LSMSWorking Paper
Number 85
Demand Analysis and Tax Reform in Pakistan
Angus Deaton and Franque Grimard
The World Bank
Washington, D.C.
Copyright © 1992
The International Bank for Reconstruction
and Development/THE WORLDBANK
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First printing February 1992
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ISSN:02534517
Angus Deaton is Professor of Economicsand Public Affairs in the Department of Economics at Princeton
University. Franque Grimard is a Ph.D. candidate at the Department of Economics at Princeton University.
Libraryof Congress Cataloging-in-PublicationData
Deaton, Angus.
Demand analysis and tax reform in Pakistan / Angus Deaton and
Franque Grimard.
p. cm. - (LSMSworking paper, ISSN 0253-4517;no. 85)
Includes bibliographical references.
ISBN0-8213-2059-9
1. Taxation-Pakistan. 2. Pricing-Pakistan. 3. Food-Prices-Pakistan. 4. Household surveys-Pakistan. I. Grimard, Franque.
II. Title. Ill. Series.
HJ5168.5.D43 1992
92-3418
336.2'05'095491-dc2O
CIP
v
ABSTRACT
Pakistan,like manyLDCs, derivesmostof governmentrevenuefrom indirecttaxation.However,
the system of taxes and subsidieshas grown up piecemealover the years, and it is unlikely that it cannot
be improved. Anytax reform proposal must deal with the basic issuesof equity and efficiency.Changes
in taxes benefit or hurt people according to their demand and supply patterns, while the effects on
government revenue depend on the way in which supply and demand respond to prices. Empirical
demand analysis can inform the debate by delineating consumptionpatterns, and by estimatingthe
responsivenessof demandto price. Previous exercisesin price reform for Pakistanhave been forcedto
make very restrictiveassumptionsaboutconsumerpreferences,and have typicallyused demandsystems
that prejudge what are the desirable directionsof price reform.
In this paper, the methodologyof Deaton (1988, 1991)is extended and applied to the 1984-85
HouseholdIncome and ExpenditureSurvey.A theoryof quality variationbased on separablepreferences
is developed,and the implicationsfor welfare and empiricalanalysislaid out. The prices of oils and fats
and of sugar do not vary very much in the survey data, and the symmetry and homogeneityrestrictions
from the theory play an importantpart in obtainingsharp estimatesof own and cross-priceelasticities.
The parameterestimatessuggestthat there are significantcross-priceelasticitiesbetweenthe high-calorie
foods, wheat, rice, sugar, and oils, and the presenceof these substitutionpatterns meansthat the effects
of potentialprice reforms are quite differentfrom those that wouldbe estimatedusing the traditionaland
more restrictiveassumptions.Basedon demandpatternsalone, it wouldbe desirableto raise government
revenue by raising the consumerprice of rice. However, in Pakistan it is not generally possible to
decouplethe producer and consumerprices of rice, so that a full analysisof policy changewould also
dependon the supply responses,which are not consideredin this study.
vi
ACKNOWLEDGEMENTS
We are grateful to Harold Alderman, Valerie Kozel, David Newbery, Nicholas Stern, and
especiallyDave Coady, for help in the preparationof this paper. Deaton is grateful to the Lynde and
Harry Bradley Foundation for research support, and to the Department of Applied Economics,
Cambridge, and ST/ICERDat the London Schoolof Economicsfor hospitality.
vii
FOREWORD
This paper is about "getting prices right." It is an empirical examinationof food prices in
Pakistan, and of what changes in prices would mean for the allocation of resources and for the real
incomesof consumers,many of whom are very poor. The results show how importantit is to take into
account substitutionbetweendifferentfoods when consideringa reform to the price of one of them. For
the case of Pakistan,the low consumerprice of rice is desirableon neither efficiencynor distributional
grounds although remedying the situation in practice is likely to affect producer prices and producer
incentives,the effects of which are not dealt with in this paper.
This work is part of a broader program of research in the Population and Human Resources
(PHR) Departmenton the extent of poverty in developingcountriesand on policies to reduce poverty,
especiallyin the context of general price and policy reform. Aside from the substantive findings for
Pakistan, one of the objectivesof this and similar work is to demonstratethe usefulness of household
surveydata for policy discussionsin developingcountries.
Ann 0. Hamilton
Director
Populationand Human ResourcesDepartment
ix
TABLEOF CONTENTS
1
Section 1.
Introduction .
.............................................
Section2.
DemandAnalysisof the 1984-85HIES ............................
4
Section3.
The Analysisof Tax and Price Reform ............................
27
References .
37
............................................
Appendix:AlternativeMethodsof Estimation .......................
39
LIST OF TABLES
5
Table 1
Structure of the 1984-85HIES Sample ................
Table 2
Budget Shares, Unit Values, and Fractions Consumingand Buying .......
. ....
6
Table 3
Price Variation by Province,Quarter, and Village: Rural Pakistan 1984-85 ..... .
. 8
Table 4
Income and Household Size Coefficients in Share and Unit Value Regressions ....
11
Table 5
Estimatesof Own and Cross-PriceElasticities:Pakistan1984-85 ....
........
19
Table 6
Estimatesof Own and Cross-PriceElasticities:Pakistan 1984-85 ....
........
25
Table 7
EfficiencyAspectsof Price Reform: Rural Sector ........
Table 8
Equity and Cost-benefitRatiosfor Tax Increase ........
Table Al
AlternativeEstimatesof Total Expenditureand Price Elasticities ....
..
..
............
33
.............
35
........
42
Introduction
As is the case in manydevelopingcountries,the governmentof Pakistanderives
most of its tax revenuefrom indirecttaxation. In the 1970's and 80's, more than 80%
of federal governmentrevenue was collectedfrom indirecttaxes, some half of which is
accountedfor by customsduties, see Ahmad and Stern (1991, Table 2.5). The tax and
subsidysystem generates major distortionsin relative prices. In the mid-80s, domestic
wheatand rice prices were approximately70% of worldprices at official exchangerates,
while the price of refined sugar was more than 60% aboveworld prices. Since the tax
and subsidypolicies that accountfor these differentialshave grown up piecemealover
the years, the structure can almost certainly be improved, even given the revenue
requirements of the government. The theory of tax reform has been extensively
developedin recent years, and Ahmad and Stern's work applies that theory to the case
of Pakistan. The basic ingredientsare the usual ones of equity and efficiency. Changes
in taxes benefit or hurt people dependingon how much they buy or sell of the goods in
question,so that the effects on equitydependon demand and supplypatterns, as well as
on the extent to which the governmentis concernedto use taxes and subsidiesas a tool
of welfare policy. The efficiencyeffects, by contrast, dependon how demandresponds
to price changes, the estimationof which is the main topic of this paper.
