1. + PHOE004BP1FHSA and the Effective Federal Funds Rate By: Anissa Khan

2. + What is PHOE004BP1FHSA anyway??? Title : New private housing units authorized by building permits: 1 unit structures for Phoenix-Mesa-Glendale, AZ (Metropolitan Statistical Area) Frequency : monthly, 1988 to 2016 Seasonally adjusted: Yes Stationary: No Importance: Economic well-being Population PHU= Private housing units authorized

3. + What is the Effective Federal Funds Rate? Definition : the interest rate banks use to charge each other for overnight loans so that they can meet their reserve requirements. Frequency: monthly, 1988 to 2016 Seasonally Adjusted: No Stationary: No Importance : Economic well-being FFR = Federal Funds Rate

4. + Dealing with Non-Stationarity: 1.Private Housing Unit Authorizations How do I know? Local Trends ACF ADF Test ADF P-values: 1 lag: 0.2771 4 lags: 0.2107 8 lags: 0.1692

5. + Dealing with Non-Stationarity: 1.Effective Federal Funds Rate How do I know? Local Trends ACF ADF Test ADF P-values: 1 lag: 0.5445 4 lags: 0.7776 8 lags: 0.99

6. + Dealing with Non-Stationarity: How do I fix it? Difference Stationary  take the difference (Difference(log(series))*100 = Monthly growth rate

7. + Summary Statistics VariableMinimum1 st QuartileMedianMean3 rd QuartileMaximum PHU- 43.6 %- 7.8 %-0.38 %0.06 %7.9 %45.6 % FFR- 91.1 %- 2.9 % 0.00 %- 0.89 % 2.4 %69.3 % FFR = Effective Federal Funds Monthly Growth Rate PHU = Private Housing Unit Authorizations Monthly Growth Rate On average: fairly constant Widely spread

8. + Histogram of FFR Monthly Growth Rate Kurtosis: 23.43 Skewness: -1.99 Centered at 0

9. + Scatterplot of X and Y Question: Is this relationship statistically significant?

10. + Bivariate Regression Model 1: CoefficientEstimateT-valueP-value 0.08970.1240.902 0.03890.6610.509 Positive relationship BUT: statistically insignificant THEREFORE: no relationship

11. + Residual Plot: Average predicted PHU: 0.056 Residual = y - y predicted

12. + Outliers Why are they a problem? Outliers can cause regression results to be incorrect. How to identify outliers: Calculate studentized residuals Those larger than 1.96 are outliers Does this series have outliers? YES: there are 20

13. + What happens when outliers are removed? Positive Relationship Statistically significant The outliers had been affecting results Model 2: Equation is the same, data is different CoefficientEstimateT-valueP-value 0.13450.2270.820 0.13752.6550.008

14. + Level-Level vs. Log-Level vs. Log-Log What is the difference? The interpretation Equation : Level-Level Model: PHU=difference(PHU) FFR=difference(FFR) Log-Level Model: PHU = 100*difference(log(PHU)) FFR = difference(FFR) Log-Log Model: Same as Model 1 PHU=100*difference(log(PHU)) FFR=100*difference(log(FFR))

15. + Level-Level CoefficientEstimateT-valueP-value - 4.505- 0.3160.753 - 33.913- 0.4490.653 CoefficientEstimateT-valueP-value - 0.1788- 0.3060.760 - 1.9038- 0.6090.543 CoefficientEstimateT-valueP-value 0.13450.2270.820 0.13752.6550.008 Log-Level Log-Log Note: Outliers have been excluded Which is best?

16. + Quadratic Regression CoefficientEstimateT-valueP-value.12950.2160.829.14071.8850.060 7.396e-050.0610.952 Model 3: Note: Outliers have been excluded

17. +

18. + Groupwise Regressions CoefficientEstimateT-valueP-value 0.02790.0370.971 0.17593.5550.0005 CoefficientEstimateT-valueP-value - 0.1902- 0.2630.793 - 0.2872- 1.4200.158 Models 4 and 5: Before January 2000 After January 2000 Note: Outliers have been excluded

19. + FFR Group Summary Statistics On average, the FFR growth rate is larger post 2000 FFRMinimum1 st QuartileMedianMean3 rd QuartileMaximum pre 2000- 14.58 %- 1.71%- 0.12 % - 0.004 % 1.96 %11.91 % post 2000- 91.1 %- 6.26 %0.00 % - 2.66 % 3.65 %35.67 %

20. + Concluding Remarks Most appropriate model Linear log-log: interpretation, significance However 1. Results differ when sample differs Larger sample 2. Questionable robustness OVB? Most likely no causal relationship

21. + Questions?