Q1. Consider the following macro model: (1) y ? m ? p ? ?y ? y ?? t t t ? t(2) mt m t ? ?? (3) ? ? t...

Question

Q1. Consider the following macro model: (1) y ? m ? p ? ?y ? y ?? t t t ? t(2) mt m t ? ?? (3) ? ? t pt Et pt y ? ? ?1 ? where 2 ~ (0, ) t N ? ? ? where y, p and m, are the logs of real output, prices and the money supply respectively and ?t is a monetary shock . a) Identify three methods for solving rational expectations models? [10 marks] b) Using your chosen method, find the rational expectations solution for prices (p) and output (y). [50 marks] c) Using a maximum of 150 words discuss the policy implications of your results for monetary policy. [40 marks]
	
Document Preview: ECON30611:  Macroeconomics IIIA XXXXXXXXXX/13 
Semester:  Autumn

Assessed Coursework

Q1.  Consider the following macro model: 
 
y?m? p???y?y??
 (1)  
t t t t
m?m??
 (2)  
t t
y???p?E p?
 (3)  
t t t?1 t
2
  where  ?? ~ N(0, ) 
t?
    
where y, p and m, are the logs of real output, prices and the money supply 
respectively and ? is a monetary shock .   
t
 
a) Identify three methods for solving rational expectations models? 
         [10 marks] 
 
b) Using your chosen method, find the rational expectations solution for 
prices (p) and output (y).   
[50 marks] 
 
c) Using a maximum of 150 words discuss the policy implications of 
your results for monetary policy.       
  
[40 marks]

Note: Submitted work should be well structured, clearly presented and 
typed using a word processor of your choice. 
 
Your work should be submitted to Leo Wells in the undergraduate office 
th
by 2.00 pm on Wednesday 14 November. If you require feedback on 
your submission you MUST submit two copies.

David · Accepted Answer

Ans. 
The Given system of equations:
a. As discussed in class, the three methods of solving this system of equations are: 
The Substitution Method: 
Case: 
We have our AS/AD equations, where demand depends on present year’s state variables, and 
past year’s expectations of present year.
Sargent’s Method of Repeated Substitution:  
Aggregate Demand is a function of next year’s expected Inflation. 
    ̅      (               )
Use reduced form, apply forward substitution, repeatedly. Apply stability conditions.
Muthian Method of Undetermined Co-efficients: 
For same problem as Sargent’s. 
Write a proposed difference equation,  take expectations, iterate the equation one period 
forward, homogenise, and collect the co-efficients.
b.   We use  Substitution Method: 
Substitute:        (    
 )   (         )  
Take Expectations at t-1: 
 ̅                    [ (    
 )]
   (             ) 
           By law of iterated expectations at t-1.  
             Now, ϒ(0)=0,

Q1. Consider the following macro model: (1) y ? m ? p ? ?y ? y ?? t t t ? t (2) mt m t ? ?? (3) ? ? t pt Et pt y ? ? ?1 ? where 2 ~ (0, ) t N ? ? ? where y, p and m, are the logs of real output,...

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