The effectsof a tax changeon tax revenuedependon how much of the good is
consumed (or supplied), and on how the demand for the good and for other goods
changesin response to the price change. It is generallyimportantto consider not only
own-priceresponses,but also cross-priceeffects. In principle,it is clearthat substitution
effectsbetweengoodsmean that changesin the price of one may have substantialeffects
on the tax yields from others. Theoreticalwork has also shown that both optimaltax
structures and desirable directions of tax reform are sensitive to the way in which the
price effects are specified. For example,if it is assumedthat cross-priceelasticitiesare
negligible, efficiency considerationswill make it desirable to tax more highly those
goods whose price elasticities are low, a prescription that would typically lead to
differential tax rates. But such a result is not at all robust. Equally plausible
assumptionsabout preferences can easily generate recommendationsfor uniform tax
rates, see Deaton(1981, 1987a),even in the absenceof any concernfor the distribution
of income. One much used set of preferences, the linear expendituresystem, implies
that it will always be desirable to increase taxes on lowly taxed goods, and decrease
2
taxes on highlytaxed goods. In this case, not only is uniformitydesirable, but any move
towards uniformity is itself welfare improving. Given these widely different results, it
is importantthat proposalsfor tax reform should be firmly based on measurement,and
not on arbitrary prior assumption.
Whilefew woulddenythe desirabilityof measurementin principle,there remain
formidabledifficulties in the way of estimatingprice responsesin Pakistanas in most
otherdevelopingcountries. Demandanalysisin developedeconomieshas typicallyrelied
on intertemporalprice variationto identifydemand responses. Accurate estimationof
a full set of own and cross-price elasticities typically requires a large number of
observations,and such time-seriesdata are not availablefor most countriesin the world.
There are a number of solutionsto this problem. The first is to make a greater use of
theoretical assumptions,so that lesser requirementsare placed on the data. This is the
route followedby Ahmad and Stern, who use a variant of the linear expendituresystem
described in full in Ahmad, Ludlow and Stern (1988). The second is to make use of
spatial variation in prices. Alderman(1988) has followedthis route and has estimated
a versionof Deatonand Muellbauer's(1980a)almostideal demandsystemusing expenditure data from 1979and 1982householdsurveysmatchedto independentregionalprice
information. These prices are for 12 selected urban areas only, so that for rural
households, or for urban householdsfar from collectioncenters, the match may be a
poor one and the price inaccurate.
In this paper, we apply and extendthe methodologyof Deaton (1988, 1991)ito
data from the 1984-85 Household Income and Expenditure Survey (HIES). As in
Alderman'swork, we rely on spatialvariationin price to identifythe demandresponses.
However, rather than using the independentprice data, which is all that was available
to Alderman, we use the price data collectedin the HIES itself. Each householdwho
buys a good reports the amountbought as well as the amount paid, so that a price, or
at least a unit value, can be derived. While these unit values are not prices and cannot
be treated as such, so that the econometricanalysisis not completelystraightforward,
there are as manyunit valuesas there are householdspurchasingeach good, so that there
are a very large number of observationsto work with. Section 2, which is the main
sectionof the paper, showshow the methodologycan be applied,and works throughthe
calculations. We also explain how demand analysis with unit values is related to
standarddemandtheory, and howthe restrictionsfrom the theory canbe used to estimate
a completedemand system using data for only a subset of goods.
3
Section 3 examinesthe implicationsof the empiricalresults for tax reform in
Pakistan, tracing out the efficiency and distributionalconsequencesof possible price
changes. The results are quite differentfrom what would be obtainedwithouta flexible
methodfor estimatingthe effectsof price changes. Commoditiessuch as wheathave low
price elasticitiesand low incomeelasticities,so that they are good candidatesfor taxation
on one count, and poor candidateson the other. But our estimatessuggestthat edible
oils are income inelastic but price elastic, so that taxes are undesirable on both
distributionaland efficiencygrounds. The estimatesalso suggestthat there are important
interactionsamongthe goods whose prices are distorted, particularlywheat, rice, oils,
and sugar, so that policiesthat changethe price of one will have quantitativelyimportant
effects through the taxes and subsidieson the others. A brief Appendixconsiderssome
alternativeprocedures, includingAlderman's, and comparesthe results.
4
Demand Analysis of the 1984-85 HIES
The householdsurvey that is used here is the National HouseholdIncome and
ExpenditureSurvey which collecteddata from 9,119 rural and 7,461 urban households
in Pakistan betweenJuly 1984and June 1985. Table 1 shows the distributionof both
urban and rural sample households over the four provinces of Pakistan. For each
provinceand sector, the householdsare distributedapproximatelyequallyover the four
quarters of the sample year. The table also shows the numbers of "clusters" in the
survey, and their distributionby sector and province. These clustersplay an important
part in the demandanalysisbelow. The HIESof Pakistan,like other householdsurveys,
minimizestravel costs by selecting,not individualhouseholds,but villages or, in urban
areas, blocks, and then interviewsgroups of householdswithineach cluster. Sincethese
householdsare locatednearto one another,and are interviewedwithin a few days of one
another, it is reasonableto assume that they face the sameprices for the goods that they
buy, particularly in rural areas, where there is often a single villagemarket. Note that
there are between 10 and 12 householdsin each cluster. Such figures are common in
householdsurveys; for surveysof different sizes, it is typicallythe number of clusters
that varies, with the size of each cluster much the same.
This paper is concerned with the demand for seven foods, listed in Table 2,
which also shows the fractionsof total consumptionaccountedfor by each. Note that
these budget shares are not the shares in the aggregate of consumption over all
households,but the average of the budgetshares for each of the 9,119 rural and 7,461
urban households. Householdswith zero budgetshares are included;the analysisof tax
reform requires the effects of price changeson demand averaged over all households,
whether they purchase or not. Rural householdsspend 51 % of their budget on food,
urban householdsrather less at 43% Apart from the catchallcategoryother food, wheat
(includingbread) and dairy products are the two largest categoriesin the table.
Means of unit values are also shown in the Table. These are computedfrom
those householdswho make market purchases of the commodityunder consideration.
The columnslabelled "%b," show the fractions of householdsin each sector who make
such purchases while the larger fractions, labelled "%c," are those who report
consumptionof each good, either from market purchases or from own-production.
Althoughthe surveycontainsboth quantityand value informationfor consumptionfrom
own-production,we use only the market purchases in computingunit values, and treat
5
Table 1: Structure of the 1984-85HIES Sample
(numbersof householdsand clusters)
Households
Clusters
Province
Rural
Urban
Rural
Urban
Punjab
Sindh
N.W. Frontier
Baluchistan
5,474
1,755
1,402
488
3,793
2,270
994
404
440
152
110
55
316
196
92
44
Total
9,119
7,461
757
648
as missing the unit values for those observationswhere consumptionis entirely from
own-production. The budget shares are computed from all households, and zero
consumption, own-production consumption, and market consumption are treated
identically.
On average, consumerspaid 2.4 rupees per kilo for wheat, either as grain or
as bread, and almosttwice as muchper kilo for rice. Meat and edible oils and fats cost
more than 14 rupees per kilo. The degree of price variationbetween households, as
measuredby the coefficientof variation,is very differentfor differentcommodities. For
sugar, and for edibleoils and fats, wherethere is a good deal of stateprice control, there
is very little variationin unit valuesacross the sample. For wheat, rice, meat, and other
foods, as well as for food as a whole, the cross-sectionalstandarddeviationis between
20 and 30% of the mean. For dairy produce, the coefficientof variation is very large
in both sectors. The definitionof this group may be less than ideal, since it contains
goods with very different unit values. Much of this can be accountedfor (and is
accountedfor) by the estimationproceduresbelow, but there will be difficultiesif the
composition within the group has a strong spatial component, which is capable of
generatinga quite spuriousrelationshipbetweenquantity and unit value.
