Applied Methods for Analysis of Economic Structure and Change

T

O

Centre for Regional Science Research

Applied Methods

for Analysis of

Economic Structure

and Change

Christer A nderstig

CERUM RAPPORT/CERUM REPORT 1988:2.

APPLIFD METHODS FOR ANALYSES OF ECONOMIC

STRUCTURE AND CHANGE

AKADEMISK AVHANDLING

som for avläggande av filo s o fie doktorsexam en

vid sam h ällsvetensk apliga fa k u lteten vid Um eå u n iversitet

fram lägges till o ffe n tlig granskning

fredagen den 10 juni 1988 kl 13.00

i hörsal E, H um anisthuset, U m eå u n iversitet

ABSTRACT

Applied methods for analyses of economic structure and change

Languuge: English and Swedish, 276 pages

by Christer Anderstig, Department of Economics,

University of Umeft, Sweden

The thesis comprises five papers and an introductory overview o f applied

models and methods. The papers concern interdependences and interrela­

tions in models applied to empirical analyses o f various problems

related to production, consumption, location and trade. Among different

definitions of 'structural analysis' one refers to the study of the

properties o f economic models on the assumption of invariant structural

relations, this definition is close to what is aimed at in lire present case.

Although the subjects cover widely differing aspects of the economic system,

applied models and methods, i.e. entropy maximizing (information minimizing)

models and random utility maximizing models, are in many cases closely

connected.

Tlic first paper reports on a regional input-ouput study applied to

Norrbotten, Sweden. The paper is mainly concentrated on developing and

estimating an econometric model, describing the structural interdependences

in the Norrbotten economy. The chapter is composed of three parts. The first

part concerns the theoretical basis of the model, the main fields of

application and principal problems in connection with the estimation. The core

of the estimated model is defined by the intersectoral dependences in the

Norrbotten economy. This model can be viewed as a part of a more general

model of the regional economy, and such a general model is briefly outlined.

The second part reports on the collection and arranging of data, and the

methods used for the estimation of the model. In the third part the results

are presented. A special interest concerns the effects of production changes

in the basic industries in the county, as to the expected impact on different

industries and occupational groups.

The second paper concerns some aspects of the problem of predicting trade flows

in the forest sector. The model, based on information theory, is predicting

current trade flows by adjusting the historical, a priori, trade flows to

satisfy current export and import totals.

In the third paper an entropy model is employed to decompose the interregional

and intraregional employment change in Sweden and Stockholm, during the period

1960 - 1980, into effects attributed to regions (zones), industries, occupations

and interaction effects.

The fourth paper presents an empirical analysis o f housing choice, based on

individual data of households in Stockholm. The consumer choice is regarded as

a complex choice from a finite set of discrete alternatives and a probabilistic

choice mode! (multinomial logit) is employed, where secondary dwelling is

included in the housing choice decision.

In the final paper spectral analysis is used for identifying the significant

components of cycle behaviour in time series of Swedish exports o f forest

products over a twenty year time period.

Keywords:

Economic structure

Input-output models

Information theory

Multinomial logit

Housing choice

Spectral analysis

Urban development

Distribution and author's address

CFKUM, U niversity of Um eâ, S-901 87 Um eâ

ISSN Ü282-Ü277 1 SUN 91-7174-366-9

P la ce of publication: U m eâ

Year o f publication: 1988

Applied methods for analyses of economic structure and change

Language: English and Swedish, 276 pages

hy Christer Anderstig, Department of Economics,

University of Umeâ, Sweden

The thesis comprises five papers and an introductory overview of applied

models and methods. The papers concern interdependences and interrela­

tions in models applied to empirical analyses of various problems

related to production, consumption, location and trade. Among different

definitions o f ’structural analysis’ one refers to the study of the

properties of economic models on the assumption of invariant structural

relations, this definition is close to what is aimed at in the present case.

Although the subjects cover widely differing aspects of the economic system,

applied models and methods, i.e. entropy maximizing (information minimizing)

models and random utility maximizing models, are in many cases closely

connected.

rITie first paper reports on a regional input-ouput study applied to

Norrbotten, Sweden. The paper is mainly concentrated on developing and

estimating an econometric model, describing the structural interdependences

in the Norrbotten economy. The chapter is composed of three parts. The first

part concerns the theoretical basis of the model, the main fields of

application and principal problems in connection with the estimation. The core

of the estimated model is defined by the intersectoral dependences in the

Norrbotten economy. This model can be viewed as a part of a more general

model of the regional economy, and such a general model is briefly outlined.

The second part reports on the collection and arranging of data, and the

methods used for the estimation of the model. In the third part the results

are presented. A special interest concerns the effects of production changes

in the basic industries in the county, as to the expected impact on different

industries and occupational groups.

The second paper concerns some aspects of the problem of predicting trade flows

in the forest sector. The model, based on information theory, is predicting

current trade flows by adjusting the historical, a priori, trade flows to

satisfy current export and import totals.

In the third paper an entropy model is employed to decompose the interregional

and intraregional employment change in Sweden and Stockholm, during the period

1960 - 1980, into effects attributed to regions (zones), industries, occupations

and interaction effects.

The fourth paper presents an empirical analysis of housing choice, based on

individual data of households in Stockholm. The consumer choice is regarded as

a complex choice from a finite set of discrete alternatives and a probabilistic

choice model (multinomial logit) is employed, where secondary dwelling is

included in the housing choice decision.

In the final paper spectral analysis is used for identifying the significant

components of cycle behaviour in time series of Swedish exports of forest

products over a twenty year time period.

Keywords:

Economic structure

Input-output models

Information theory

Multinomial logit

Housing choice

Spectral analysis

Urban development

Preface

This thesis contains papers written during the past ten years, in connection with manifold

research projects relating to regional development, the forest sector, the building sector, urban

development and the housing market. The early papers were written during years on the staff on

the Department of Economics at University of Umeå, while two papers of more recent date have

been produced at the Regional Planning Office in Stockholm.

Diregarding the general view where everything depends on everything, it may seem an awkward

task to find the link between research efforts in these disparate fields. Yet there are at least two

kind of links that I would like to point at. First, the financial support given by the Swedish Council

of Building Research to next to all research projects. Second, the personal link, involving several

people.

