Elena Lasarte Navamuel
Dusan Paredes Araya
Esteban Fernández Vázquez
Serie de Documentos de Trabajo en Economía - UCN
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A true cost of living index for Spain using a
microeconomic approach and censored data
A TRUE COST OF LIVING INDEX FOR SPAIN USING A
MICROECONOMIC APPROACH AND CENSORED DATA
Elena Lasarte Navamuel1
Dusan Paredes Araya2
Esteban Fernández Vázquez1
Resumen
Un verdadero costo de la vida (COL) mide la proporción de los gastos por
mantener un nivel de utilidad para dos vectores de precios. Su aplicación y la
comprobación empírica ha sido, en general, focalizada desde una perspectiva
temporal. El objetivo de este trabajo es calcular un COL espacial entre las
regiones de Espanha. Para este propósito se utilizaran los microdatos de la
Encuesta
de
Hogares
Presupuesto 2010
(EPF,
Encuesta
de
PresupuestosFamiliares) proporcionado por el Instituto Español de Estadística
(INE, InstitutoNacional de Estadística).
Vamos a denominar a este costo Índice espacial del Costo de Vida (SCOL).
Utilizamos un enfoque microeconómico que mantiene el nivel de los hogares
de la constante utilidad y permite la sustitución entre las diferentes canastas de
bienes a través del espacio. Los resultados revelan grandes diferencias en
SCOL a través de las regiones españolas. Las estimaciones del índice de
SCOL permite reconsiderar las comparaciones regionales en materia de
salarios medios. Aun cuando las cifras nominales de las cuentas regionales
muestran grandes disparidades regionales, las diferencias regionales son en
gran parte moderada cuando las cifras salariales son corregidos por nuestra
SCOL.
Palabras clave: Índice espacial del Costo de Vida, AIDS, estimación en dos
etapas para datos censurados, España.
Código JEL: R21, C36
1
2
REGIOLab. University of Oviedo, Spain.
Universidad Católica del Norte, Chile.
1
Abstract
A true Cost of Living (COL) index measures the expenditure ratio of maintaining
a utility level for two price vectors. Its application and empirical testing has
been, generally, focalized on a temporal perspective. The aim of this paper is to
calculate a spatial COL for the regions of Spain. For this purpose, we will use
the microdata from the 2010 Households Budget Survey (EPF, Encuesta de
Presupuestos Familiares) provided by the Spanish Statistical Institute (INE,
Instituto Nacional de Estadística).
We will denominate this index Spatial Cost of Living Index (SCOL). This type of
analysis is not usually made by the national statistical agencies and Spain is not
an exception. We use a microeconomic approach that keeps the households’
level of utility constant and allows substitution among different baskets of goods
across space. The results reveal large differences in SCOL across the Spanish
regions. The estimates of the SCOL index allows for reconsidering regional
comparisons in terms of average wages. Even when nominal monetary
magnitudes for Regional Accounts show great regional disparities, regional
differences are largely moderated when the wage figures are corrected by our
SCOL.
Keywords: Spatial cost of living index, AIDS, two-step estimation for
censored data, Spain.
JEL Classification: R21, C36
2
1.
Introduction.
A true Cost of Living (COL) index measures the expenditure ratio of
maintaining a utility level for two price vectors. The COL index is broadly used
as an indicator useful to asses changes in welfare: if the COL index is equal to
one, then the price change does not affect the consumer surplus. Otherwise,
the consumer should be compensated, namely in a positive or negative sense,
in order to keep constant the level of utility. Computing a spatial version of the
COL index (SCOL index) is an issue of great interest since it allows measuring
expenditure differentials across regions, which have important implications for
the assessment of welfare policies. This kind of analysis is not usually made by
national statistical agencies where its application has been limited to a temporal
perspective (Koo et al., 2000 and Molina, 1997). Comprehensive regional cost
of living data are not available from a governmental source, neither for U.S.
states, nor for European regions (Suedekum, 2006). Most of works use an
approximation to the SCOL index, for example, the ACCRA3 index or the CPI
(Koo et al., 2000; Curran et al., 2006 and Jolliffe, 2006) and, other works
estimates its own SCOL index according to different approaches: (i) estimation
of a regression model of the factors that explain COL in an area (Kurre, 2003),
(ii) estimation of COL data from expenditure data (Voicu and Lahr, 1999); and
(iii) estimation of a complete set of demand equations (AIDS) for all
commodities in all places (Paredes and Iturra, 2011). While this approach is
strongly grounded on the consumer theory, it is considered very complicated
and typically is not operational due to data requirements.