Since we are going to use the spatial price variation to estimate the demand
responses,it is worth looking in more detail at the behaviorof the unit values. The top
panel of Table 3 shows the coefficientsobtained by regressing the unit values on
dummiesfor Sindh, Punjab, and North West Frontier Province, omittingBaluchistan,
and on dummies for each of the first three quarters in the survey, omittingthe fourth.
The bottom panel showsF-statisticsand degreesof freedomfor cluster (village)dummy
6
Table 2: BudgetShares, Unit Values, and Fractions Consumingand Buying
Rural
Urban
share
%c
%b
u.v.
c.v.
share
%c
%b
u.v.
c.v.
Wheat
Rice
Dairy
Meat
Oils & Fats
Sugar
Other Food
12.8
2.7
12.7
3.7
4.1
2.9
12.2
96
68
97
88
85
90
100
68
54
41
85
85
89
100
2.4
5.4
6.0
14.3
14.2
8.2
4.9
29
30
150
31
5
7
19
9.0
2.0
9.5
5.3
4.3
3.0
10.2
95
77
97
95
96
96
99
92
76
90
94
96
96
98
2.3
5.8
5.916.4
14.0
8.3
5.3
16
26
100
34
4
6
28
All Food
51.0
100
100
5.5
29
43.3
99
99
5.9
23
Note: Share is the mean of the percentage budget share over all households, %c is the percentage of people
who consume the good, i.e. who buy it, %b, or consume from own production, u.v. is unit value, i.e. the
average rupees per kilo spent on the commodity by households buying it, and c.v. is the coefficient of variation
of the unit value. Unit values for other food and for total food are computed as geometric means of the unit
values of goods purchased with weights equal to the budget shares of the individual goods. (*) One outlier is
excluded from the mean unit value of dairy products.
variables, separatelyfor each of the four provinces. The top panel shows how prices
vary betweenprovinces and over time, the bottompanel the extent to which they vary
from village to village within each province. Note that since every household in each
cluster is interviewedat the same time, there is no need to interact cluster with time
dummies. For all seven foods, there are pronouncedinter-provinceprice differences.
Apart from wheat,which is more expensivein Sindh and NWFP than in Baluchistan,all
province means are lower than those in Baluchistan. In accord with the calculationsin
Table 2, the differences are relatively small for oils and fats and for sugar and, to a
lesser extent, for wheat, while dairy products show very large provincialdifferences.
Rice is very muchcheaper in Sindhthan elsewhere. The seasonaldifferencesare much
less marked, at least in 1984-85;they show no obvious pattern of price increase over
time.
The bottom panel of Table 3 showsthat there is typically a great deal of intervillage variation in unit values. All of the F-statistics are significantat conventional
significancelevels. However, the samplesizes are large, and a better indicationof the
strength of the inter-villagevariation is whether the F-statistics are larger than the
logarithmof the sample sizes in each case, (see Schwartz (1978)). For wheat in all
7
provinces but Baluchistan,the F-tests are smaller than this criterion, and the same
happensin a few other cases, rice in Sindh, dairy in Punjab, meat in Punjab and NWFP,
and sugar in Punjab. In all other cases, the inter-villagespatial variationis large enough
to meet even this stringentcriterion. In order to save space, we have not includedthe
results for the urban sector correspondingto Table 3. The province effectsare broadly
similar to those in the rural sector, and once again, the seasonaleffects are much less
pronounced. TheF-statisticsfor the clustersare againlarge by conventionalcriteria, but
they are not as large as those for the rural sector. Since city blocks are not as
geographicallyseparated as are villages, and since the large cities have many urban
blocks each, this result is to be expected.
The model that we use to estimateprice elasticitiesis a standardone in which
demand is a function of prices, total consumption,and household demographics. In
addition, it is recognizedthat the observedunit values, while movingwith prices, will
also vary from householdto householdbecausedifferentconsumerswill typicallychoose
different qualitieswithin the same commoditygroup. We therefore needtwo equations,
one for the budget shares, and one for the unit values. These are written as follows,see
Deaton (1990: equations 1-2):
N
W,ac =
'{G
+E nx. +jQ.Z.
0
OGHI'PHC
+ (fC
+
+
UG)
(1)
H-1
N
Invac=
CgG+O'lnx.)e.+ y
+
i
AGHI'PH + uGiC-
(2)
H1.1
The relationshipbetween these equations and standard demand functions is
exploredlater in this section. In equation(1), w., is the budgetshare of good G in the
budget of household i, living in cluster c. By analogy with the almost ideal demand
system, the share is assumedto be a linear functionof the logarithmof total household
expenditure,x, and the logarithmsof the N prices, as well as of a vector of household
characteristicsz. The remainingterms representthe residual betweenthe share and its
conditionalexpectation. The first component,f,,, is a cluster fixed effect for good G,
assumed to be orthogonalto the prices, while the idiosyncraticterm u° representsnot
only taste variations, but also measurementerror in the share. From an econometric
point of view, the non-standardfeature of equation (1) is that the prices are not
observed. Instead, we have data on the unit values v, which are not identical to the
prices, but are relatedto them by equation(2). The logarithmof unitvalue is a function
Table 3: Price Variationby Province, Quarter, and Village: RuralPakistan 1984-85
(regressionsof unit values on provincialand seasonaldummiesANOVAby village)
Wheat
Rice
Dairy Products |
Meat
|Oils
& Fats
|
Sugar
|Other
Food
REGRESSION PARAMETER ESTIMATES
Punjab
-8.0
(4.5) -68.7
(16)
-22.1
(16)
-2.0
(8.5)
-6.6
(22.)
7.3
(5.2) -43.1
(22) -78.3
(15)
-13.8
(9.5)
-2.6
(10)
(9.0)
NWFP
6.3
(4.7)
-2.8
(1.4) -26.0
(5.4)
-31.1
(21)
-1.3
(5.0)
(11-)
-6.3
(6-9)
Quarter 1
Quarter 2
Quarter 3
-2.1
-2.4
0.0
(2.6)
(3.0)
(0.0)
0.4
-1.0
-2.0
(0.4)
(0.8)
(1.6)
2.0
-1.5
-3.0
(0.7)
(0.5)
(1.1)
-1.4
-3.4
-1.9
(1.6)
(4.1)
(2.2)
-0.2
-0.5
-0.3
(1.4)
(2.9)
(1.8)
-2.9
-3.7
0.3
-0.2
0.3
-9.7
-11.8
(12)
Sindh
-7.2
(6.0)
(1.7)
(1.1)
(1.5)
0.9
-4.3
-6.9
(1.7)
(8.4)
(13)
ANOVA
F
R2
F
F
R2
F
R2
F
R2
F
R2
F
R2
Punjab
Sindh
NWFP
Balu'stan
4.02
5.42
6.06
9.14
0.334
0.526
0.408
0.582
9.14
4.40
7.12
8.52
0.593
0.435
0.572
0.610
3.07
9.44
10.63
17.70
0.385
0.776
0.673
0.798
7.85
8.61
4.46
10.97
0.454
0.475
0.304
0.607
13.7
10.4
13.5
7.74
0.608
0.508
0.541
0.500
7.2
19.9
13.9
18.0
0.420
0.662
0.586
0.695
12.8
14.1
10.8
17.9
0.528
0.571
0.477
0.691
All
5.65
0.432
10.83
0.646
6.46
0.590
9.30
0.498
12.39
0.571
14.0
0.588
13.79
0.556
(13)
00
Notes: The figures in brackets are absolute t-values. The number of observations in each regression or analysis of variance is the number of rural
households who report expenditure on the good in question.
