SOU 2005:57

Consumer Demand and Labor Supply in

Sweden 1980-2003

Bengt Assarsson

Department of Economics

Uppsala University

Box 513, SE-751 20 Uppsala

Sweden

E-mail: bengt.assarsson@nek.uu.se

2004-03-11

Abstract

This paper analyses the demand for consumer goods and leisure in Sweden for the period 1980-2003. A dynamic version of the AIDS demand system is used. An error correction model is used where a form of habit formation is applied. The results show reasonable estimates of price and income elasticities for the consumer goods. Also, the labor supply elasticity is in line with previous results using micro data.

1 Introduction

The estimation of demand elasticities has a long tradition in applied economics. During the 1970ies and 1980ies demand systems based on speci…c utility or cost functions were estimated and e¤ort was put on deriving attractive functional forms of these systems. The most successful demand systems were those with a ‡exible functional form, such as the Translog 1 or the AIDS (Almost Ideal Demand System) 2 . Demand systems were often estimated with aggregate time series data, though the theory from which the systems were derived considered the behavior of a single consumer or household. Initially, systems like the Translog and AIDS were static. Later, dynamic versions of these models were used and …t the data better.

The purpose of this paper is to estimate demand elasticities for the most recent Swedish aggregate consumption data. The elasticities can be used for example for estimating deadweight losses for di¤erent tax schedules or for computing optimal tax rates according to the Ramsey or inverse rule 3 , i.e. tax rates being set inversely to the compensated price elasticity of demand 4 . These elasticities must also include the price elasticities (own and cross price elasticities) of leisure time. If leisure time is excluded, the implicit assumption is that the cross-price elasticities between leisure and other goods is zero, in which case a uniform tax is optimal. Therefore, the estimated demand systems include Swedish consumption goods and leisure time.

The paper is organized as follows. The next section gives a brief introduction to the theory of consumer demand and some of the problems that occur in this type of exercise. The third section discusses the problems of specifying the demand system, which in this case is a dynamic version of the AIDS model. The fourth section gives a detailed description of the data and how the treatment of leisure time is done. The …fth section gives the main empirical results, while detailed tables can be found in the Data appendix. The last section gives the conclusions.

2 Theory of consumer demand

A general description of the consumer’ decision problem is given in the life cycle hypothesis. There, the consumer maximizes expected discounted utility from a bundle of consumption goods and services as well as leisure time - given an intertemporal budget constraint. With many goods and services and demand dependent on many expected future discounted prices this problem becomes very complex and di¢ cult to handle in empirical applications. Various assumptions have to be done in order to keep the problem manageable. Rather than starting from the most general and compley theory, here the most simple static model is used but extended with some dynamics. This is one of the ways in which the

1 See Christensen, Jorgensen and Lau (1979).

2 See Deaton and Muellbauer (1980).

3 See Atkinson and Stiglitz (1980), p. 369.

4 The compensated price elasticity of demand for good i with respect to a change in the

p j

@ q i

price of good j is de…ned as " ij =

, where q i
belongs to a bundle of goods,
q
, which

@p j
q
i

gives the same utility as before the price change, i.e.

0
):

u(q ) = u(q

1

p j q j

P p i q i

@x q i

development has proceeded in the literature 5 .

Generally, the consumer maximises the expected utility

T t

X

max (1 + r) (1+ ) E t fu(q t+ )g
(1)

=0

subject to an intertemporal budget constraint

A t+1 = A t + ! t h t p t q t
(2)

where the horizon is from t to T, r is the real rate of interest, is the rate of time preference, E is the expectations operator, u is the utitilty function, A t is wealth at time t, ! t is the wage rate, h t is the number of hours worked, p t = p 1t ; :::; p nt is a vector of prices and q t = q 1t ; :::; q nt a vector of quantities. Assuming intertemporal separability, and for convenience dropping the time subscript, the problem can be stated

X

max u(q) subject to x =
p i q i
(3)

where x is total expenditure. The solution to this problem gives the Marshallian demand functions q i = g i (x; p). If these demand functions are substituted into the direct utility function u(q) the indirect utility function u = '(x; p) is obtained. The indirect utility function shows the highest possible utility that can be attained for alternative prices and total expenditure. The dual problem is to minimize the total expenditure required to obtain a given utility level, which can be stated as

min x = pq
(4)

subject to

u = v(q)
(5)

The solution to this problem gives the Hicksian demand functions as q i = h i (u; p) which may simply be derived as the partial derivative of the cost function x = c(u; p) w.r.t. p i . The cost function shows the minimum cost to obtain utility level u at prices p. Substituting the indirect utility function (which is the inverse of the cost function) into the Hicksian demand functions gives the Marshallian demand functions. In this paper the dual approach to obtain the demand functions is used.

The total expenditure elasticity is de…ned as E i = @q i x and shows the percentage change of the demand for good i following a one percentage change in total expenditure (often also referred to as the income elasticity). Letting

w i = denote the budget share of the i-th good we have the general

P

property that w i E i = 1: The uncompensated 6 price elasticity of demand is

de…ned as e ij = @q i p j and shows the percentage change of the demand for good i

@p j q i

following a one percentage change in the price of good j. For i = j we refer to the own-price elasticity and for i 6= j to the cross-price elasticity. Another general

5 See Deaton and Muellbauer (1980b) and Edgerton et al (1996) where various dynamic versions of the AIDS model were developed.

6 Uncompensated implies that the consumer is not compensated for the loss in income induced by a price increase.

2

P

property is that j e ij + E i = 0: Finally, the compensated 7 price elasticity is

s

de…ned as e ij = e ij + w j E i which shows the percentage change of the demand for good i following a one percentage change in the price of good j - at constant utility.

2.1 Static and dynamic model

The consumer’ decision problem with respect to both consumption goods and leisure is dynamic and is probably best analysed within the life-cycle model framework. The literature using aggregate data however tend to divide the problem into a dynamic optimization problem about aggregate consumption and a (more or less) static optimization problem about the allocation between di¤erent consumer goods. Once leisure - or labor supply - is considered the problem is clearly a dynamic one. Typical for the aggregate consumption problem is the constant marginal utility condition governing the Euler equations in this area. This condition can also be used for the allocation of the individual

consumption items, i.e. the demand functions could be stated in terms of marginal utility as q i = h i ( @u @c ; p) , as in Blundell et al (1994). However, here we

follow the simpler route and introduce simple dynamics in an otherwise static framework.

Particular problems also arise in the context of durable goods, i.e. goods which are not consumed within the data period one quarter of a year. The consumption of Housing is for rental apartments estimated as rents in nominal and …xed prices, while for owner-occupied housing a rental equivalent is computed. However, capital gains are not included. For other durables like vehicles, household equipment, etc. consumption is estimated as purchases in current and …xed prices. Some studies have chosen to exclude durables and some to include them as here. In this study durables measured as purchases account for approximately 8-9 percent of total expenditure including Leisure.

2.2 Utility tree and multi-stage budgeting

The number of goods available to the consumer and the number of observations present in the data obviously poses a problem, particularly to the researcher occupied with time-series data. At the most there are about 90 observations available in this study (75 for the data up to 1998). This put a restriction on the number of goods that can be included. A system with 10 goods to be estimated with FIML has 10 10+20=120 free parameters to estimate without any dynamics. Various +restrictions therefore must be imposed on the systems in order to make estimation possible. Restrictions like Slutsky symmetry clearly helps to some extent. A more radical approach is the idea of multi-stage budgeting, a procedure previously dealt with in the literature 8 . Consider a two-stage budgeting process in which the consumer is supposed to decide in two di¤erent stages. The …rst stage considers n groups of goods, r=1,...n and in the second stage the r th group consists of i=1,...,m goods. Then the consumer’ preferences

7 Compensated implies that the demand is calculated at the point where the consumer is compensated for the loss in income induced by the price change so that the utility is the same as before the price change. The compensated demand hence measures the pure price e¤ect.

8 See Gorman (1959), Pollak (1971), Deaton and Muellbauer (1980a, Ch. 5.2), Pudney (1981), Varian (1982), Laisney (1991) or Edgerton et al.(1996).

3

are said to be weakly separable if they can be represented by a utility function of the form

u = f [v 1 (q 1 ); :::; v n (q n )]
(6)

where q r represents the vector of quantities in the r th group. Utility maximization now means maximizing the functions v r (q r ) separately, using the standard tools of demand analysis but replacing total expenditure by group expenditure x r : The Marshallian demand functions now can be written

q ri = g ri (p 1 ; :::; p n ; x r )
(7)

P

where p r denotes the price vector of the r th group and x r = i p ri q ri is the total expenditure of the group. The …rst stage allocation of total expenditure into group expenditure is a problem since the price vectors p r must be replaced by some price indices p r : Deaton and Muellbauer (1980a) show that an approximation exists such that the demand function above can be replaced by

Q r = g r (P 1 ; :::; P n ; x)
(8)

where Q r is a quantity index - or expenditures expressed in constant prices - and P r a price index, where the latter could be an approximation to a true cost of living index. Though the assumption of weak separability means that one can study the consumer’ optimization problem at separate stages it has implications for the e¤ect of a price change on a certain group belonging to group r on the demand for another good belonging to another group s. In addition, the expenditure elasticity depends both on the …rst stage elasticity and the elasticity within the group at lower stages of the budgeting process. If a price of a particual good increases it will a¤ect the demand for all goods in the group to which the good belong. But the price index of the group - P r - is also a¤ected and hence the demand for all other goods belonging to groups outside r. The relationships are uncovered in Edgerton (1992, 1993) and Edgerton et al (1996, p. 71-72). If q ri is expenditure in constant prices and p ri the implicit price derived by dividing expenditure in current prices with expenditure in constant prices then the price index can be written

P r =
c(u; p r )

c(u; )

where is the unit vector, x r = P r Q r , x =
r x r

substitution we obtain the Marshallian demand
as

P

(9)

P

and Q r = i Q ri . By

q ri = g ri [p r ; P r g r (P 1 ; :::; P n ; x)] = g ri (p 1 ; :::; p n ; x):
(10)

Following Edgerton et al (1996) and using the de…nitions E (r)i for the within group expenditure elasticity, E (r) for the group expenditure elasticity, and E i for the total expenditure elasticity and similarly for price elasticities - e ij for the

uncompensated and e ij for the compensated price elasticity - and budget shares we obtain the following de…nition of elasticities:

E i
= E (r) E (r)i
(11)

e ij
= rs e (r)ij + E (r)i w (s)j ( rs + e (r)(s) )

= rs e ij + E (r)i w (s)j e (r)(s)

e ij
= rs e (r)ij
+ E (r)i w (s)j e (r)(s)

4

where rs = 1 for r=s and zero otherwise 9 . How should these de…nitions be interpreted? The expenditure elasticities are straightforward. The price elasticity is composed of two parts which can be labelled the direct and indirect e¤ects. The direct e¤ect - rs e (r)ij - is the within group price elasticity measured in the usual way. The indirect e¤ect measures how much the price change of a certain good a¤ects the allocation among groups. It depends on the three factors

E (r)i - the within group expenditure elasticity

w (s)j - the budget share of the good which price changes and rs + e (r)(s) - the price elasticity between groups r and s

The …rst factor measures the e¤ect of the change in group expenditure (due to the price change) on the expenditure on the i th good. The second factor measures the relative change of the group price index caused by the change of the price of the i th good, which is measured by the budget share of the price changing good. The third factor measures the e¤ect on the demand for group r - on Q r - of a change in the price index of group s - of P r .

Note that if the latter own price elasticity equals -1 the elasticity collapses to e ij = e (r)ij . On the other hand, if e (r)(r) = 0 then the price change implies a

proportional change in the expenditure of the group and e ij = e (r)ij : Note also that the total price elasticity is well approximated by the within group price elasticity if the within group budget share of the price changing good is small or within group expenditure elasticities are small.

3 Speci…cation of demand system

The estimation of elasticities requires a speci…cation of the demand model. Several alternatives exist in the literature. In Edgerton et al (1996) di¤erent speci…- cations are evaluated empirically. The …nally chosen model is the AIDS (Almost Ideal Demand System) model which is commonly applied in the empirical literature.

