What how did fed interest rate target respond to this

Question

Monetary Economics Assignment

1. Take our benchmark model in which households maximize utility, firms maximize profits, firms and households interact with one another in the labor market, goods market, asset (loan), and money markets. Assume that wages and prices are perfectly flexible. Using diagrams of the labor market to determine real wages, the goods market to determine the real interest rate, and the money market to determine the price level use the model to make predictions what would happen to equilibrium real wages, real interest rates, output, consumption, investment, work, and the price leveleffort if the following events occur:

a. There is a permanent increase in productivity (but assume that this increase in productivity does not change marginal products of labor or capital).

b. There is a temporary increase government spending financed with lump sum taxes.

c. There is an increase in the money supply.

2. Use the IS/LM model to predict what would happen to equilibrium real and nominal interest rates and output, if
a. There is a temporary increase in government spending.

b. There is an increase in the money supply.

c. Expected inflation (next period) rises.

3. Consider the following model. There is an expectations augmented short-run Phillips curve:

π_t = π^e_t + (1/θ) (y_t - yⁿ_t),

where y_t is (the logarithm of) output, yⁿ_t is natural level of output, π_t is inflation, and π^e_t is expected inflation.

There is also an equation that describes the growth rate in aggregate demand:

dg_t = π_t + ( y_t - y_t-1 ) ,

where dgt is the growth rate in aggregate demand.

a. Take the above two equations and derive equations that solve for inflation (π_t) and output ( y_t ) as functions of yⁿ_t, π^e_t, dg_t, and y_t-1.|

b. Suppose that households have adaptive expectations, π^e_t= π_t-1 . Assume yⁿ_t = 0 . Let θ = 1. Using the equations solved for in part a, answer the following questions.

(i) Policymakers increase demand growth from 0 to 8 and keep it there.

Complete the following table.

t	dgt	Yt-1	πet	πt	yt
0	0	0	0	0	0
1	8	0
2	8
3	8
4	8

Based on the table is it possible of get output above the full-employment level of output? Is it possible get output above full-employment level indefinitely? What is the cost of in terms of inflation of trying to increase output?

(ii) Policymakers increase demand growth from 0 to 8 for two periods and then reduce demand growth back to zero in order to keep inflation from getting high. Complete the following table.

t	dgt	Yt-1	πet	πt	yt
0	0	0	0	0	0
1	8	0
2	8
3	0
4	0

Based on the table what are the costs of temporarily trying to increase output above the full-employment level of output?

c. Suppose that households have rational expectations. Derive equations for equilibrium inflation an output. Hint: right in terms of expectations of dg_t, dg^e_t, assume that households know y_t-1 and ynt.

(i) Policymakers increase demand growth from 0 to 8 and keep it there. Suppose that the increase in time period 1 was not anticipated, but was correctly anticipated from time period 2, 3, .... Complete the following table.

t	dgt	Yt-1	πet	πt	yt
0	0	0	0	0	0
1	8	0
2	8
3	8
4	8

(ii) Policymakers increase demand growth from 0 to 8 for two periods and then reduce demand growth back to zero in order to keep inflation from getting high. Suppose that each time the change in growth was unanticipated. Complete the following table.

	t	dgt	Yt-1	πet	πt	yt
0		0	0	0	0	0
1		8	0
2		8
3		0
4		0

Based on the table what are the costs of temporarily trying to increase output above the full-employment level of output?

4. Instead of assuming policymakers can control the growth rate of aggregate demand directly, assume that policymakers target interest rates. Thus our model of the economy is as follows:

Expectations augmented short-run Phillips curve:

π_t = π^e_t + (1/θ) (y_t - yⁿ_t),

where y_t is (the logarithm of) output, yⁿ_t is natural level of output, π_t is inflation, and π^e_t is expected inflation.

IS curve for aggregate demand:

y_t - yⁿ_t = σ(R_t - π^e_t+1 - ρ) + e_t

where Rt is nominal interest rate, π^e_t+1 is expected inflation, ρ is the long-run real interest rate, and e_t is a shock to aggregate demand.