9
of lnx, so that , is the elasticityof quality with respectto total expenditure,and of the
characteristicsz, since householdfeaturesmay affect quality choice. The unobservable
prices appear through the matrix p. In the simplest case, this matrix would be the
identitymatrix, the other variableswouldbe absent, and prices wouldequal unit values.
The extra generalityallows for quality "shading"in responseto price change, so that we
might expect q,, < 1, with some non-zerooff-diagonalterms. Not surprisingly,theip
matrix is not identifiedwithout further assumptions,and in Deaton (1987b, 1988), a
theoretical model is developed that provides suitable prior information,see also the
discussion below. In practice, k is close to the identity matrix, so that a simple
procedureworks as if the approximationwere correct, and to makewhateveradjustments
are necessaryat the end.
Readers who would like to see a completedevelopmentof the econometric
methodologybefore turning to the results should consultDeaton (1990). In the current
paper, we develop the procedure in an intuitiveway, presenting results alongside the
discussion of the methodology. To begin, note that the a, ,B, and y parameters in
equations(1) and (2) can be estimatedstraightforwardlyby OLS if we allowfor cluster
fixed effects by including dummy variables for each cluster. Since the prices are
assumedto be the same in each village,the dummyvariableswill allowfor them, as well
as for the fixed effectsf0G, and the cluster meansof the idiosyncraticerrors. However,
we see from Table 1 that there are 757 rural and 648 urban clusters,and most computer
programs will not allow regressionswith so manydummyvariables. However, several
estimationprogramsallowfor analysisof variancewith continuousregressorsand a large
number of classes. Alternatively,and more transparently,equations(1) and (2) can be
estimatedby calculatingthe mean of each variablefor each cluster, and then running a
regression using the deviations from the cluster means of all the variables. Standard
OLS gives the correct parameter estimates,althoughthe usual standard errors have to
be multipliedby V(N-k)I(N-k-C+ I ) where k is the numberof regressors,N the sample
size, and C the numberof clusters. This correctionallows for the fact that (C-1) degrees
of freedom are removedwhen the cluster means are subtractedout. Given the figures
in Table 1, the correctionis quite small; standard errors should be increased by about
four percent.
A selectionof the results from this first stage of the estimationare given in
Table 4. Householdcompositioneffects, the z's in equations(1) and (2), are modelled
by entering, together with the logarithmof total householdexpenditure,the logarithm
10
of total household size, and the thirteen ratios, n. In, where nj is the number of people
on age and sex groupj, and n is total household size. There are seven age groups for
each sex, makingfourteen in all; these sum to unity, so only thirteenneed be included
in the regression. The Table shows only the coefficients on total expenditure and
householdsize; the demographicratiosare typicallyimportantin the share equation- the
structure of the household affects demandpatterns - but much less so in the unit value
equation. The first two rows of the table show the coefficientsof the logarithmsof total
household expenditureand total householdsize in the budget share equation (1). The
rural results are shown in the top panel, and the urban in the lower panel. The third row
shows the total expenditureelasticityfor the good, calculatedaccordingto the formula
e,=
_i-' +0w,.
(3)
Note that expenditureon each good respondsto total outlay, not only through the effect
on quantity, the usual expenditureelasticityei, but also through the quality effect, j,
which must also be allowedfor in (3).
The figures shown in the table are evaluatedat the samplemeansof the budget
shares as reported in Table 2. Negativevaluesof A correspondto expenditureelasticities
less than unity, and this is the case for all goods exceptdairy products and meat. Wheat
and edible oils and fats are the least elastic of the goods in the table, and the only ones
with elasticitiesless than a half. These figures imply an expenditureelasticity for food
as a whole of approximately0.8 in both sectors. In all cases, the coefficient on
householdsize is of the oppositesign to that on total expenditure;increasesin household
size, with compositionheld constant, affect the pattern of demand as do decreases in
expenditure. Indeed, in several cases, and most preciselyfor wheat,the coefficientsare
close to being equal and opposite, so that, conditionalon household composition,it is
only per capita household expenditure that matters. Changes in household size that are
matchedby proportionalchangesin total expenditurehave no effect on the share of the
budget devotedto wheat. This is only approximatelytrue for the other foods. Note the
very close correspondencebetweenthe rural and urban estimates;there is no particular
reason why this has to be happen, but large differences would have called for some
explanation.
Quality elasticitiesare estimated from the effect of (the logarithm of) total
expenditureon the (logarithmof the) unit value. These estimatesare shown in line 4 of
Table 4: Income and HouseholdSize Coefficientsin Share and Unit Value Regressions
(withinclusterregressions)
Wheat
Rice,
Dairy
Meat
Oils & Fats
|
Sugar
Other Food
RURAL
w:Inx
w:lnhhs
elasticity wrt x
Inv:lnx
Inv:lnhhs
-0.068
0.070
0.374
0.095
-0.033
(56)
(49)
(15)
(4.3)
-0.006
0.007
0.684
0.107
-0.062
(7.6)
(8.8)
-0.004
0.006
0.711
0.111
-0.075
(6.8)
(11)
(12)
(6.3)
0.024
-0.007
1.053
0.139
-0.031
(13)
(3.2)
(6.4)
(1.3)
0.009
-0.006
1.095
0.154
-0.099
(14)
(8.0)
0.009
-0.000
0.938
0.242
-0.156
(11)
(0.5)
(24)
(13)
-0.024
0.013
0.417
0.000
0.000
(42)
(19)
(0.4)
(0.0)
-0.004
0.002
0.865
0.006
-0.004
(8.2)
(4.1)
-0.011
0.009
0.648
-0.000
-0.000
(27)
(20)
(4.6)
(2.8)
-0.040
0.020
0.593
0.076
-0.033
(40)
(17)
(21)
(7.9)
URBAN
w:lnx
w:lnhhs
elasticity wrt x
Inv:lnx
Inv:lnhhzs
-0.053
0.054
0.388
0.027
-0.028
(53)
(47)
(7.6)
(6.7)
(16)
(10)
0.001
0.008
1.001
0.010
-0.023
(0.7)
(5.0)
(0.9)
(1.9)
(34)
(19)
-0.023
0.019
0.470
0.003
-0.002
(44)
(31)
(2.6)
(2.1)
(0.3)
(0.1)
-0.030
0.020
0.580
0.129
-0.076
(32)
(19)
(26)
(13)
Notes: w is the budget share, Inv the unit value, x total expenditure, and hhs household size so that w:lnx is the regression coefficient of the regression
of w on hx, and similarly for the other rows. The elasticity in row 3 is the total expenditure elasticity of quantity; the total expenditure elasticity of
expenditure on the commodity is the sum of this and the quality elasticity in the next row. Absolute values of t-values are given in parentheses.
12
each panel, and the correspondingcoefficientof the logarithmof householdsize in line
5. With the exceptionof sugar in the urban sector, where the coefficientis essentially
zero, all of these estimatesare positive, as is to be expected,but none are very large.