3.1 The AIDS model

The AIDS uses the time period t cost function

Y

X
1
XX

log c(u t ; p t ) = 0 + k log p kt +

log p kt log p jt +u
0
p k
(12)

2
kj

kt

k
k j

k

where u is the utility level, p is a price vector, p kt is the price of the k-th good. If prices are normalised to unity (12) collapses into 0 + 0 . u then can be seen as an index of utility, 0 u 1 , where for u = 0, 0 can be seen as the cost of subsistence while for u = 1, 0 + 0 can be seen as the cost of bliss.

As described in section 2, taking the partial derivative w.r.t. the k-th price gives the Hicksian demand for the k-th good, which upon substitution of the indirect utility function gives the Marshallian demand as

9 rs is the so called Kronecker’s delta.

5

w it = i + X j
ij log p jt + i (log x t log P t )

where P
= 0
+
k
k log p kt + 1
k j

kj
log p k log p j :
kj
= 1

t

2

2
ij

and w it =
p it q it

the budget share for the i-th good.

p jt q jt

P

(13)

+ ji

3.2 Linear AIDS

A linear version of the AIDS model was suggested by Deaton and Muellbauer (1980) where the price index P t was replaced by the index

X

P t = 0 + w kt log p kt
(14)

k

This approximation has become very popular in the literature. Here, both linear and nonlinear versions have been used. Though the linear version of AIDS has proven accurate in a number of studies 10 I have …nally chosen the nonlinear version. The additional computational burden is small and the results not particularly sensitive to the a priori choice of the parameter 0 . 11 . The linear version was evaluated here but it was the nonlinear version that was …nally chosen.

3.3 Dynamic AIDS

The simplest static model is not likely to perform well with time series data. Di¤erent dynamic versions of the model have been used in the literature. A

dynamic demand system suggested by Assarsson (1991), Alessie and Kapteyn (1991) and Kesavan et al (1993) can be derived from a dynamic form of the cost function. Using the principle of demographic translation, as suggested by Pollak and Wales (1981), results in demand functions

X X

w it = i + ij w jt 1 + ij log p jt + i (log x t log P t ) (15)

j j

where

0

X

1

X

XX

(16)

P

X @

A

1

=
0
+

k
+

kj
w
jt 1

+

k
log p
kt
+

kj
log p
k
log p
j

t

k

j

k

2
k j

This type of system was evaluated here and short and long run elasticities

were derived. The restriction

k kj
=
j kj
= 0 was used, where the …rst

10

Alston et al (1994),Buse (1994) or Edgerton et al (1996).

See for example Chalfant (1987), P

P

11 The parameter 0 was set to 30 percent of the log of total expenditure in 1995, the base year in which prices was normalised to unity.

6

sum implies adding-up and the second identi…cation. The restriction kj = jk , for all k,j, was rejected and the further restriction that is diagonal, was also rejected in this particular speci…cation.

3.4 AIDS in error correction form

Another alternative, which was …nally chosen, is the error correction form, which has become very popular recently and seems to …t the data well. It allows both short term and long term as well as feedback responses to be estimated and it can be derived from the basically static AIDS framework through the method of demographic translation. The long run equilibrium can be desribed by (13) above and the error correction form as

w

=
X j { ij log p jt + ' i
log(x=P ) +

(17)

it

1

t
X j
ij it 1

where P t

X

XX

(18)

=
0 + k log p kt +

kj log p k log p j

k

2
k
j

kj
=
1
ij + ji

(19)

2

and it 1
=
w it 1 i X j
ij log p jt 1 i (log x t 1 log P t 1 )(20)

The matrix should be restricted in order for the system to be theoretically

consistent. In particular, it is su¢ cient if i ij =
j ij = 0 for adding up and

be coherent (and possible to estimate

identi…cation to hold. For the system to P
P

e.g. with Full Information Maximum Likelihood) parameters have to be further restricted. Di¤erent speci…cations were tested and the …nally chosen system is a restricted version which allows six commodity groups to be included. The preferred speci…cation use a single scalar as the error correction term. The model can be rewritten in level form as

w it = i + X j { ij log p jt + ' i log(x=P ) t + (1 + )w it 1 +

X j ij log p jt 1 + i log(x=P ) t 1
(21)

which can be derived from the AIDS expenditure function (12) by translating the parameter i into

i = i + (1 + )w it 1 + X j kj log p jt 1 + i log(x=P ) t 1
(22)

and the long run parameters be derived as

ij
=
{ ij + ij
;
i
=
' i + i
:
(23)

This is the speci…cation …nally used for estimating the elasticities and can be viewed as a compromise which on the one hand saves parameters through

7

various restrictions derived from economic theory but on the other hand is ‡exible enough to allow for the most important dynamics.

3.5 Elasticities

The long run elasticities in the model are then given by (22) - (26):

l

i

E i
=
1 +

w i

l

ij

i
j +
2 1
k kj + jk

log p k

e ij
=

P w i

ij

e l ij
= e ij l + w j E i l

and the short run elasticities by (27) - (29):

s

' i

E i
=
1 +

w i

s

{ ij

' i
j + 1
k ({ kj + { jk ) log p k

e ij
=

2
P w i
ij

s
=
s

s

e ij
e ij
+ w j E i

(24)

(25)

(26)

(27)

(28)

(29)

where ij is Kroneckers delta. Seasonal dummies are included in the estimations but for simplicity have been excluded in the formulas above.

Note that the short run elasticities are not directly identi…ed due to the loss of the constant term in the di¤erence form. The parameter i is interpreted as the budget share for a household at the subsistence level and is identi…ed in the derivation of the long run elasticities. The short run elasticities are identi…ed by assuming that i in the short run is equal to the long run value.

4 Data

The data used is quarterly national accounts running from 1980-2003. For the period 1980-1998 data are from the old SNA de…nitions and the base year is 1991. For the period 1993-2003 data are based on the latest SNA de…nitions and comply better with international accounting systems. The de…nitions in some commodity groups are quite di¤erent and it has not been possible to adjust the data for the earlier period so that it completely matches with data for the later period. However, the best possible revisions were done and the data for the earlier period linked with the later period to give a longer data series. The series were then used in the estimations and compared with estimations run for the period 1980-1998. It turned out that the estimates with the consistent data series for 1980-1998 were more reasonable, both in terms of …t and theoretical consistency 12 .

12 Compensated own-price elasticities were negative and the goodness of …t were better for most equations. It could not be ruled out that this result were due to the inability to consistently link the old with the new series. Hence, the older but longer series was chosen.

8

4.1 Utility tree and speci…cation of categories

With quarterly data for the period 1980-1998 there are 76 observations. The static AIDS model with seasonal dummies and no theoretical restrictions implies 40 parameters in a system with 5 goods and 135 parameters in a system with 10 goods. Hence, it is clear that the dimension of the system must be kept small. With the dynamic speci…cation, 6 goods appear to be the limit, but the theoretical homogeneity and symmetry restrictions were applied and the dynamics kept simple.

The design of the two-stage budgeting system is governed by the demand from the public inquiry (Mervärdesskattesatsutredningen). It takes account of the design of the present system of the VAT system in which some goods are exempted, and tax rates vary across di¤erent commodities and services. Some a priori considerations are also done and some aggregation as done by Statistics Sweden in the SNA is kept here. Some di¤erent aggregations were tried and in particular estimates where some groups tend to have positive ownprice elasticities were avoided. The aggregation …nally considered is

Table 1. Goods in two-stage budgeting system

1
Food, beverages, and health care
1_1
Food including light beer

1_2 Alchohol and tobacco

1_3
Restaurant

1_4
Health care

2
Housing, fuel, and furniture
2_1
Housing, fuel, and furniture

3
Household and personal care
3_1
Clothing and shoes

3_2
Household utensils

3_3 Post and telephone

3_4
Hotels

4
Transports, vacation travel
4_1
Vehicles including fuel

4_2
Transports

4_3 Foreign travel and consumption

4_4 Recreation including cultural activities

5
Miscellaneous goods and services
5_1
Goods for recreation

5_2
Games

5_3 Books and magazines

5_4
Miscellaneous goods

5_5
Insurance

6
Leisure
6_1
Leisure

with budgeting in two stages. The …rst-stage has 6 goods and the second stage betweem one and …ve goods in each category. Leisure is obviously a single good and the good with largest budget share. We now turn to its measurement, which is an important issue.

4.2 The measurement and treatment of leisure

Suppose the n-th good in the system of demand equations above is leisure time, such that p n is the price of leisure and q n the number of leisure hours. The

budget share of leisure then is w n = Pp n q n : The price of leisure has been

j p j q j

9

measured as the wage rate less the average marginal tax rate 13 . The budget restriction then can be written

X n 1

p i q i = p n h + A;
(30)

i=1

where p n h is labor income, h is the total number of hours worked and A is non-labor income 14 . The budget restriction can be rewritten by taking account of the time restriction T = ml + z + s + n + q n , where T is the total number of hours available, ml = h is total numbers of hours, where m is mean hours and l the number of employed. z is the number of hours used for home production, s is the number of hours used for labor search, n is the number of subsistence hours and q n is leisure time. The budget restriction then becomes

X n

i=1 p i q i = p n (T ml z s n) + A M
(31)

where M usually is referred to as full or potential income 15 . The problem then is how to estimate leisure time. The daily budget for an individual consumer could simply be determined as (24-h-0-0-8), the number of total hours less the number of hours worked less the assumed 8 hours used for sleeping 16 .

The number of daily hours is then aggregated to the total number of quarterly leisure hours for the adult population, b. The conversion factor from daily to quarterly hours is , the number of days each quarter. These have been estimated as the number of ordinary working days, i.e. …ve days for an ordinary week and also exclusive of all "red" days. The simplest measure of the total number of quarterly leisure hours is therefore (24 8) b ml. However, we also assume that some of the time of the unemployed is used for home production and labor search. If the the number of unemployed persons are labelled u, then the labor force is l + u and we assume that 1 mu hours is used for home production and labor search. Similarly, we assume that the elderly - or the adult population outside the labor force - use some time for home production and labor search, which is 2 m(b (l + u)). Finally, there is the number of subsistence hours, which are related to sleeping, eating and for some health care, etc. which are di¢ cult to determine. We denote this by bn. The total number of quarterly leisure hours then can be determined as

24 b ml 1 mu 2 m(b (l + u)) nb
(32)

where the respective terms are

13 The hourly compensation paid by employers have been obtained as the total compensation divided by the total number of hours worked, as described in the National Accounts. The data on average marginal tax rates have been obtained from Gunnar du Rietz, Ratio. The relative

wage
(1 t 2 )

1 t 2

1 t 2

price of leisure is determined by
(1+t 1 )
= wage

= p n where

p f (1+t 3 )

p f
(1+t 1 )(1+t 3 )
p i
(1+t 1 )(1+t 3 )

is the total tax wedge., where wage is the compensation paid by the employer, t 1 is the payroll tax rate, t 2 is the income tax rate and t 3 is the indirect tax rate. All prices in this study are measured including indirect taxes and wages excluding payroll taxes. The price on leisure is therefore simply the wage rate net of the average marginal tax rate.

14
The simplest formulation would be to use the budget restriction
P
n

i=1 p i q i = p n T + A;

for T = h + q
n
:

15

See Dowd (1992) or Madden (1995) for similar treatments.

16 An alternative would be to measure non-labor income as is done by Dowd (1992). He measures A as the di¤erence between private disposable income and labor income and sets

T = 24.

10

24 b= the total number of hours available ml= the number of hours worked

1 mu= the number of hours worked in home production and labor search by those unemployed

2 m(b (l+u))= the number of hours worked in home production and labor search by those outside the labor force

nb= the number of subsistence hours worked in home production, sleeping, etc. by the adult population

The formula can be simpli…ed to

(24 n) b m [l 1 u 2 (b (l + u))]
(33)

Data are available on all variables less i and n, for which some assumptions are necessary. The basic assumption is ( 1 = 0:5; 2 = 0:2; n = 12). For a fully employed person this means that the daily leisure time is (24-12-8=4) hours, for an unemployed person it is (24-12-4=8) hours and for a pensionist (24-12-1.6=10.4) hours. As alternatives in a sensitivity analysis we also use 1 = 0:4&0:6; 2 = 0:1&0; 3; n = 11&13, a total of 27 combinations. On the whole, elasticities were not very sensitive to this choice. The …nal choice was done on a judgemental basis in which the requirement of theoretically correct signs on the parameters was the most important.

5 Empirical results

5.1 Estimated equations

The empirical results are presented extensively in the data appendix. Here some summary results from the estimations are presented. In general the goodness of …t of the estimated equations are satisfactory, which can be seen in Table 2.

