church, curram - 1996 - forecasting consumers' expenditure a comparison between econometric and...

8/13/2019 Church, Curram - 1996 - Forecasting Consumers' Expenditure a Comparison Between Econometric and Neural Net

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ELSEVIER International Journal of Forecasting 12 (1996) 255-267

F o r e c a s t in g c o n s u m e r s e x p e n d i tu r e :A c o m p a r i s o n b e t w e e n e c o n o m e t r i c a n d n e u r a l n e t w o r k

m o d e l sK e i t h B . C h u r c h a * , S t e p h e n P . C u r r a m b

aESRC Macroeconornic Modelling Bureau, University of Warwick, Coventry CV4 7AL, UKbWarwick Business School, University of Warwick, Coventry CV4 7AL, UK

Abstract

This paper i s mot iva ted by the d i f f icu l t i es f aced by fo recas ter s in p red ic t ing the dec l ine in the g rowth r a te o fco n s u m e r s ' ex p en d i t u r e i n t h e l a t e 1 9 8 0 s . T h e eco n o m e t r i c s p eci fi c a ti o n s o f f o u r co m p e t i n g ex p l an a t i o n s a r er ep l i c a t ed an d t h e s t a ti c fo r eca s t s co m p ar ed w i t h t h e ac t u a l o u tt u r n s . T h e s am e d a t a a r e t h en u s ed t o e s t i m a t en eu r a l n e t w o r k m o d e l s . T h e m a i n i s s u e i s w h e t h e r t h e n eu r a l n e t w o r k t e ch n o l o g y can ex t r ac t an y m o r e f r o m t h ed a t a s e t s p r o v i d ed t h an t h e eco n o m e t r i c ap p r o ach . I t is f o u n d t h a t t h e n eu r a l n e t w o r k m o d e l s d e s c r i b e t h e d ec l i n ei n t h e g r o w t h o f co n s u m p t i o n s i n ce t h e l a t e 1 9 8 0 s a s w e ll a s , b u t n o b e t t e r t h an , t h e ec o n o m e t r i c s p ec if i ca t i on si n c l u d ed i n t h e ex e r c is e , an d a r e s h o w n t o b e r o b u s t w h en f aced w it h a sm a l l n u m b er o f d a t a p o i n t s. H o w e v e r ,w h i ch ev e r ap p r o a ch i s ad o p t ed , i t is t h e s ki ll o f ch o o s in g t h e m en u o f ex p l an a t o r y v a r i ab l e s w h i ch d e t e r m i n e s t h esuccess of the f inal resul ts .Keywords: Consumers' ex penditure; Econom etric m odelling; Neural networks; Forecasting

1 I n t r o d u c t i o n

T h i s p a p e r c o m p a r e s t h e f o r e ca s t s f r o mm o d e l s o f U K c o n s u m e r s ' e x p e n d it u r e w h i cha r i s e f r o m c o m p e t i n g e c o n o m e t r i c a n d n e u r a ln e t w o r k s p e c i f i c a t i o n s . T h e m o t i v a t i o n f o r t h ise x e r c i s e c o m e s f r o m t h e d i f f i c u l t y i n e x p l a i n i n gt h e p e r s i s t e n t d o w n t u r n i n c o n s u m e r s ' e x p e n d i -t u r e t h a t o c c u r r e d d u r i n g t h e l a t e 1 9 8 0 s a n d e a r l y1 9 9 0 s . T h e f a i l u r e t o p r e d i c t t h e s e e v e n t s p r o b a -b l y le d t o p o l i c y m a k e r s t a k i n g d e c i s i o n s t h a t

* Corresponding author. Tel: 01203 523934; fax : 01203523032; e-m ail: [email protected].

m a d e t h e s u b s e q u e n t r e ce s s io n d e e p e r a n d m o r ep r o l o n g e d t h a n i t m i g h t o t h e r w i s e h a v e b e e n .F o r e c a s t e r s u s in g e c o n o m e t r i c a n d o t h e r m e t h -o d s b a s e d m o r e o n j u d g e m e n t w e r e e q u a l l yp r o n e t o t h e s e f o r e c a s t fa i lu r e s. T h e u s e o f a ne c o n o m e t r i c m o d e l e n t a i l s a n e x p l i c i t s t a t e m e n to f t h e m o d e l d e t e r m i n i n g e x p e n d i t u r e a n d e n -a b l e s c o m p a r a b l e n e u r a l n e t w o r k m o d e l s t o b ec o n s tr u c te d . T h e p a p e r e x a m i n e s w h e t h e r t h ee s t i m a t i o n o f p o t e n ti a l l y h i g h ly n o n - l i n e a r n e u r a ln e t w o r k m o d e l s u s i n g t h e s a m e v a r i a b l e s f e a -t u r e d i n t h e c o n v e n t i o n a l c o n s u m p t i o n f u n c t i o n sc a n h e l p e x p l a i n c o n s u m e r s ' b e h a v i o u r .

T h e c o n s u m e r s ' e x p e n d i t u r e e q u a t i o n s u s e d in0169-2070/96/ 15.00 (~) 1996 Elsevier Scienc e B.V. All rights rese rvedSSDI 0 1 6 9 - 2 0 7 0 ( 9 5 ) 0 0 6 3 1 - 1


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256 K.B . Church, S.P. Curram / International Journal of Forecasting 12 1996) 255 -267t h is c o m p a r i s o n a r e b a s e d o n t h o s e e s t i m a t ed b yt h e L o n d o n B u s i n e s s S c h o o l ( L B S ) , t h e N a t i o n a lI n s t i t u t e o f E c o n o m i c a n d S o c ia l R e s e a r c h( N I E S R ) a n d t h e B a n k o f E n g la n d ( B E ) , t h r e eo f t h e l a r g e -s c a le q u a r t e r l y m o d e l s o f t h e U Ke c o n o m y r e g u l a r l y d e p o s i t e d a t t h e E S R C M a c -r o e c o n o m i c M o d e l l i n g B u r e a u , t o g e t h e r w i t h as p e c i f i c a t i o n b a s e d o n a s a v i n g s r a t i o e q u a t i o ne s t i m a t e d b y G o l d m a n S a c h s ( G S ) . W e h a v ec h o s e n t o l o o k a t t o t a l e x p e n d i t u r e r a t h e r t h a nt h e d i s a g g r e g a t e c o m p o n e n t s . T h e s e e q u a t i o n se x a c t l y c o r r e s p o n d t o t h o s e d e s c r i b e d a n d e v a l u -a t e d i n C h u r c h e t a l . ( 1 9 9 4 ) . T h a t p a p e r c o n -c l u d e s t h a t d e s p i t e r e c e n t d e v e l o p m e n t s a n di m p r o v e m e n t s i n m o d e ll in g c o n s u m p t i o n , n o n eo f t h e m o d e l s c a n c o m p l e t e l y e x p l a i n t h e f a l l i ne x p e n d i t u r e g r o w t h o f t h e l a te 1 9 8 0s a n d e a r l y1990s .