The unit value of meat rises with total expenditure,with elasticitiesof 0.15 in the rural
and 0.24 in the urban sector. There are severalother cases (rice, other food, wheatand
dairy producein the rural sector)with qualityelasticitiesaround 10%. Note that for the
two essentiallyhomogeneousgoods, sugar and edible oils, the elasticitiesare zero, as
they should be. As was the case for the budget shares, increases in household size
typicallyact in muchthe sameway as decreasesin expenditure. This is the major effect
of demographicson quality;conditionalon total expenditureand householdsize, age and
sex compositionhave little effect on quality choice.
The estimates in Table 4 are the final estimates for the effects of total
expenditure and the demographics. Note that they are derived entirely from within
cluster information. The next step is to use the between cluster informationin the data
to estimate the price responses. We first use the estimates from the first stage to
calculate cluster averages of the shares and unit values "purged" of expenditureand
demographiceffects. Define:
g°
=
S (WGC - #Glnxr,
ne
(4)
YG
iEc
YC
I I 1
(InvGi, ~' ri)Xic
-
(5)Zc)
nGc i'c
where n, is the numberof householdsin cluster c, n* is the numberof householdswho
purchasegood G (and thus report unit values)and superimposedtildes indicateestimates
from the first, within-clusterstage. As the number of observationsin the first-stage
regressionincreases,the estimateswill tendto their true values,so that g° and y' will
tend to the true cluster means, which, by (1) and (2), can be written:
0
0
CIOg
=
+E
0
06
GHtnPIk +fc + u(6)
YG I=C %+4GHnH+G.(7)
(G +
AGMInpv, +u la
where uO and uI are the cluster means of the errors in (1) and (2). Note that in the
constructionof (4) and (5), the right hand side variablesdo not have the meansexcluded;
13
the cluster means containthe informationabout the prices that must be excluded from
the first stage regressions,but must be includedin the betweencluster regressionsif the
price effects are to be identified.
If the matrix I were the identitymatrix, and if the cluster means u° andulc
were zero, the columnsof the matrix e of price effectscouldbe estimatedby regressing
each yc on the matrix of correctedprices y,. This is in fact very close to what we do.
Given that the quality effects in Table 4 are not large, the correctionfor the 'I matrix
is not the most importantone, but it is necessaryto correct for the fact that the sample
clusters are not large enoughto allowus safelyto ignore the averages of the measurement errors. The procedure is a standarderrors in variablesone, which allows both for
the measurement error in the prices, and any possible correlation between the
measurementerrors in the price and share equations.
To see howthis works, definethe varianceand covariancematricescorresponding to (6) and (7):
qGH =
Cov(YCCYHC), SCH=
rCH
=
(8)
(YCoXv
YHC),
,YH)-
cov(y
By the definitionof ordinaryleast squares,the OLS estimatorwouldbe S-1R, a feasible
version of which is S-'A, where the tildes show that the covariancesin (8) are evaluated
using the estimates in (4) and (5) rather than (6) and (7). The problem with these
estimatorsis that the variancecovariancematrix S overestimatesthe variancecovariance
matrix of the true prices, becauseit includesthe effectsof the measurementerror in (7);
similarly R is contaminatedby any covariancesin the measurementerror betweenthe
two equations. But the variances and covariancesof the errors can be estimatedfrom
the first stage regressions,and the estimatesused to makethe correction. Leteji, j=1,2
be the residual for householdi, cluster c, good G, from the first stage share regression
( = 0) or unit value regression ( 1). Define:
aGH
= (n-C-k)'
E eofeH%i
WGII =
(nG-C-k)
cC
EYGH
= (n4-C-k)-1EEe'
c
i
ceHrc
i
(9)
14
where n is the total numberof householdsin the survey who report purchasesof good
G. Denote the matricesdefined in (9) by , . and fr, and their limits E, n, and r.
Then from (6) and (7):
S = *M¶ + S2N+-, R =
*MO'+rN-1,
(10)
where M is the unobservable variance covariance matrix of the true price vector,
NI = pIimC-' D(n )-l, D(n;) is a diagonalmatrix formedfrom the elementsof
and N-1 is the correspondingmatrix formed from the ne's. To eliminatethe effects of
the measurementerror, we need to correct OLS by removingthe second terms on the
right hand side of (10). This leads to the estimator:
A
=
(S-0N2)-'(A-rFr')
(11)
where &-I and jV1 correspondto the sampleaveragesinsteadof the probabilitylimits.
From (10), it is immediatethat, taking probabilitylimits as the sample size goes to
infinity but with the cluster sizes remainingfixed:
plimB = B = (*")-'e'.
(12)
To interpretthese results, start with the last, equation(12). If * is the identity
matrix, B convergesto the transposeof the matrix of price responses0, which is what
we want. If k • I, then B is all that can be identifiedwithoutfurther theory, and we
cannot go further with the data alone. From (11) we see that, in the absence of
measurementerror, in which case the matrices 9 and r would be zero, the estimator
reducesto the ordinary least squares estimator,as it should. Even if these matricesare
not zero, large cluster sizes will make the post-multiplyingdiagonalmatrices small, so
that, once again, we approachthe OLS estimator. In this case, averagingover clusters
is enough to removethe measurementerror and the price responsematrix can simplybe
estimated by least squares once the expenditure and demographiceffects have been
removed at the first stage. The present procedure is more general and allows for the
possibilitythat measurementerror is sufficientlysevere, or cluster size small enough, so
that even the averages are contaminated. This seems wise, since cluster sizes are often
in single figures, and the number of purchasersof a good in each cluster will often be
only two or three.
15
A full discussionof how to obtainthe variancecovariancematrix of A is given
in the Appendix of Deaton (1990). The formulae are complex because a complete
treatment requires that allowancebe made for the facts (i) that the error covariance
matrices and in (12)are estimated,not known, and (ii)that the calculatedvariances
and covariancesof the "purged" sharesand prices also containestimatesof the first stage
parameters. However, it seems that these considerationshave very little effect on the
calculationsin practice, and they certainlydo not do so in the current case, presumably
becausethe first-stageparametersare so very well-determined. The main contribution
to the variance is the samplingvariability of the cluster fixed effectsf in (1), which are
analogousto the disturbancesin the between-clusterregression. Of course, the standard
OLSvariance-covariancematrix formulaehave to be modifiedfor the errors in variables
case. From equation (A.12) in Deaton (1990), we have:
rn
V{vec(A)}
where A = (S-oN;'),
C-'(P'HPOA-IJHJ'A-') + C-'(P'HJ'A-'
J = (ONI IN), and P' = (I IN Be.
A-'JA J'A-')K
(13)
The matrices H and A are
formed from the variance covariancematrices of the measurementerrors and the data
accordingto:
-g=
RI|RQ A= Ir
Q|
(14)
K is the 2AT2
x 2N2 commutationmatrix; it is the matrix of ones and zeros with the
propertythat Kvec(A) = vec(A') for an arbitrary conformablematrix A. Equation (13)
is not exact; it ignores the samplingvariability of the first-stage estimates, but it has
proven accurate in other applications, and the additional terms make no noticeable
difference in the current case.
Together with the first stageresults, the matrixB yieldseverythingthat we need
to know. However, it is usual as well as convenientto present the results of demand
analysisin terms of elasticities,and a little further work is neededto convert the results
to that form. Note first that, since the budgetshare is the product of quantityand unit
value divided by outlay, its derivatives with respect to the logarithms of the prices
containsterms representing,not only the responseof quantityto price, but also of unit
16
value with respect to price. If WG is differentiatedwith respect to InpH,rearrangement
gives:
(15)
eGH = -IGH + OGHWG*
Given appropriateseparabilityassumptions,it is possibleto expressthe responsesof unit
value to prices, the * matrix, in terms of the total expenditureelasticitiesof quality.
