A Taylor Rule with Monthly Data

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Presentation transcript:

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

Fed Funds 1957-2005

Unemployment Rate 1957-2005

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

CPI, All Items, 1957 - 2005

Standard Approaches Random Walk rt = α + βrt-1 + ε Taylor Model rt = α + β1CPI + β2(CPI-2) + β3(Un-4) + ε (or, rt = 1 + 1.5CPI + .5Gap + ε ) Econometric Models rt = α + β1rt-1 + β2(CPI-2) + β3(Un-4) + ε

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

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 rt : the Fed Funds rate at time t, the dependent variable CPIt-1 : the Consumer Price Index at time t-1 Adjusted CPIt-1 : CPI minus 2 at time t-1 Unt-1 : the Unemployment Rate at time t-1 Gapt-1 : the Unemployment Rate minus 4 at time t-1

Variables Per Model rt-1 CPIt-1 Gapt-1 Random Walk X Taylor Econometric Neural Net

Data Sets Data Set Training Validation Total PreGreenspan 319 36 355 Jan 58 to Jul 87 319 36 355 Greenspan Aug 87 to Nov 05 197 22 219 rt-1 : 0 to 5 24 243 rt-1 : 5.01 to 10 27 270 rt-1 : over 10 55 6 61

Random Walk Intercept Coefficient of r at t-1 PreGreenspan 0.177 0.973 0.006 0.995 High 1.481 0.879 Medium 0.021 Low 0.022

Taylor Equation Original Equation rt = 1 + 1.5*CPI + .5*Gap Calculated Equation Intercept CPI Gap PreGreenspan 2.334 0.789 0.296 Greenspan 1.797 1.477 -0.935 High 5.005 0.564 0.910 Medium 5.755 0.197 0.161 Low 2.837 0.496 -0.490

Econometric Model Intercept Fed Funds Adj. CPI Gap PreGreenspan 0.291 0.965 0.019 -0.035 Greenspan 0.047 0.994 -0.007 -0.024 High 1.442 0.862 0.066 -0.027 Medium 0.007 1.002 -0.003 -0.019 Low 0.125 0.983 0.018 -0.022

Neural Networks Significance of Variables PreGreenspan Greenspan Low Medium High Fed Funds CPI UnRate

Mean Squared Error Comparisons on Validation Sets Model / Data Set PreGreenspan Greenspan Low Medium High Random Walk 0.676 0.034 0.122 0.271 0.574 Taylor 10.036 8.392 6.651 9.701 16.754 Taylor2 6.793 3.001 0.985 2.221 1.263 Econometric 0.657 0.030 0.124 0.262 0.613 Neural Network 1.121 0.129 0.104 0.269 0.372