The aim of this paper is to provide an estimation of the SCOL index. The
SCOL index is calculated by estimating an Almost Ideal Demand System
(AIDS) developed by Deaton and Muellbauer (1980) following a microeconomic
approach, which is consistent with the consumer theory. The data are obtained
from the Household Budget Survey of 2010. The AIDS estimates an
expenditure function as a function of prices and a given utility level. After the
parametric construction, the expenditure ratio between the average prices of
two regions is directly estimated. We should keep in mind that the data
available present several limitations. First, the SCOL index is calculated only for
3
American Chamber of Commerce Researchers Association.
3
the food group because we need information about physical quantities and
monetary expenditure across spatial units. This information allows for
recovering prices, something that cannot be achieved in the rest of the
expenditure groups excepting energy products. Additional, the food group is the
most important group in terms of household consumption, with an expenditure
of 14.37% on total household budget. Second, our analysis only estimates the
SCOL for the 17 Spanish NUTS II regions (Autonomous Communities) since
the survey does not allows for more detailed spatial scale. At this geographical
disaggregation level we find large differences in the SCOL across regions: the
differences in cost of living between regions around 20%.
The paper is organized as follows: section 2 reviews the literature on
cost of living index and describes the methodology applied. Section 3 provides
details about the database used for our empirical exercise for the Spanish
regions. The estimation results are reported in section 4. Finally, section 5
concludes the paper with the final remarks.
2. Methodology for constructing a Spatial Cost of Living Index.
The Spanish National Institute of Statistics (INE) estimates the Price
Consumer Index (CPI) to measure variations in prices of goods and services
purchased by Spanish households. The CPI index is calculated as a chainLaspeyres index between the current period and the base period. It can be
considered as an approximation of the COL, given that the CPI does not
maintain a constant utility level as the COL does. In other words, the CPI is only
a proxy of the true cost of living because it imposes a fixed basket of goods and
services to all households in all spatial units. Keeping fixed the quantities
consumed instead of the utility level generates a substitution bias derived from
ignoring the substitutions made by consumers in response to price variations.4
The substitution bias is more significant in spatial comparisons than in a time
series context. The reasons are (i) because transportation costs affect prices in
4
We can highlight the importance of the existing bias between the two indices taking into
account the words of Allan Greenspan in 1995 before the U.S. Congress. He declared that he
suspected that the Price Consumer Index overstated the Cost of Living by 0.5 to 1.5% point
annually. The bias of 1.1% a year up to 2006 would generate an increase of US$ 691 billion in
the public deficit (Lucia Fava, V., 2010).
4
different ways across space even in the same period of time; and, (ii) because
the consumption basket is affected by geographical and weather factors
(Paredes & Iturra, 2012). For these reasons, the assumption that the
consumption basket is fixed across the space could be an unrealistic
assumption when spatial price variations are studied.
The theory of the COL was initially developed for Konüs (1924). The
author focused his theory on comparing two periods of time: a household which
faces two different price levels tries to adjust its commodity basket in order to
maintain a constant level of utility with the minimum expenditure cost. However,
due to practical reasons this approach is not the most commonly used. When
instead of utility the baskets are fixed, such as in the case of CPI, the resulting
index is called Axiomatic. This approach is preferred over COL because its
calculation does not require estimating an expenditure function. Its main
disadvantage is the existence of a potential spatial substitution bias. For
example, if two prices are extremely different across space, then the consumers
will change the quantity that is not captured by the axiomatic approach.