Deaton (1988) derivesthe formula:
QGff
=GH
(16)
+GeGHeG
where er is the total expenditureelasticity. Equations (15) and (16) can be used to
eliminatethe matrix of price elasticities,yieldinga relationshipbetween * and 0. But
equation (12) also links * and e with the estimatedmatrix B, so that both 0 and *,
and thus the matrix of price elasticities E, can be calculated from the estimated
parameters. In matrix notation the formulasare:
0 = B'{I-D(Q)B'+D(Q)D(w)}-'
(17)
E = {D(w)-'B'-I} {I-D(Q)B'+D(Q)D(w)}-'
(18)
where w is the vector of budget shares, and the elementsof
=G
{(1-
G)WG+f
lP} '
t
are given by
(19)
In order to save space, we report only the estimatesof the elasticitymatrices, together
with their standarderrors. These can be derived from the variance covariancematrix
of B, (13), using the formula:
V{vec(E')} = {(D(w)-'+ED(Q))®G} V{vec(B)}{(D(w)-1+D(Q)E')® G' } (20)
G = {I-D()+DQ)D(w)}-'.
17
This expression, like that for the variances of the B matrix, ignores the sampling
variabilityof the first-stageestimates. Again, see Deaton (1990)for a full treatment.
We cannow summarizethe secondstageof the estimationas follows. The firststage parameterestimatesare used to calculateequations(4) and (5), giving a "purged"
unit value and budget share for each good for each cluster. Clusters that do not have a
completeset of unit values are dropped. Note that we are thereby dropping only those
clusterswhere at least one of the goodsis bought by no one; it need not be the case that
anyonebuys all of the goods. Even so, 137 rural clusters are lost, leaving 620 for the
estimation; only 10 clusters are lost in the urban sector, leaving 638. It is the large
number of missingunit values at the individuallevel that makes it attractiveto average
over clusters at this stage. Because prices are assumed to be the same within each
cluster, the averaging does not lose price information,and, althougha more efficient
estimationtechniquemight be based on the individualhouseholddata, it would have to
deal with the very large numbers of missing values at that level. The first-stage
equations are also used to calculatethe estimatesof the measurementerror variances
according to (9). We assume that the off-diagonalterms in all three of these matrices
are zero. There is no difficultyin principle in generalizingthis, although in practice,
the off-diagonalterms are typicallyvery small.
A decisionalso has to be made aboutthe extent of spatial and temporalvariation
that the prices are asked to explain. The issue is whetherthere are broad regional taste
differencesthat we do not wishto attributeto regional price differences. To the extent
that the inhabitantsof, say, the North West Frontier have different tastes from those in
Sindh, we should allow (at the least) for dummy variables for those regions. Within
provinces, many of the spatial differences in prices will be of long standing, so that
consumers have had a great deal of time to adjust to them. In consequence, our
proceduresare likely to estimatelong-runprice responses,which would not be expected
to be the same as the seasonal responsesto short term price changes. We therefore
allow for dummyvariables for each of the quarters of the survey. The econometric
proceduresremain as discussedabove, but having calculated(4) and (5), these cluster
means are first regressed on provinceand quarterly dummies, and the residualscarried
forward for further analysis.
The estimatesof the matrix of price elasticities,evaluatedat the sample means
of the budgetshares, are shown in Table 5. The top panel refers to the rural sector, the
bottom the urban sector. The final row and column, for non-food, is derived in a
18
manner that will be discussedbelow. The estimatesare typically well-determined,at
least in comparisonto estimatesfrom time-seriesdata. All of the diagonal terms, the
own-priceelasticities,are negative,and several(rice and edibleoils in both sectors, and
dairy products in the urban sector) are less than -1. There is again a good deal of
conformitybetweenthe rural and urban estimatesof these own-priceelasticities. The
effects of the sugar and edible oil prices, columns five and six, have relatively large
standarderrors; recall from Table 2 that theseprices show little variation in the sample.
Particularly in the urban sector, these two columns contain several estimatesthat are
large in absolutevalue. For example, wheat, rice and meat are all estimatedas being
very (positively)elasticto the oil price, and rice (negatively)to the sugar price. These
figures have large standarderrors and shouldbe treated accordingly.
Apart from the effects of the oil and sugar prices, the cross-priceterms are
typically not very large. The urban estimatesshow a large substitutioneffect of the
wheatprice on rice purchases, an effect that is muchsmaller, and not at all significant,
in the rural estimates. In the rural matrix, oil and sugar apart, the numericallylargest
cross-priceelasticitiesare -0.43 for the price of other food on dairy products, and 0.43
for the meat price on rice purchases, and the latter effect is even stronger in the urban
estimates.
None of these cross-priceeffects, except possiblythat betweenwheat and rice,
are large enough, or precise enough, to change, by itself, the way in which we might
think abouttaxes. However, the configurationof these elasticitiesis very differentfrom
what would be the case if alternative assumptionshad been made. In particular, the
assumptionof additivepreferences, as for examplein the linear expendituresystem, not
only restricts the cross-priceelasticitiesto be small, as indeed is mostly the case here,
but also enforcesan approximateproportionalitybetweentotal expenditureand own-price
elasticities. This proportionalityhas dramatic effects for tax policy, because it means
that goods that are attractive to tax on efficiency grounds, those with low price
elasticities,are those most heavilyconsumedby the poor, and are thusthe least attractive
on distributionalgrounds. There is therefore a balance between equity and efficiency
that tends to drive taxes towards uniformity. The estimates in Table 5 show no such
proportionality. Table 3 estimatesthat meat and dairy produce are luxuries and rice a
necessity, and yet Table 5 estimatesthat rice is much more price elastic than is either
dairy produce or meat. Taxing rice is therefore doubly unattractivecompared with
taxing either of the other two goods. We shall return to these issues in more detail in
19
Table 5: Estimatesof Own and Cross-PriceElasticities:Pakistan 1984-85
Wheat
Rice
Dairy
Produce
Meat
Oils &
Fats
Sugar
Other
Food
RURAL
Wheat
Rice
Dairy
Meat
Oils & Fats
Sugar
Other Food
-0.51
(0.09)
0.30
(0.29)
0.04
(0.12)
-0.28
(0.20)
0.22
(0.13)
0.14
(0.17)
0.18
(0.08)
0.08
(0.04)
-1.59
(0.13)
0.13
(0.05)
0.14
(0.09)
0.23
(0.06)
0.29
(0.08)
0.05
(0.03)
0.03
(0.02)
-0.11
(0.08)
-0.87
(0.03)
-0.06
(0.05)
0.04
(0.04)
0.04
(0.05)
0.01
(0.02)
0.01
(0.06)
0.43
(0.20)
-0.15
(0.08)
-0.57
(0.13)
0.24
(0.09)
0.22
(0.11)
0.11
(0.05)
-0.04
(0.29)
-0.18
(0.97)
0.19
(0.40)
-1.54
(0.66)
-2.04
(0.44)
-0.99
(0.56)
-0.44
(0.25)
0.04
(0.22)
-0.39
(0.75)
0.84
(0.31)
-0.62
(0.51)
-0.31
(0.34)
-0.07
(0.44)
0.21
(0.20)
0.09
(0.09)
-0.32
(0.30)
-0.43
(0.13)
0.34
(0.21)
0.08
(0.14)
0.16
(0.18)
-0.35
(0.08)
-0.86
(0.13)
1.44
(0.24)
-0.22
(0.12)
-0.20
(0.16)
0.09
(0.10)
-0.05
(0.15)
0.18
(0.09)
0.08
(0.05)
-1.83
(0.10)
-0.18
(0.05)
-0.08
(0.07)
0.08
(0.04)
0.14
(0.06)
-0.03
(0.04)
-0.07
(0.05)
-0.45
(0.09)
-1.10
(0.04)
0.21
(0.06)
-0.01
(0.04)
-0.06
(0.05)
-0.00
(0.04)
-0.21
(0.09)
0.64
(0.17)
0.07
(0.08)
-0.33
(0.11)
-0.09
(0.07)
-0.14
(0.10)
-0.03
(0.06)
2.26
(0.74)
1.96
(1.41)
0.58
(0.68)
2.66
(0.95)
-1.17
(0.58)
0.20
(0.85)
0.06
(0.55)
0.41
(0.35)
-2.40
(0.66)
0.60
(0.32)
-0.22
(0.45)
-0.13
(0.27)
-0.81
(0.40)
-0.20
(0.26)
-0.05
(0.11)
0.14
(0.20)
-0.14
(0.10)
-0.03
(0.14)
-0.04
(0.08)
-0.41
(0.12)
-0.34
(0.08)
URBAN
Wheat
Rice
Dairy
Meat
Oils & Fats
Sugar
Other Food
Note: The rows refer to the good being affected, and the columns to the price being changed. Hence, row
2, column 7 for the rural sector estimates that a 1 % increase in the price of other food will decrease the
quantity purchased of rice by 0.32% The figures in parentheses are standard errors.