N e u r a l n e t w o r k s a r e a f a m i l y o f m o d e l s w h i c ha r e l o o s e l y b a s e d o n t h e s t r u c t u r e o f n e u r o n s i nt h e b r a i n . T h e y a r e m a d e u p o f s i m p l e p r o c e s s -i n g u n i t s w h i c h c o n n e c t t o f o r m s t r u c t u r e s t h a ta r e a b l e t o l e a r n r e l a t i o n s h i p s b e t w e e n s e t s o fv a r i a b l e s . I n i t i a l r e s e a r c h o n n e u r a l n e t w o r k sf o c u s e d o n d i s c o v e r i n g t h e w a y t h a t t h e b r a i nw o r k s , b u t t h e y h a v e s i n c e b e e n e x p l o i t e d f o rt h e i r m a t h e m a t i c a l p r o p e r t i e s a s s i g n a l p r o -c e s sor s a nd s t a t i s t i c a l mode l s . In r e c e n t ye a r st h e r e h a s b e e n i n c r e a s i n g i n t e r e s t i n t h e u s e o fn e u r a l n e t w o r k s f o r f o r e c a s t i n g p u r p o s e s . F o rf u r t h e r e x a m p l e s s ee D e p a r t m e n t o f T r a d e a n dIndus t ry (1993) , Smi t h (1993) , Az of f (1994) .

T h e p a p e r p r o c e e d s a s f o ll o w s . I n S e c ti o n 2 w ed i s c u s s t h e t h e o r y b e h i n d t h e c h o i c e o f v a r i a b l e su s e d i n b o t h t h e e c o n o m e t r ic a n d n e u r a l n e t w o r km o d e l s a n d h o w t h e f i n a l s p e c i f i c a t i o n s a r ec h o s e n . S e c t i o n 3 p r e s e n t s t h e r e s u lt s o f t h ee s t im a t i o n a n d s o m e p r o p e r t i e s o f t h e p r e f e r r e dn e u r a l n e t w o r k m o d e l a r e e x a m i n e d i n S e c t i o n 4 .S o m e c o n c l u s i o n s a r e d r a w n i n S e c t i o n 5 .

2 . M odel l ing cons umers expen itureT h e d i f f e r e n t m o d e l s p r e s e n t e d i n t h i s c o m -

p a r i s o n r e f l e c t t h e d i f f e r i n g o b j e c t i v e s o f t h em o d e l b u i ld e r s. I n th e c a s es o f t h e L B S , N I E S Ra n d B E s p e c i f i c a t i o n s , t h e e q u a t i o n s a r e d e -

s i gne d t o fo rm a sma l l pa r t o f a l a rge - sc a l em a c r o e c o n o m i c m o d e l . T h e m o d e l p r o p r i e t o r sa r e t h e r e f o r e n o t o n l y c o n c e r n e d w i t h e s t i m a t i n ga s i ng l e r e l a t i onsh i p t ha t g i ve s a good de sc r i p t i ono f t h e d a t a b u t a l s o in t h e w a y t h a t t h is e q u a t i o ni n t e r a c t s w i t h t h e o t h e r s i n t h e m o d e l t o d e -t e r m i n e f u l l m o d e l p r o p e r t i e s . F o r e x a m p l e , t h eB E e q u a t i o n u s e d i n t h i s c o m p a r i s o n d o e s n o ta p p e a r i n t h e v e r s i o n o f t h e m o d e l c u r r e n t l y h e l db y t h e B u r e a u b e c a u s e p r o b l e m s i n m o d e l l i n gn e t l iq u i d a s s e t s, o n e o f i ts e x p l a n a t o r y v a r i a b l e s ,l e a d s t o u n w e l c o m e s i m u l a t i o n p r o p e r t i e s i f i t i su s e d . I n a d d i ti o n t o t h e p r o b l e m o f e n d o g e n e i t yo f p o s s i b l e r i g h t- h a n d s i d e v a ri a b l e s , t h e m o d e l -l e r m a y w i s h t o i m p o s e c e r t a i n f e a t u r e s i m p l i e db y t h e o r y b u t i m p o s e d a t t h e e x p e n s e o f g o o d -n e s s o f f i t , s t a t i c h o m o g e n e i t y o f c o n s u m p t i o nw i t h r e s p e c t t o i n c o m e a n d w e a l t h b e i n g o n ee x a m p l e . I n c o n t r a s t, t h e o b j e c t i v e w h e n b u i l d -i n g t h e n e u r a l n e t w o r k m o d e l o f c o n s u m e r se x p e n d i t u r e i s s i m p l y t o p r o d u c e t h e b e s t f o r e -c a s t i n g m o d e l , a l t h o u g h t h e m o d e l l i n g p r o c e s si t s e l f c a n g i ve some gu i da nc e a s t o t he r e l a t i vei m p o r t a n c e o f e a c h o f t h e i n p u t s.2 . 1. E c o n o m e t r i c a p p r o a c h

M o s t m o d e r n e c o n o m e t r i c c o n s u m p t i o n f u n c -t i o n s o r i g i n a t e f r o m t h e l i f e - c y c l e t h e o r y w h i c he x p l a i n s h o w a n i n d i v i d u a l s m o o t h s h i s / h e r e x -p e n d i t u r e g i v e n t h e a m o u n t o f w e a l t h a c c u m u -l a t e d o v e r a l i f e t i m e . H e n d r y e t a l . ( 1 9 9 0 ) s h o wh o w a s t a n d a r d o p t i m i z a t i o n e x e r c i s e y i e l d s al o g - l i n e a r c o n s u m p t i o n f u n c t i o n d e p e n d i n g o nf a c t o r s s u c h a s i n c o m e , w e a l t h a n d t h e r e a l r a t eo f r e tu r n , b u t t h e n p o i n t o u t t h a t t h is n e g l e c t sp o s s i b l e r o l e s f o r i n c o m e u n c e r t a i n t y , c r e d i tc o n s t r a i n t s , d e m o g r a p h i c c h a n g e s , l i q u i d i t y a n dd y n a m i c a d j u s t m e n t . T h e f i n a l s p e c i f i c a t i o n c o n -t a i n s v a r i a b l e s t h a t t h e r e f o r e r e f l e c t b o t h t h e o -re t i c a l c ons i de ra t i ons a nd , t o a c e r t a i n e x t e n t ,t h e o p i n i o n s o f t h e m o d e l l e r . T h e m o s t im p o r -t a n t d i f f e r e n c e s i n t h e m o d e l s a r e i n t h e c h o i c eo f t h e m e a s u r e o f n o n - h u m a n w e a l th . T h e B Emode l use s ne t l i qu i d a s se t s a s i t s we a l t h va r i -a b l e , whi c h i s t he na r rowe s t de f i n i t i on a nd i se n c o m p a s s e d b y t h e m e a s u r e o f n e t f i n a n c i a lw e a l t h o f t h e p e r s o n a l s e c t o r u s e d b y a l l t h e


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K.B. Church, S.P. Curram / International Journal of Forecasting 12 1996) 255-267 2 5 7other models. The NIESR model has a tempor-ary effect from the change in liquid assets. TheLBS and GS models also consider physicalwealth to be important and include differentmeasures of the value of the housing stock.There is also disagreement on the role of interestrates. T hey do not feature in explanations of BEand GS but the real bank base rate appears inthe NIESR specification and the after-tax versionof the same variable in the LBS model. Variousother variables are used to capture the factorsmentioned above which are neglected in thelife-cycle theory. The GS model uses differencesin the unemployment rate to try to captureincome uncertainty. The influence of shifts in thedemographic structure is addressed explicitly inthe LBS model by a term measuring the propor-tion of the population aged between 45 and 64.The estimation method used is OLS with atwo-stage Engle and Granger (1987) techniqueemployed by the LBS and GS models. The two-stage technique involves first estimating a coin-tegrating relationship. This relationship is thenembodied in the second-stage dynamic model.The approach involves examination of the time-series properties of each of the variables. Theorder of integration of a series is the number oftimes that differencing is required to make itstationary. The variables in the cointegratingregression should all be integrated of order one.The cointegrating relationship exists if the re-siduals from this regression are stationary. Theseresiduals then appear in the second-stage regres-sion which should only contain stationary vari-ables using differencing where necessary. Typi-cally the cointegrating relationship embodies thelong-run or equilibrium relationship betweenconsumption, income and wealth, but stationaryvariables from outside the cointegrating regres-sion may also enter the long-run solution of themodel. The time series and cointegrating prop-erties of the variables used in these models iscovered in Section 3.