This paper follows Konüs’ idea but studying price differentials across the
space. Despite the vast literature on cost of living indices over time, the spatial
dimension has received less attention (Desai, 1969; Howard Nelson, 1991;
Timmins, 2006 and Atuesta and Paredes, 2011). For the specific case of Spain,
no previous attempt of computing a SCOL has been made. In this paper this
gap is covered estimating a SCOL index for Spanish regions. In order to
calculate the SCOL with the economic approach we need to observe prices,
quantities and a utility function. Prices and quantities are directly observable
from sample data, but we cannot observe the form of the utility function. To
address this problem an Almost Ideal Demand System (AIDS), proposed by
Deaton and Muellbauer (1980), is estimated.
The estimation of the AIDS is used to recover the expenditure function
and to calculate the COL for the median household in each region. The analysis
starts with a definition of a SCOL index between regions i and j as:
5
=
and
Where
̅,
̅ ,
,
(1)
are the prices paid by the reference consumer in the regions i
and j, respectively. The AIDS defines a cost or expenditure function consistent
with the microeconomic theory that defines the minimum expenditure necessary
to attain a utility level at given prices:
,
= 1−
log
+ log "
(2)
where c is the expenditure function, p is the price vector, u is the utility level,
and
log
&
= #$ + % # log
'(
log "
&
&
1
+ % % * log
2
'( '(
= log
+ +$ ,
-
log
(3)
(4)
If (3) and (4) are substituted in the cost function (2), and applying the
Shepard’s lemma, the demand functions can be obtained directly from this
equation:
. /01
. /01
,
2 32
=
,
=4
(5)
Where4 is the budget share of good i:
&
4 = # + % * log
+ + +$ ,
'(
-
(6)
If u is defined in (2) as a function of prices and total expenditure and
substitute the result into (6), the shares are obtained as a function of p and x,
6
plus a set of parameters to be estimated. These shares are the AIDS demand
functions:
&
+ + log56⁄7 9
4 = # + % * log
'(
(7)
Where α, β and γ are parameters of the model; 4 is the budget share of good
i;6is the total expenditure on the food groups and P is a price index defined as:
log 7 = #$ + ∑&'( # log
+ ∑&'( ∑&'( * log
(
;
log
(8)
The parameters of the AIDS model satisfy the adding-up restriction
(∑ 4 = 1), are homogeneous of degree zero in prices and total expenditure
taken together, and the total expenditure satisfies the Slutsky symmetry. These
properties of the demand consumer theory can be imposed in the following way:
∑&'( # = 1,
∑&'( * = 0,
∑&'( * = 0,
∑&'( + = 0
* =*
(9)
(10)
(11)
The model to be estimated in our case is a particular case of the AIDS
model because it has censored data, caused by those households that report
zero consumption. Not accounting for the zero consumption biases the
estimation of the parameters of the model. To address the problem of biased
estimation we will follow the two-step method proposed by Shonkwiler and Yen
(1999) which improves a previous two-step estimation procedure of Heien and
Wessells (1990). In the first step we estimate a probit regression with a
dependent binary variable that represents the decision of consuming and a set
of socioeconomic variables are used as regressors. The probit model
determines the probability that a given household consumes a given good and it
is used to estimate the cumulative (Φ) and the density (=) functions.
7
The second step incorporates the cumulative function as a scalar in the
equations for shares, whereas the density function is included as an extra
variable:
&
4 = Φ 6 ># + % * log
'(
+ + log56⁄7 9? + %
@
AA@ + B= 6
@
(12)
AA@ are dummy variables for the 17 Spanish regions (NUTS II) that
Where
represent unobservable heterogeneity across spatial units and idiosyncratic
components;
@
is a parameter associated to the regional dummy
is an extra parameter associated with the density function.
AA@ ; and, B
The set of C– 1 equations like (11) conforms the demand system, where
n is the number of shares and the last share is recovered as a residual of the
remaining C– 1 ones. Once this demand system is estimated, the parameters
are used to recover the expenditure function of a representative household for
each spatial unit and the SCOL index defined in(1) is calculated.
3. Data.
The data used in this analysis are obtained from the 2010 Household
Budget Survey (EPF), a survey that provides information about Spanish
household’s
patterns
of
consumption,
income
and
other
household
socioeconomic characteristics5. The data sample is formed by 22,346
observations at a household level and for the 17 regions.