My thesis adviser, Âke E Andersson, has convinced me that the disparate papers have to do

with structural analysis (albeit of a less modern kind) and has during past years offered support

and encouragement to complete the work, even if the structure of papers has changed. Börje

Johansson, who has acted as leader for some projects, has likewise been supporting and

encouraging, not least by the regular question: Have you finished yet? Björn Hårsman, co­

author of chapter four, and Lennart Fridén, both at the Regional Planning Office, have gratefully

been understanding to my situation in the last months.

I have benefitted greatly from Lars Lundberg, co-author of chapter two, as to his excellent

guidance into applied economics.

A great many people at the Department of Economics in Umeå and at the Regional Planning

Office have made contributions in many respects, not least typing the various manuscripts. I

want to thank you all!

1. APPLIED METHODS FOR ANALYSES OF ECONOMIC

STRUCTURE AND CHANGE - AN OVERVIEW

2. ECONOMY AND EMPLOYMENT IN NORRBOTTEN -

A REGIONAL INPUT-OUTPUT STUDY (*)

3. ACTUAL AND PREDICTED TRADE FLOWS OF

FOREST PRODUCTS

4. ON OCCUPATION STRUCTURE AND LOCATION PATTERN

IN THE STOCKHOLM REGION

5. RESIDENTIAL LOCATION, TENURE AND SECONDARY

DWELLING - A MODEL OF HOUSING CHOICE APPLIED

TOSTOCKHOLM

6. SPECTRAL ANALYSIS APPLIED TO SWEDISH EXPORTS

OF FOREST PRODUCTS (*)

SUMMARY

APPLIED METHODS FOR ANALYSES OF ECONOMIC

STRUCTURE AND CHANGE - AN OVERVIEW

1. INTRODUCTION

2. AGGREGATIVE VERSUS DISAGGREGATIVE ANALYSIS

3. INFORMATION MINIMIZATION AND RANDOM

UTILITY MAXIMIZATION

4. ANALYZING THE STRUCTURE OF REGIONAL PRODUCTION

1. I N T R O D U C T I O N In this th es i s f i v e p a p e r s a r e c o l l e c t e d , i n c l u d i n g as m a n y s u bj ects: 11) A r e g i o n a l i n p u t - o u t p u t study, (II) A m o d e l f o r p r o j e c t i o n of i n t e r n a t i o n a l t ra d e f l o w s of f o r e s t p r o d u c t s , (III) M o d e l s r e f e r i n g to Inter- a n d l n t r a r e g i o n a l l o c a t i o n a l a n a l y s i s , (IV) A n a n a l y s i s of h o u s i n g c h o i c e a n d (V) A n a p p l i c a t i o n of s p e c t r a l a n a l y s i s to e x p o r t s e ri es of f or e s t prod uc t s. Si n c e the p a p e r s r e p r e s e n t w i d e l y d i f f e r i n g a s p e c t s of the e c o n o m i c

s ys tem, an o p e n i n g q u e s t i o n c o n c e r n s the a i m a n d p r i n c i p l e of the

c o l l e c t i o n . As a p r e l i m i n a r y a n d g e n e r a l a n s w e r it c o u l d be sai d that

all p a p e r s ar e f o c u s e d on e m p i r i c a l a n a l y s e s of e c o n o m i c s t r u c t u r e s ,

a n d that the m e t h o d s e m p l o y e d a r e c l o s e l y related.

As to the d e f i n i t i o n a n d use of the a m b i g u o u s c o n c e p t 'structure'

a r e m a r k b y M a c h l u p (1963) c o u l d b e q u o t e d : "In g e n e r a l , the ter m

Is m o r e o f t e n u s e d as a n u n n e c e s s a r y Ja r go n a n d as a p l a i n w e a s e l w o r d

than it Is u s e d as a t e c h n i c a l t e r m w i t h c l e a r l y d e f i n e d m e a ni n g. T h i s

s h o u l d be r e a s o n e n o u g h for a v o i d i n g it." Now, M a c h l u p ' s d i s c o u r a g i n g

a t t i t u d e r e fe r s to c o n t e x t s w h e r e structure' is u s e d fo r a p o l o g e t i c

alms, w h i l e in the p r e s e n t c as e a t e c h n i c a l t e r m is a i m e d at.

But e v e n w i t h r e s p e c t to ' s t ru c tu ra l a n alysis' t h e re a r e s e v e r a l

d e f i n i t i o n s , a n d let us b r i e f l y t o u c h on the d i s t i n c t i o n s b e t w e e n

th re e m e a n i n g s of this con c ep t. Fi r s t , w i t h i n m o d e r n m a t h e m a t i c s the

a n a i y s i s of s t r u c t u r a l s t a b i l i t y has d u r i n g the last d e c a d e s b e c o m e a

c l e a r L y d e f i n e d sub j ec t, b a s e d on b i f u r c a t i o n a n d c a t a s t r o p h e th eory,

g e n e r a l l y c o n c e r n i n g the s t r u c t u r a l s t a b i l i t y of d y n a m i c mod el s.

In this f i e i d one ca n f i n d s e v e r a l w o r k s r e f e r i n g to e c o n o m i c

2

to the s t u d y of the p r o p e r t i e s of e c o n o m i c m o d e l s o n the a s s u m p t i o n

of I n v a r i a n t s t r u c t u r a l r el a ti o n s . T h i s d e f i n i t i o n a p p l i e s to m u c h

of the w o r k in the t r a d i t i o n of i n p u t - o u p u t a n a l y s i s , a n d c o m e s v e r y

c l o s e to w h a t is a i m e d at in the p r e s e n t case. T o a v o i d c o n f u s i o n of

ideas, the t it l e thus r e f e r s to a n a l y s e s of e c o n o m i c s tr u ct u r e ,

i n s t e a d of s t r u c t u r a l an a l y s i s .

In the p r e s e n t c a s e the g e n e r a l a p p r o a c h a p p l i e d c o u l d be i l l u s t r a ­

ted b y a s t a t e m e n t by B r o d y (1970, p. 18): "By a s s u m i n g a p p r o x i m a t e

m e a s u r a b i l i t y w e d o n o t a s s u m e t hat i n p ut c o e f f i c i e n t s a r e stable.