20
Section3, but for now noteonly that the results in Table 5 have different implicationsfor
tax structures in Pakistan from previous estimatesbased on models such as the linear
expendituresystem.
The results in Table 5 are not all that we needto know aboutdemand responses
in order to evaluateprice reform proposals. The demand for non-foodswill generally
be affectedby price changesin foods, and the demandfor food will dependon the prices
of non-foods. For most non-foodswe do not have data on physical quantities,and so
the methodspresented above cannot yield the estimatesthat are required to close the
system. However, it is possible to use the results of consumer demand theory to
completethe system, at least for a single aggregateof non-foods. The completesystem
has to satisfy the budget constraint, which yields one set of restrictions, and it must be
homogeneousof degree zero, which yields another. We show below that providedwe
can make a reasonable guess for the quality elasticityof non-foodsas a whole, adding
up and homogeneityallow us to add another row and column to the matricesof price
elasticitiesin Table 5. In fact, it is possible to do better than this, by using the Slutsky
symmetry restriction of demand theory. In the current context, the use of these
restrictions is particularly attractive. As we have seen from Table 5, the elasticitiesin
the "sugar" and "oils and fats" columnsare not very well determined,an outcomethat
reflectsthe low varianceof sugar and oils prices in the sample. But other prices do vary
a great deal, and symmetryallows us to use, for example, the well-determinedeffects
of rice prices on sugar and oils to measure more precisely the effects of sugar and oils
prices on rice. Further, the symmetryrestrictionis testable, somethingthat is not true
of homogeneitywhen we have data on only a subset of goods. The remainderof this
section explainshow to complete the system, and how adding up, homogeneity,and
symmetrywork in a model with quality as well as quantity and price. The econometric
extensionsare also presented.
A full discussion of the theory of quality and quantity will be presented
elsewhere,and only the bare essentialsare given here. The basic idea is that quality is
an attribute of commodity aggregates, so that, for example, a higher unit value for rice
means that there are more expensivevarieties and fewer cheaper varieties in the rice
"bundle" under consideration. There is therefore a group of rice goods, and the way in
which rice expenditures are allocated within the group varies systematicallywith the
outlay of the spender. Preferencesare assumed to be (weakly)separable between the
various commoditygroups, so that there exist sub-utilityfunctionsfor each subgroup,
21
represented here by the subgroup cost functions, CG(uG,PG)each of which gives the
minimum expenditureon group G necessaryto reach uGat group prices given by the
vector PG. Following Deaton and Muellbauer (1980, pp. 130-2), we use these cost
functionsto define group quantity indicesQGand group unit value indicesVG by
(21)
QG = CG(UG
0 PG)
VG =
CG(UG,PG)IC(UGPG)
The vector p° is some convenientbase vector that is used to measure quantity: it need
not necessarily be a price, and quantities can be measured in physical units, or in
calories. The quantity index QG is a standard one, and for fixed p0 is a monotone
increasingfunctionof uG. The unit value vG is linearlyhomogeneousin the price vector
PG, as should be any sensible price index, but it is also a function of the group utility
level uGand thus of QG. It is the dependenceof the unit value on group consumption
levels that generates the quality effects, and it is a straightforwardexercise to use the
second part of (21) to prove the relationshipbetween unit value and price used in
equation (16) above, at least under the simplifyingassumptionthat prices in the group
move proportionately.
The really useful fact about the definitions in (21) is that they can be used to
write the consumer's maximizationproblem as:
Max u = V(Q 1, Q2,
I QG
S.t. E VQG= x
QN)
(22)
This reformulationworks because utilityis a functionof the sub-utilities,which arejust
monotonetransformationsof the Q's, and because total expenditurehas to be the sum
of the costs on each subgroup. Of course, the familiar formulahides the unfamiliarfact
that the "prices" VG are not prices at all, but unit values, which dependon the very Q's
that are the solution to the problem. This makes (22) an unsuitable vehicle for
calculation,but it neverthelessshowsthat it is possibleto writedown "standard" demand
functions, with quantitiesfunctions of x and the unit values, and that these demand
functionssatisfy all the functionalrestrictionswith which we are familiar. In particular,
we can adopt an "almost ideal" systemfunctionalform and write:
WI = O{G+
OGln(x/v) +E cHI,nvH
H
(23)
22
where v is a (linearlyhomogeneous)index of all the unit values. Note again that (23)
is more complicatedthan it looks, becausethe unitvalues are functionsof the quantities,
and therefore cannotbe econometricallyexogenous. The equationmust be supplemented
with an equationthat links the unit valueswith total outlay and prices, an equationgiven
by (2), which in skeletalform is
IlnvG =
cG
+ / Inx + E 6GH1rP
(24)
H
The substitutionof (24) in (23) yields equation (1), which has been the basis for the
estimation. However, the great value of equation (23) is that it tells us exactly what
restrictionsshouldbe satisfiedby the system. Adding-upimpliesthat the fl's in (23) add
to zero, as does each of the columnsof the C-matrix. Homogeneityis equivalentto the
rows of C addingto zero, and symmetryto the symmetryof C.
To translatethese statementsinto statementsabout the parametersestimatedin
this paper, we need to specifythe index v, and then explicitlymake the substitutionof
(24) into (23). We adapt Deaton and Muellbauer's suggestionand approximatelnv by
the inner product W.lnv,where the bar denotesthe mean over the sample. We can then
match the parametersin (1) and (2) with the parametersin (23) and (24, whereby
=
(C - w) = D ', say
=
=
(25)
-D':'.