The AIDS is estimated for ten sub-groups belonging to the group of Food
and non-alcoholic beverages in the EPF classification: (1) Bread and cereals,
(2) Meat, (3) Fish, (4) Milk, cheese and eggs, (5) Oil, (6) Fruits, (7) Vegetables,
(8) Sugar, (9) Coffee, tea and cacao; and (10) Mineral water and other soft
drinks. The observed budget shares 4 of equation (12) for each household are
calculated dividing the expenditure of the household in each of the ten food
groups by the total household expenditure in food.
5
More details in
http://www.ine.es/jaxi/menu.do?type=pcaxis&path=%2Ft25%2Fp458&file=inebase&L=0
8
The estimation of the AIDS requires data on prices, quantities purchased
and household expenditure. A problem arising due to zero consumption is that
prices are not available for all the items and all the households. Due to the fact
that all the prices must be observable to estimate the AIDS system, the
individual prices at which households purchase the commodities are recovered
by dividing expenditures by quantities. In the cases where the quantities are not
reported by a household, the price of the item is replaced by a geometric mean
of the prices of this item in the same region, distinguishing if this item is
purchased by a household situated in a capital city or not. In the first case, the
price is replaced by the average price of the same item in the same capital city.
In the second case, the price is replaced by the average price of the item in the
region. This procedure to determine missing prices implies that the households
that do not consume an item are facing the average commodity prices.
Although the household expenditure is the main variable in the survey,
the EPF also recovers other socioeconomic variables (size of the household,
sex, marital status and age of the head household, income level and education
level) that will be used to estimate the probit model in the first step of the
process. It is assumed that these characteristics influence the decision of
consuming a particular good.
4. Estimation and results.
The estimates of the probit model for the first step of the Shonkwiller and
Yen (1999) methodology are shown in Appendix 1. A binary variable which
represents the decision of consumption of each of the ten food groups of the
data sample is regressed as a function of the socioeconomic variables
described in section 3, demographic variables represented as region dummies,
population size of the municipality and one dummy which takes the values of 1
if the household is situated in a capital city and 0 otherwise. The results of the
probit model are used to calculate the cumulative (B) and the density (=)
functions included in the estimation of the AIDS.
The parameters of the model are estimated by applying Nonlinear
Seemingly Unrelated Regression that fits a system of nonlinear equations by
Feasible Generalized Nonlinear Least Squares (FGNLS). The parameters
9
estimated are shown in Appendix 2. These estimates are necessary to recover
the expenditure function (2) for the representative household in each region
and, then this expenditure function is used to calculate the SCOL. As a
representative household we take the household with the median income in
each region. The results of the SCOL are shown in Table 1.
Table 1.The Spatial Cost of Living Index by regions.
REGION
SCOL
ANDALUCIA
ARAGON
ASTURIAS
BALEARES
BASQUE COUNTRY
CANARY ISLANDS
CANTABRIA
CASTILLA LA MANCHA
CASTILLA LEON
CATALONIA
EXTREMADURA
GALICIA
LA RIOJA
MADRID
MURCIA
NAVARRA
VALENCIA
0.915
0.971
0.929
0.960
1.093
1.019
0.964
0.835
0.900
1.082
0.912
0.917
0.981
1.000
1.008
1.093
0.979
The region of Madrid is taken as reference, which explains why the index for
Madrid takes the value 1. The results are sorted in alphabetical order, showing
the smallest value (0.835) in Castilla-La Mancha and the highest one (1.093) in
the Basque Country and Navarra. The results could be interpreted as follows:
the cost in food products required to attain the same utility level for the median
households in Madrid is around 17% higher than the equivalent household in
Castilla-La Mancha, for example6. Similarly, is 9.3% lower than in the Basque
Country and Navarra. Differences in the COL seem to be quite relevant among
regions, especially if we take into account the relative small size of the country
and the proximity between some pairs of regions. A positive correlation is
observed between the COL estimated and the regional dynamics, since the
most developed regions in Spain (Catalonia, the Basque Country and Navarra)
6
Note that differences in consumption patterns are allowed between these two households,
provided that their utility level is the same.