11

Table 2. Summary statistics for estimated demand systems.

2
Mean of
Standard error
p-value in

System
dep. var.
of regression
autocorrelation test

R

Stage 1: 1
0.97
0.15
0.0036
0.08

2
0.95
0.16
0.0037
0.31

3
0.95
0.08
0.0029
0.08

4
0.70
0.11
0.0060
0.08

5
0.94
0.07
0.0031
0.63

6
0.97
0.43
0.0065
0.68

Group 1: 1_1
0.90
0.65
0.0077
0.01

1_2
0.79
0.18
0.0059
0.36

1_3
0.78
0.14
0.0088
0.02

1_4
0.96
0.03
0.0016
0.18

Group 2: 2_1
0.95
0.16
0.0037
0.31

Group 3: 3_1
0.55
0.47
0.0130
0.11

3_2
0.41
0.40
0.0093
0.11

3_3
0.79
0.11
0.0057
0.29

3_4
0.91
0.03
0.0010
0.14

Group 4: 4_1
0.89
0.56
0.0127
0.82

4_2
0.68
0.11
0.0043
0.05

4_3
0.85
0.23
0.0130
0.19

4_4
0.96
0.10
0.0031
0.13

Group 5: 5_1
0.92
0.42
0.0098
0.03

5_2
0.89
0.11
0.0064
0.11

5_3
0.98
0.14
0.0050
0.07

5_4
0.72
0.25
0.0067
0.00

5_5
0.92
0.08
0.0034
0.04

Group 6: 6_1
0.97
0.43
0.0065
0.68

The …rst column shows the goodness of …t of the individual equations in

2

each system. In stage 1 R for all equations except Transports are around 0.95. For Transports it is 0.70. The second column shows the mean of the dependent variable revaling that the mean of the budget share of goods consumption for 1980-1998 is 57 percent while for leisure it is 43 percent. The percentage standard error (of the regression) is around 0.35 for all goods except Transports for which it is 0.6 percent. For leisure the standard error is 0.65 percent. The fourth column of Table 2 shows tests for autocorrelation in the individual equations. This test is done by running an unrestricted VAR with 2 lags on the estimated residuals of the systems. The number of observations times R 2 is then treated as chi-square distributed with degrees of freedom equal to the number of variables on the right-hand side of each equation, i.e. a LM test 17 . The autocorrelation tests show no sign of autocorrelation in the six equations in Stage 1.

Turning to Stage 2 it can be noted that the …t is generally somewhat lower. In Group 1 Food is the biggest category, accounting for 65 percent within the

group and totally (0.65 0.15) 100 = 9.8 percent with a 0.8 percent standard

2

error. The R = 0:9 for Food but there is some autocorrelation in this equation.

17 See Engle (1984).

12

However, the other equations in Group 1 show no sign of autocorrelation so that autocorrelation in the group as a whole can be statistically rejected.

The …t of the Housing - Group 2 - equation is 0.95 and the standard error is 0.4 percent. The budget share is 16 percent, 28 percent of total consumption (less leisure). In Group 3 autocorrelation is rejected in all equations. However, the …t is rather poor in this group. In Group 4 there is autocorrelation in 4_2 - Transports. The …t is rather poor in this category - 0.68. Finally, in Group 5 there is autocorrelation in three of the …ve groups: 5_1, 5_4 and 5_5, while there is no sign of autocorrelation in the aggregate as revealed in the equation for Group 5 in the Stage 1 estimation.

5.2 Estimated elasticities

Estimated elasticities are presented in the data appendix. Here, some summary results are presented. In Table 3, the total elasticities de…ned in (11) are shown. The within-group elasticities - also de…ned in (11) - are presented in the data appendix.

Table 3. Total long run compensated own-price and total expenditure elasticities. Estimated at mean values for the period 1994-1998.

Compensated
Total expen-

own-price
diture

Item
elasticity
elasticity

Food including light beer
-0.36
0.55

Alchohol and tobacco
-0.88
0.58

Restaurant
-0.43
0.96

Health care
-0.36
0.53

Housing, fuel, and furniture
-0.28
0.21

Clothing and shoes
-0.26
2.61

Household utensils
-0.31
2.65

Post and telephone
-0.72
1.80

Hotels
-0.52
2.29

Vehicles including fuel
-1.87
2.30

Transports
-1.39
2.99

Foreign travel and consumption
-1.56
5.40

Recreation including cultural activities
-1.57
2.93

Goods for recreation
-1.19
2.35

Games
-1.30
1.83

Books and magazines
-1.55
1.94

Miscellaneous goods
-0.79
1.69

Insurance
-0.80
4.62

Leisure
-0.09
0.49

All compensated own-price elasticities are negative and all total expenditure elasticities are positive. Food, Housing and Leisure are necessities and all other goods luxuries. Price elasticities are relatively low for necessities and relatively high for luxuries which is in line with the intuition. The demand is price inelastic for all goods belonging to the …rst three groups of Stage 1 and for Miscellaneous goods, Insurance and Leisure. It is elastic for Travel and recreation and for

13

Books and magazines. The VAT on books were recently reduced from 25 to 6 percent which eventually would lower prices by some 15 percent and consequently increase demand by almost 25 percent in the long run (the compensated own-price elasticity is -1.55). However, notice in Table 4 below that the short run elasticity is only -0.15.

Table 4. Total short run compensated own-price and total expenditure elasticities. Estimated at mean values for the period 1994-1998.

Compensated
Total expen-

own-price
diture

Item
elasticity
elasticity

Food including light beer
-0.34
0.30

Alchohol and tobacco
-0.40
0.59

Restaurant
-0.62
0.82

Health care
-0.62
0.38

Housing, fuel, and furniture
-0.16
0.23

Clothing and shoes
-0.82
1.50

Household utensils
-1.19
1.37

Post and telephone
-0.64
1.27

Hotels
-1.21
1.22

Vehicles including fuel
-0.88
2.16

Transports
-0.72
0.80

Foreign travel and consumption
-1.09
0.84

Recreation including cultural activities
-0.35
1.00

Goods for recreation
-1.68
1.18

Games
-0.99
0.92

Books and magazines
-0.15
0.98

Miscellaneous goods
-1.27
0.85

Insurance
-0.65
2.32

Leisure
-0.09
1.23

Table 4 shows the corresponding short run elasticities. These are the direct e¤ects of changes in prices and total expenditure, i.e. that occur within a quarter. In most cases the absolute value of the elasticity is smaller in the short than in the long run. This supports the interpretation of adjustment costs or habit formation in the demand for these goods. This applies to all total expenditure elasticities except Leisure for which the short run elasticity is 1.23 - a luxury - while being only 0.49 in the long run - a necessity. The short run compensated own-price elasticities are abolutely higher than the corresponding long run elasticities for 8 of the 19 goods, i.e. for all goods in Group 3.

Why would the short run elasticity overshoot and exceed the long run elasticity? This would likely occur for goods where demand is very ‡exible and the degree of habit formation low. These e¤ects are particularly strong for Clothing and shoes, Household utensils, and Hotels. For these categories the response to a change in the relative price has a large immediate e¤ect but declines in the long run. For the categories Housing, Transports and Miscellaneous the initial response is instead relatively small but increases to reach a peak at the long run value.

14

Figure 1. Short and long run own-price elasticities at temporary and permanent price changes.

We can distinguish not only between long and short run elasticities but also between the response to temporary and permanent changes in prices and total expenditure (full income). In Figure 1 the dynamic response to relative price changes are shown. The charts show the own-price elasticities as a response to temporary and permanent changes in relative prices 18 . The elasticities in the …gure converge to the long run uncompensated own-price elasticities estimated

18 The shocks are one-percentage shocks in the relative prices in the …rst quarter in 1994 and the responses are measured as the percentage change in demand and shown for the remainder of the sample period (elasticities).As can be seen in the charts, the long run e¤ects are reached within approximately 2 years.

15

in Stage 1 and given in Table B1 in the data appendix. A temporary price change has a temporary demand e¤ect which lasts for about 2 years. The overshooting property can be seen particularly for Household and personal care and Leisure. The response which could be expected due to the presence of adjustment costs can be noticed in particular for Housing, fuel and furniture, Transports and vacation travel and Miscellaneous goods and services.

The elasticities also vary over time due to variations in budget shares, prices and full income, as apparent from the de…nitions of elasticities in (22) - (29). These variations are illustrated in Figures 2 and 3 which show long run compensated own-price elasticities and total expenditure elasticities, respectively.

As can be seen in Figure 2 the long run compensated own-price elasticities are all negative and fairly stable during the sample period. For some categories there seems to be a shift in the beginning of the 90ie. In absolute terms, the elasticity decreases for Food and Household and personal care and increases for Transports, Miscellaneous and Leisure. For Food and Household and personal care the elasticity decreases from approximately -0.4 to -0.25 while for Miscellaneous goods and services the elasticity decreases from about -1.6 to -2.1. The labor supply elasticity is low but become more elastic during the sample period and increases from about 0.05 to 0.1. This could be due to the tax reform in the beginning of the 90ies which shifted taxes from labor to goods. We tried to include a dummy for the period before 1990 but it was not statistically signi…cant.

In Figure 3 the long run total expenditure elasticities are shown. They are all positive and lowest for the Food, Housing and Leisure categories. The elasticity drops from about 0.75 to 0.6 for Food, increases from .1 to .2 for Housing and from .4 to .5 for Leisure. Though the elasticities vary they are fairly stable during the sample period.

5.3 Labor supply elasticities

The responses shown in Figure 1 indicate that the initial labor supply response is quite large but declines in the long run. The short run uncompensated response is about -.6 while in the long run the elasticity is about -.4. The compensated response is quite lower - around -.09. The relatively high short run …gures may be interpreted as a response in hours to temporary changes in demand with a corresponding change in compensation. In many occupations this increase in compensation may be more or less automatic (and negotiated) and hence both wages and labor supply become ‡exible with respect to excess demand in the short run. These results are in line with what previously have been found by Blomquist (1983) and Blomquist and Hansson-Brusewitz (1990) for Swedish household data on mens’and womens’labor supply 19 .

It is interesting to compare the results for demand systems with and without Leisure, since the measurement of Leisure in itself seems uncertain. We do that by estimating the Stage 1 demand system with and without Leisure. The results are presented in Table 5.

19 Surveys of labor supply are Pencavel (1986) and Killingsworth and Heckman (1986).

16

Table 5. Comparison of uncompensated price

and total expenditure elasticities with and without Leisure in Stage 1. At mean values 1994-1998.

1
2
3
4
5
6

1
-0.34
-0.12
-0.25
-0.15
0.53
-0.28

-0.44
-0.01
0.09
0.19
0.17

2
-0.07
-0.31
-0.29
0.07
0.05
0.33

-0.00
0.08
-0.15
-0.03
0.11

3
-0.54
-0.87
-0.45
0.53
0.15
-1.28

0.25
-0.27
-0.67
0.21
0.47

4
-0.30
-0.10
0.31
-1.84
0.11
-1.37

0.34
0.13
0.15
-0.42
-0.19

5
1.09
0.04
0.18
0.23
-2.12
-1.70

-0.01
-0.13
0.82
0.25
-0.93

6
-0.13
-0.07
-0.00
0.11
-0.08
-0.32

x/P
0.62
0.21
2.47
3.19
2.27
0.49

0.45
0.53
1.45
1.80
1.50

First, the classi…cation of necessities and luxuries are the same 20 , though the total expenditure elasticities are higher particularly for the groups 3, 4, and 5. This depends on Leisure being classi…ed as a necessity with a large budget share. Own-price elasticitities are all negative in the system with Leisure but 2 - Housing, fuel and furniture - has a positive, but insigni…cant, elasticity in the system without Leisure. Own-price elasticities for groups 4 and 5 are more elastic in the system with Leisure. Notice also that the high positive crossprice elasticity between 5 and 1 - 1.09 - is -0.01 in the system without Leisure. Another high cross-price elasticity in the system with Leisure is between 3 and 2 - -0.87 - which is lower, -0.27, in the system without Leisure.

5.4 Comparison with previous results

The results are compared to previous empirical results in Table 6. The table is incomplete and only presents a small sample from the literature. Generally, it seems as if the elasticities estimated here are fairly reasonable.

20 Note however that strictly the classi…cation should be done with respect to the compensated elasticities.

19

Table 6. Comparison of uncompensated price and total expenditure elasticities estimated in di¤erent models in Stage 1.

