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

2. Fed Funds

3. Unemployment Rate

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

5. CPI, All Items,

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

7. 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

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
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

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

14. 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

17. 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

18. 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

19. 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

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

21. 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