10
are those that present the highest SCOL indices. In these regions the cost of
food products is higher than in the region of Madrid, which is the region with the
largest city of Spain. Even when large city sizes are normally linked to higher
incomes and, consequently, higher costs, one should bear in mind that the
results are only observable at the NUTS II level. In other words, the results are
just an average of all the households living in the region of Madrid, which
comprises Madrid City but much smaller towns and villages as well. Catalonia,
the Basque Country and Navarra do not contain such a large city as Madrid,
even when Barcelona in Catalonia or the metropolitan area of Bilbao in the
Basque Country are considerably large. However, they are regions that
comprise many more urban areas on average than the region of Madrid.
Furthermore, these regions are located in the so-called Ebro-Axis, which is the
area with the most developed Spanish regions, traditionally. One interesting
exception is the case of the Canary Island, where the cost in food products is
estimated to be larger than in Madrid. Even when this could be somehow
surprising, since Canary Island are considered as relatively poor within Spain,
this could be an consequence of higher transport costs.
5. Concluding remarks: some implications on regional economics.
Economic indicators of regional income do not normally take into account
geographical differentials in cost of living. Not adjusting these nominal indicators
and transforming them into real values inevitably yields misleading results. For
example, policies designed to alleviate regional income disparities that do not
consider potential geographical differences in cost of living could result in
benefits to regions that in real terms would not need these benefits. As an
illustrative example, Table 3 shows the average wages across regions in
nominal terms for 20107 and the same values when they are adjusted by the
estimated SCOL.
7
Information on regional wages can be founded at:
http://www.ine.es/jaxi/menu.do?type=pcaxis&path=/t22/e308_mnu&file=inebase&N=&L=0
11
Table 3.Nominal and adjusted wages in 2010 by regions.
REGION
ANDALUCIA
ARAGON
ASTURIAS
BALEARES
CANARY ISLANDS
CANTABRIA
CASTILLA LEON
CASTILLA LAMANCHA
CATALONIA
VALENCIA
EXTREMADURA
GALICIA
MADRID
MURCIA
NAVARRA
BASQUE COUNTRY
LA RIOJA
Nominal Wage
18,839
20,623
20,691
19,708
17,552
19,459
18,205
19,272
23,871
19,575
17,795
18,815
25,785
18,744
22,862
25,596
21,127
Wage adjusted by
SCOL
20,580
21,236
22,273
20,526
17,224
20,178
20,228
23,071
22,056
19,998
19,508
20,513
25,785
18,591
20,914
23,419
21,527
Second column shows the average wage per worker in 2010 according
to the Regional Accounts disseminated by INE. The last column to the right
shows these same values but adjusted by the SCOL index estimated in the
previous section, i.e., expressed in equivalent Euros of Madrid. By applying this
adjustment is relatively easy to detect that the regional disparities in wages are
considerably lower. For example, the mean wage in Madrid in 2010 was
approximately 37% higher than in Andalucia; however if differences in cost of
living are corrected by using the estimated SCOL, this difference is only of 25%.
The possibility of making such analysis is the main motivation for this
paper, which proposes a cost of living index for the case of Spain. Although the
Consumer Price Index is the usual measure taken as reference for quantifying
changes in cost of living, it cannot be considered a true cost of living index
because it suffers from a variety of conceptual and practical problems. Our
Spatial Cost of Living Index (SCOL) is based on microeconomic foundations
and is estimated from an Almost Ideal Demand System in order to maintain
constant the level of utility of the consumer instead of fixing the basket. The
estimation of the AIDS considers the potential bias generated by zero
consumption observations, a very usual in the expenditure surveys. Using this
methodology the expenditure ratio is calculated for two representative
consumers in two different spatial units. While most of the literature has
12
computed the cost of living index over time, we computed the index in a spatial
context where a substitution bias problem due to the heterogeneity of the
consumers belonging to different spatial units. The empirical results, using food
microdata of the Spanish Household Budget Survey for 2010, show huge
differences in cost of living across regions. Our estimates show that the
difference between the most expensive and the cheapest region, Basque
Country and Castilla La Mancha, respectively, is more than26%.These
differences in the SCOL provide some new insights when wage differences
across the 17 NUTSII regions are analyzed. The results are undoubtedly
limited, since they only study differences in cost of living regarding food –due to
data availability-, but allow for comparing living standards across regions from a
different perspective, not commonly considered in traditional regional analysis.