1
2
3
4
5
6

1
-0.34
-0.12
-0.25
-0.15
0.53
-0.28

a
-0.54

-0.01
0.27
0.23

b
-0.32

c
-0.45

d
-0.65

e
-0.20

2
-0.07
-0.31
-0.29
0.07
0.05
0.33

a

b

-0.15

d

-0.7

3
-0.54
-0.87
-0.45
0.53
0.15
-1.28

a
-0.64

-0.81
0.04
0.48

b

-0.57

c

-0.96

4
-0.30
-0.10
0.31
-1.84
0.11
-1.37

a
-0.04

-0.14
-0.71
-0.44

b

-0.34

c

-1.09

5
1.09
0.04
0.18
0.23
-2.12
-1.70

a
-0.18

-0.04

-0.90

c

-1.62

6
-0.13
-0.07
-0.00
0.11
-0.08
-0.32

c

-0.06

x/P
0.62
0.21
2.47
3.19
2.27
0.49

a
0.27

0.04
1.57
1.58

b
0.37

0.75
0.44

e
0.96

Note. a) Anderson and Blundell (1983)

b) Blanciforti and Green (1983)

c) Kaiser (1993)

d) Pollak and Wales (1992)

e) Assarsson (1996)

The own-price elasticities for Food and Housing are similar to those found in other studies. This is true also for Household and personal care though this category is probably not directly comparable with other studies. The Transports and Miscellaneous categories turn out to be relatively elastic here with the elasticities -1.84 and -2.12 respectively, which can be compared to the next highest which are -1.09 and -1.62 in Kaiser (1993). Again, these categories may not be directly comparable.

The total expenditure elasticity for Food is in line with other studies while those for Household and personal care, Transports and Miscellaneous seem to be relatively high here. Again, this is not quite comparable to the results in other studies since most of them use total expenditure less the consumption

20

value of Leisure, while here full income is used.

6 Summary and conclusions

This paper has analysed the demand for consumer goods and services as well as the demand for leisure in a simultaneous equations model for Swedish aggregate time series data. The usual weak separability assumption between leisure and consumption goods has not been adopted here. A dynamic version of the Almost Ideal Demand System in error correction form has been estimated and price and total expenditure elasticities for consumption goods and leisure have been estimated simultaneously. All goods and leisure have been divided into 19 categories in a two-stage budgeting process in which the …rst stage comprises 6 categories of which Leisure is one.

The price of leisure time is estimated as the wage rate net of the average marginal tax rate. The estimate of ’full’income is then conditional on the measurement of leisure time which is subject to a sensitivity analysis in which the number of hours used for home work and labor search is varied across di¤erent population groups.

Even if weak separability is assumed when demand is estimated within the di¤erent consumption categories there are relationships beween the categories that can be explored. This is done here and within-group elasticities as well as total elasticities are estimated. Estimations are carried out with the dynamics speci…ed as an error correction model. Homogeneity as well as symmetry restrictions are imposed. Restrictions are also imposed on the dynamic speci…cation in order to arrive at a coherent system. A weak test of weak separability is done in the form of Hausman-Wu tests for simultaneity bias. Tests for autocorrelation is also carried out. Equations - in budget share form - are with some exceptions estimated with good …t and the elasticities turn out with the correct signs and with reasonable precision. All long run as well as short run compensated as well as uncompensated own-price elasticities are negative and all total expenditure elasticities are positive. Categories classi…ed as necessities with total expenditure elasticities less than one have generally lower price elasticities than luxury goods, as is usually the case also in other studies. Necessities are typically Food and Housing. On the other hand, categories like Travel or Books are classi…ed as luxury goods and have long run compensated price elasticities well above minus unity.

The price elasticity for Leisure is the labor supply elasticity (with opposite sign). The long run compensated labor supply elasticity is here 0.1 which is in line with previous estimates for Swedish households on micro data. The short run elasticity is higher than the long run elasticity which might re‡ect strong short run intertemporal substitution.

In the context of optimal taxation the cross-price elasticities are interesting, especially those between Leisure and the various consumption goods. Generally, these elasticities use to be estimated with much less precision than the own-price elasticities and this is the case here also. Most of the cross-price elasticities are fairly close to zero with some notable exceptions.

21

References

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23

Data appendix

Table
Type of elasticity
At value

A1
Long run uncompensated price elasticities
Mean

Long run total expenditure elasticities
Mean

A2
Long run compensated price elasticities
Mean

A3
Long run uncompensated price elasticities
1994-1998

Long run total expenditure elasticities
1994-1998

A4
Long run compensated price elasticities
1994-1998

A5
Short run uncompensated price elasticities
Mean

Short run total expenditure elasticities
Mean

A6
Short run compensated price elasticities
Mean

A7
Short run uncompensated price elasticities
1994-1998

Short run total expenditure elasticities
1994-1998

A8
Short run compensated price elasticities
1994-1998

A9
Stage 1. Long run uncompensated price elasticities
1994-1998

Stage 1. Long run total expenditure elasticities
1994-1998

Stage 1. Long run compensated price elasticities
1994-1998

B1
Stage 1. Standard errors of uncompensated price elasticities
1994-1998

Stage 1. Standard errors of total expenditure elasticities
1994-1998

B2
Stage 1. Standard errors of compensated price elasticities
1994-1998

B3
Stage 2. Group 1. Standard errors of uncompensated price elasticities
1994-1998

Stage 2. Group 1. Standard errors of total expenditure elasticities
1994-1998

B4
Stage 2. Group 1. Standard errors of compensated price elasticities
1994-1998

B5
Stage 2. Group 3. Standard errors of uncompensated price elasticities
1994-1998

Stage 2. Group 3. Standard errors of total expenditure elasticities
1994-1998

B6
Stage 2. Group 3. Standard errors of compensated price elasticities
1994-1998

B7
Stage 2. Group 4. Standard errors of uncompensated price elasticities
1994-1998

Stage 2. Group 4. Standard errors of total expenditure elasticities
1994-1998

B8
Stage 2. Group 4. Standard errors of compensated price elasticities
1994-1998

B9
Stage 2. Group 5. Standard errors of uncompensated price elasticities
1994-1998

Stage 2. Group 5. Standard errors of total expenditure elasticities
1994-1998

B10
Stage 2. Group 5. Standard errors of compensated price elasticities
1994-1998

24

Table A1. Long run uncompensated price elasticities. Calculated at mean values.

1_1
1_2
1_3
1_4
2_1
3_1
3_2
3_3
3_4
4_1
4_2
4_3
4_4
5_1
5_2
5_3
5_4
5_5
6_1

1_1
-0.448225
0.118271
-0.033555
-0.020143
-0.095611
-0.085266
-0.075873
-0.026533
-0.004936
-0.067569
-0.013220
-0.027922
-0.012865
0.168872
0.044326
0.058058
0.102253
0.032629
-0.219177

1_2
0.437165
-0.902909
-0.022525
0.094479
-0.098183
-0.087564
-0.077912
-0.027238
-0.005066
-0.069382
-0.013578
-0.028683
-0.013205
0.173466
0.045535
0.059532
0.105019
0.033514
-0.225086

1_3
-0.172767
-0.031848
-0.422304
-0.074093
-0.172760
-0.154243
-0.137094
-0.047554
-0.008904
-0.122362
-0.023903
-0.050300
-0.023254
0.305338
0.079618
0.105183
0.184931
0.058663
-0.396261

1_4
-1.306355
0.318120
0.824625
-0.181017
-0.086881
-0.077452
-0.068991
-0.024383
-0.004479
-0.061407 -0.012039 -0.025400 -0.011718
0.153432
0.040613
0.052760
0.092975
0.029795
-0.199416

2_1
-0.033293
-0.009025
-0.007480
-0.001842
-0.247773
-0.139790
-0.123592
-0.040947
-0.008055
0.035044
0.006826
0.014624
0.006548
0.029474
0.007269
0.009890
0.017699
0.005428
0.354049

3_1
-0.337674
-0.091219
-0.073238
-0.017908
-0.777453
-0.394171
-0.153953
-0.060311
0.044606
0.276361
0.054187
0.114625
0.052885
0.051208
0.013734
0.017778
0.031114
0.010114
-1.142741

3_2
-0.343984
-0.092928
-0.074593
-0.018238
-0.791876
-0.175581
-0.424276
0.130077
-0.104809
0.281527
0.055192
0.116742
0.053855
0.052160
0.013985
0.018102
0.031691
0.010298
-1.163913

3_3
-0.194416
-0.052386
-0.042739
-0.010555
-0.452427
-0.214830
0.416496
-0.689223
0.173237
0.158870
0.031505
0.066720
0.030848
0.029899
0.008264
0.010530
0.018246
0.006058
-0.665916

3_4
-0.297803
-0.080415
-0.064573
-0.015767
-0.685308
1.167471
-1.171452
0.030933
-0.523916
0.243631
0.047758
0.101090
0.046612
0.045148
0.012102
0.015672
0.027430
0.008916
-1.007526

4_1
-0.176687
-0.047760
-0.037133
-0.009092
-0.066248
0.102177
0.090692
0.030726
0.005876
-1.996960 0.104168 0.160538 0.379566
0.027008
0.007172
0.009345
0.016405
0.005267
-1.028290

4_2
-0.224550
-0.060709
-0.047281
-0.011573
-0.084515
0.130330
0.115773
0.039391
0.007506
0.411491
-1.437583
-0.430576
-0.267863
0.034542
0.009210
0.011972
0.020994
0.006766
-1.311953

4_3
-0.420920
-0.113704
-0.088160
-0.021661
-0.158496
0.242831
0.215455
0.072820
0.013929
-0.258634
-0.306768
-1.718644
-0.924651
0.063818
0.016924
0.022207
0.038797
0.012407
-2.441924

4_4
-0.219858
-0.059415
-0.046291
-0.011332
-0.082909
0.127722
0.113496
0.038640
0.007359
0.946193
-0.324142 -0.688106 -1.622606
0.033814
0.009027
0.011756
0.020559
0.006630
-1.285406

5_1
0.554654
0.150605
0.122685
0.030337
0.042044
0.062401
0.055754
0.020000
0.003667
0.109958
0.021534
0.045543
0.020926
-1.176970
-0.257902
-0.176276
-0.216589
-0.119443
-1.349936

5_2
0.407308
0.110673
0.090703
0.022510
0.030673
0.045809
0.040986
0.014890
0.002699
0.080369
0.015793
0.033475
0.015359
-0.863059
-1.323463
1.010034
-0.078059
-0.168760
-0.992239

5_3
0.462637
0.125414
0.102108
0.025241
0.034961
0.052096
0.046568
0.016703
0.003063
0.091717
0.017969
0.037941
0.017519
-0.429179
0.755445
-1.518805
-0.485472
0.053848
-1.125435

5_4
0.404094
0.109792
0.089261
0.022065
0.030708
0.045451
0.040577
0.014507
0.002668
0.080207
0.015697
0.033176
0.015227
-0.208318
-0.040110
-0.245297
-0.792080
-0.134167
-0.983390

5_5
1.174490
0.318715
0.257227
0.063595
0.089461
0.132061
0.117606
0.041401
0.007707
0.234838
0.045729
0.095951
0.044361
-1.147075
-0.605477
-0.300789
-1.398194
-0.696398
-2.854161

6_1
-0.082497
-0.022299
-0.017840
-0.004381
-0.085079
-0.000331
-0.000414
-0.000280
-3.78E-05
0.063531
0.012276
0.025812
0.011846
-0.031457
-0.007999
-0.010676
-0.018960
-0.005943
-0.269607

Long run total expenditure elasticities. Calculated at mean values.

0.606488
0.622620
1.103916
0.547218
0.124946
2.382054
2.426567
1.371819
2.099997
2.423232
3.088628
5.754376
3.024870
2.057008
1.504297
1.715660
1.499930
4.378952
0.444333

Table A2. Long run compensated price elasticities. Calculated at mean values.

