Does Money Matter?An Artificial Intelligence Approach

Peter Tino – CERCIA, University of Birmingham, UK

a collaboration with

J. Binner – Aston Business School, Aston University, UK

B. Jones – State University of New York, USA

G. Kendall – Nottingham University, UK

J. Tepper – Nottigham Trent University, UK

Does Money Matter?

Motivations

• What is money?

Traditional interpretation of what money is capturing:

– Store of value

– Unit of account

– Medium of exchange

• Changing environment

– New monetary assets

– Banks blend with Building Societies, etc.

• Need to adequately measure money ...

... in order to construct money supply (monetary policy), but ...

– how to combine and measure different objectives in a changing

environment?

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 1

Does Money Matter?

Our framework

• How do we know if we have been successful or not?

– Inflation targeting - one of the main monetary policy tools.

– Macroeconomists: having robust measures of money will help

us in predicting inflation.

• In the past ...

– We used to know how much money there was in the economy.

– Stable relationship between the quantity of money and prices.

– Macroeconomic control through targeting money supply.

• ... but then ... ”the case of missing money”

– Financial innovation distorted formerly stable relationships.

– Major economies abandoned monetary targeting in the late

1980s.

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 2

Does Money Matter?

Divisia Money - Bank of England

Aggregate mcertain

• Assets where we know the value (rate of return)

• Personal sector monetary aggregate containing:

1. Notes and coins

2. Non-interest bearing time deposits

3. Interest bearing savings (short term)

4. Interest bearing time deposits (long term)

5. Building society deposits (long term)

Interest rate captures liquidity: L ↓ =⇒ IR ↑

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 3

Does Money Matter?

Money Stock Mismeasurement?

• Traditional simple sum index

M =∑

i∈Aggregate

mi (Fisher, 1922)

mi - the amount of asset i

• Weighted average index (such as Divisia)

– weighted by interest rate si

takes the degree of liquidity into account

DM =∑

i∈Aggregate

si · mi

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 4

Does Money Matter?

Divisia Monetary Index

• Capture ”services” provided by monetary assets

• ”consumer price index” for money

• Compare with a high yielding non-monetary asset -

what else we could have done with the money ...

• more liquid monetary asset =⇒ more services

Rt - max. rate of return on non-monetary asset at time t

ri,t - rate of return on monetary asset i at time t

price/value: pi,t =Rt − ri,t

Rt + 1= 1 −

ri,t + 1

Rt + 1

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 5

Does Money Matter?

• Normalize across monetary assets j in the whole economy

mi,t - quantity of monetary asset i at time t

νi,t =pi,t · mi,t

∑

j pj,t · mj,t

• Capture the flow of values of money - share weight

si,t =1

2(νi,t − νi,t−1)

• Discrete-time approximation of the continuous flow (in log-scale)

ln Mt − ln Mt−1 =∑

i

si,t · (ln mi,t − ln mi,t−1)

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 6

Does Money Matter?

Predicting Inflation Rates - Data

• Monthly data

• 4 Levels of aggregation: M1, M2, MZM, M3

– aggregation levels currently monitored in USA

– narrow → broad

• At each aggregation level:

– Simple sum

– Weighting

∗ non-monetary benchmarks

- BAA (a long bond in USA)

- upper envelope

∗ St Louis Fed Reserve Bank style

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 7

Does Money Matter?

Data - Cont’d

• Interest rates

– short term

– long term

– Important?

Short term IR are currently used in UK to control inflation.

• Training: Jan ’61 - Feb ’97

• Validation: Mar ’97 - Apr ’01

• Test: May ’01 - Jun ’05

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 8

Does Money Matter?

US Inflation Rates

0 50 100 150 200 250 300 350 400 450 5000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16inflation rate

trainvalidatetest

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 9

Does Money Matter?

Predicting Inflation Rates - Models

• Evolutionary (FF) Neural Networks

– ES - crossover + Gaussian mutation

– evolve a population of neural networks

– finite length input window (finite input memory)

• Recurrent Neural Networks

– self-recurrent internal state units

– dynamically construct internal representations of temporal de-

pendencies

– trained via BPTT

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 10

Does Money Matter?