By a s s u m i n g the e x i s t e n c e a n d m e a s u r a b i l i t y of the s p e e d of a car

w e d o not d e n y a c c e l e r a t i o n . W e a r e c o n c e r n e d o n l y in the i n t e r ­ d e p e n d e n c e a n d r e g u l a r i t i e s a m o n g the c o e f f i c i e n t s t h e m s e l v e s , e m e r g i n g in t he c o n t e x t of a g i v e n m o m e n t . " Th u s , a c c e p t i n g this f i x e d pr o p o r t i o n s ' a p p r o a c h , the p r e s e n t a n a l y ­ ses of e c o n o m i c s t r u c t u r e s a r e c o n c e r n i n g I n t e r d e p e n d e n c i e s a n d i n t e r ­ r e l a t i o n s in s p e c i f i c m o d e l s , a p p l i e d to e m p i r i c a l a n a l y s e s of v a r i o u s p r o b l e m s r e l a t e d to p r o d u c t i o n , c o n s u m p t i o n , l o c a t i o n a n d trade.

2

.

T h e m o d e l s d i s c u s s e d a r e a ll r e f e r i n g to the m e s o or m i c r o le ve l

of the e c o n o m y a n d all m o d e l s a r e m o r e or less d i s a g g r e g a t e d . T h e

e m p h a s i s put on d i s a g g r e g a t i o n is p a r t l y a c o n s e q u e n c e of the a u t h o r ' s i n t e r e s t in a n d p r e d i s p o s i t i o n to this k i n d of a p p l i e d e c o n o m i c s , i r r e s p e c t i v e of the p r e s e n t p o s i t i o n as r e s e a r c h w o r k e r at a r e g i o n a l p l a n n i n g office. Bu t w h a t is m o r e i n t e r e s t i n g than h a v i n g t h e se s u b j e c t i v e r e a s o n s is to c o n s i d e r the a g g r e g a t i o n p r o b l e m In r e l a t i o n to e c o n o m i c s as a b e h a v i o u r a l scienc e . F r i e d r i c h v o n H a y e k h as put the a g g r e g a t i o n p r o b l e m v e r y c o n c i s e l y : "In fact, n e i t h e r a g g r e g a t e s no r a v e r a g e s d o a c t u p o n o n e a n o t h e r ” . O t h e r s h a v e g i v e n the p r o b l e m a m o r e s y s t e m a t i c t r e a t m e n t , e.g.

1

)

C o n s i d e r i n g the i n f l u e n c e tha t p h y s i c s has h a d o n e c o n o m i c s ,

a c o m p a r i s o n of th e r e s p e c t i v e a g g r e g a t i o n p r o b l e m tu rn s out

I n t e r es t in g . A s r e m a r k e d b y L a n c a s t e r (1966a, p. 2 0 1 ) , " . . . the l evel

of d i r e c t a w a r e n e s s in e c o n o m i c s is at the i n d i v i d u a l (micro-) level,

w h i l e the a g g r e g a t e s ( m a c r o - v a r i a b l e s ) a re a b s t r a c t i o n s . T h e r e v e r s e is t y p i c a l l y t rue of p hy s i c s , w h e r e , fo r e x a m p l e , the p r e s s u r e of a gas ( a g g r e g a t e b e h a v i o r of m o l e c u l e s ) is o b s e r v a b l e a b o u t as d i r e c t l y as a n y p h y s i c a l p h e n o m e n o n , w h i l e the b e h a v i o r of a s i n g l e m o l e c u l e In that a g g r e g a t e is o b s e r v a b l e o n l y in an i n d i r e c t f a s h i o n . ” As far as a p p l i e d e c o n o m i c s is c o n c e r n e d the c o n c l u s i o n is o b v i o u s - in g e n e r a l the m o d e l s m u s t be c o n f i n e d to m a c r o - v a r i a b l e s , b a s e d on m o r e or less a g g r e g a t e d m i c r o - v a r i a b l e s . 1) See a l s o A l l e n (1956).

4

W h i l e the f i r s t p ar t of the a r g u m e n t r e p r e s e n t s the e s t a b l i s h e d

o p i n i o n , the c o n c l u s i o n is less r e c o g n i z e d . T h e a g g r e g a t i o n

p r o b l e m h a s m o r e o f t e n b e e n o v e r l o o k e d th an l o o k e d over, and, as

L e i j o n h u f v u d (1968, p. Ill) puts it, "the a g g r e g a t e s u s e d t en d to

b e c o m e p r o f e s s i o n a l c o n v e n t i o n s w h i c h a r e s e l d o m e x a m i ne d" .

As n o t e d b y A l l e n (1956), the s e r i o u s d i s c u s s i o n a b o u t the a g g r e g a t i o n

p r o b l e m w a s s t a r t e d w i t h a s e r i e s of a r t i c l e s b y K l e i n a n d o t h e r s in

1946. In r e t r o s p e c t , the d i s c u s s i o n at tha t tim e ca n be s e e n as a

p r e l i m i n a r y to the c o m i n g m a c r o - e c o n o m i c m o d e l - b u i l d i n g t r a di ti o n.

It is i n t e r e s t i n g to not e , t hat w h i l e the d i s c u s s i o n of a g g r e g a t i o n

p r o b l e m s a n d s p e c i f i c a t i o n e r r o r s a r o s e f r o m the a d v a n c e of m a c r o - e c o n o m i c m o d e l - b u i l d i n g , this t r a d i t i o n p r o v i d e d , a c c o r d i n g to G r i l i c h e s (1974), a n ' e r r o r s - c a n c e l - o u t - i n - a g g r e g a t e s ' j u s t i f i c a t i o n for no t d e a l i n g w i t h e r r o r s in v a r i a b l e s . T h i s p o i n t s to the g e n e r a l p r o b le m, d i s c u s s e d in e.g. A l o n s o (1968), of a c o n f l i c t b e t w e e n s p e c i f i c a t i o n e r r o r s a n d m e a s u r e m e n t e r r o r s , the f o r m e r d e c r e a s i n g a n d the l a t t e r i n c r e a s i n g w i t h d i s a g g r e g a t i o n a n d m o d e l co m p l e x i t y . F u r t h e r , as e x e m p l i f i e d in G r u n f e l d a n d G r i l i c h e s (1960), in c as e

the b e h a v i o u r is i n f l u e n c e d b y v a r i a b l e s at the a g g r e g a t e level,

1

the m a c r o - r e l a t i o n m a y p e r f o r m e v e n b e t t e r t h a n the m i c r o - r e l a t i o n .