1_1
1_2
1_3
1_4
2_1
3_1
3_2
3_3
3_4
4_1
4_2
4_3
4_4
5_1
5_2
5_3
5_4
5_5
6_1

1_1
-0.388986
0.134276
-0.021124
-0.017144
-9.56E-05
-0.062463
-0.055850
-0.020144
-0.003648
-0.030749
-0.006139
-0.012883
-0.006042
0.188001
0.048988
0.064564
0.113744
0.036125
0.039570

1_2
0.497956
-0.886472
-0.009762
0.097558
-0.000143
-0.064148
-0.057352
-0.020681
-0.003744
-0.031581
-0.006306
-0.013238
-0.006202
0.193103
0.050320
0.066198
0.116813
0.037103
0.040579

1_3
-0.064249
-0.002527
-0.399707
-0.068641
0.000962
-0.112531
-0.100501
-0.035963
-0.006555
-0.055378
-0.011038
-0.023078
-0.010862
0.340350
0.088101
0.117115
0.205970
0.065031
0.073502

1_4
-1.253274
0.332477
0.835831
-0.178295
-0.000392
-0.056951
-0.050979
-0.018588
-0.003324
-0.028225 -0.005644 -0.011836 -0.005554
0.170582
0.044823
0.058594
0.103287
0.032942
0.034526

2_1
-0.021878
-0.005981
-0.005016
-0.001188
-0.226619
-0.135462
-0.119711
-0.039502
-0.007810
0.042371
0.008292
0.017558
0.007997
0.033040
0.008238
0.011259
0.019908
0.006127
0.408376

3_1
-0.110260
-0.029803
-0.024741
-0.006139
-0.399340
-0.307222
-0.077178
-0.034852
0.049571
0.419914
0.082151
0.174376
0.079969
0.124038
0.032025
0.042880
0.075054
0.023750
-0.114192

3_2
-0.112274
-0.030349
-0.025189
-0.006250
-0.406744
-0.086971
-0.346051
0.156007
-0.099751
0.427775
0.083677
0.177599
0.081438
0.126375
0.032618
0.043670
0.076465
0.024189
-0.116235

3_3
-0.066018
-0.017812
-0.015007
-0.003767
-0.232141
-0.166329
0.459625
-0.674173
0.176053
0.241214
0.047737
0.101440
0.046615
0.070558
0.018774
0.024760
0.042883
0.013861
-0.068275

3_4
-0.097184
-0.026260
-0.021801
-0.005403
-0.352136
1.244112
-1.103778
0.053369
-0.519535
0.370237
0.072415
0.153807
0.070494
0.109373
0.028223
0.037810
0.066177
0.020941
-0.100861

4_1
0.058005
0.015634
0.012236
0.002949
0.317879
0.192661
0.170213
0.056342
0.010961
-1.851061 0.132370 0.219953 0.406833
0.102673
0.025839
0.035452
0.062047
0.019164
0.009851

4_2
0.073733
0.019879
0.015584
0.003755
0.405311
0.245172
0.216796
0.072077
0.013971
0.597111
-1.401598
-0.354585
-0.233041
0.130593
0.032994
0.045175
0.078970
0.024476
0.013629

4_3
0.137731
0.037094
0.028958
0.007003
0.755260
0.458355
0.404759
0.133619
0.026003
0.087392
-0.239955
-1.578746
-0.859966
0.243854
0.061282
0.084678
0.147518
0.045369
0.019791

4_4
0.072183
0.019453
0.015257
0.003677
0.397010
0.240096
0.212383
0.070651
0.013687
1.127843
-0.288914 -0.613717 -1.588469
0.127801
0.032326
0.044349
0.077313
0.023978
0.013095

5_1
0.750581
0.203651
0.164612
0.040542
0.368630
0.137582
0.122087
0.042044
0.007951
0.234193
0.045731
0.097258
0.044297
-1.114189
-0.242131
-0.154851
-0.178754
-0.107706
-0.461526

5_2
0.549429
0.149167
0.121315
0.029986
0.270147
0.100305
0.089133
0.031094
0.005813
0.171093
0.033525
0.071452
0.032502
-0.817634
-1.311922
1.025558
-0.050651
-0.160205
-0.340106

5_3
0.626211
0.169630
0.137039
0.033742
0.307630
0.114729
0.101858
0.035075
0.006634
0.195132
0.038119
0.080939
0.037046
-0.376852
0.768606
-1.500776
-0.453897
0.063643
-0.384507

5_4
0.547187
0.148557
0.119845
0.029508
0.268637
0.100408
0.089031
0.030560
0.005796
0.170843
0.033338
0.070855
0.032237
-0.162433
-0.028615
-0.229695
-0.764432
-0.125610
-0.336019

5_5
1.595897
0.432766
0.346577
0.085349
0.782985
0.294381
0.260307
0.087948
0.016884
0.499536
0.096992
0.204677
0.093783
-1.011647
-0.571867
-0.254686
-1.316622
-0.671450
-0.971810

6_1
-0.040271
-0.010877
-0.008798
-0.002185
-0.014639
0.015869
0.013884
0.004457
0.000885
0.090260
0.017490
0.036977
0.016891
-0.017909
-0.004587
-0.006030
-0.010785
-0.003405
-0.077226

Table A3. Long run uncompensated price elasticities. Calculated at 1994-1998 mean values.

1_1
1_2
1_3
1_4
2_1
3_1
3_2
3_3
3_4
4_1
4_2
4_3
4_4
5_1
5_2
5_3
5_4
5_5
6_1

1_1
-0.404202
0.130199
-0.014933
-0.012761
-0.108791
-0.091947
-0.086122
-0.042391
-0.005893
-0.073185
-0.015316
-0.033169
-0.015200
0.185218
0.062189
0.065389
0.114216
0.043000
-0.250577

1_2
0.477653
-0.891326
-0.001908
0.105132
-0.111936
-0.094622
-0.088617
-0.043569
-0.006061
-0.075301
-0.015759
-0.034133
-0.015630
0.190633
0.063998
0.067168
0.117534
0.044241
-0.257813

1_3
-0.024345
0.007313
-0.453544
-0.053921
-0.188651
-0.159546
-0.149334
-0.073477
-0.010206
-0.127110
-0.026578
-0.057361
-0.026375
0.321109
0.107728
0.113798
0.198183
0.074451
-0.434795

1_4
-0.871735
0.276410
0.669282
-0.362975
-0.104351
-0.088187
-0.082632
-0.040679
-0.005646
-0.070242 -0.014693 -0.031830 -0.014576
0.177810
0.059707
0.062651
0.109583
0.041243
-0.240478

2_1
-0.041792
-0.011469
-0.010710
-0.002914
-0.312351
-0.116901
-0.109295
-0.053497
-0.007514
0.037428
0.007868
0.017188
0.007719
0.021019
0.007011
0.007253
0.012948
0.004841
0.334372

3_1
-0.358787
-0.098008
-0.090851
-0.024725
-0.918709
-0.338630
-0.159745
-0.031955
0.050077
0.297622
0.062440
0.135255
0.062224
0.063558
0.021406
0.022761
0.039311
0.014920
-1.355090

3_2
-0.364794
-0.099653
-0.092359
-0.025135
-0.934010
-0.171897
-0.382846
0.173286
-0.106871
0.302595
0.063482
0.137496
0.063249
0.064621
0.021760
0.023135
0.039971
0.015169
-1.377646

3_3
-0.247713
-0.067424
-0.062698
-0.017071
-0.633917
-0.071202
0.358398
-0.740365
0.123171
0.205025
0.043031
0.093395
0.042993
0.043820
0.014770
0.015805
0.027131
0.010322
-0.935313

3_4
-0.315349
-0.086138
-0.079870
-0.021716
-0.807332
1.167450
-1.127660
0.067362
-0.528818
0.261463
0.054872
0.118917
0.054675
0.055878
0.018816
0.020004
0.034566
0.013125
-1.191033

4_1
-0.134685
-0.036819
-0.033728
-0.009312
-0.075704
0.090997
0.085141
0.041925
0.005824
-2.006127 0.111567 0.168793 0.397719
0.031668
0.010641
0.011355
0.019600
0.007390
-0.990528

4_2
-0.174549
-0.047712
-0.043780
-0.012063
-0.098009
0.118083
0.110529
0.054481
0.007573
0.399026
-1.426531
-0.431185
-0.264456
0.041138
0.013830
0.014752
0.025455
0.009616
-1.285348

4_3
-0.316092
-0.086347
-0.078932
-0.021843
-0.178133
0.213483
0.199712
0.098264
0.013633
-0.223383
-0.298458
-1.707033
-0.881024
0.074042
0.024892
0.026737
0.045858
0.017261
-2.321870

4_4
-0.171327
-0.046808
-0.042970
-0.011837
-0.096300
0.115997
0.108611
0.053564
0.007441
0.888850
-0.313151 -0.670373 -1.596716
0.040378
0.013586
0.014529
0.024988
0.009446
-1.262291

5_1
0.707266
0.193977
0.180256
0.048915
0.043836
0.076701
0.071813
0.035383
0.004965
0.125802
0.026389
0.057254
0.026147
-1.241913
-0.321148
-0.209508
-0.267725
-0.155030
-1.754118

5_2
0.549827
0.150885
0.140345
0.038065
0.034054
0.059648
0.055867
0.027490
0.003859
0.097832
0.020521
0.044566
0.020337
-0.822043
-1.309687
0.747179
-0.150009
-0.172324
-1.364163

5_3
0.585420
0.160289
0.148913
0.040406
0.036140
0.063544
0.059520
0.029381
0.004116
0.104076
0.021835
0.047297
0.021726
-0.498310
0.752903
-1.562299
-0.541112
0.032938
-1.451246

5_4
0.508540
0.139585
0.129572
0.035170
0.031602
0.055122
0.051574
0.025393
0.003568
0.090484
0.018978
0.041159
0.018755
-0.263093
-0.068504
-0.272595
-0.815668
-0.159071
-1.261246

5_5
1.387323
0.380607
0.352471
0.096093
0.085237
0.150292
0.140648
0.069087
0.009682
0.247561
0.051837
0.111913
0.051324
-1.164668
-0.671396
-0.332797
-1.319993
-0.822099
-3.438299

6_1
-0.081713
-0.022337
-0.020685
-0.005692
-0.073809
-0.001593
-0.001532
-0.000832
-0.000114
0.060671
0.012697
0.027434
0.012498
-0.029843
-0.009990
-0.010487
-0.018439
-0.006924
-0.316765

Long run total expenditure elasticities. Calculated at 1994-1998 mean values.

0.554274
0.570315
0.962661
0.531339
0.208797
2.606926
2.650449
1.797841
2.290790
2.304284
2.989149
5.399232
2.934384
2.350738
1.827750
1.944464
1.690676
4.615177
0.487457

Table A4. Long run compensated price elasticities. Calculated at 1994-1998 mean values.

1_1
1_2
1_3
1_4
2_1
3_1
3_2
3_3
3_4
4_1
4_2
4_3
4_4
5_1
5_2
5_3
5_4
5_5
6_1

1_1
-0.360933
0.142048
-0.004040
-0.009774
-0.012375
-0.076106
-0.071342
-0.035178
-0.004885
-0.039577
-0.008273
-0.017882
-0.008286
0.197497
0.066287
0.069707
0.121804
0.045828
0.005481

1_2
0.522167
-0.879128
0.009305
0.108205
-0.012764
-0.078315
-0.073404
-0.036154
-0.005025
-0.040713
-0.008511
-0.018399
-0.008518
0.203269
0.068215
0.071603
0.125341
0.047150
0.005676

1_3
0.050928
0.027911
-0.434665
-0.048733
-0.021015
-0.132004
-0.123655
-0.060951
-0.008458
-0.068743
-0.014358
-0.030924
-0.014381
0.342455
0.114847
0.121330
0.211383
0.079361
0.009672

1_4
-0.830292
0.287759
0.679724
-0.360106
-0.011891
-0.072988
-0.068446
-0.033757
-0.004681
-0.038018 -0.007943 -0.017174 -0.007952
0.189595
0.063641
0.066787
0.116861
0.043954
0.004927

2_1
-0.025434
-0.007045
-0.006663
-0.001776
-0.275396
-0.110938
-0.103717
-0.050731
-0.007137
0.050051
0.010493
0.022775
0.010329
0.025668
0.008573
0.008977
0.015834
0.005908
0.430229

3_1
-0.155900
-0.042518
-0.039599
-0.010738
-0.465550
-0.264607
-0.090566
0.001940
0.054804
0.455236
0.095529
0.207390
0.094932
0.120967
0.040652
0.043215
0.074787
0.028222
-0.148196

3_2
-0.158495
-0.043228
-0.040252
-0.010916
-0.473298
-0.096630
-0.312513
0.207748
-0.102065
0.462851
0.097126
0.210828
0.096497
0.122992
0.041325
0.043925
0.076044
0.028692
-0.150629