• Kernel regression

– linear in parameters

– linear techniques in ”feature space”

– finite length input window (finite input memory)

– Kernel width, input lag and other model hyperparameters are

set on the validation set

– Kernel Recursive Least Squares - Kernelized version of the

classical Recursive Least Squares (RLS) technique

– Other kernel-based regression techniques used:

∗ Kernel Partial Least Squares

∗ Relevance Vector Machine

∗ Gaussian Process

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 11

Does Money Matter?

Kernel Recursive Least Squares

1K(x ,x) X

2K(x ,x)

3K(x ,x)

4K(x ,x)

F

R

Σi

F(x) = w K(x ,x)ii

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 12

Does Money Matter?

Baseline - Random Walk

• y(t) - the actual observed inflation rate at time t.

y(t) - inflation rate predicted to occur at time t by our model.

• Predict that in T months (prediction horizon) we will observe

the current inflation rate:

y(t + T ) = y(t)

• Corresponds to random walk hypothesis with moves governed

by a symmetrical zero-mean density function.

• It measures ”the degree to which the efficient market hypothesis

applies”.

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 13

Does Money Matter?

Evaluation Methods

• Root Mean Square Error

RMSE =

√

√

√

√

1

N

N∑

t=1

(y(t) − y(t))2

• Improvement in RMSE over baseline (RW)

IORW (M) =RMSE(RW ) − RMSE(M)

RMSE(RW )× 100%

=

(

1 −RMSE(M)

RMSE(RW )

)

× 100%

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 14

Does Money Matter?

Our Hypothesis

• USA MSI (divisia) - superior indicators of monetary conditions.

• Such evidence could reinstate monetary targeting.

• Most empirical studies based on cointegration techniques (Stracca

2003).

• We use artificial intelligence techniques to model regularities in

past inflation rates and monetary indexes.

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 15

Does Money Matter?

Results

• RMSE(RW) = 0.008827

• All models implicitly included past inflation rates as input vari-

able.

• Does inclusion of measures of money (or interest rates) improve

predictive performance?

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 16

Does Money Matter?

Evolved Neural Networks

Evol NN M TB BAA Recurrent IORW

M1 - No No Yes :-(

M2 - No No No :-(

M3 M3 No No No :-(

M4 DM3 BAA Yes No Yes :-(

:-( means worse than baseline

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 17

Does Money Matter?

Recurrent Neural Networks

RNN M TB BAA # Hidden IORW

M1 Envelop M1 Yes No 25 11.28

M2 - No No 5 10.81

M3 SS M3 Yes No 10 13.61

M4 - Yes Yes 10 14.13

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 18

Does Money Matter?

Kernel Recursive Least Squares

KRLS In Lag KW ν λ IORW

M1 10 1.5 0.21 0.1 7.09

M2 10 1.2 0.27 0.1 39.62

M3 10 1.2 0.28 0.1 35.77

M4 12 1.2 0.27 0.1 43.42

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 19

Does Money Matter?

KRLS - Predicted Inflation Rates

0 100 200 300 400 500 6000

0.05

0.1

0.15

0 10 20 30 40 50 600.01

0.02

0.03

0.04Val

0 5 10 15 20 25 30 35 40 45 500.01

0.02

0.03

0.04Tst

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 20

Does Money Matter?

Lessons Learnt

1. When controlling model complexity appropriately, it is possible

to beat baseline RW model quite considerably.

2. It seems that enough information is present in the inflation rates

alone, no standard additional measures of money are helpful.

3. Need to deal with model complexity issues in a more profound

way.

4. Other compound measures of money may be useful, but they may

be

• model/task dependent

• non-linear in nature

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 21

Does Money Matter?

Conclusions and Future Work

• All approaches are valid, and all try to solve the same task –

prediction of inflation rate.

• The assumptions the models make about the structure of the

data are different - this is the first shot.

• Further work required to develop the construction of Divisia.

• Hybrid approaches & apply to different datasets (e.g. Risk ad-

justed Divisia).

P. Tino, J. Binner, B. Jones, G. Kendall, J. Tepper 22

Does Money Matter?

Conclusions and Future Work

policy implementation

• Bank of England – need to be transparent and accountable with

their funding.

• Rule Extraction

• Need to understand better how each technique influences the

results.

• We may able to influence Bank of England to pursue new av-

enues of research and adopt new ways of constructing money,

still transparent (e.g. non-linearities).

• Philipp’s Curve...

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