T h e c o n c l u s i o n is no t v e r y s e n s a t i o n a l : E a c h a g g r e g a t i o n p r o b l e m

m u s t b e s o l v e d in its o w n w ay, a n d as to the p r e s e n t study, a

s t a t e m e n t b y J o h a n s e n (1964, p.l) m a y g i v e the g u i d i n g p r i n c i p l e :

" Indeed, X d o not b e l i e v e that in g e n e r a l the a p p l i c a t i o n of the

a n a l y s i s in t e rm s of less a g g r e g a t e d c o n c e p t s is s u p er io r . T h e d e g r e e of a g g r e g a t i o n to a p p l y a n d the c o n c e p t s to u s e d e p e n d o n the p r o b l e m s w h i c h on e w a n t s to e x a m i n e , a n d t h e r e is c e r t a i n l y a n e e d for b o t h a g g r e g a t i v e a n d d i s a g g r e g a t i v e a n a l y s e s . " N e x t f o l l o w s a n a c c o u n t of h o w this g e n e r a l 'principle' h a s b e e n i m p l e m e n t e d . Fi rs t , the r e f e r e n c e m a d e to m o d e l s o n the m i c r o le v el a c t u a l l y r ef e rs

to the p a p e r on h o u s i n g c h o i c e (IV). A n d e v e n in th i s c a s e the micro'

da ta , that is the f a m i l y e x p e n d i t u r e a n d i n c om e da ta , h a v e b e e n

a g g r e g a t e d o v er i n d i v i d u a l f a m i l y m e m b e rs . T h e o t h e r f o u r p a p e r s a r e

r e f e r i n g to w h a t is l a b e l e d the m e s o level, b e t w e e n m i c r o a n d macro.

In the f irst p ap e r (I) a r e g i o n a l i n p u t - o u t p u t s t u d y is p r e s e n t e d .

At the time the s t u d y w a s p e r f o r m e d , it wa s p r i m a r i l y a i m i n g at

a n a n a l y s i s of the im p a c t on the r e g i o n a l e c o n o m y of e s t a b l i s h i n g

a n e w s t eel mill. A n i n p u t - o u t p u t m o d e l w a s c h o s e n s i n c e this m o d e l

Is b a s e d o n w h a t is c r u c i a l in the im p a c t a n a l y s i s , viz. the i n t e r ­

d e p e n d e n c e b e t w e e n i n d u s t r i e s in the r e g i o n a l eco no m y.

Now, in c o m p a r i s o n to a n a l t e r n a t i v e r e p r e s e n t a t i o n of the e c o n o m y ,

e.g. an e c o n o m i c b a s e mo d e l , the i n p u t - o u t p u t m o d e l is d i s a g g r e g a t i v e ,

by d e f i n i t i o n . But w h a t is true of i n p u t - o u t p u t t a b l e s in g e n e r a l ,

a n d the p r e s e n t on e in p a r t i c u l a r , is sti ll a c o n s i d e r a b l e d e g r e e

of a g g r e g a t i o n . In the p r e s e n t s i n g l e r e g i o n m od e l, the f l o w s are

c o m p l e t e l y a g g r e g a t e d o v e r g o o d s a n d s e r v i ce s , a n d a c t i v i t i e s a r e

6

the p r e s e n t c a s e the b a s i s h a s b e e n the p r o b l e m of p r e d i c t i n g

s p e c i f i c t r a d e flows. T h e m od e l , b a s e d on i n f o r m a t i o n t h e o ry , is p r e d i c t i n g c u r r e n t t r a d e f l o w s s i m p l y b y a d j u s t i n g the h i s t o r i c a l , a p r i o r i , t r a d e f l o w s to s a t i s f y c u r r e n t e x p o r t a n d i m p o r t totals. T h e r e s u l t s s u g g e s t that a c o n s i d e r a b l e d e g r e e of i n e r t i a is c h a r a c t e r i s t i c of s ome of the h i s t o r i c a l t r a d e p a t t e r n s , e s p e c i a l l y w i t h r e s p e c t to S w e d i s h expor ts . T h e t r a d e n e t w o r k b e i n g h i g h l y a g g r e g a t e d m ea n s , h o w e v e r , t ha t the 1) F o r a t h e o r e t i c a l d i s c u s s i o n of a g g r e g a t i o n p r o b l e m s in input - o u t p u t a n a l y s i s , see Moriraoto (1970). H ö g l u n d (1966) p r e s e n t s a n e m p i r i c a l s t u d y of r e l a t e d inte re s t.

s i g n i f i c a n c e of this r e s u l t is u n c l e a r a n d that the m o d e l p r i m a r i l y s er v e s a n i l l u s t r a t i v e purpo s e. A l s o the t h i r d p a p e r (III), s t u d y i n g S w e d i s h e m p l o y m e n t c h a n g e s I960 - 1980 b y d e c o m p o s i t i o n a n a l y s i s , is d r a w i n g on i n f o r m a t i o n theory. A n e n t r o p y m o d e l is u s e d to d e c o m p o s e e m p l o y m e n t c h a n g e s i nto e f f e c t s of r e g io n, i n d u s tr y, o c c u p a t i o n a n d i n t e r a c t i o n eff ec ts . By a d d i n g a n o c c u p a t i o n e f f e c t to the t r a d i t i o n a l e f f e c t s of r e g i o n a n d i n du st r y, the d e c o m p o s i t i o n p r o v i d e s i m p o r t a n t i n f o r m a t i o n that o t h e r w i s e w o u l d not be a v a i l a b l e , e v e n at a v e r y d e t a i l e d d i s a g g r e g a t i o n of ind u st ri e s.

T h e r e is o n e issue that is of s p e c i f i c i n t e r e s t to p e r f o r m this

a n a l y s i s , viz. the s p a t i a l i m p l i c a t i o n s of the p r o d u c t c y c l e theory.