Dendrites

The neural network used for these experi-ments is the multilayer perceptron developed

by Rumelhart et al. (1986). The network takescontinuous-valued input variables and learnstheir relationship to continuous-valued targetvalues, a method known as supervised learning.The network is data driven in that it learns onlyfrom the training data presented to it and has nounderlying parametric model. This means thatthe model produced is only as good as the dataused, so the choice of explanatory variables is asimportant as for any other approach. Neuralnetworks do, however, have the ability to ignorevariables which do not contribute to the modelso that some experimentation with potentialvariables can be done, though care must betaken not to swamp the network with too manyirrelevant variables.

The basic building block of the neural networkis the neuron. A single neuron is a simpleprocessing unit based on the structure of neuronsin the brain. Fig. 1 shows a biological neuron.The neuron collects input signals through thedendrites and passes them to the soma or pro-cessor. If the combined signals reach somethreshold then the neuron is activated and passesa signal on to other neurons via the axonal path.The sensitivity of a neuron is controlled by thisactivation threshold. While a single neuron isslow, it is the interconnection of over 100 billionneurons which gives the brain its power.

An artificial neural network is made up oflayers of neurons as shown in Fig. 2. The inputlayer and output layer represent the input andoutput variables of the model. Between them lieone or more hidden layers which hold thenetwork s ability to learn non-linear re lation-ships. The greate r the number of neurons in thehidden layers, the more the network is able to

2.2. Neural network approach

F i g 1 A b r a i n n e u r o n


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258 K.B. Church, S.P. Curram / International Journal of~Forecasting 12 1996) 255-267Input Layer Hidden Layer Output Layer

Fig. 2. A 3 2 1 multilayerperceptron.

cope with non-linear relationships. Each neuronin a layer has weighted connections to eachneuron in the next layer. The weights multiplythe signal between pairs of neurons and can havepositive and negative values. This means thatthey can control the strength of the connectionand whether there is a positive or negativerelationship between neurons. Each neuron alsohas a bias term which acts like the intercept in aregression. An individual neuron works as fol-lows: the values of inputs entering the neuronare summed and added to the bias term; thistotal then passes through an S-shaped squashing(or sigmoid) function to give the activation of theneuron in the range 0 to 1. The activation valueis then passed on to all the neurons in the nextlayer of the network via weighted connectionsor, in the case of the output layer, represents theoutput of the network.

The data to be used with the network areusually scaled. The output from a neuron, andthus the network as a whole, is in the range 0 to1, so data for the dependent variable must bescaled to within this range. Moreover, we scaledthe dependent variable from 0.2 to 0.8. This wasdone for two reasons. First, as Smith (1993)points out, the sigmoid function becomes in-creasingly non-linear as it approaches 0 and 1,which makes it increasingly difficult to representlinearly scaled variables as their values approachthese extremes, and so slows learning. Second,the regime allows the possibility of forecast

values which are outside the range of the originaltraining data, as may be required for new data orsensitivity analysis.

The explanatory variables do not need to bescaled, but scaling is usually desir able. Hart(1992) notes that scaling variables to the sameorder of magnitude prevents those variables witha higher magnitude from 'swamping' the netw orkin the initial stages of training. This swampingeffect can slow or inhibit the training of thenetwork. Typical ranges for scaling explanatoryvariables are 0 to 1 o r - 1 to 1 (Hart , 1992;Smith, 1993; DTI, 1994a). In our case the range0.2 to 0.8 was used, since for one model a laggedversion of the dependent variable, consumerexpenditure, was used as an explanatory vari-able, and it was thought desirable to maintain a1:1 relationship between the two.A general overview of the training process isproduced below. However more technical de-scriptions of the training algorithm are given bySmith (1993) and summarized by Lippmann(1987). Training involves repeatedly presentingthe data to the network. Learning is achieved inthe network by altering the values of weightedconnections between neurons and bias valueswithin neurons to bring the output of the net-work closer to the desired target value. Theoverall aim is to reduce the mean-squared error(MSE) for the training data. The errors betweenoutput and target values are propagated backthrough the network to attribute them to theweights in the network. These are then alteredusing the steepest descent method which aims toreduce the MSE by following the steepest gra-dient on the error surface. The rate o f learning iscontrolled by gain and momentum parameters.The gain parameter specifies the magnitude ofchanges to the weights. A small gain term resultsin slow network learning while a large gain termcan miss key features on the error surfaceleading to oscillation or convergence to localminima. Past changes which have been made toa particular weight are stored as an exponentiallysmoothed average, known as the momentum. Aproportion of this momentum is used in futurechanges of the weight so as to smooth learningand reduce oscillation.


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K.B. Church, S.P. Curram / International Journal of Forecasting 12 1996) 255-267 259Two key disadvantages of the multilayer per-

ceptron are its slow learning speed and its abilityto converge to local minima. These are par-ticularly affected by the choice of value for thegain parameter. To help overcome the difficultyin setting the gain parame ter we used the adapta-tions suggested by Vogl et al. (1988). Here thegain term is not fixed but is allowed to varydepending on the success of the learning. Whilethere is an improvement in the MSE, the gainterm is allowed to increase, representing in-creased confidence in the direction of learning. Ifthe MSE worsens by more than some small givenpercentage, the gain term is reduced, themom ent um terms are ignored so that past weightchanges are not allowed to affect the currentweight changes, and the calculated weight andbias changes for that iteration are not used. Themomentum term is switched back on when asuccessful learning iteration occurs.

A key aspect in setting up the network isdeciding on the number and size of the hiddenlayers. The more complex the interactions be-tween the variables, the more the hidden unitsrequired. If too few hidden neurons are used,the network will fail to learn the richness of therelationships; if too many are used then the datamay be overfitted, fitting to individual datapoints rather than the trend and so reducing thenetwork's ability to generalize. There are nohard and fast rules for deciding on the number ofhidden neurons to use. It has been found thatgenerally only one hidden layer is required forforecasting problems. However, the actual num-ber of neurons required in that layer must befound by trial and error.

We used an alternative to optimizing thenumber of hidden nodes, which is to use anindepe ndent validation step in the training of thenetwork as described by Hoptroff (1993). Herethe network is required to have sufficient nodesto fit the trend but is not streamlined to preventoverfitting. Hoptroff suggests that 10 nodes inthe hidden layer are usually sufficient for mostforecasting problems. More nodes can be usedbut usually result in slower learning without animprovement in results.

The approach requires that independent vali-

dation data are used to test how well the net-work is able to generalize to unseen data. Thevalidation data are taken out from the trainingdata and should be representative across therange of outcomes. A larger validation set islikely to be more representative. However thisdoes take data away from the training set. It is,therefore, necessary to strike a balance betweenthe training and validation data set sizes. Whenlarge amounts of data are available the selectionof validation data can be done using a simplerandom choice. In our case, the amount of datawas limited, so we used a stratification approach.Here the data were ordered by ascending valueof the dependent variable and partitioned intogroups of roughly equal size, one for eachvalidation point required. One validation pointwas then selected at random from each group.This stratification approach tries to ensure thatthe validation data are representative by choos-ing across the range of values for the dependentvariable.Hoptroff (1993) suggests that the validationdata should comprise 10-25 of the availabledata, and at least 10 data points. We used a moreconservative 30 with a minimum of 15 datapoints. It is important to stress that these valida-tion data were independent and were not usedfor actual training examples, nor were they takenfrom test data used for the final forecastingperiod.