3_3
-0.107781
-0.029289
-0.027364
-0.007425
-0.320927
-0.020378
0.405937
-0.716815
0.126441
0.313688
0.065855
0.143248
0.065603
0.083338
0.028034
0.030000
0.051582
0.019517
-0.103263

3_4
-0.137030
-0.037371
-0.034815
-0.009432
-0.409227
1.232460
-1.066910
0.097155
-0.524661
0.399971
0.083959
0.182356
0.083424
0.106301
0.035718
0.037966
0.065731
0.024815
-0.130408

4_1
0.044982
0.012334
0.011375
0.003115
0.326037
0.156889
0.146639
0.071862
0.009988
-1.866718 0.140734 0.231823 0.426464
0.082731
0.027715
0.029526
0.051153
0.019130
0.074221

4_2
0.058371
0.016004
0.014785
0.004041
0.422760
0.203421
0.190208
0.093320
0.012977
0.579785
-1.388675
-0.349197
-0.227114
0.107287
0.035960
0.038303
0.066325
0.024850
0.096587

4_3
0.105240
0.028838
0.026542
0.007285
0.764583
0.367948
0.343844
0.168341
0.023372
0.103018
-0.230227
-1.560127
-0.813669
0.193708
0.064926
0.069622
0.119852
0.044743
0.172161

4_4
0.057277
0.015697
0.014509
0.003964
0.415071
0.199691
0.186779
0.091686
0.012743
1.066195
-0.276005 -0.589918 -1.560017
0.105260
0.035312
0.037714
0.065081
0.024399
0.094561

5_1
0.890142
0.244113
0.226557
0.061536
0.451753
0.143617
0.134311
0.065897
0.009231
0.268130
0.056273
0.122483
0.055575
-1.190072
-0.303798
-0.191258
-0.235717
-0.143041
-0.665732

5_2
0.691897
0.189855
0.176368
0.047880
0.351107
0.111683
0.104486
0.051195
0.007174
0.208514
0.043759
0.095337
0.043229
-0.781738
-1.296185
0.761347
-0.125137
-0.163004
-0.517766

5_3
0.736746
0.201707
0.187154
0.050828
0.374027
0.118755
0.111107
0.054617
0.007639
0.221610
0.046515
0.101086
0.046131
-0.455527
0.767249
-1.547047
-0.514668
0.042851
-0.550780

5_4
0.640157
0.175697
0.162885
0.044252
0.324856
0.103322
0.096561
0.047343
0.006640
0.192943
0.040488
0.088088
0.039881
-0.225764
-0.056032
-0.259530
-0.792620
-0.150448
-0.478720

5_5
1.746695
0.479168
0.443184
0.120932
0.887480
0.282129
0.263719
0.128919
0.018039
0.527047
0.110413
0.239159
0.108972
-1.062589
-0.637253
-0.296827
-1.256969
-0.798594
-1.303624

6_1
-0.043821
-0.011955
-0.011099
-0.003073
0.010811
0.012286
0.011435
0.005494
0.000768
0.090158
0.018885
0.040934
0.018599
-0.019087
-0.006389
-0.006689
-0.011802
-0.004438
-0.091019

Table A5. Short run compensated price elasticities. Calculated at mean values.

1_1
1_2
1_3
1_4
2_1
3_1
3_2
3_3
3_4
4_1
4_2
4_3
4_4
5_1
5_2
5_3
5_4
5_5
6_1

1_1
-0.392119
-0.021573
0.003704
0.072312
-0.016574
-0.019793
-0.017641
-0.006175
-0.001153
-0.003320
-0.000661
-0.001384
-0.000662
0.055480
0.014492
0.019098
0.033587
0.010675
-0.094832

1_2
-0.071136
-0.428579
-0.054568
-0.088110
-0.031692
-0.037796
-0.033711
-0.011855
-0.002204
-0.006367
-0.001268
-0.002658
-0.001271
0.105880
0.027751
0.036502
0.064110
0.020429
-0.180775

1_3
-0.082678
-0.035796
-0.634526
-0.210622
-0.046473
-0.055927
-0.049783
-0.017268
-0.003246
-0.009301
-0.001850
-0.003855
-0.001851
0.156905
0.040687
0.054078
0.095011
0.029997
-0.269397

1_4
-1.102920
0.305634
0.922220
-0.519518
-0.019560
-0.023339
-0.020825
-0.007373
-0.001358
-0.003999
-0.000797
-0.001668
-0.000797
0.065511
0.017267
0.022518
0.039682
0.012675
-0.111735

2_1
-0.000280
-7.58E-05
-0.000371
-0.000122
-0.114392
0.021209
0.018599
0.006052
0.001194
-0.051697
-0.010008
-0.021220
-0.009710
-0.012573
-0.003324
-0.004227
-0.007592
-0.002466
0.046979

3_1
-0.089878
-0.024279
-0.019491
-0.004767
0.079150
-0.873219
-0.021649
-0.262860
-0.033578
-0.005306
-0.001030
-0.002197
-0.000982
0.161211
0.042525
0.055981
0.097838
0.031372
-0.561894

3_2
-0.082675
-0.022335
-0.017921
-0.004382
0.072784
0.005085
-1.212402
0.088649
0.022581
-0.004881
-0.000947
-0.002020
-0.000903
0.148281
0.039080
0.051466
0.089981
0.028833
-0.516666

3_3
-0.072927
-0.019690
-0.015862
-0.003888
0.064374
-0.883780
0.328919
-0.477546
0.067744
-0.004307
-0.000838
-0.001788
-0.000800
0.130865
0.034755
0.045587
0.079499
0.025613
-0.457187

3_4
-0.073555
-0.019854
-0.015947
-0.003890
0.064786
-0.053985
0.253475
0.040307
-1.213827
-0.004357
-0.000846
-0.001805
-0.000806
0.131875
0.034761
0.045802
0.080031
0.025669
-0.459638

4_1
-0.017758
-0.004803
-0.003513
-0.000835
-0.172445
-0.009144
-0.007973
-0.002594
-0.000499
-1.005608
-0.011242
-0.021744 -0.304484
0.110283
0.028424
0.038304
0.066894
0.020966
-0.877262

4_2
-0.006330
-0.001713
-0.001248
-0.000299
-0.062227
-0.003299
-0.002879
-0.000944
-0.000180
0.050037
-0.724716
0.167614
0.025391
0.039668
0.010272
0.013844
0.024122
0.007554
-0.316113

4_3
-0.006307
-0.001706
-0.001257
-0.000295
-0.063205
-0.003298
-0.002887
-0.000956
-0.000182
0.116666
0.063627
-1.123679
0.444474
0.040755
0.010597
0.014000
0.024680
0.007853
-0.324433

4_4
-0.007966
-0.002150
-0.001570
-0.000375
-0.078752
-0.004075
-0.003560
-0.001162
-0.000222
-0.172830
-0.347332
0.242373
-0.330530
0.049957
0.012981
0.017736
0.030410
0.009554
-0.399841

5_1
0.250435
0.067996
0.055255
0.013646
-0.084615
0.188673
0.167954
0.059415
0.010992
0.171085
0.033637
0.071392
0.032629
-1.613771
-0.249829
0.187762
0.148098
-0.086656
-0.572020

5_2
0.183732
0.049919
0.040813
0.010116
-0.062136
0.138217
0.123219
0.044152
0.008074
0.125403
0.024741
0.052624
0.024020
-0.731014
-0.960924
-0.585562
1.316001
-0.217663
-0.420311

5_3
0.208887
0.056623
0.045988
0.011355
-0.070545
0.157239
0.140034
0.049530
0.009165
0.142588
0.028044
0.059425
0.027295
0.575748
-0.518973
-0.179871
-1.129338
-0.094301
-0.476804

5_4
0.182495
0.049581
0.040211
0.009928
-0.061654
0.137599
0.122393
0.043155
0.008007
0.124741
0.024508
0.051984
0.023731
0.232463
0.476317
-0.615446
-1.232295
-0.038460
-0.416767

5_5
0.530946
0.144074
0.115991
0.028642
-0.179220
0.401278
0.355962
0.123505
0.023202
0.363837
0.071118
0.149771
0.068867
-0.463898
-0.141127
-0.672400
-1.633193
-0.531502
-1.210262

6_1
-0.137429
-0.037160
-0.029281
-0.007142
-0.286500
-0.017430
-0.015356
-0.005060
-0.000990
-0.008997
-0.001725
-0.003625
-0.001654
-0.032371
-0.008088
-0.010987
-0.019487
-0.006021
-0.615450

Short run total expenditure elasticities. Calculated at mean values.

0.366537
0.697319
1.045893
0.428384
0.144023
1.433055
1.318391
1.161258
1.171806
2.175032
0.781446
0.805554
0.987353
1.147921
0.836580
0.957911
0.837509
2.454409
1.244752

Table A6. Short run compensated price elasticities. Calculated at mean values.

1_1
1_2
1_3
1_4
2_1
3_1
3_2
3_3
3_4
4_1
4_2
4_3
4_4
5_1
5_2
5_3
5_4
5_5
6_1

1_1
-0.355896
-0.011796
0.011236
0.074120
0.040936
-0.005856
-0.005427
-0.002342
-0.000367
0.018996
0.003609
0.007658
0.003446
0.067191
0.017309
0.023074
0.040614
0.012796
0.060701

1_2
-0.002391
-0.410038
-0.040236
-0.084669
0.077820
-0.011347
-0.010519
-0.004548
-0.000712
0.036084
0.006858
0.014565
0.006555
0.128103
0.033113
0.044059
0.077447
0.024461
0.115393

1_3
0.021389
-0.007687
-0.613073
-0.205468
0.117508
-0.015939
-0.014774
-0.006366
-0.001001
0.054327
0.010309
0.021786
0.009842
0.190518
0.048722
0.065505
0.115185
0.036050
0.173167

1_4
-1.060899
0.316994
0.931017
-0.517391
0.047875
-0.007109
-0.006594
-0.002869
-0.000446
0.022054
0.004198
0.008905
0.004010
0.079109
0.020562
0.027129
0.047847
0.015147
0.070462

2_1
0.012991
0.003470
0.002485
0.000626
-0.090251
0.026252
0.023108
0.007697
0.001480
-0.043210
-0.008319
-0.017806
-0.008047
-0.008406
-0.002208
-0.002656 -0.005023 -0.001657
0.109474

3_1
0.047713
0.012898
0.009746
0.002324
0.306181
-0.820430
0.024883
-0.247598
-0.030577
0.081253
0.015767
0.033629
0.015257
0.205427
0.053536
0.071140
0.124474
0.039592
0.054786

3_2
0.043978
0.011889
0.008981
0.002141
0.281581
0.053694
-1.169564
0.102679
0.025343
0.074760
0.014503
0.030928
0.014031
0.188995
0.049210
0.065418
0.114504
0.036397
0.050531

3_3
0.038092
0.010288
0.007792
0.001859
0.248814
-0.841300
0.366420
-0.465107
0.070167
0.065772
0.012798
0.027301
0.012390
0.166455
0.043673
0.057828
0.100959
0.032264
0.043533

3_4
0.039059
0.010546
0.007977
0.001897
0.250281
-0.010855
0.291500
0.052783
-1.211369
0.066473
0.012896
0.027540
0.012480
0.168032
0.043761
0.058204
0.101811
0.032393
0.044591

4_1
0.191887
0.051859
0.040834
0.009939
0.171990
0.071498
0.063017
0.020461
0.004059
-0.874568
0.014171
0.032244
-0.279907
0.177787
0.045158
0.061515
0.107583
0.033452
0.057020

4_2
0.068789
0.018606
0.014617
0.003581
0.062049
0.025552
0.022538
0.007373
0.001448
0.096879
-0.715583
0.186882
0.034215
0.063789
0.016278
0.022182
0.038701
0.012022
0.020082

4_3
0.070605
0.019118
0.015189
0.003665
0.063886
0.026182
0.023137
0.007603
0.001501
0.165227
0.073104
-1.103187
0.453625
0.065504
0.016781
0.022417
0.039570
0.012491
0.023582

4_4
0.086999
0.023455
0.018486
0.004519
0.078325
0.032311
0.028545
0.009316
0.001835
-0.113742
-0.335828
0.266702
-0.319313
0.080394
0.020587
0.028439
0.048828
0.015217
0.024923

5_1
0.360928
0.097874
0.078704
0.019335
0.097061
0.231173
0.205375
0.071620
0.013401
0.240523
0.047085
0.100046
0.045613
-1.578198
-0.241008
0.199905
0.169508
-0.080069
-0.078874

5_2
0.263623
0.071529
0.057874
0.014269
0.070608
0.168926
0.150291
0.053091
0.009819
0.175934
0.034561
0.073590
0.033509
-0.705353
-0.954491
-0.576790
1.331463
-0.212878
-0.059576

5_3
0.301178
0.081539
0.065534
0.016096
0.081219
0.192661
0.171240
0.059707
0.011174
0.200416
0.039250
0.083261
0.038148
0.605410
-0.511608
-0.169648
-1.111463
-0.088801
-0.065315

5_4
0.263231
0.071425
0.057325
0.014080
0.070780
0.168681
0.149741
0.052049
0.009767
0.175428
0.034319
0.072873
0.033187
0.258473
0.482750
-0.606599
-1.216643
-0.033656
-0.057210

5_5
0.769536
0.208572
0.166183
0.040825
0.208322
0.493390
0.436780
0.149398
0.028385
0.512424
0.099739
0.210288
0.096448
-0.386887 -0.122249 -0.646178 -1.586865 -0.517446
-0.160665

6_1
-0.016978
-0.004599
-0.003817
-0.000972
-0.089778
0.028960
0.025446
0.008135
0.001633
0.066415
0.012837
0.027352
0.012394
0.006489
0.001484
0.002259
0.003880
0.001139
-0.082279

Table A7. Short run uncompensated price elasticities. Calculated at 1994-1998 mean values.