H e r e e m p l o y m e n t f i g u r e s a r e u s e d to d i f f e r e n t i a t e b e t w e e n v a r i o u s e c o n o m i c a c t i v i t i e s , i n c l u d i n g d i f f e r e n t p h a s e s in the p r o d u c t cycle. In this c o n t e x t d e f i n i n g a c t i v i t i e s b y i n d u s t r y is i n a d e q u a t e si n c e a n industry' is a n a g g r e g a t e o v e r al l k i n ds of e s t a b l i s h m e n t s a n d a c t i v i t i e s , w h e t h e r , e.g., m a n u f a c t u r i n g in b r a n c h p l a n t s or R & D in c o r p o r a t e h e a d q u a r t e r s . D e f i n i n g a c t i v i t i e s b y o c c u p a t i o n m a k e s it p o s s i b l e , h o w e v e r , to d i f f e r e n t i a t e b e t w e e n , e.g., k n o w l e d g e i n t e n s i v e a n d g o o d s h a n d l i n g o c c u p a t i o n s , c a t e g o r i e s that c a n b e c o n c e i v e d as c o u n t e r p a r t s to

p h a s e s in the p r o d u c t cycle. As f o r the s p a t i a l d i m e n s i o n , r e g i o n s

h av e b e e n c o n s t r u c t e d a c c o r d i n g to the level of i n t r a r e g i o n a l

a c c e s s i b i l i t y , a p r i n c i p l e d e r i v e d f r o m p r o d u c t c y c l e th e ory.

In g e n e r a l , region s , i n d u s t r i e s a n d o c c u p a t i o n s h a v e b e e n c o n s t r u c t e d

on the b a s i s of h o m o g e n e i t y p r i n c i p l e s , a c c o r d i n g to c h a r a c t e r i s t i c s

8

i l l u s t r a t i o n , i m p l y a m o d e l of h o u s i n g d e m a n d w h e r e a ll h o u s i n g a t t r i b u t e s a r e l u m p e d t o g e t h e r i nt o o n e s i n g l e - v a l u e d c o m m o d i t y , h o u s i n g s e r v i c e s ' , a n d w h e r e h o u s e h o l d s a r e n o t g r o u p e d at all. G i v e n th e s e a l t e r n a t i v e s , w e m a y w i t h o u t f u r t h e r e l a b o r a t i o n c o n c l u d e t ha t the d i s a g g r e g a t e d a p p r o a c h g i v e s a b e t t e r u n d e r s t a n d i n g of the d e m a n d f or h o u s i n g a n d the b e h a v i o u r of a h o u s i n g m a rk e t. Now, it s h o u l d b e a d m i t t e d t ha t th is e x t r e m e l y a g g r e g a t i v e a p p r o a c h in f act h a s no r e l a t i o n w i t h m o d e r n re s e a r c h , n o r w i t h m o d e r n m a c r o m o d e l i n g in c o n n e c t i o n w i t h r e g i o n a l a n d lo cal p l a nn in g . S i n c e the s e v e n t i e s a c o n s i d e r a b l e p ar t of the r e s e a r c h in h o u s i n g e c o n o m i c s h a s b e e n f o c u s e d o n d i s a g g r e g a t e d i s c r e t e c h o i c e m o d e l s , the r e s e a r c h s t r e a m to w h i c h the p r e s e n t p a p e r b e l o n g s . E v e n m a c r o level a p p r o a c h e s , in r e s e a r c h as w e l l as in p l a n n i n g a n d p o l i c y c o n t e x t s , a r e c o u c h e d in t e r m s p a r t l y r e f l e c t i n g th e h e t e r o g e n e i t y 1) of h o u s i n g a n d the i n f l u e n c e of li fe c y c l e f a ct or s . B e i n g a p o l i c y f i e l d of g r e a t i m p o r t a n c e , a n d g i v e n the i n c r e a s i n g l y

s o p h i s t i c a t e d r e s e a r c h a t the m i c r o level, the m o s t r e c e n t h o u s i n g

r e s e a r c h is c o n c e r n i n g the li nk b e t w e e n m i c r o a n d m a c r o p e r s p e c t i v e s F or e x a m p l e , A n a s et al. (1987) h a v e d e v e l o p e d a p r o t o t y p e m o d e l of the S w e d i s h h o u s i n g m a r k e t , d r a w i n g o n a s i m i l a r m o d e l in US, A n a s (1982), w h e r e the li nk b e t w e e n m i c r o a n d m a c r o b e h a v i o u r s is d i s c u s s e d . In t h e s e s t u d i e s it is a r g u e d that lo gi t m o d e l s , b a s e d on I n d i v i d u a l c h o i c e th eory, ca n b e m e a n i n g f u l l y a n d a c c u r a t e l y e s t i m a t e d u s i n g sma ll a g g r e g a t i o n u n i t s a n d r e l a t i v e f r e q u e n c y d a t a of ch oices. 1) Cf. H å r s m a n (1981) 2) A r e v i e w is f o u n d in C l a r k a n d V a n L i e r o p (1986)

10

b e h a v i o u r in ti m e series. In the p r e s e n t e x p l o r a t i v e pap e r, the

e s t i m a t e d s p e c t r a a r e b a s e d o n q u a r t e r l y d a ta , 1961 - 1979, for

S w e d i s h e x p o r t s of 158 f o r e s t p r od u c t s . T h i s m e a n s t h a t m o s t

p r o d u c t s a r e r e a s o n a b l y h o m o g e n e o u s w i t h r e s p e c t to p r o d u c t i o n ,

u s e s a n d t r a n s p o r t a t i o n c h a r a c t e r i s t i c s . A n d a f i n e c l a s s i f i c a t i o n

of p r o d u c t s m a y b e ju s ti fi e d, as d i f f e r e n t q u a l i t i e s w i t h i n a g g r e ­

g a t e s as 's a wnwood', 'pulp' etc. e x h i b i t m a r k e d l y d i f f e r e n t sp ectra.

1) O v e r v i e w s of r e l a t e d s t a t i s t i c a l m o d e l s in thi s f i e l d a r e f o u n d in e.g. W r i g l e y a n d B r o u w e r (1986) a n d W r i g l e y (1985).

