1. A Taylor Rule with Monthly Data A.G. Malliaris Mary.E. Malliaris Loyola University Chicago

2. Fed Funds 1957-2005

3. Unemployment Rate 1957-2005

4. CPI-All Items 12 month logarithmic change rate Jan 1957-Nov 2005

5. CPI, All Items, 1957 - 2005

6. Standard Approaches Random Walk r t = α + βr t-1 + ε Taylor Model r t = α + β 1 (CPI-2) + β 2 (Un-4) + ε Econometric Model r t = α + β 1 r t-1 + β 2 (CPI-2) + β 3 (Un-4) + ε

7. Neural Network Architecture Input, Hidden and Output Layers with sigmoid function applied to weighted sum w1 w2 w3 w16 w17 w18 w19 w20 w21 F(sum inputs*weights)=node output F(sum inputs*weights)=output

8. Network Process The neural network adjusts the weights and recalculates the total error. This process continues to some specified ending point (amount of error, training time, or number of weight changes). The final network is the one with the lowest error from the sets of possible weights tried during the training process

9. Variable Designations r t : the Fed Funds rate at time t, the dependent variable CPI t-1 : the Consumer Price Index at time t-1 Adjusted CPI t-1 : CPI minus 2 at time t-1 Un t-1 : the Unemployment Rate at time t-1 Gap t-1 : the Unemployment Rate minus 4 at time t-1

10. Variables Per Model r t-1 CPI t-1 Gap t-1 Random WalkX TaylorXX EconometricXXX Neural NetXXX

14. Data Sets Data SetTrainingValidationTotal PreGreenspan Jan 58 to Jul 87 31936355 Greenspan Aug 87 to Nov 05 19722219 r t-1 : 0 to 521924243 r t-1 : 5.01 to 1024327270 r t-1 : over 1055661

17. Random Walk InterceptCoefficient of r at t-1 PreGreenspan 0.1770.973 Greenspan 0.0060.995 High 1.4810.879 Medium 0.0210.995 Low 0.0220.995

18. Taylor Equation Original Equation r t = 2 + 1.5*CPI +.5*Gap Calculated Equation InterceptCPIGap PreGreenspan 2.3340.7890.296 Greenspan 1.7971.477-0.935 High 5.0050.5640.910 Medium 5.7550.1970.161 Low 2.8370.496-0.490

19. Econometric Model InterceptFed FundsAdj. CPIGap PreGreenspan 0.2910.9650.019-0.035 Greenspan 0.0470.994-0.007-0.024 High 1.4420.8620.066-0.027 Medium 0.0071.002-0.003-0.019 Low 0.1250.9830.018-0.022

20. Neural Networks Significance of Variables PreGreenspanGreenspanLowMediumHigh Fed Funds CPI UnRateCPI UnRate CPIUnRate Fed Funds

21. Model / Data Set PreGreenspanGreenspanLowMediumHigh Random Walk 0.6760.0340.1220.2710.574 Taylor 10.0368.3926.6519.70116.754 Taylor2 6.7933.0010.9852.2211.263 Econometric 0.6570.0300.1240.2620.613 Neural Network 1.1210.1290.1040.2690.372 Mean Squared Error Comparisons on Validation Sets

22. Summary Several approaches to modeling Econometric approach best when applied to pre-Greenspan and Greenspan Neural Network best when sample is divided to low, medium and high