Each iteration of the training process is asfollows. The network is presented with a set oftraining examples from which weight and biasadjustments are made. Then the network istested using independent validation data to findthe ability of the network to fit unseen data.Training is stopped at the iteration where theMSE for the validation data is minimized. Thisrepresents the point in training where the net-work is best able to generalize.

In practice, it has been found that the MSE ofthe validation data can go up but then improveagain. To overcome this, training is usuallycontinued for some time after the optimum pointhas been reached to ensure that no furtherreduction in the MSE will occur. In our case, thenetwork weights and biases are saved every time


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26 K.B. Church, S.P. Curtain / International Journal of Forecasting 12 1996) 255-267t h e M S E o f t h e v a l i d a t i o n s e t i s r e d u c e d , a n dt r a i n i n g o f t h e n e t w o r k i s s t o p p e d i f 2 0 0 0 i t e r a -t io n s o c c u r w i t h o u t a n i m p r o v e m e n t . T h i s m e a n st h a t t h e f i n a l s a v e d n e t w o r k r e p r e s e n t s t h eop t i ma l t r a i n i ng po i n t whi l e t he e x t ra i t e ra t i onso f f e r a l ar g e s a f e t y m a r g in t o e n s u r e t h a t a b e t t e rs t o p p i n g p o i n t w i ll n o t h a v e b e e n m i s s e d . I f th eM S E o f t h e v a l i d a t i o n s e t d o e s n o t p e r m a n e n t l yg e t w o r s e ( i . e . n o o p t i m u m p o i n t i n t r a i n i n g i sr e a c h e d ) , t h i s s u g g e s t s t h a t t h e n e t w o r k d o e s n o tc o n t a i n e n o u g h n o d e s t o o v e r f i t t o t h e d a t a a n di s un l i ke l y t o be a b l e t o p i c k up t he fu l l unde r l y -i ng t r e nd . In t h i s s i t ua t i on t r a i n i ng i s r e s t a r t e du s i n g m o r e n o d e s i n t h e h i d d e n l a y e r .

T h e r e a s o n i n g b e h i n d t h e i n d e p e n d e n t v a l i d a -t i o n a p p r o a c h i s t h a t t h e u n d e r l y i n g t r e n d l ie sc l o s e r t o t h e n e t w o r k s t a r t i n g p o i n t t h a n a m o d e lw h i c h h a s b e e n f i t t e d t o i n d i v i d u a l d a t a p o i n t s .S i n c e t h e s t e e p e s t d e s c e n t m e t h o d t r i e s t o m i n i -mi z e t he f i t t i ng e r ro r i n a s shor t a d i s t a nc e f romt he s t a r t i ng po i n t a s poss i b l e , i t w i l l f i t t heu n d e r l y i n g s t r u c t u r e b e f o r e t h e d e t a i l o f t h ei nd i v i dua l da t a po i n t s . Thus s t opp i ng t r a i n i ng a tt h e r i g h t t i m e p r e v e n t s o v e r f i t t i n g f r o m o c c u r -r i ng . S i nc e t he va l i da t i on da t a a re no t use d i nt r a i n i n g , t h e p o i n t w h e r e i t r e a c h e s i t s m i n i m u mM S E s h o u l d r e p r e s e n t t h e p o i n t w h e r e t h ege ne ra l i z i ng a b i l it i e s o f t he mo de l a re m a xi -m i z e d .

3 E s t i m a t i o n a n d f o r e c a s ti n gI n t h i s s e c t i o n w e p r e s e n t e s t i m a t e s o f e a c h o f

t h e f o u r c o n s u m p t i o n f u n c t i o n s u s i n g t h e t w oa l t e r n a t i v e a p p r o a c h e s t o m o d e l b u i l d i n g . T h ee x t e n t t o w h i c h e a c h s p e c i f ic a t io n c a n e x p l a i n t h ed o w n t u r n i n e x p e n d i t u r e a f t e r 1 9 8 8 i s t h e ne x a m i n e d . T h e t y p e o f e c o n o m e t r i c m o d e l u s e da nd i t s unde r l y i ng a s sumpt i ons a re a l l f a i r l yf a m i l i a r a n d c a n , t h e r e f o r e , b e s e e n a s a b e n c h -m a r k a g a i n s t w h i c h t h e n e u r a l n e t w o r k m o d e l sc a n b e j u d g e d . T h e f u n c t i o n a l f o r m s o f t h ee c onome t r i c spe c i f i c a t i ons a re t hose o r i g i na l l yu s e d b y t h e m o d e l b u i l d e r s , a n d s o t h e i r d e c i -s i o n s o n c h o i c e o f v a r i a b l e s a n d d y n a m i c s tr u c -t u r e a r e a d o p t e d . T h e m o d e l s a r e d e s i g n e d t oc a p t u r e s h o r t - r u n b e h a v i o u r , s o t h e d e p e n d e n t

v a r i a b l e i s t h e c h a n g e i n t h e l o g o f c o n s u m e r se x p e n d i t u r e . S i n c e t h e n e u r a l n e t w o r k i s n o tb a s e d o n a n u n d e r l y i n g e c o n o m i c m o d e l w e u s et h e s a m e e x p l a n a t o r y v a r i a b l e s a s t h e i n p u t t ot h e n e t w o r k t o e n a b l e a d i r e c t c o m p a r i s o n . T h ed a t a u s e d a r e t h e s a m e f o r b o t h a p p r o a c h e s a n da r e a v a i l a b l e f r o m t h e a u t h o r s o n r e q u e s t . T h esourc e s fo r a l l t he da t a a re t he C e nt ra l S t a t i s t i c a lOf f i c e pub l i c a t i ons , Economic Trends a n d t h eMonthly Digest of Statistics.3.1. Econometric modelling

T h e O L S e s t i m a t e s o f t h e f i r s t - s t a g e r e g r e s -s i o n s a r e s h o w n i n T a b l e 1 w h e r e t h e t w o - s t e pm e t h o d i s a d o p t e d . D e t a i l e d t e s t s o f t h e t i m e -se r i e s p rope r t i e s fo r a l l t he se r i e s t ha t a ppe a r i nt h e l o n g - r u n s o l u t i o n s a r e p r e s e n t e d i n C h u r c h e ta l . (1994) . The t e s t s show t ha t a l l t he va r i a b l e suse d i n t he f i r s t - s t a ge re gre s s i ons a pa r t f rom t heu n e m p l o y m e n t t e r m i n t h e G S m o d e l a r e i n t e -g r a te d o f o r d e r o n e . T h e s t a ti o n a r y u n e m p l o y -m e n t t e r m s h o u l d n o t r e a l l y a p p e a r i n t h ec o i n t e g r a t i n g r e l a t i o n s h i p b u t d o e s f o r m p a r t o ft h e lo n g - r u n e c o n o m i c re l a ti o n s h i p . T h e i n t e r e s tr a t e v a r i a b l e s a n d L B S d e m o g r a p h i c t e r m a r e a l ls t a t i ona ry a nd so a re c ons i s t e n t wi t h i nc l us i on i nt h e s e co n d s ta g e . T h e D i c k e y - F u l l e r ( D F ) a n da u g m e n t e d D i c k e y - F u l l e r ( A D F ) t e s t s q u o t e d i nT a b l e 1 i n d i c a te s o m e e v i d e n c e f o r c o i n t e g r a t i o ni n b o t h L B S a n d G S m o d e l s , a l t h o u g h t h e c a s e i sw e a k e r f o r t h e G S s p e c i f i c a t i o n . T h e N I E S Rm o d e l i m p o s e s t h e f i r s t - s t a g e r e l a t i o n s h i p , a n dt h i s p r o v e s t o b e t h e c o i n t e g r a t i n g v e c t o r w h i c hs h o w s t h e s t r o n g e s t e v i d e n c e t h a t t h e r e s i d u a l sa re s t a t i ona ry .

