ECON 5010 Solutions to Problem Set #3

Transcription

1 ECON 5010 Solutions to Problem Set #3 Empirical Macroeconomics. Go to the Federal Reserve Economic Database (FRED) and download data on the prime bank loan rate (r t ) and total establishment nonfarm employees (h t ) over the period 1960 through Transform each series into a quarterly frequency. Use r t and h t to answer the following questions. 1. Do the time series appear stationary? If necessary, detrend each series using three di erent methods and comment on the results. Use the detrended data in the questions below. Solution. Total employees (h t ) appears nonstationary, while the loan rate (r t ) appears stationary. See below. 2. Provide a single graph of r t and h t over the sample period. Using macroeconomic theory as a guide, comment on the relationship between the two over the business cycle. Solution. Judging by the graph below, h t+j and r t are inversely correlated. In accordance with macro theory, an increase in the interest rate increases the incentive of rms to invest. The additional investment leads to increased employment with a lag of j periods. 3. Estimate an AR(4) for both time series. Do the empirical autocorrelations and partial autocorrelations match those of an AR(4) process? Are the residuals random noise? Solution. The employee growth rate correlations and partial correlations indicate an AR process, possibly an AR(2). The employee growth rate residuals are close to random noise except for the signi cant correlation at lag 8. The loan rate correlations and partial correlations indicate an AR process, possibly an AR(2). The loan rate residuals are close to random noise except for the signi cant correlation at lag Use the AR(4) to forecast for How do the forecasts perform? Solution. The employee growth rate forecasts are good for the 1st quarter of The loan rate forecasts are poor because the bank loan rate is at at 3.25 while the forecasts are trending upward over Estimate a VAR(2). Use the results to (a) calculate the impulse response functions for r t and h t, and (b) test for Granger causality. Comment on the results. Solution. The bank loan rate Granger causes total employee growth and the employee growth rate Granger causes the bank loan rate. 1

2 Thousands of Employees #1 & #2. HP-Filtered Total Employees and the Bank Loan Rate ( ) 10 5 Loan Rate vs. HP Filtered Total Employees h detrended r #3. AR(4) Regressions Estimation Range: 1961:02 to 2009:04 Forecast Range: 2010:01 to 2011:04 Box-Jenkins - Estimation by Gauss-Newton Convergence in 3 Iterations. Final criterion was < Dependent Variable LNH Quarterly Data From 1961:02 To 2009:04 Usable Observations 195 Degrees of Freedom 190 Centered R** R Bar ** Uncentered R** T x R** Mean of Dependent Variable Std Error of Dependent Variable Standard Error of Estimate Sum of Squared Residuals Regression F(4,190) Significance Level of F Durbin-Watson Statistic Q(36-4) Significance Level of Q CONSTANT AR{1} AR{2} AR{3} AR{4}

3 Total Employee Growth Rates -- Correlations and Partial Correlations Total Employee Growth Rate Residuals -- Correlations and Partial Correlations - - -

4 Estimation Range: 1961:02 to 2009:04 Forecast Range: 2010:01 to 2011:04 Box-Jenkins - Estimation by Gauss-Newton Convergence in 3 Iterations. Final criterion was < Dependent Variable R Quarterly Data From 1961:02 To 2009:04 Usable Observations 195 Degrees of Freedom 190 Centered R** R Bar ** Uncentered R** T x R** Mean of Dependent Variable Std Error of Dependent Variable Standard Error of Estimate Sum of Squared Residuals Regression F(4,190) Significance Level of F Durbin-Watson Statistic Q(36-4) Significance Level of Q CONSTANT AR{1} AR{2} AR{3} AR{4} Interest Rate -- Correlations and Partial Correlations - - -

5 Interest Rate Residuals -- Correlations and Partial Correlations #4. Forecasts 5 Total Employees Growth Forecasts HHAT LNH

6 5.25 Bank Loan Rate RHAT R #5. Impulse Response Function and Granger Causality VAR/System - Estimation by Least Squares Dependent Variable LNH Quarterly Data From 1960:03 To 2011:01 Usable Observations 202 Degrees of Freedom 197 Total Observations 203 Skipped/Missing 1 Centered R** R Bar ** Uncentered R** T x R** Mean of Dependent Variable Std Error of Dependent Variable Standard Error of Estimate Sum of Squared Residuals Durbin-Watson Statistic LNH{1} LNH{2} R{1} R{2} Constant F-Tests, Dependent Variable LNH Variable F-Statistic Signif LNH R Dependent Variable R Quarterly Data From 1960:03 To 2011:01 Usable Observations 202 Degrees of Freedom 197 Total Observations 203 Skipped/Missing 1

7 Centered R** R Bar ** Uncentered R** T x R** Mean of Dependent Variable Std Error of Dependent Variable Standard Error of Estimate Sum of Squared Residuals Durbin-Watson Statistic LNH{1} LNH{2} R{1} R{2} Constant F-Tests, Dependent Variable R Variable F-Statistic Signif LNH R Responses to Shock in LNH Entry LNH R Responses to Shock in R Entry LNH R