13
14
Appendix 1: Probit estimation for censored consumption
Share1
Share2
Share3
Share4
Share5
Expenditure
0.0956***
0.4184***
0.5976***
0.4344***
0.3317***
Stratification Level
0.0192***
-0.0643***
-0.0588***
-0.0389***
-0.0672***
Household Size
0.4471***
0.2687***
0.1859***
0.2910***
0.2240***
Number of Employed
-0.0435***
0.0661***
0.0215***
-0.0952***
-0.0051***
Head Age
0.0015***
0.0093***
0.0135***
0.0046***
0.0065***
Head Sex
0.0167***
0.0146***
0.0127***
0.0339***
0.0107***
Head Marital Status
0.0065***
0.0091***
-0.0274***
-0.0118***
-0.0100***
Education Level
-0.0915***
-0.0818***
-0.0461***
-0.0303***
-0.0513***
Municipality Size
-0.0181***
-0.0811***
-0.0165***
-0.0470***
-0.0395***
Capital of Province
0.0003
0.0288***
0.0099***
0.0203***
0.0003
Andalucia
-0.0194*
0.0356***
0.4222***
0.1613***
0.2780***
Aragon
0.0370***
0.0352***
0.4058***
0.2057***
0.1826***
Asturias
-0.2127***
-0.1673***
0.1519***
0.1410***
-0.0843***
Baleares
-0.0291***
-0.0169*
0.0194***
0.1414***
-0.0027
Canarias
0.0292***
-0.0416***
0.0882***
-0.0102
0.1470***
Cantabria
0.1461***
0.2914***
0.5006***
0.2764***
Castilla-León
0.1624***
0.0135*
0.2635***
-0.0164*
-0.0869***
Castilla-La Mancha
0.1851***
-0.1087***
0.1872***
-0.0129
-0.2003***
Cataluña
-0.0039
-0.0462***
0.1040***
0.1609***
0.0641***
Valencia
-0.1055***
-0.0392***
0.1775***
-0.0440***
-0.1864***
Extremadura
-0.2004***
0.0259***
0.3508***
0.0877***
0.3017***
Galicia
0.3446***
0.2021***
0.2996***
0.4242***
0.0175***
Madrid
-0.0249**
0.0428***
0.4208***
0.1733***
0.3379***
Murcia
-0.0503***
0.1610***
0.3648***
0.1368***
0.2952***
Navarra
0.0468***
-0.1298***
0.0782***
-0.3568***
-0.0831***
Pais Vasco
0.1554***
0.0246***
0.1782***
0.0613***
0.0735***
La Rioja
0.0267**
Ceuta y Melilla
-0.3618***
0.3226***
-0.0977***
0.2836***
Madrid City
-0.1373***
0.0420***
0.3402***
0.0633***
0.2350***
Constant
0.5872***
-3.0732***
-5.7930***
-3.0416***
-3.3013***
(1) *, ** and *** represent the level of significance to 10%, 5% and 1%, respectively.
(2) Number of observations 16261421 (weighted).