3. I N F O R M A T I O N M I N I M I Z A T I O N A N D R A N D O M U T I L I T Y M A X I M I Z A T I O N

T h e d i s c u s s i o n a b o v e w a s c l o s e d b y p o i n t i n g at the the analogue,, in

a s t a t i s t i c a l d e c o m p o s i t i o n c o n t e x t , b e t w e e n s p e c t r a l a n a l y s i s a n d e n t r o p y m o d e l i n g . A m o r e i n t e r e s t i n g q u e s t i o n c o n c e r n s the c o n n e c ­ ti on b e t w e e n m o d e l s u s e d in p a p e r s I - IV. A c t u a l l y , w h e n p r o j e c t i n g t r a de f l o w s (II), d e c o m p o s i n g e m p l o y m e n t (III) a n d a n a l y z i n g h o u s i n g c h o i c e (IV), the t h e o r e t i c a l p e r s p e c t i v e s d i f f e r b u t th e m o d e l f o r m s ar e q u i t e or a l m o s t i d e n ti c al . F u r t h e r m o r e , s o m e m o d e l s a r e of g e n e r a l i n t e r e s t in e s t i m a t i n g a n d p r o j e c t i n g i n p u t - o u t p u t c o e f f i ­

cient s , a l t h o u g h n o t u s e d in this case.

First, the i n f o r m a t i o n t heory, or e n t r o p y m o d e l a p p r o a c h e s u s e d in

p a p e r s II a n d III a r e q u i t e i de nt i c a l . In a n o v e r v i e w b y B a t t e n a n d

B o y c e (1986) this a p p r o a c h is r e l a t e d to a l a r g e r f a m i l y of s p a t i a l

i n t e r a c t i o n models. E v e n if t h is c o n n e c t i o n d o e s not i m p l y that

e n t r o p y m o d e l s a r e i n a p p l i c a b l e in o t h e r f i e l d s of e c o n o m i c s , the

mo st f r e q u e n t a p p l i c a t i o n s d o r e l a t e to r e g i o n a l s c i e nc e , e.g. in

sp a t i a l f o re c a s t i n g .

In this c o n t e x t R o y (1987) p o i n t s out that tw o a l t e r n a t i v e a p p r o a c h e s

ar e a v a i l a b l e , k n o w n as the S h a n n o n a n d the K u l l b a c k a p p r o a c h e s . It is 1)

the latter, a l s o k n o w n as the m i n i m u m i n f o r m a t i o n p r i n c i p l e , or e n t r o p y

m a x i m i z a t i o n w i t h n o n - u n i f o r m p r i o r p r o b a b i l i t i e s , th at is u s e d in p a p e r s II a n d III. T h us , in p r o j e c t i n g tr a d e f l o w s (II) a n d e s t i m a t i n g e m p l o y m e n t c h a n g e s (III), a r e v i s e d d i s t r i b u t i o n (of i n t e r r e g i o n a l t r a d e f l o w s a n d e m p l o y m e n t b y regi on , i n d u s t r y a n d o c c u p a t i o n , r e s p e c t i v e l y ) is i n f e r r e d f r o m a p r i o r d i s t r i b u t i o n u p o n the i n t r o d u c t i o n of n e w e x o g e n e o u s d a t a (t otal r e g i o n a l e x p o r t s a n d im p o r t s a n d t o t a l n u m b e r of e m p l o y e d in r eg i on s, i n d u s t r i e s , o c c u p a t i o n s etc ., r e s p e c t i v e l y ) . I) See S n i c k a r s a n d W e i b u l l (1977), W e b b e r (1979)

12

T h e e s t i m a t e s of a n y e n t r o p y m o d e l m a y he c h a r a c t e r i z e d as a t ype of

s t a t i s t i c a l i n f e r e n c e , see e.g. B a t t e n a n d B o y c e (1986). O n e may, h o w ­

e ver, m a k e a f u r t h e r d i s t i n c t i o n b e t w e e n the t w o a p p r o a c h e s in this

respect. T h e S h a n n o n a p p r o a c h d i f f e r s f r o m the K u l l b a c k p r o c e d u r e b y a s s u m i n g u n i f o r m p r i o r p r o b a b i l i t i e s , e . g., a s s u m i n g tha t i n t e r r e g i o n a l t r a d e f l o w s a r e e q u a l l y p r o b a b l e . Now , t h e r e is e m p i r i c a l e v i d e n c e t h a t the K u l l b a c k p r o c e d u r e h a s s u p e r i o r p r e d i c t i v e c a p a b i l i t y , a t l e ast w i t h r e s p e c t to h i s t o r i c a l data. A c c o r d i n g to R o y (1987), thi s a p p r o a c h m a y (thus) b e c l a s s i f i e d a (the) s t a t i s t i c a l I n f e r e n c e ap p r o a c h .

On the o t h e r han d , the S h a n n o n a p p r o a c h is a l l e g e d to h a v e a l a r ge r

e x p l a n a t o r y powe r , b y the f o l l o w i n g reason. U s i n g the S h a n n o n a p p r o a c h ,

the e s t i m a t e d m o d e l is b a s e d on a set of e x p l a n a t o r y c h a r a c t e r i s t i c s

and, h e n c e , the p a r a m e t e r s c a n b e u s e d at the f o r e c a s t i n g stage,

a c c o u n t i n g fo r the e f f e c t s of c h a n g e d c h a r a c t e r i s t i c s . A p p l i e d to,

e .g ., i n t e r r e g i o n a l t r a d e fl o ws , the e s t i m a t e d f l o w p a t t e r n c o u l d be

b a s e d on i n f o r m a t i o n s u c h as t r a n s p o r t a t i o n co s t s a n d o t h e r t r a d e

i m p e d i m e n t s / a f f i n i t i e s , as in the c l a s s i c a l g r a v i t y m odel. A f l o w

p a t t e r n f o r e c a s t c o u l d thus r e f l e c t the e f f e c t s of a l t e r e d t r a n s p o r ­

t a t i o n c osts, ta ri f f b a r r i e r s et c., p r o v i d e d t hat t his i n f o r m a t i o n

is a v a i l a b l e . A s to the e x p l a n a t o r y p o w e r of the K u l l b a c k p r o c e d u r e , R o y a r g u e s t ha t it “s u b s t i t u t e s d i r e c t p r o j e c t i o n f r o m the p r i o r d i s t r i b u t i o n f o r the e s t i m a t i o n p h a s e of the S h a n n o n m o d e l . . ( a n d is t h e r e f o r e ) ..i n c a p a b l e of c o n s i d e r i n g a n y c h a n g e s in the c o n f i g u r a t i o n of c h a r a c t e r i s t i c s i n f o r m a t i o n b e t w e e n the e s t i m a t i o n (prior) ti m e p e r i o d a n d the f o r e c a s t i n g p e ri o d " . T h u s , s t a r t i n g f r o m the c o n c e p t i o n of the K u l l b a c k a n d S h a n n o n a p p r o a c h ­ es h a v i n g c o m p l e m e n t a r y m e r i t s , R o y p r e s e n t s a n e w f o r e c a s t i n g a p p r o a c h , a t t e m p t i n g to c o m b i n e t h e s e m e ri t s. A s r e g a r d s o ur d i s c u s s i o n ,

R o y

paper la of interest primarily by the discussion of the

advan-1)

tages and disadvantages associated with respective approach.