T h e s e c o n d - s t a g e r e g r e s s i o n s a n d d y n a m i cm o d e l o f t h e B E a r e g i v e n in T a b l e 2 . V i r t u a l lya l l t he e s t i ma t e d c oe f f i c i e n t s a re a t l e a s t t wi c et h e m a g n i t u d e o f t h e i r s ta n d a r d e r r o r s a n d t h eon l y d i a gnos t i c t e s t f a i l e d i s t ha t o f t he B Em o d e l f o r a u t o c o r r e l a t i o n . T h e f a c t t h a t a l l t h em o d e l s p a s s t h e R e s e t t e s t i n d i c a t e s t h a t t h el o g - l i n e a r f u n c t i o n a l f o r m i s p r o b a b l y a na d e q u a t e d e s c r i p t i o n o f t h e d a t a , a l t h o u g h g i v e nt h e g e n e r a l n a t u r e o f th i s t e s t a m o r e c o m p l i -c a t e d m o d e l r e m a i n s a p o s s i b i l i t y . A l t h o u g h t h ee q u a t i o n s a r e r e p l i c a t e d o n s e a s o n a l l y a d j u s t e d


7/13

K . B . C h u r c h , S . P . C u r r a m / I n t e rn a t i o n a l J o u r n a l o f F o r e c a s ti n g 1 2 1 9 9 6 ) 2 5 5 - 2 6 7 261T a b l e 1F i r s t - s t a g e r e g r e s s i o n s

L B S G SD e p e n d e n t v a r i ab l e ln ( C ) I n ( C )S a m p l e p e r i o d 6 9 : 1 - 9 0 :1 7 1 : 2 - 8 9 : 4E s t im a t i o n m e t h o d O L S O L SC o n s t a n t 1 .3 1 0 . 9 1 3

( 0 . 2 9 ) ( 0 . 3 3 2 )I n ( Y ) 0 . 7 5 7 0 . 8 2 8

( 0 . 0 3 9 ) ( 0 . 0 4 6 )l n ( H W ) 0 . 0 5 9 0 . 0 4 6

( 0 . 0 1 6 ) ( 0 . 0 2 0 )l n ( F W ) 0 . 0 9 3 0 . 0 5 9(o.oo8) (O.OLO)A ( U ) - 0 . 0 3 0(0.008)R 2 0 . 9 9 1 0 . 9 8 9t r 0 . 0 1 6 0 . 0 1 5D W 1.06 1 .27D F - 5 . 3 * * - 5 . 9 4 *A D F 4 ) - 2 . 9 * - 2 . 6 9N o t e s f o r T a b l e s I a n d 2 :c T o t a l c o n s u m e r s ' e x p e n d i t u r eY R e a l p e r s o n a l d i s p o s a b l e i n c o m eH W H o u s i n g w e a l thF W F i n a n c i a l w e a l t hI N T I n t e r e s t r a t eU U n e m p l o y m e n td e m P r o p o r t i o n o f t h e p o p u l a t i o n a g e d b e t w e e n 4 5 - 6 4w e a l t h T o t a l w e a l t hR B C h a n g e i n s t o c k o f l i q u i d a s s e t sA L i q u i d a s s e t sE C M E r r o r c o r r e c t i o n m e c h a n i s mR a t h e r t h a n e s t i m a t e a n E C M , i n t h e N I E S R m o d e l t h er e l a t i o n s h i p b e l o w i s u s e d i n t h e s e c o n d - s t a g e r e g r e s s i o nE C M = l n ( C - I O O A S C C / P C ) - I n ( Y )w h e r eS C C S t o c k o f c o n s u m e r c r e d i tP C C o n s u m e r ' s e x p e n d i t u re d e f l a t or* * S i g n i f i c a n t a t 1 l e v e l* S i g n i f i c a n t a t 5 l e v e l

1992 v i n t a ge da t a , t he sa mpl e pe r i od o r i g i na l l yuse d i n e a c h c a se i s r e t a i ne d t o t ry a nd re p l i c a t ea s c l o s e l y a s p o s s i b l e t h e p u b l i s h e d e q u a t i o n o fe a c h o f t h e i n s ti t u ti o n s r e p r e s e n t e d .M o r e d e t a i l e d r e s u l t s a n d t e s t i n g a r e c o n t a i n e di n C hur c h e t al . (1994) . On e of the c onc l us i onso f t h a t p a p e r i s t h a t f o l lo w i n g t h e l a st b r e a k d o w ni n c o n s u m e r s e x p e n d i t u r e e q u a t i o n s , a s d e -s c r i b e d i n C a r r u t h a n d H e n l e y ( 1 9 9 0 ) , t h e r e l a -

t i o n s h ip s o f t h a t e r a h a v e s i n ce b e e n s u c c e s sf u l lya u g m e n t e d s o t h a t t h e r i s e i n e x p e n d i t u r e b e -t w e e n 1 9 8 5 a n d 1 9 8 7 i s n o w a d e q u a t e l y d e -s c r i b e d . T h i s h a s b e e n a c h i e v e d t o a c e r t a i ne x t e n t b y p l a c i n g g r e a t e r e m p h a s i s o n t h e r o l e o ft h e h o u s i n g m a r k e t . A l t h o u g h t h e s e i n n o v a t i o n sh a v e h e l p e d t o e x p l a i n o n e d i f f i c u l t p e r i o d t h e ya r e f o u n d t o b e u n a b l e t o c a p t u r e t h e f a l l i ne xpe ndi t u re t ha t oc c ur re d i n t he e a r l y 1990s .T h i s i s d e m o n s t r a t e d b y e s ti m a t i n g t h e m o d e l sup un t i l t he l a s t qua r t e r o f 1988 a nd t he nc a l c u l a t i ng s t a t i c fo re c a s t s . The se fo re c a s t s t o -g e t h e r w i t h t h e a c t u a l c h a n g e s i n e x p e n d i t u r e a r eshown i n F i g . 3 .3 .2 . N e u r a l n e t w o r k m o d e l l in g

T h e e s t i m a t i o n o f t h e n e u r a l n e t w o r k m o d e l sp r e s e n t e d h e r e r e q u i r e a n a p p r o p r i a t e s o f t w a r ep a c k a g e . T h e s o f t w a r e u s e d w a s d e v e l o p e d b yt h e a u t h o r s a n d c o n t a i n s t h e f e a t u r e s d e s c r i b e di n S e c t io n 2 , h o w e v e r d e t a i ls o f s e v e r a l p a c k a g e st h a t a r e c a p a b l e o f r e p e a t i n g t h is e x e r c i s e a r eg i v e n i n D T I ( 1 9 9 4 b ) . T h e n e u r a l n e t w o r k w a suse d a s a r e gre s s i on t oo l t o l e a rn t he r e l a t i onsh i pb e t w e e n a s e t o f e x p l a n a t o r y v a r i a b l e s a n d t h ed e p e n d e n t v a r i a b l e , n a m e l y t h e c h a n g e i n c o n -s u m e r e x p e n d i t u r e . T h u s t h e n e u r a l n e t w o r k i su s e d i n a s i m i l a r w a y t o t h e O L S m e t h o d , b u ta l l ows h i gh l y non- l i ne a r r e l a t i onsh i ps t o be f i t t e di f t h e y e x i s t. T h e s e t o f e x p e r i m e n t s w i t h t h en e u r a l n e t w o r k s i n v o l v e d t r a i n i n g m o d e l s u s i n ge x a c t l y t h e s a m e e x p l a n a t o r y v a r i a b l e s a n d d a t as e ts a s f o r e a c h o f th e e c o n o m e t r i c m o d e l s . A s ac o n s e q u e n c e t h e n e u r a l n e t w o r k i s s u b j e c t t o t h esa me i nsuf f i c i e nc i e s i n t he da t a a s t he e c ono-m e t r i c m o d e l s .

