance¡ and time independent and finite autocovariances.

Part  1.d  (8  poimts).

Does this process have a steady state?  Please explain in detail. Your argument must be convincing in a disciplined way. In terms of being convincing,  more is not necessarily better, but you should be as thorough as needed to make your point including, of course, showing any math work you deem necessary to include in as much detail as you judge necessary.

  • HINT: Recall that in steady state there are no shocks and you can get rid of time subscripts since the value of all variables are constant across time.

Part  1.e  (8  poimts).   Suppose  you  were  to  estimate  this  process  for  the  purposes  of forecasting. Do you have a preference of what representation you would use: ARMA, MA, or AR? Please explain in detail. Your argument must be convincing in a disciplined way. In terms of being convincing, more is not necessarily better, but you should be as thorough as needed to make your point including, of course, showing any math work you deem necessary to include in as much detail as you judge necessary.

  • NOTE: The idea here is for you to just express an informed opinion as if you were explaining this to someone that understands the material but has not looked at this process in as much detail as you have so far.  代考宏观计量经济学

Part  1.f  (8 poimts).  Consider 4 in period t = 0 and assume the value of o was zero in all periods t c 0. Moreover, in period t = 0 the value of o is oO = fi and thereafter the value of o is zero for all periods t > 0. Derive the value of 4 in any arbitrary period N > 0. Note: your derived value of 4N must be in terms of parameters, only. Please show your work in detail (you are deriving IR5N for N > 0).

  • NOTE: We‘ve gotten at IRFs in different ways throughout the class, but no matter what path we take the IRF is always the same. Therefore, take the approach you are most comfortable with.
代考宏观计量经济学
代考宏观计量经济学

Problem  2  (22  poimts  total).    代考宏观计量经济学

Consider  a  VAR  with  two  variables:   4fi,t  and  4X,t.   In particular, assume

代考宏观计量经济学
代考宏观计量经济学

where εt is white noise and the µs and ∅s are parameters. Establish with mathematical precision the conditions under which the steady state values of y1 and y2 are finite.

  • HINT:What you need to do.hereΣis solve for the ste.ady state firstΣ.  Then, focus on the parameters in the vector and the matrix
    What you are looking to do here is state values and/or conditions for these parameters such that y1is not equal to plus or minus ∞.

Problem  3  (15  poimts).

Consider a VAR with two variables:  y1,t  and y2,t.  In particular, assume

代考宏观计量经济学
代考宏观计量经济学

where εt is white noise and the Øs are parameters. Assume that the matrix of coefficients Φ1 is upper triangular. Given this information, establish with mathematical precision the conditions for this VAR to be stable.

  • Himt:   the  solution  to  this  problem  involves  the  companion  matrix  and  eigenvalues (problem 4 of the Lesson fi practice problems with solutions has an example of how to get at eigenvalues), and the Lesson 1 notes go over what an upper triangular matrix is on page 10.

Problem 4 (20 poimts total).

The Stata dataset Midcerm_5_.dta contains five variables: time (a string variable that nonetheless shows the quarterly frequency ordering of the data); apl (U.S. average product of labor index, seasonally adjusted at an annual rate, 2009=100); u (U.S. unemployment level in thousands, seasonally adjusted); lf (U.S. labor force level in thousands, seasonally adjusted); v (U.S. vacancy level in thousands, seasonally adjusted).

The variable

where θ  is the Greek letter ”theta™ is the ratio of aggregate vacancies to aggregate unem- ployment. Empirically, there is a negative relationship between vacancies and unemployment called the Beveridge curve. Furthermore, θ is often referred to as mavhet tsghtness: the higher θ is, the higher the tightness in the labor market or, in other words, the better the labor market is doing as there are many open positions per job seeker. All the questions that follow below revolve around modeling the behavior of market tightness. Please put theamswer to all your questioms im a simgle .do file called VAÆtheta.do amd put this file imto your .zip file.  Please clearly mark im your .do file what questiom you are amswerimg where.  代考宏观计量经济学

Part 4.a (15 poimts).  In theory, market tightness is a function of the average product of labor. Model θ and the average product of labor as a recursive VAR in:

levels (i.e. using θ and ap1); log levels (i.e., ln (θ) and ln (ap1)); growth rates (i.e., d ln (θ) and d ln (ap1)); using the cyclical component of the natural logarithm of θ and the average product of labor obtained with a smoothing parameter equal to 1600; and using the cyclical component of the natural logarithm of θ and the average product of labor obtained with a smoothing parameter equal to 105.  Please  explaim  im  your  code,  usimg  commemts,  all  the  decisioms  you that guide your recursive modelimg.

Part 4.b (5 poimts).  Which of the VARs that you ran in (1) would you prefer to use? Also, would it be the case that you definitely do not want to use one or more of these VARs? Explain using comments in your Stata code, and adding any supporting Stata coding that you might think is appropriate (although adding extra coding is not necessary if you think the sort of output you obtained is self explanatory in terms of which model is best and only words are needed to convey the message).

 

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代考宏观计量经济学
代考宏观计量经济学

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