15
Share6
Share7
Share8
Share9
Share10
0.4575***
0.4716***
0.3895***
0.3755***
0.2810***
-0.0374***
-0.0866***
-0.0750***
-0.0488***
-0.0472***
0.1854***
0.2660***
0.2511***
0.2177***
0.2771***
-0.0135***
-0.0461***
-0.0002
0.0121***
-0.0113***
0.0169***
0.0098***
0.0024***
0.0045***
-0.0085***
0.0302***
0.0290***
0.0142***
0.0148***
-0.0019***
-0.0536***
-0.0315***
0.0157***
0.0051***
0.0137***
0.0054***
0.0349***
-0.0001
-0.0239***
-0.0447***
-0.0585***
-0.0791***
-0.0365***
-0.0309***
-0.0735***
0.0152***
0.0097***
0.0194***
0.0135***
0.0110***
0.5216***
0.4443***
0.1767***
0.4110***
0.5427***
0.4487***
0.3648***
0.1676***
0.2763***
0.1972***
0.0685***
0.0752***
0.0174***
-0.0046
-0.0272***
0.3482***
0.3735***
0.1014***
0.0311***
0.4978***
0.3232***
0.1685***
0.2359***
0.3316***
0.7011***
0.1183***
0.1144***
0.1631***
0.2114***
0.2203***
0.3737***
-0.0297***
-0.1611***
-0.1375***
-0.1226***
0.2976***
0.2206***
-0.1429***
-0.0737***
0.1423***
0.3965***
0.3315***
0.0426***
0.0795***
0.3759***
0.1883***
0.3188***
-0.0849***
-0.0653***
0.3191***
0.2380***
0.1680***
0.3296***
0.5185***
0.3672***
0.2436***
0.1485***
0.0754***
0.0049
0.0708***
0.6353***
0.3948***
0.1264***
0.2695***
0.4389***
0.2889***
0.2508***
0.1743***
0.4004***
0.4882***
0.0979***
0.2015***
-0.0260***
0.0596***
-0.1745***
0.2330***
0.1584***
0.1333***
0.0120***
-0.1767***
0.1119***
0.0703***
0.1851***
0.3375***
0.4579***
0.6053***
0.3559***
0.1921***
0.3031***
0.3485***
-4.2029***
-3.8425***
-3.7123***
-4.0518***
-1.7106***
Appendix 2: Coefficients of the Almost Ideal Demand System.
Coeff.
(
;
0.00125***
#(
#;
Coeff.
0.0042***
+(
+;
Coeff.
-0.0660***
*((
*(;
Coeff.
0.0665***
-0.0440***
+E
#E
*(E
-0.0200***
E
+
#
*
-0.0101***
F
F
F
(F
+
#
*
-0.0011***
G
G
G
(G
+H
#H
*(H
-0.0010***
H
+I
#I
*(I
-0.0008***
I
+J
#J
*(J
0.0010***
J
+K
#K
*(K
0.0015***
K
*;;
0.0374***
($
*;E
0.0163***
((
*;F
-0.0096***
(;
*;G
0.0026***
(E
*;H
0.0077***
(F
*;I
-0.0013***
(G
*;J
-0.0014***
(H
*;K
-0.0004***
(I
*
0.0056***
(J
EE
*EF
0.0001***
*EG
0.0012***
*EH
-0.0014***
*EI
0.0077***
*EJ
0.0000***
*EK
-0.0001***
*FF
0.0242***
*FG
-0.0018***
*FH
0.0013***
*FI
-0.0008***
*FJ
-0.0010***
*FK
-0.0010***
*GG
-0.0039***
*GH
0.0037***
*GI
-0.0010***
*GJ
-0.0014***
*GK
0.0009***
*HH
-0.0097***
*HI
-0.0034***
*HJ
0.0019***
*HK
0.0022***
*II
-0.0063***
*IJ
0.0009***
*IK
0.0020***
*JJ
0.0030***
*JK
-0.0020***
*KK
-0.0032***
(1) *, ** and *** represent the level of significance to 10%, 5% and 1%, respectively.
0.00121***
0.00143***
0.00157***
0.00091***
0.00125***
0.00127***
-0.00007***
0.00110***
0.00049***
0.00283***
0.00080***
0.00251***
0.00190***
0.00194***
0.00232***
0.00134***
0.00377***
0.3775***
0.2498***
0.0959***
0.0514***
0.0770***
0.0811***
0.0043***
0.0172***
0.0610***
0.0560***
-0.0174***
0.0110***
0.0044***
-0.0013***
-0.0043***
-0.0009***
16
B(
B;
BE
BF
BG
BH
BI
BJ
BK
Coeff.
-0.0202***
0.2578***
0.2617***
0.1525***
0.0642***
0.2262***
0.1170***
0.0146***
0.0223***
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18