T h e s h a p e o f th e n e u r a l n e t w o r k is d e p e n d e n to n t h e n u m b e r o f v a r i a b l e s , w h i le t h e h i d d e nl a y e r i s r e q u i r e d t o h a v e s u f f i c i e n t n o d e s t om o d e l t h e r e l a t i o n s h i p b u t n e e d n o t b e o p t i -m i z e d t o p r e v e n t o v e r f i t t i n g , s i n c e i n d e p e n d e n tv a l i d a t i o n i s b e i n g u s e d . O u r n e t w o r k s u s e d 1 0n o d e s i n t h e h i d d e n l a y e r w h i c h w a s f o u n d t o b esuf f i c i e n t fo r a l l t he mode l s . The f i na l t r a i ne dn e t w o r k r e p r e s e n t s t h e r e l a t i o n s h i p s b e t w e e n t h ee x p l a n a t o r y v a r i a b l e s a n d t h e d e p e n d e n t v a r i -a b l e . T h e r e w a s a w i d e v a r i a t i o n i n t h e n u m b e r


8/13

262 K . B . C h u r c h , S . P . C u r r a m / I n t e r n a ti o n a l J o u r n a l o f F o r e c a s ti n g 1 2 1 9 9 6 ) 2 5 5 - 2 6 7Tab le 2Second-s tage regress ionsDependen t va r i ab leSample pe r iodEs t ima t ion me thod

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o f i t era t io ns required t o rea ch t he o pt ima l po intf r o m 6 7 89 f o r t h e B E m o d e l 4 7 08 f o r t h e G S5 7 8 fo r t he NIE SR a nd 1 67 f o r t he L B S.O b serv a t io n o f t he erro rs dur ing training sho w edthat in a ll m ode ls both tra ining and va l idat ionset errors fe l l quickly during the ini t ia l s tages ofl e ar n i n g. F o r t h e N I E S R a n d L B S m o d e l s apo int wa s qu ick ly rea ched where t he t ra in ingerror cont inued to fa l l but the va l idat ion errorbeg an to r ise steadi ly indicat ing that the net -work was start ing to f i t the noise rather than theunder ly ing t rend . In t he ca se o f t he G S a nd B Em o de l s t he reduc t io n o f t rain ing a nd v a l ida tio nerro rs wa s s lo w bu t s t ea dy unt il t he v a lida t io nerro r beg a n t o s lo wly r i se . T he mo re s t ea dylearning suggests that tra ining took longer to f i tt he t rend but wa s l e s s a f f ec t ed by no i se . T het e s t da t a i s a ppl i ed t o t he ne t wo rk in t he sa mewa y as the tra ining data exce pt that the weightsand biases are f ixed at their f ina l va lues . Theo ut put o f t he ne t wo rk f o r ea ch se t o f v a r ia b le sf ro m t he t e s t se t i s t hen re sca led t o f o rm t hef o reca s t v a lue .

T he s t a t i c o ne - s t ep- a hea d f o reca s t s f ro m t hen e u r a l n e t w o r k m o d e l s a r e c o m p a r e d t o t h o s ef ro m t he eco no met r i c spec i f i ca t io n in F ig s . 4 - 7 .T he eco no met r i c mo de l s ha v e a s l i g ht a dv a nt a g ebeca use t he cho ice o f v a r ia b le s i s ba sed o n t heresu l t s o f e s t ima t io n o v er t he f u l l sa mplespec i f i ed in T a ble 2 . T here f o re t he cho ice o fspeci f icat ion is inf luenced by the data points thatare to be forecast . By contrast a l though theneura l ne t wo rk mo de l use s t he sa me r ig ht - ha nds ide v a r ia b le s no n e o f t he f o reca s t da t a a re used

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F i g . 5 . N I E S R m o d e l . C h a n g e i n t o t a l c o n s u m e r s e x p e n d i -t u r e ; a c t u a l a n d f o r e c a s t v a l u e s .

in e i ther tra ining or va l idat ing the f ina l spe-c i f icat ion used.

G en era l ly t he ne t w o rk fo reca s t s f o l lo w c lo se lyt h o s e g e n e r a t e d b y t h e e c o n o m e t r i c m o d e l s . T h eneura l ne t wo rk mo de l us ing t he L B S cho ice o fv a r ia b le s per f o rms ev en wo rse t ha n i t s e co no -met r i c equiv a lent f a i ling t o pred ic t a ny do w -

0.03 . . . . .

0.01 ...-

0

- 0.01

1~ 1M6 Igg? 1~8 1~ 1~ 1991 a992

F i g . 6 . B E m o d e l . C h a n g e i n t o t a l c o n s u m e r s e x p e n d i t u r e ;a c t u a l a n d f o r e c a s t v a l u e s .


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264 K .B. Chu rch, S .P. Curram I In ternat ional Journa l o f Forecas t ing 12 1996) 25 5-2 67

0 . 0 3

2

0 .0 1 ~\ ~

- 0 . 0 1 . . . , , * * . . . . . . . . . . . . . . . . . . . . . . .

- 0 ~ ~ I M 0 I S 6 7 I ~ 1 S i n I S l m I N 1 I ~

~ w

Fig. 7. GS model. Change in total consumers expenditure;actual and forecast values.

nturn. In the NIESR example it is the model-based forecast which is slightly better at the startof the forecast period and the neural networkwhich is preferable towards the end. The com-parison with the BE model does not allow a clearpreference to be made, with both models over-predicting badly from 1989 to the start of 1991.The neural network does come close to capturingthe low point of the recession, but both modelssubsequently return to overprediction.

The GS choice of explanatory variables provesto be the best for both econometric and neuralnetwork specifications. Fig. 7 shows that theeconometric model picks up the downturn well,actually forecasting a larger downturn in con-sumption growth than was actually witnessedbetween the third quarter of 1989 and the startof 1991. Subsequently, the model is slightly toooptimistic about the speed of the recovery. Oneof the main reasons why the GS model performsbetter than the other models is the inclusion ofterms in the change and rate of change of theunemployment rate. The actual profile of theforecast is sensitive to the functional form that ischosen for the unemployment rate. Similar spe-cifications in Church et al. (1994) which use thelogarithm of the rate tend not to capture theinitial downturn as accurately, but do not over-predict at the end of the forecast. The neuralnetwork is designed to fit a model to the overalltrend shown in the data rather than any noise. Inthe GS example, the network forecast followsthe actual data down without picking up in-dividual peaks and troughs. The model does notunderpredict in the way of its econometric equiv-

alent, but nor does it fully pick up the lowestpoint of the downturn. It shares the overpredic-tion seen in the final few periods.

