Question 3: The Phillips Curve and Inflation Expectations
(8 points)
Consider the following two modifications to the Phillips Curve equation we studied in
class
i. The Federal Reserve has been successful in achieving stable inflation around its
target rate of 2% per year. Therefore, we may expect inflation expectations to be
"anchored" in the sense that private sector agents expect inflation to eventually
return to target over the long-run after any economic shocks. Suppose that
inflation expectations are not adaptive, but are anchored to the inflation target as
follows:
pi _(t)^(e)=(1-
ho )/(b)ar (pi )+
ho pi _(t-1)
This equation says that firms forecast inflation as a weighted average of the
inflation target /bar (pi ) and yesterday's inflation pi _(t-1). Note that adaptive expectations
are a special case of this where the weight on yesterday's inflation
ho =1.
ii. Many economists have documented that the empirical Phillips Curve is almost
flat. Therefore, suppose that the Phillips Curve does not depend on the current
state of the economy.Question 3: The Phillips Curve and Inflation Expectations
(8 points)
Consider the following two modifications to the Phillips Curve equation we studied in class
i. The Federal Reserve has been successful in achieving stable inflation around its
target rate of 2% per year. Therefore, we may expect inflation expectations to be
"anchored" in the sense that private sector agents expect inflation to eventually
return to target over the long-run after any economic shocks. Suppose that inflation
expectations are not adaptive, but are anchored to the inflation target as follows:
pi _(t)^(e)=(1-
ho )/(b)ar (pi )+
ho pi _(t-1)
This equation says that firms forecast inflation as a weighted average of the
inflation target /bar (pi ) and yesterday's inflation pi _(t-1). Note that adaptive expectations
are a special case of this where the weight on yesterday's inflation
ho =1.
ii. Many economists have documented that the empirical Phillips Curve is almost flat.
Therefore, suppose that the Phillips Curve does not depend on the current state
of the economy.
Assume that the rest of the AS/AD model is the same as in class. Additionally, consider
the following parameter values: /bar (pi )=2%,
ho =0.4(,)/(b)ar (m)=0.5(,)/(b)ar (b)=0.5,ar (a) =0.
Assume the economy starts at potential (in t=0,pi _(0)()/(b)=ar (pi ) and tilde(Y)_(0)=0 ). In period 1(t=1),
the economy is hit by a cost-push shock, /bar (o_(1))=2%, lasting one period. Answer the
following questions:
A. Compute the value of short-run output and inflation for the first 5_() periods after the
shock. (Hint: solve the AS-AD system of two equations in two unknowns, pi _(t),tilde(Y)_(t),
for t going from 1 to 5 .) Graphically illustrate the dynamics of the economy.
B. How does your answer change if we assume inflation expectations are more firmly
anchored to the inflation target? (Hint: what does this imply for the value of
ho ?
Increase/decrease this parameter by 0.1 and recompute your answer from part A)
Question 3: The Phillips Curve and Inflation Expectations (8 points)
Consider the following two modifications to the Phillips Curve eguation we studied in class
i.
The Federal Reserve has been successful in achieving stable inflation around its target rate of 2% per year.Therefore,we may expect inflation expectations to be "anchored" in the sense that private sector agents expect inflation to eventually return to target over the long-run after any economic shocks.Suppose that inflation expectations are not adaptive, but are anchored to the inflation target as follows:
T=(1-P)+PTTt-1
This equation says that firms forecast inflation as a weighted average of the inflation target it and yesterday's inflation T.-1. Note that adaptive expectations are a special case of this where the weight on yesterday's inflation p = 1.
ii.
Many economists have documented that the empirical Phillips Curve is almost flat. Therefore, suppose that the Phillips Curve does not depend on the current state of the economy.
Assume that the rest of the AS/AD model is the same as in class. Additionally, consider the following parameter values: tt = 2%, p = 0.4, m = 0.5, b = 0.5, a = 0.
Assume the economy starts at potential (in t = 0,iTo = tt and Y, = 0). In period 1 (t = 1), the economy is hit by a cost-push shock, = 2%, lasting one period. Answer the following questions:
A. Compute the value of short-run output and inflation for the first 5 periods after the shock. (Hint: solve the AS-AD system of two equations in two unknowns, It, Yt for t going from 1 to 5.) Graphically illustrate the dynamics of the economy
B. How does your answer change if we assume inflation expectations are more firmly anchored to the inflation target?(Hint: what does this imply for the value of p? ncrease/decrease this parameter bv o.1 and recompute vour answerfrom partA