The Kullback procedure discussed so far may in fact be seen as a

special case of the minimum information principle, as presented in

Snickars and Weibull (1977). There, e.g., the 'new gravity model'

makes use of explanatory characteristics (travel time) information

as well, in addition to the information of a prior probability

distribution and the probability sum information. Thus it seems as

If the difference between a Shannon approach (the classical gravity

model) and a Kullback approach (the new gravity model) is not a

matter of explanatory power, as the same characteristics are used

In both approaches, but a matter of the amount of information used,

being less in the Shannon approach.

Now, turning to the connection between information theory approaches

and the multinomial logit model (MNL) approach used in paper IV, Anas

(1983) gives one proof that the Shannon approach and the (simple) MNL

may yield identical estimates. It may therefore be instructive to

draw on parts of Anas' paper. Assume the problem of deriving the

h

choice probabilities P

, where h =l—

H denotes choosers and j=l...J

J

denotes the discrete alternatives forming the choice set (as in, e.g.,

a housing choice problem). The information available makes it possible

to formulate the following information minimizing problem, using the

Shannon approach:

h

h

Min 1 1 P In P

(1)

h 1

J

j

I ;

The problem resembles the traditional forecasting problem, as

discussed, from a users perspective, by e.g. Chambers et al. (1971);

'The superior short term accuracy of techniques based on stochastic

models of time series, while causal ('explanatory') methods are to

prefer in long term forecasting.

14

_J

J

J

6

G i v e n e q u i v a l e n t i n f o r m a t i o n , a c h a n g e f r o m the i n f o r m a t i o n - m i n i m i -

z a t i o n a p p r o a c h to a r a n d o m u t i l i t y m a x i m i z a t i o n a p p r o a c h m e a n s t h a t

the c ho i ce p r o b a b i l i t i e s , c o r r e s p o n d i n g to (6), c o u l d b e d e r i v e d as

f o l l o w s .

It is assumed that the choosers have similar preferences and that

the random utility function is linear in parameters and additive in

variables :

h

h

h

U =

+ I'

X

+

i

(7)

j

oj

k

k jk

J

h

where U

is the perceived utility of alternative j for chooser h;

3

n is a vector of utility coefficients, among which a

are alter­

ed

native specific constants, measuring the unspecified part of utility,

h

and

*

is the vector of random utility. The random component (

is

3

assumed to be statistically independent and identically distributed

according to the extreme value distribution

h

-<

Prob( (

<= < ) = expl-exp

).

(8)

3

by this assumption the utllity-maximization choice probabilities will

have the form

h

h

h

P

* Prob( U

> U

;

V

3 i i)

i

i

3

h

h

= exp( (i

+ - u X

) / £ exp( (\

+ £ <r X

)

(9)

oi

k k ik

3

o3

k k 3k

16

c r e t e ch o ice. O n e c a u s e f o r the o p p o s i t e o p i n i o n m a y be the f act, that

a p p l i e d r a n d o m u t i l i t y - m a x l m i z a t i o n m o d e l s a r e t r a d i t i o n a l l y d i s a g g r e ­

g a t e d , w h i l e i n f o r m a t i o n - m i n i m i z a t i o n m o d e l s a r e g e n e r a l l y e s t i m a t e d

f r o m a g g r e g a t e data. T h i s f a c t d o e s not, h o w e v e r , p r o v i d e a s o u n d b a s i s

f o r c o m p a r i n g the two a p p r o a c h e s .

O n e i m p o r t a n t p r o p e r t y of the M N L m o d e l is t e r m e d ' i n d e p e n d e n c e f r o m

i r r e l e v a n t a l t e r n a t i v e s ' (IIA). T h i s p r o p e r t y , i m p l y i n g that the r e l a ­

t ive od d s for the c h o i c e of a n y two a l t e r n a t i v e s is i n d e p e n d e n t of the

a t t r i b u t e s of a n y o t h e r a l t e r n a t i v e , is a d i r e c t c o n s e q u e n c e of the

a s s u m p t i o n of I n d e p e n d e n t l y d i s t r i b u t e d r a n d o m terms. T hus, in c a se s

w h e r e the u n o b s e r v e d a t t r i b u t e s of a l t e r n a t i v e s (the r a n d o m terms) a r e

c o r r e l a t e d , the a s s u m p t i o n of the M N L m o d e l is v i o l a t e d . In t hese

c a s e s a n e s t e d l ogit m o de l , as in p a p e r IV, m a y p r o v i d e a p r a c t i c a l w a y

of d e a l i n g w i t h the II A p ro b le m. M a y it h e r e s u f f i c e to s a y th at the

n e s t e d logit m o d e l is a n a p p r o a c h that m a k e s it p o s s i b l e to a c c o m o d a t e

v a r y i n g d e g r e e s of s i m i l a r i t y b e t w e e n a l t e r n a t i v e s .

S i n c e the (simple) M N L m o d e l a n d the S h a n n o n a p p r o a c h m od el , a c c o r ­

d i n g to t h e p r e s e n t a t i o n a b o v e le a ds to the s a m e f o r m a l r e p r e s e n t a t i o n

of the b e h a v i o u r , the I I A p r o b l e m is i m p l i e d a l s o w i t h r e s p e c t to the

i n f o r m a t i o n - m i n i m i z a t i o n a p p r o a c h . In t h is c o n t e x t it is i n t e r e s t i n g

to n o t e th e d e v e l o p m e n t of m o d e l s u s i n g the S h a n n o n a p p r o a c h w h e r e

the s t r u c t u r e of the m o d e l s ha r e s th e f r e e d o m f r o m the II A r e s ­

t r i c t i o n in t h e sam e w a y as t h e n e s t e d log i t mo d e l , see e.g. B o y c e

Now, it s h o u l d b e c l e a r f r o m a b o v e th at i n f o r m a t i o n - m i n i m i z a t i o n is a

m o r e g e n e r a l p r i n c i p l e t h a n t h e S h a n n o n a p p r o a c h u s e d in (1) - (4).