A final exercise was conducted which pre-sented the network with the inputs used in all themodels (25 in total) to examine if the provisionof all the information used can yield betterresults than in any one of the models. Thisapproach is only valid using the neural networkmodel as the quality of the forecast is the onlyconcern with this method. The specification ofthe econometric model is constrained by theneed to be consistent with economic theory. Th eforecasts for the combined model are shown inFig. 8. This model shares several of the charac-teristics of the GS specification. The downturn iscaptured adequately and in this case coincideswith the bottom of the cycle. The magnitude ofthe recovery is again overstated. The resultsfrom this final exercise show that the neuralnetwork is able to pick out the important fea-tures from a large number of variables toproduce a model which performs better than anyof the encompassed models. Howeve r, great caremust be taken to use a representative validationset since the high parameterization offered bythe large number of variables leads to a modelwhich is more sensitive to the training process.There are several points emerging from thissection. The first is that neural networks do notrequire vast quantities of data for effectiveforecasting performance. The neural networkproduces similar forecasts to the econometricmodels and does not outperform them, indicat-ing that the process underlying the behaviour of

0 . 0 3

0 . 0 2

0 .0 1

0

- 0 . 0 1

- 0 . 0 2I S e 6

~ t t * ~

Fig. 8. Total model. Change n total consumers expenditure;actual and forecast values.11116 1987 11181 1~ IT~IO II i91 1992


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K . B . C h u r c h , S . P . C u r r a m / I n t e r n a ti o n a l J o u r n a l o f F o r e c a s ti n g 1 2 1 9 9 6 ) 2 5 5 - 2 6 7 2 6 5

c o n s u m e r s ' e x p e n d i t u r e i s n o t h i g h l y n o n - l i n e a r .F i n a l ly , i f t h e i n f o r m a t i o n r e q u i r e d t o m a k e a na c c u r a t e f o r e c a s t is n o t c o n t a i n e d w i th i n t h e d a t as e t , n o f o r e c a s t i n g m e t h o d w i l l p r o d u c e a d e q u a t ep r e d i c t i o n .

4 P r o p e r t ie s o f a n e u r a l n e t w o r k m o d e lT h e e c o n o m e t r i c m o d e l s i n t h i s c o m p a r i s o n a l lc o n t a i n e s t i m a t e s o f p a r a m e t e r s t h a t w i ll b e o f

i n t e r e s t t o e c o n o m i s t s , t h e m a r g i n a l p r o p e n s i t yt o c o n s u m e b e i n g o n e e x a m p l e . T h e s o l e o u t p u to f t h e n e u r a l n e t w o r k i s th e f o r e c a s t a n d r e v e a l sn o t h i n g a b o u t t h e u n d e r l y i n g e c o n o m i c p r o p -e r t ie s . A f u r t h e r c o m p a r i s o n b e t w e e n e c o n o -m e t r i c a n d n e t w o r k m o d e l s c a n b e m a d e b yp e r t u r b i n g o r s h o c k i n g e a c h o f t h e n e t w o r ki nput s t o ga uge t he se ns i t i v i t y wi t h re spe c t t oe a c h va r i a b l e . Th i s i nvo l ve s t e s t i ng t he ne ura ln e t w o r k m o d e l w i t h t h e a v e r a g e v a l u e s f r o m t h ec o m p l e t e d a t a s e t t o f i n d t h e f o r e c a s t f o r t h ed e p e n d e n t v a r i a b l e s ; e a c h v a r i a b l e i s t h e ns h o c k e d , o n e a t a t i m e , t o f i n d t h e d e g r e e t ow h i c h t h e s h o c k a f f e c t s t h e f o r e c a s t o f t h ed e p e n d e n t v a r i a b l e . T h e s e r e s u l t s c a n b e d i r e c t l yc o m p a r e d t o t h e e l a s t i c i t i e s i n t h e e c o n o m e t r i cs p e c i f i c a t i o n . T a b l e 3 s h o w s t h e i m p a c t o n t h ec h a n g e i n e x p e n d i t u r e i n t h e G S m o d e l o fi n c r e a si n g e a c h o f t h e l o g g e d in p u t s b y o n e p e rc e n t a n d t h e u n e m p l o y m e n t t e r m s b y o n e p e r -T a b l e 3R e s p o n s e o f A I n C ) t o a o n e p e r c e n t i n c r e a s e i n ri g h t - h a n ds i d e v a r i a b l e s

G S N e u r a ln e t w o r k

l n C ) , _ l - - 0 . 2 1 8 - - 0 . 1 1 6I n Y ) , _ 1 0 . 1 8 0 0 . 1 2 3l n H W ) t _ ~ 0 . 01 0 - 0 . 0 1 7l n F W ) , _ l 0 . 0 13 0 . 0 2 0A(U),_~* -0.645 -0.906A n(Y) 0.189 0.200A n(H W ) 0.101 0.034A n(FW ) 0.030 0.018AA(U)* -3.161 -2.018N o t e : * O n e p e r c e n t a g e p o i n t i n c r e a s e i n u n e m p l o y m e n tr a t e .

c e n t a g e p o i n t f r o m t h e i r a v e r a g e v a l u e s f o r b o t he c o n o m e t r i c a n d n e u r a l n e t w o r k m o d e l s .

T h e r e a r e s e v e r a l k e y f e a t u r e s s h a r e d b y t h et w o c o m p e t i n g e x p l a n a t i o n s . T h e o n l y ' c o e f f i -c i e n t ' s i gn t ha t d i f fe r s i s t ha t fo r hous i ng we a l t hi n t he l ong run , whi c h ha s a ne ga t i ve e f fe c t i n t hen e u r a l n e t w o r k m o d e l . T h e d y n a m i c t e r m s i ni nc om e a re o f ve ry s i mi l a r s iz e , whi l e c ha nge s i nw e a l t h h a v e s m a l l e r i m p a c t i n t h e n e t w o r k m o d e lb u t t h e r e l a ti v e i m p o r t a n c e o f h o u s i n g a n df i n a n c i a l w e a l t h i s c o m p a r a b l e . T h e m a g n i t u d e so f th e c o n s u m p t i o n a n d i n c o m e r e s p o n s e s a r es m a l l e r i n t h e n e t w o r k m o d e l b u t v i r t u a l l y e q u a la nd oppos i t e , sugge s t i ng a l ong- run un i t e l a s t i c i -t y. U n e m p l o y m e n t h a s a l r ea d y b e e n s e e n t o p l a ya n i m p o r t a n t r o l e i n e x p l a i n i n g t h e d o w n t u r n i ne x p e n d i t u r e . C h a n g e s i n t h e u n e m p l o y m e n t r a t eg i v e a l a r g e r d e c r e a s e i n e x p e n d i t u r e g r o w t h i nt h e n e t w o r k m o d e l w h i l e t h e e c o n o m e t r i c s p e -c i f i c a t i on i s more re spons i ve t o t he ra t e o f t h i sc h a n g e . T h e o v e r a l l i m p a c t o f a o n e p e r c e n t a g ep o i n t i n c r e a s e i s s m a l l e r i n t h e n e t w o r k v e r s i o nw h i c h h e l p s t o e x p l a i n w h y t h e e c o n o m e t r i cmode l a c t ua l l y fo re c a s t s a more ra p i d fa l l i ne x p e n d i t u re g r o w t h t h a n t h e n e t w o r k m o d e l ( a n dt h e a c t u a l o u t c o m e ) f r o m t h e e n d o f 1 9 8 9 t o t h es ta r t of 1991.

