Project II

Troy DewittEmelia Bragadottir

Christopher WildermanQun Luo

Dane Louvier

Scope of analysis

• Does monetary policy affect the U.S. Economy?• What is going to be the status of U.S. economy

upon graduation – will we be able to get a job?• Will inflationary pressures force the Federal

Reserve to raise the interest rate?• Use univariate model to forecast the federal fund

rates• Use univariate model to forecast the

unemployment rate• If causality exists between the two variables use

a VAR model to forecast the data

0

5

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2519

54

1957

1959

1962

1964

1967

1969

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1987

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1994

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2007

%

UNEMPLOYMENT FFR

Trace Unemployment Rate and Federal Funds Rate - It appears that changes in the unemployment rate lag changes in the federal funds rate

Correlogram for FFR Correlogram for Unemployment

Both time series have a unit root – Meaning we have to difference the data to eliminate the data’s dependence on time

ADF Test Statistic -3.230898 1% Critical Value* -3.4432

5% Critical Value -2.8665

10% Critical Value -2.5694

ADF Test Statistic -1.543935 1% Critical Value* -3.4432

5% Critical Value -2.8664

10% Critical Value -2.5694

FFR - only at 1% level

Unemployment rate

Differenced Time Series

Correlogram of differenced FFRCorrelogram of differenced

unemployment rate

Unit Root Test

dFFR

dUnemployment rate

ADF Test Statistic -8.295159 1% Critical Value* -3.4432

5% Critical Value -2.8665

10% Critical Value -2.5694

ADF Test Statistic -16.43205 1% Critical Value* -3.4432

5% Critical Value -2.8665

10% Critical Value -2.5694

Univariate ARMA Output

Correlogram of ResidualsdFederal Funds Rate dUnemployment Rate

Correlogram of Residauls SquareddFederal Funds Rate dUnemployment Rate

ARCH LM TestdFederal Funds Rate dUnemployment Rate

ARCH GARCH ModeldFederal Funds Rate dUnemployment Rate

Actual Fitted Residual GraphsdFederal Funds Rate dUnemployment Rate

Correlogram of ResidualsdFederal Funds Rate dUnemployment Rate

Correlogram of Residuals Squared

dFederal Funds Rate dUnemployment Rate

Forecasts of Univariate Models

Causality

Does the unemployment rate Granger cause the federal funds rate?

Does the federal funds rate Granger cause the unemployment rate?

Is there two-way causality between these two variables?

Cross Correlogram: Differenced Unemployment Rate and Differenced Federal Funds Rate (Evidence of Two-Way Causality)

Granger Causality Test

Pairwise Granger Causality Tests

Date: 05/31/07 Time: 15:10

Sample: 1954:07 2007:12

Lags: 24

Null Hypothesis: Obs F-Statistic Probability

DFEDFUNDS does not Granger Cause DUNEMPLOYMENT

609 2.14998 0.00129

DUNEMPLOYMENT does not Granger Cause DFEDFUNDS 2.94100 4.7E-06

Both variables are significant, however the unemployment rate is more significant

Funds Unemployment

Funds 1, 2, 4, 7, 8, 9, 13, 16 7, 11, 18, 22Unemployment 1 2, 3, 4, 12, 15, 19, 24

Summary of Significant Lags of Vector Autoregressive Estimates

Impulse Response VAR Estimates (Unemployment appears to have significant effects on the Federal Funds rate for five months)

Impulse Response VAR Estimates (Federal Funds rate has an insignificant effect on the unemployment rate)

Test of the models ability to accurately forecast Apr 06 – Apr 07

Test of the models ability to accurately forecast Apr 06 – April 07

VAR Forecast May 07 – Dec 07

VAR forecast of May 07 – Dec 07

Forecast Comparison

Questions?