Li ke w i s e , the M N L m o d e l is Just a s p e c i a l ca s e of d i s c r e t e c h o i c e

models. T h i s b r i n g s A n a s (1983) to c l o s e his p a p e r b y s t a t i n g the

c o n v i c t i o n that the e q u i v a l e n c e b e t w e e n i n f o r m a t i o n - m i n i m i z a t i o n a n d

d i s c r e t e c h o i c e t h e o r y d o e s n o t e n d w i t h the M N L model.

R e f r a i n i n g f r o m a n y a t t e m p t s in th i s respe ct , t h e r e is, h o w e v e r , o n e

q u e s t i o n th a t s ho u ld , at least, b e r a i s e d in th i s c o n t e x t , viz. the

c o r r e s p o n d e n c e to the K u l l b a c k a p p r o a c h (the m i n i m u m i n f o r m a t i o n p r i n ­ ciple) in a d i s c r e t e c h o i c e t h e o r y f ra me w o r k . A l t h o u g h a p r i o r p r o b a ­ b i l i t y d i s t r i b u t i o n c a n be d e r i v e d b y m o d e l i n g e f f o r t s , see S n i c k a r s a n d W e i b u l l (1977), the d i r e c t u s e of h i s t o r i c a l d a t a is the c o m m o n p r o c e d u r e , as in p a p e r s II a n d III. A3 d i s c u s s e d b y F i s c h e r a n d N i j k a m p (1987) in a r e c e n t 'State of the Art' r e view, s ev e r a l i m p o r t a n t m e t h o d o l o g i c a l is su e s a r e r a i s e d w h e n c h o i c e b e h a v i o u r o v e r t ime is i n c o r p o r a t e d in d i s c r e t e c h o i c e m o d e l l ­

ing. O n e k e y issue is the p r o b l e m of d i s t i n g u i s h i n g b e t w e e n the i n f l u ­

en ce of tr ue ( st ru c tu r al ) s t a t e d e p e n d e n c e a n d s p u r i o u s s t a t e d e p e n ­

d e n c e in the m o de l i n g . F o l l o w i n g H e c k m a n (1981), th e s e i n f l u e n c e s a re

r e l a t e d to two d i s t i n c t e x p l a n a t i o n s fo r the e m p i r i c a l r e g u l a r i t y of

c u r r e n t b e h a v i o u r b e i n g d e p e n d e n t on pa st b e h a v i o u r .

One e x p l a n a t i o n is t h a t the p r e v i o u s c h o i c e h a s a g e n u i n e b e h a v i o u r a l

e f f e c t on the c u r r e n t ch o ice, as a c o n s e q u e n c e of, e. g., a l t e r e d p r e ­

ferenc e s. In this c a s e t h e r e is a tr ue st a t e d e p e n d e n c e of c u r r e n t on

past b eh a v i o u r . A s e c o n d e x p l a n a t i o n for the p h e n o m e n o n is t ha t the

p r e v i o u s c h o i c e m a y a p p e a r to i n f l u e n c e the c u r r e n t c h o i c e o n l y

18

£ a

X Y

j t

k k Jkt

3* 33' 3 <t-l>

3

3t

w h e r e U is the u t i l i t y of a l t e r n a t i v e J for c h o o s e r h at t ime p e r i o d h jt t; X is the v a l u e of th e k : t h a t t r i b u t e for a l t e r n a t i v e j a n d c h o o s e r jkt h h, w h i c h m a y v a r y in time, C * 1 if c h o o s e r h c h o o s e s a l t e r n a t i v e j (t-1) ^ h J in the p r e v i o u s p e r i o d (t-1) a n d 0 o t h e r w i s e , t is an e r r o r c o m p o -j * h n e n t that v a r i e s a m o n g c h o o s e r s b u t is t i m e - i n v a r i a n t a n d < is an Jt e r r o r c o m p o n e n t tha t v a r i e s a m o n g b o t h c h o o s e r s a n d t i m e p e r i od s . T h e i n c l u s i o n of the s e c o n d t e r m in (10) a l l o w s c h o i c e in a p r e v i o u s p e r i o d to i n f l u e n c e c h o i c e in the c u r r e n t pe r iod. If t h e e s t i m a t e of the p a r a m e t e r

V

33

V

(

JJ

J

d i r e c t l y to the d y n a m i c c h o i c e p r o b l e m ; e . g ., o n the a s s u m p t i o n that * h

(

^ h

Second, if it can be assumed that

7

= 0 for all h and J but that

3

some

Ì

f 0, we have a true state dependence model. In this case

3 3

previous choices are explicitly considered but, since the error terms

are assumed to be independent across time periods, the usual type of

discrete choice models can still be applied directly.

„h

Third, turning the assumptions the other way round, i.e.

<

f 0 for

3

some h and 3, and

)’

* 0 for all h,3 and 3, we have a spurious state

33

dependence model. In this case previous choices are not considered,

but, since some unobservables are assumed to remain constant across

time pericds, the error terms are serially correlated and, hence,

current and previous choices are statistically dependent.

Consequently, the usual estimation procedures are no longer valid.

In these circumstances there are two approaches available to deal

with the error terms; The 'fixed effects' approach, in which the

^ h

t

terms are specified as alternative-specific constants for each

3

chooser, or the 'random effects' approach, in which the complex error

1)

variable structure is dealt with directly.

To conclude, by raising the question of the correspondence to the

Kuliback approach in a discrete choice theory framework, the discussion

has been carried to a generalization of the discrete choice model in a

dynamic context. Whether there is a meaningful answer to the opening

question has not been considered, but there is one specific reason for

2 )

bringing dynamic discrete choice modeling up for discussion.

L) See Heckman (1981) for details. The model presented by Heckman may

be considered as a further generalization of the discrete choice

model.

2) The link between entropy models and discrete choice models has

been discussed in other contexts, see e.g. Nijkamp and Reggiani

(1986).