Wi t h a l og- l i ne a r spe c i f i c a t i on , t he e c onome t -r i c mode l s wi l l ha ve c ons t a n t e l a s t i c i t i e s a nd noi n t e ra c t io n s b e t w e e n v a r ia b l e s . H o w e v e r , if t h ed e t e r m i n a t i o n o f c o n s u m e r s ' e x p e n d i t u r e i s h i gh -l y n o n - l i n e a r t h e n w e m i g h t s u s p e c t t h a t a 1 0s h o c k w o u l d n o t b e e q u a l t o 1 0 t i m e s a 1shoc k . To i nve s t i ga t e , va r i a n t s i mul a t i ons a rec o n d u c t e d o n t h e n e u r a l n e t w o r k m o d e l w h e r es h o c k s o f b e t w e e n m i n u s a n d p l u s 2 0 i n u n i ti n t e r v a l s a r e a p p l i e d t o t h e v a r i a b l e s e n t e r e d i nl o g g e d f o r m . T h e u n e m p l o y m e n t r a t e i s d e -c r e a s ed b y t w o p e r c e n t a g e p o i n t s a n d t h e ni n c r e a s e d b y 0 .1 u n t i l t h e r a t e i s t w o p e r c e n t a g epoi n t s a bove ba se . The re su l t s a re i l l us t ra t e d i nF i g . 9. A s a m p l e o f f o u r v a r i a b le s f r o m t h e G Sm o d e l s h o w s h o w t h e g r o w t h r a t e o f c o n s u m p -t i o n c h a n g e s w i t h t h e s i z e o f s h o c k . T h e c u r v a -t u re se e n i n t he p l o t s i l l us t ra t e s t he de gre e o fnon- l i ne a r i t y i n t he re l a t i onsh i p . Typi c a l l y , fo rs m a l l c h a n g e s i n t h e e x p l a n a t o r y v a r i a b l e s t h ee f f e c ts a r e n e g l ig i b le b u t w h e n l a r g e r s h o c k s a r e


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266 K.B. Church, S.P. Curram International Journal of Forecasting 12 1996) 255-267A l n ( R P O I )

. 4 o - t o o ~ ] DShark I o ~ ~ ( z )

A l n ( W )

= u6

ln(m'Dz)E

- -2 ]

. ~ ,~x k t o ; n ~a e n d q m t ~ ( ~ )

~ J

t2 -1S ho ck to ; n a s c e n t ~ i o a J e ( ~ ~ l s )Fig. 9. Response of expenditure to changes in explanatoryvariables.

applied then the slight curvature does lead tonoticeable differences. The income variablesshow the largest non-linearity as seen by thedifference in the absolute effects when theshocks of plus and minus 20 are applied.Shocks of this size are rarely seen in reality,however. Further experiments where two vari-ables are shocked simultaneously also indicatethat the combined effects are little different tothe sum of the outcome o f the individual shocks.Overall, the conclusion is that a log-linear econo-metric model is probably adequate for describingthe data in this case.

5 ConclusionsSeveral points emerge from this paper. The

common belief that neural networks require avast number of dat a points to be effective can bediscounted and the forecasts produced are noworse than those using standard econometricmethods. Indeed, despite the possibility of fittinga highly non-linear model, it appears that theneural network produces a very similar specifica-

tion to the econometric method. None of themodels here can completely explain the dow-nturn in consumers' expenditure after 1988. Inthe case of the LBS and NIESR equations itappears that the information required to solvethe forecasting problem is not in these data sets.The BE and particularly the GS models performbetter and this seems to be due to the inclusionof terms involving the unemployment rate.

While the economic model builder is expectedto satisfy statistical criteria and tests down from ageneral to a specific model in which all thecoefficients are significantly different from zero,the neural network contains no underlying as-sumptions and even when presented with a largenumber of inputs can discriminate betweenthem, giving low weight to irrelevant informa-tion.The overall conclusion is that every forecastingmethod is dependent on the quality and natureof the data used. If the answer is not in thechosen data, then no method can extract it. Theneural network technology is easier to applybecause the model builder does not need toworry about the economic properties of the finalspecification. In both methods, the role of judge-ment in choosing the appropriate explanatoryvariables is the most important factor. The userof the neural network has the additional task ofensuring that the type and quantity of data usedin the validation is sufficient and typical of thedata as a whole.

AcknowledgementsThe authors are grateful to Ajay Patel, whoseMSc dissertation demonstrated the initialfeasibility of this project. We also thank Ken

Wallis and two anonymous referees for com-ments on the paper, but as ever we take re-sponsibility for the accuracy and interpretationof all the results.

e f erences

Azoff , E.M . , 1994, Neural Network Time Series Forecastingof Financial Markets Wiley, Chichester) .


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K.B . C hurch, S.P. Curtain / International Journal of Forecasting 12 1996) 25 5-2 67 267Carruth, A. and A. Henley, 1990, Can existing consumptionfunctions forecast consumer spending in the late 1980s?,Oxford Bulletin of Economics and Statistics, 52, 211-222.Church, K.B. , EN. Smith and K.F. Wailis, 1994, Econo-metric evaluation of consumers expenditure equations,

Oxfor d Rev iew o f Economic Po l i cy , 10, 71-85.Department of Trade and Industry, 1993, Neural ComputingApplications Portfolio (DTI, London).Department of Trade and Industry, 1994a, Best PracticeGuidelines for Developing Neural Computing Applications(DTI, London).Department of Trade and Industry, 1994b, Directory ofNeural Computing Suppliers, Products and Sources ofInformation (DTI, London).Engle, R.F. and C.W.J. Granger, 1987, Cointegration anderror correction: Representation, estimation and testing,Econometrica, 55, 179-197.Hart, A., 1992, Using neural networks for classificationtasks-some experiments on datasets and practical advice,Journal of Operational Research Society, 43, 215-226.Hendry, D.F. , J.N.J. Muellbauer and A. Murphy, 1990, Theeconometrics of DHSY, in: J.D. Hey and D. Winch, eds.,A Century of Economics: I00 years of the Royal Eco nomicSocie ty and the Economic Journal (Basil Blackwell, Ox-ford) 298-334.Hoptroff, R.G., 1993, The principles and practice of time

series forecasting and business modelling using neuralnetworks, Neural Computing and Applications, 1, 59-66.Lippmann, R.P., 1987, An introduction to computing withneural nets, IEEE A S S P , 4(2), 4-22.Rumelhart, D.E., G.E. Hinton and R.S. Williams, 1986,Learning internal representations by error propagation, in:D.E. Rumelhart, J.L. McLelland and the PDP ResearchGroup, eds., Parallel Distributed Processing (MIT Press,Cambridge, MA) 318-362.Smith, M., 1993, Neural Networks for Statistical Modeling(Van Nostrand, New York).Vogl, T.E , J.K. Mangis, A.K. Rigler, WIT. Zink and D.L.Alkon, 1988, Accelerating the convergence of the back-propagation method, Biological Cybernetics, 59, 257-263.

Biograph i e s Keith CHURCH is a Research Associate in theESRC Macroeconomic Modelling Bureau at the Universityof Warwick. His research interests are concerned withexplaining the difference in properties across large-scalemacroeconometric models of the UK economy.Stephen CURRAM is a lecturer in Operational Researchand Systems at the Warwick Business School. His researchinterests include the application of neural networks formanagement decision making and the representation ofintelligent decision making in computer simulation models.

church, curram - 1996 - forecasting consumers' expenditure a comparison between econometric and...

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