Taylor rule for the interest rate:

R_t = ρ + π*_t + γπ (π_t - π*_t) + γ_y(y_t - yⁿ_t)

a. Suppose people have adaptive expectations, so that π^et = π_t-1 and π^e_t+1 = π.

Combine the IS curve and the Taylor rule to get an equation for inflation that is a function of the output gap (y_t - yⁿ_t), π*_t, and e_t. The resulting expression is our new DG curve.

b. Use the new DG curve and the Phillips curve, find equations that describe n equilibrium π_t and output gap (y_t - yⁿ_t).

c. Suppose θ = 1, σ = 1, ρ = 0, γ_π = 1.5 , γ_y = 0.5 , and n = 0 . Suppose that in time period 1, there was shock to aggregate demand. The shock lasts only one period. Fill out the table below to trace out the dynamics of inflation, output, and interest rates.

t	et	Π*t	Πt-1	πt	yt	Rt
0	0	4	4	4	0	4
1	4	4
2	0	4
3	0	4
4	0	4

What how did Fed interest rate target respond to this demand shock?

d. Suppose θ = 1, σ = 1, ρ = 0, γ_π = 1.5 , γ_y = 0.5 , and yⁿ_t = 0 . Suppose that starting in time period 1, the Fed lowered its inflation target from 4 to 0. Fill out the table below to trace out the dynamics of inflation, output, and interest rates.

t	et	Π*t	Πt-1	πt	yt	Rt
0	0	4	4	4	0	4
1	0	0
2	0	0
3	0	0
4	0	0

What happened to to interest rates when the Fed changed its desired inflation rate?

5. In the Excel spreadsheet 4386HW2F16.xls, worksheet "Q5. Phillips Curve" contains quarterly data on inflation and unemployment rate from 1960 to 2015.

a. Construct a scatterplot with inflation on the vertical axis and unemployment on the horizontal axis. From the scatterplot, what does the relationship between the inflation and unemployment appear to be?

b. To get a sense of the quantitative relationship, take the same data plotted in (a) and run a linear regression with inflation as the dependent variable and unemployment rate as an independent variable (be sure to include an intercept/constant in the regression). What is the sign of the coefficient on unemployment rate and is this coefficient statistically significant? To do this you need to add-in the Analysis ToolPak in Excel.

c. As the model suggests that one might want to control for expected inflation, create a measure of expected inflation that is a moving average of inflation over the previous four quarters: π^e_t = (1/ 4)(π_t-1 + π_t-2 + π_t-3 +π_t-4 ) . From this create, a column in your spread sheet that represents inflation less inflation expectations: π_t - π^e_t. In another column, create a variable that represents deviations of unemployment from the natural rate: u_t - uⁿ_t.

Taking these new data series, construct a scatterplot with π_t - π^e_t on the vertical axis and u_t - uⁿ_t on the horizontal axis. What is the apparent relationship between inflation and unemployment as implied by the scatterplot? With these same variables, run a regression π_t - π^e_t as the dependent variable and u_t - uⁿ_t as an independent variable (include a constant in the regression as well). What is the sign of the coefficient on u_t - uⁿ_t and is the coefficient statistically significant?

d. In addition to inflation expectations shifting the Phillips curve, supply shocks might shift the Phillips curve. In order to control for supply shocks, run a regression with π_t - π^e_t as the dependent variable with u_t - uⁿ_t and the average growth rate in oil prices over the past year as independent variables (include a constant in the regression as well). To run this regression in Excel, add a new column right behind the column with u_t - uⁿ_t that contains the average growth rate in oil prices over the last four quarters (including the current quarter).

What happens to coefficient on u_t - uⁿ_t (compared to that found in part c) and is it statistically significant? What is the sign of the coefficient on oil prices and is it statistically significant?

Attachment:- 4386hw2f16.xls