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

Fed Funds

Unemployment Rate

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

CPI, All Items,

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

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

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

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

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

Data Sets Data SetTrainingValidationTotal PreGreenspan Jan 58 to Jul Greenspan Aug 87 to Nov r t-1 : 0 to r t-1 : 5.01 to r t-1 : over

Random Walk InterceptCoefficient of r at t-1 PreGreenspan Greenspan High Medium Low

Taylor Equation Original Equation r t = *CPI +.5*Gap Calculated Equation InterceptCPIGap PreGreenspan Greenspan High Medium Low

Econometric Model InterceptFed FundsAdj. CPIGap PreGreenspan Greenspan High Medium Low

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

Model / Data Set PreGreenspanGreenspanLowMediumHigh Random Walk Taylor Taylor Econometric Neural Network Mean Squared Error Comparisons on Validation Sets

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