1_1
1_2
1_3
1_4
2_1
3_1
3_2
3_3
3_4
4_1
4_2
4_3
4_4
5_1
5_2
5_3
5_4
5_5
6_1

1_1
-0.366802
-0.012518
0.018300
0.082457
-0.018925
-0.020976
-0.019668
-0.009728
-0.001350
-0.004395
-0.000913
-0.001966
-0.000925
0.059041
0.019817
0.020886
0.036419
0.013696
-0.095901

1_2
-0.018636
-0.408494
-0.031927
-0.083246
-0.036899
-0.040880
-0.038353
-0.018995
-0.002635
-0.008575
-0.001782
-0.003842
-0.001806
0.115072
0.038649
0.040718
0.070958
0.026714
-0.186801

1_3
0.073401
-0.014805
-0.637305
-0.175452
-0.050992
-0.056674
-0.053097
-0.026231
-0.003639
-0.011882
-0.002466
-0.005288
-0.002498
0.159498
0.053483
0.056592
0.098463
0.036931
-0.259613

1_4
-0.732091
0.266393
0.738806
-0.621932
-0.023709
-0.026283
-0.024656
-0.012188
-0.001691
-0.005545
-0.001151
-0.002481
-0.001164
0.074123
0.024884
0.026113
0.045681
0.017178
-0.120293

2_1
-0.012608
-0.003455
-0.003280
-0.000885
-0.198998
0.017301
0.016109
0.007782
0.001094
-0.046329
-0.009705
-0.021073
-0.009594
-0.014457
-0.004851
-0.005026
-0.008918
-0.003393
0.074242

3_1
-0.095400
-0.026060
-0.024156
-0.006577
0.092120
-0.859016
-0.025559
-0.296927
-0.036968
-0.005192 -0.001097 -0.002391 -0.001069
0.179991
0.060531
0.064349
0.111288
0.042075
-0.670446

3_2
-0.087203
-0.023827
-0.022080
-0.006012
0.084203
0.003653
-1.224176
0.083621
0.023011
-0.004744 -0.001002 -0.002184 -0.000976
0.164544
0.055332
0.058794
0.101733
0.038454
-0.612827

3_3
-0.080800
-0.022053
-0.020456
-0.005570
0.078020
-0.620567
0.203304
-0.658572
0.044327
-0.004408
-0.000931
-0.002030
-0.000907
0.152363
0.051249
0.054563
0.094234
0.035647
-0.567777

3_4
-0.077805
-0.021250
-0.019710
-0.005357
0.075170
-0.058713
0.244546
0.032426
-1.211195
-0.004258
-0.000900
-0.001963
-0.000876
0.146772
0.049349
0.052460
0.090778
0.034352
-0.546784

4_1
-0.004664
-0.001286
-0.001113
-0.000313
-0.165541
-0.007897
-0.007322
-0.003486
-0.000488
-1.006645
-0.012303
-0.021614 -0.316230
0.103664
0.034768
0.037003
0.064071
0.024056
-0.873480

4_2
-0.001758
-0.000485
-0.000420
-0.000118
-0.061041
-0.002932
-0.002716
-0.001291
-0.000181
0.049468
-0.733824
0.160920
0.023687
0.038227
0.012797
0.013625
0.023644
0.008852
-0.321862

4_3
-0.001768
-0.000487
-0.000424
-0.000119
-0.064122
-0.003049
-0.002831
-0.001358
-0.000190
0.110006
0.060563
-1.115346
0.414962
0.040392
0.013545
0.014212
0.024922
0.009417
-0.339660

4_4
-0.002108
-0.000580
-0.000502
-0.000141
-0.076971
-0.003585
-0.003327
-0.001585
-0.000222
-0.161806
-0.327631
0.228801
-0.367437
0.047935
0.016148
0.017485
0.029664
0.011159
-0.405831

5_1
0.313313
0.085933
0.079813
0.021659
-0.108744
0.223233
0.208700
0.102358
0.014366
0.211861
0.044484
0.096738
0.044000
-1.704034
-0.291674
0.182408
0.138425
-0.105713
-0.739965

5_2
0.243551
0.066838
0.062137
0.016853
-0.084565
0.173601
0.162361
0.079523
0.011164
0.164714
0.034583
0.075278
0.034217
-0.701165
-0.995176
-0.496764
0.994717
-0.185999
-0.575433

5_3
0.259330
0.071008
0.065934
0.017891
-0.089960
0.184545
0.172600
0.084807
0.011884
0.175215
0.036793
0.079885
0.036547
0.578871
-0.567754
-0.158035
-1.209104
-0.116860
-0.612075

5_4
0.225301
0.061843
0.057377
0.015574
-0.078200
0.160622
0.150062
0.073551
0.010335
0.152430
0.032002
0.069565
0.031570
0.240471
0.468940
-0.649430
-1.279416
-0.061200
-0.532136

5_5
0.614622
0.168625
0.156079
0.042552
-0.213351
0.438211
0.409481
0.200117
0.028053
0.416358
0.087266
0.188853
0.086264
-0.507815
-0.227208
-0.623578
-1.475273
-0.663293
-1.450870

6_1
-0.118398
-0.032375
-0.029887
-0.008227
-0.264198
-0.014556
-0.013586
-0.006646
-0.000927
-0.007436
-0.001559
-0.003368
-0.001525
-0.026938
-0.009003
-0.009440
-0.016636
-0.006218
-0.654835

Short run total expenditure elasticities. Calculated at 1994-1998 mean values.

0.303454
0.590762
0.821573
0.380007
0.226046
1.500506
1.371686
1.270363
1.222957
2.158821
0.795408
0.841334
1.000534
1.182840
0.919564
0.978478
0.850739
2.324909
1.225758

Table A8. Short run compensated price elasticities. Calculated at 1994-1998 mean values.

1_1
1_2
1_3
1_4
2_1
3_1
3_2
3_3
3_4
4_1
4_2
4_3
4_4
5_1
5_2
5_3
5_4
5_5
6_1

1_1
-0.343045
-0.006013
0.024261
0.084092
0.033887
-0.012291
-0.011575
-0.005779
-0.000798
0.014022
0.002945
0.006384
0.002854
0.065770
0.022059
0.023249
0.040582
0.015243
0.044152

1_2
0.027579
-0.395845
-0.020316
-0.080062
0.065914
-0.023986
-0.022602
-0.011299
-0.001559
0.027274
0.005731
0.012437
0.005558
0.128168
0.043013
0.045320
0.079057
0.029729
0.085890

1_3
0.137833
0.002829
-0.621201
-0.171024
0.092139
-0.033124
-0.031169
-0.015544
-0.002144
0.037984
0.007970
0.017214
0.007717
0.177739
0.059553
0.063017
0.109756
0.041119
0.119333

1_4
-0.702379
0.274534
0.746275
-0.619881
0.042420
-0.015397
-0.014506
-0.007240
-0.000999
0.017526
0.003681
0.007986
0.003566
0.082559
0.027694
0.029065
0.050895
0.019116
0.055084

2_1
0.005092
0.001337
0.001108
0.000346
-0.159058
0.023756
0.022146
0.010771
0.001502
-0.032661
-0.006861
-0.015006
-0.006768
-0.009428
-0.003162
-0.003170
-0.005797
-0.002238
0.178088

3_1
0.021415
0.005903
0.005339
0.001491
0.353026
-0.816303
0.014348
-0.277403
-0.034247
0.085618
0.017952
0.039097
0.017718
0.213118
0.071623
0.076087
0.131750
0.049732
0.023736

3_2
0.019587
0.005401
0.004883
0.001364
0.322686
0.042712
-1.187687
0.101460
0.025499
0.078274
0.016412
0.035735
0.016194
0.194832
0.065472
0.069520
0.120439
0.045453
0.021765

3_3
0.018106
0.004987
0.004513
0.001260
0.298985
-0.584442
0.237061
-0.642014
0.046633
0.072471
0.015197
0.033112
0.015006
0.180397
0.060637
0.064515
0.111555
0.042133
0.019885

3_4
0.017437
0.004804
0.004348
0.001212
0.287726
-0.023944
0.277027
0.048350
-1.208973
0.069760
0.014637
0.031907
0.014445
0.173744
0.058378
0.062018
0.107445
0.040595
0.019084

4_1
0.163416
0.044707
0.041276
0.011309
0.210057
0.053652
0.050174
0.024590
0.003422
-0.876030
0.015081
0.037924
-0.289229
0.151393
0.050740
0.053919
0.093544
0.035068
0.124986

4_2
0.060276
0.016502
0.015186
0.004166
0.077397
0.019792
0.018487
0.009042
0.001260
0.097608
-0.723734
0.182780
0.033613
0.055834
0.018678
0.019855
0.034525
0.012906
0.045826

4_3
0.063556
0.017411
0.016186
0.004402
0.081659
0.020857
0.019527
0.009609
0.001341
0.160955
0.071279
-1.091799
0.425507
0.058951
0.019754
0.020698
0.036363
0.013720
0.050025

4_4
0.075766
0.020674
0.019101
0.005231
0.097483
0.024813
0.023233
0.011408
0.001583
-0.101473
-0.314978
0.256256
-0.354855
0.069962
0.023552
0.025467
0.043284
0.016258
0.057234

5_1
0.405409
0.111154
0.103070
0.028026
0.096874
0.256968
0.240207
0.117743
0.016512
0.283503
0.059506
0.129442
0.058786
-1.677879
-0.282926
0.191627
0.154573
-0.099678
-0.192918

5_2
0.315088
0.086439
0.080228
0.021805
0.075233
0.199831
0.186869
0.091473
0.012831
0.220419
0.046263
0.100729
0.045717
-0.680832
-0.988368
-0.489607
1.007263
-0.181308
-0.150074

5_3
0.335543
0.091843
0.085144
0.023149
0.080373
0.212379
0.198608
0.097532
0.013656
0.234379
0.049200
0.106854
0.048810
0.600456
-0.560520
-0.150328
-1.195762
-0.111870
-0.159447

5_4
0.291585
0.080010
0.074111
0.020157
0.069623
0.184923
0.172743
0.084618
0.011880
0.204006
0.042815
0.093095
0.042185
0.259305
0.475228
-0.642830
-1.267787
-0.056860
-0.138808

5_5
0.795803
0.218265
0.201698
0.055098
0.191476
0.504753
0.471599
0.230315
0.032261
0.557199
0.116746
0.252723
0.115262
-0.456257 -0.209973 -0.605388 -1.443442 -0.651449 -0.376686

6_1
-0.022907
-0.006233
-0.005799
-0.001619
-0.050962
0.020444
0.019100
0.009314
0.001297
0.066839
0.014006
0.030476
0.013783
0.000206
7.06E-05
0.000120
0.000123
3.75E-05
-0.088297

Table A9. Stage 1. Long run uncompensated price elasticities. Calculated at 1994-1998 mean values.

1
2
3
4
5

1
-0.437580
-0.014277

0.087275
0.190075
0.174507

2
-0.004937
0.076203

-0.154600
-0.028122
0.111457

3
0.247319
-0.266902

-0.666418
0.212633
0.473368

4
0.340672
0.128015

0.145438
-0.419951
-0.194173

5
-0.012697
-0.130663

0.824064
0.250909
-0.931612

Long run total expenditure elasticities. Calculated at 1994-1998 mean values.

0.453754 0.527394 1.451610 1.797440 1.503694

Long run compensated price elasticities. Calculated at 1994-1998 mean values.

1
2
3
4
5

1
-0.542716
-0.160774
0.028263
0.094192

0.127281

2
-0.126692
-0.094742
-0.223159
-0.139209

0.056408

3
-0.088212
-0.736468
-0.855104
-0.093935

0.322108

4
-0.074627
-0.453923
-0.088514
-0.798582

-0.381794

5
-0.360368
-0.616612
0.628464
-0.066965

-1.088213

Statistical significance of elasticities

Stage 1: Standard errors and p-values evaluated at mean values for the period 1994-1998.

Table B1. Estimated uncompensated price elasticities and the total expenditure elasticity, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.

1
2
3
4
5
6

1
-0.34
-0.12
-0.26
-0.15
0.53
-0.27

(0.16)
(0.12)
(0.13)
(0.18)
(0.13)
(0.18)

[0.03]
[0.33]
[0.05]
[0.38]
[0.00]
[0.14]

2
-0.07
-0.31
-0.26
0.15
0.07
0.34

(0.09)
(0.10)
(0.08)
(0.11)
(0.10)
(0.15)

[0.41]
[0.00]
[0.00]
[0.20]
[0.45]
[0.02]

3
-0.53
-0.87
-0.44
0.53
0.14
-1.29

(0.24)
(0.20)
(0.35)
(0.27)
(0.38)
(0.29)

[0.03]
[0.00]
[0.20]
[0.05]
[0.69]
[0.00]

4
-0.28
-0.12
0.34
-1.83
0.11
-1.40

(0.20)
(0.18)
(0.17)
(0.31)
(0.18)
(0.30)

[0.16]
[0.50]
[0.05]
[0.00]
[0.56]
[0.00]

5
1.10
0.03
0.20
0.23
-2.12
-1.70

(0.30)
(0.28)
(0.46)
(0.37)
(0.56)
(0.37)

[0.00]
[0.90]
[0.67]
[0.53]
[0.00]
[0.00]

6
-0.13
-0.07
-0.01
0.11
-0.07
-0.31

(0.02)
(0.03)
(0.02)
(0.04)
(0.02)
(0.12)

[0.00]
[0.01]
[0.58]
[0.00]
[0.00]
[0.01]

Total
0.62
0.21
2.46
3.18
2.27
0.49

expenditure
(0.24)
(0.18)
(0.38)
(0.40)
(0.48)
(0.16)

[0.01]
[0.23]
[0.00]
[0.00]
[0.00]
[0.00]

Table B2. Estimated compensated price elasticities, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.

1
2
3
4
5
6

1
-0.27
-0.01
-0.21
-0.08
0.56
0.01

(0.15)
(0.12)
(0.14)
(0.18)
(0.13)
(0.09)

[0.08]
[0.93]
[0.12]
[0.64]
[0.00]
[0.88]

2
-0.05
-0.27
-0.24
0.17
0.08
0.44

(0.08)
(0.10)
(-0.09)
(0.11)
(0.09)
(0.08)

[0.59]
[0.01]
[0.00]
[0.12]
[0.37]
[0.00]

3
-0.22
-0.45
-0.27
0.81
0.29
-0.16

(0.22)
(0.20)
(0.36)
(0.27)
(0.37)
(0.14)

[0.32]
[0.03]
[0.45]
[0.00]
[0.44]
[0.26]

4
0.12
0.43
0.56
-1.47
0.29
0.07

(0.19)
(0.18)
(0.18)
(0.31)
(0.18)
(0.15)

[0.55]
[0.02]
[0.00]
[0.00]
[0.12]
[0.63]

5
1.38
0.43
0.36
0.49
-1.99
-0.66

(0.28)
(0.30)
(0.48)
(0.37)
(0.56)
(0.19)

[0.00]
[0.15]
[0.46]
[0.18]
[0.00]
[0.00]

6
-0.07
0.01
0.02
0.17
-0.05
-0.08

(0.02)
(0.03)
(0.02)
(0.03)
(0.02)
(0.05)

[0.00]
[0.67]
[0.23]
[0.00]
[0.01]
[0.10]

Group 1: Standard errors and p-values evaluated at mean values for the period 1994-1998.

Table B3. Estimated uncompensated price elasticities and the total expenditure elasticity, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.

1
2
3
4

1
-0.77
0.02
-0.11
-0.04

(0.03)
(0.03)
(0.05)
(0.06)

[0.00]
[0.28]
[0.04]
[0.48]

2
0.10
-1.00
-0.10
0.08

(0.10)
(0.15)
(0.19)
(0.22)

[0.33]
[0.00]
[0.60]
[0.73]

3
-0.67
-0.16
-0.62
-0.10

(0.13)
(0.16)
(0.36)
(0.32)

[0.00]
[0.33]
[0.08]
[0.76]

4
-1.21
0.17
0.57
-0.40

(0.40)
(0.39)
(0.36)
(0.37)

[0.00]
[0.66]
[0.11]
[0.28]

Total
0.89
0.92
1.55
0.86

expenditure
(0.12)
(0.36)
(0.62)
(0.77)

[0.00]
[0.01]
[0.01]
[0.27]

Table B4. Estimated compensated price elasticities, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.

1
2
3
4

1
-0.21
0.18
0.03
0.00

(0.06)
(0.03)
(0.04)
(0.05)

[0.00]
[0.00]
[0.39]
[0.99]

2
0.67
-0.84
0.05
0.12

(0.16)
(0.17)
(0.15)
(0.21)

[0.00]
[0.00]
[0.74]
[0.58]

3
0.30
0.11
-0.38
-0.03

(0.32)
(0.21)
(0.28)
(0.30)

[0.35]
[0.61]
[0.17]
[0.92]

4
-0.67
0.32
0.71
-0.36

(0.32)
(0.35)
(0.28)
(0.37)

[0.04]
[0.36]
[0.01]
[0.33]

Group 3: Standard errors and p-values evaluated at mean values for the period 1994-1998.

Table B5. Estimated uncompensated price elasticities and the total expenditure elasticity, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.

1
2
3
4

1
-0.57
-0.38
-0.14
0.03

(0.37)
(0.45)
(0.12)
(0.17)

[0.13]
[0.40]
[0.22]
[0.84]

2
-0.41
-0.61
0.06
-0.12

(0.38)
(0.54)
(0.13)
(0.16)

[0.28]
[0.26]
[0.62]
[0.44]

3
-0.23
0.20
-0.82
0.11

(0.22)
(0.30)
(0.12)
(0.11)

[0.30]
[0.49]
[0.00]
[0.33]

4
0.94
-1.30
-0.03
-0.55

(1.10)
(1.40)
(0.42)
(0.67)

[0.39]
[0.36]
[0.95]
[0.44]

Total
1.06
1.07
0.73
0.93

expenditure
(0.23)
(0.23)
(0.15)
(0.73)

[0.00]
[0.00]
[0.00]
[0.20]

Table B6. Estimated compensated price elasticities, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.

1
2
3
4

1
-0.14
0.02
0.06
0.06

(0.46)
(0.38)
(0.12)
(0.16)

[0.76]
[0.95]
[0.63]
[0.70]

2
0.03
-0.20
0.26
-0.09

(0.47)
(0.47)
(0.14)
(0.15)

[0.95]
[0.67]
[0.07]
[0.54]

3
0.07
0.48
-0.68
0.13

(0.27)
(0.26)
(0.12)
(0.11)

[0.81]
[0.06]
[0.00]
[0.24]

4
1.32
-0.94
0.15
-0.53

(1.37)
(1.21)
(0.42)
(0.65)

[0.33]
[0.44]
[0.72]
[0.42]

Group 4: Standard errors and p-values evaluated at mean values for the period 1994-1998.

Table B7. Estimated uncompensated price elasticities and the total expenditure elasticity, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.

1
2
3
4

1
-1.68
0.18
0.31
0.47

(0.17)
(0.08)
(0.13)
(0.07)

[0.00]
[0.02]
[0.02]
[0.00]

2
0.82
-1.34
-0.24
-0.18

(0.38)
(0.36)
(0.23)
(0.30)

[0.03]
[0.00]
[0.29]
[0.56]

3
0.54
-0.14
-1.36
-0.73

(0.29)
(0.11)
(0.29)
(0.22)

[0.06]
[0.21]
[0.00]
[0.00]

4
1.28
-0.22
-0.48
-1.50

(0.27)
(0.22)
(0.19)
(0.20)

[0.00]
[0.30]
[0.01]
[0.00]

Total
0.72
0.94
1.68
0.92

expenditure
(0.06)
(0.12)
(0.14)
(0.09)

[0.00]
[0.00]
[0.00]
[0.00]

Table B8. Estimated compensated price elasticities, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.

1
2
3
4

1
-1.29
0.26
0.49
0.55

(0.17)
(0.08)
(0.13)
(0.07)

[0.00]
[0.00]
[0.00]
[0.00]

2
1.32
-1.23
-0.02
-0.07

(0.38)
(0.36)
(0.24)
(0.30)

[0.00]
[0.00]
[0.95]
[0.81]

3
1.44
0.05
-0.95
-0.54

(0.29)
(0.11)
(0.30)
(0.21)

[0.00]
[0.63]
[0.00]
[0.01]

4
1.77
-0.12
-0.25
-1.40

(0.27)
(0.21)
(0.19)
(0.20)

[0.00]
[0.58]
[0.19]
[0.00]

Group 5: Standard errors and p-values evaluated at mean values for the period 1994-1998.

Table B9. Estimated uncompensated price elasticities and the total expenditure elasticity, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.

1
2
3
4
5

1
-0.78
-0.17
-0.05
0.02
-0.05

(0.05)
(0.07)
(0.05)
(0.10)
(0.04)

[0.00]
[0.00]
[0.27]
[0.87]
[0.20]

2
-0.47
-1.19
0.88
0.06
-0.09

(0.20)
(0.66)
(0.25)
(0.65)
(0.10)

[0.02]
[0.07]
[0.00]
[0.92]
[0.36]

3
-0.12
0.83
-1.39
-0.29
0.11

(0.13)
(0.25)
(0.16)
(0.29)
(0.07)

[0.36]
[0.00]
[0.00]
[0.31]
[0.10]

4
0.05
0.04
-0.14
-0.62
-0.08

(0.14)
(0.35)
(0.15)
(0.52)
(0.06)

[0.70]
[0.90]
[0.35]
[0.24]
[0.15]

5
-0.21
-0.37
-0.09
-0.73
-0.62

(0.16)
(0.27)
(0.18)
(0.35)
(0.16)

[0.19]
[0.17]
[0.61]
[0.04]
[0.00]

Total
1.03
0.80
0.86
0.74
2.02

expenditure
(0.07)
(0.25)
(0.15)
(0.18)
(0.31)

[0.00]
[0.00]
[0.00]
[0.00]
[0.00]

Table B10. Estimated compensated price elasticities, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero

1
2
3
4
5

1
-0.38
-0.03
0.09
0.27
0.05

(0.06)
(0.07)
(0.05)
(0.09)
(0.03)

[0.00]
[0.67]
[0.06]
[0.00]
[0.18]

2
-0.16
-1.08
0.99
0.26
-0.02

(0.26)
(0.66)
(0.26)
(0.61)
(0.10)

[0.55]
[0.10]
[0.00]
[0.67]
[0.88]

3
0.22
0.94
-1.27
-0.08
0.19

(0.16)
(0.24)
(0.17)
(0.27)
(0.07)

[0.17]
[0.00]
[0.00]
[0.76}
[0.01]

4
0.35
0.14
-0.04
-0.44
-0.01

(0.19)
(0.35)
(0.16)
(0.49)
(0.06)

[0.07]
[0.69]
[0.82]
[0.37]
[0.81]

5
0.59
-0.11
0.19
-0.24
-0.43

(0.20)
(0.27)
(0.17)
(0.32)
(0.16)

[0.00]
[0.69]
[0.27]
[0.46]
[0.01]