The matrix D is the matrix B defined in (12), but, since it correspondsto a complete
system of goodsthat together exhaustthe budget, has one more row and columnthan B;
hence the changeof notation. Note also that the vectors ° /3land - in the expressions
above refer to the full system, and therefore have one more element than their
counterparts earlier in the paper.
Equation (25) yieldsthe restrictionson D, and hence on B, that are required to
completethe system and to imposesymmetry. Adding-upis
*'D' = 0,
L'ff =0,
where , is the vector of units. Homogeneityrequiresthat
(26)
23
D'(t- f') +
(27)
=
while the symmetryrestrictionis that
0 I = (I-i1)D
D'(I-ljw-') +#3W
+ v'
(28)
The adding-upand homogeneityrestrictionsare used to completethe system, that is to
add the final rows and columnsto the B matrix and thence to the elasticitymatrix. The
symmetryrestriction,by contrast,generatestestablerestrictionson the matrixD and thus
ultimatelyon B.
The econometricanalysisproceedsas follows. We already have an estimateof
the B-matrix, in this case 7 x 7, as well as an estimate of V, the 49 x 49 variance
covariancematrix of the estimatesof vecB/. Adding-upand homogeneitytogetherimply
that D can be derived from B by means of
|
I7
B
[ 17
_
I#]
[0
(29)
or, in an obviousnotation,
vecD' = (J2 ®Jl)vecB' - vecJ3
(30)
which offers an immediatemeans of calculationfor the full matrix, as well as of its
variance covariancematrix. Note that we require estimatesof the last elementsgN and
j3s correspondingto the non-foodcategory. Sincethe elementsof j add to zero over
the complete set of goods, the former is easily estimated, but the quality elasticity of
non-foodcannotbe estimatedwithout(the non-existent)data on unit valuesfor non-food.
Here, we simply assume a value for AN of 0.10; giventhe general unimportanceof the
quality estimatesin this study, this need for this obviouslyarbitrary choice is unlikely
to be a serious difficulty. Note too that we are effectivelyassumingthat the first stage
parameters, j3°and j1. are known; they are treated as constantsin the calculationof D
and its standarderrors. Ideally, the first-stagesamplingvariabilityshould be taken into
account, but, just as in the evaluationof the standard errors for B, and for the same
reason, it is ignored.
24
The symmetryrestriction(28) can be convenientlywritten:
L(I-K)G[((Il-wiI)OI)vecDI
+ (wiOI)OI] = °,
(31)
where G is a 49 x 64 matrix of ones and zeros which deliversa vector containingthe top
left 7 x 7 elementsof an 8 x 8 matrix in vec form, K is the 49 x 49 commutationmatrix,
which convertsvecA into vecA/, and L is a 21 x 49 matrix which selectsfrom vecA the
elementsof the lower left trianglein the originalmatrix. This expressionis simplerthan
it looks. The restrictionL(I-K)A = 0 for some matrix A requires that the lower left
triangleof the transpose shouldbe identicalto the lower left triangleof the original, i.e.
that the original should be symmetric. It is written in this form rather in the simpler A
= KA becausethis last imposes redundantrestrictions, includingfor examplethat the
diagonalelementsequalthemselves,whichwould result in singularitieswhen calculating
the variances and covariancesof the restrictions. The G matrix is necessarybecausethe
restrictionsof adding-up,homogeneityand symmetryare not independent.The D matrix
satisfies adding-upand homogeneityby construction, so that symmetry need only be
applied to the top 7 x 7 submatrixof the left hand side of (28).
Equation (30) is substitutedinto equation (31) to generate a "standard" set of
linear restrictions
RvecB' = r.
(32)
A restrictedestimateof B is then calculatedaccordingto
vec(B * ) = vec(B') + VR/(RVR)-1(r-Rvec(A'))
(33)
with variance covariancematrix (RVR)-'. A Wald test for the symmetryrestriction is
availablefrom
W = (r-Rvec(B')'(RVR')-'(r-RvecB').
(34)
The results are shown in Table 6 for both sectors. The Wald tests for the
symmetryrestrictiontake values 58.04 in the rural sector and 80.03 in the urban sector,
both of which would be distributedas X21 if the null hypothesis were true. Although
these tests indicate rejection at any conventionalsignificancelevel, they are based on
large numbersof observations,620 rural villages, and 638 urban clusters. They are not
25
Table 6: Estimatesof Own and Cross-PriceElasticities:Pakistan 1984-85
(symmetrycontainedestimatesfor the full system)
Wheat
Rice
Dairy
Produce
Meat
Oils &
Fats
Sugar
Other
Food
NonFood
-0.51
(0.08)
0.30
(0.15)
0.00
(0.02)
-0.22
(0.14)
0.19
(0.13)
0.12
(0.17)
-0.01
(0.06)
-0.10
(0.03)
0.07
(0.03)
-1.53
(0.12)
-0.01
(0.02)
0.21
(0.07)
0.26
(0.06)
0.31
(0.07)
-0.07
(0.03)
-0.01
(0.02)
0.08
(0.02)
-0.04
(0.07)
-0.89
(0.03)
-0.08
(0.05)
0.16
(0.04)
0.10
(0.05)
0.07
(0.02)
-0.05
(0.01)
-0.04
(0.04)
0.30
(0.10)
-0.02
(0.02)
-0.61
(0.13)
0.19
(0.09)
0.18
(0.11)
0.08
(0.04)
-0.07
(0.02)
0.06
(0.04)
0.38
(0.09)
0.02
(0.01)
0.17
(0.10)
-1.59
(0.40)
-0.44
(0.35)
-0.01
(0.04)
-0.09
(0.04)
0.04
(0.04)
0.34
(0.18)
0.01
(0.01)
0.13
(0.09)
-0.29
(0.25)
0.03
(0.40)
0.03
(0.04)
-0.09
(0.04)
0.01
(0.05)
-0.34
(0.13)
0.01
(0.02)
0.20
(0.13)
0.02
(0.13)
0.10
(0.17)
-0.40
(0.08)
-0.13
(0.03)
-0.08
(0.13)
-0.10
(0.28)
-0.17
(0.05)
-0.91
(0.29)
0.65
(0.51)
-1.27
(0.62)
-0.28
(0.12)
-0.68
(0.10)
-0.69
(0.12)
0.97
(0.17)
-0.08
(0.04)
-0.22
(0.10)
0.10
(0.10)
-0.07
(0.14)
0.10
(0.06)
-0.06
(0.03)
0.22
(0.04)
-1.85
(0.10)
-0.11
(0.02)
0.10
(0.04)
0.11
(0.04)
0.13
(0.06)
-0.01
(0.03)
-0.00
(0.01)
-0.03
(0.04)
-0.50
(0.08)
-1.11
(0.04)
0.18
(0.05)
0.05
(0.04)
-0.03
(0.05)
0.01
(0.03)
0.02
(0.01)
-0.10
(0.06)
0.28
(0.12)
0.10
(0.03)
-0.32
(0.10)
-0.05
(0.07)
-0.15
(0.10)
0.00
(0.05)
-0.05
(0.02)
0.05
(0.05)
0.22
(0.09)
-0.00
(0.02)
-0.07
(0.06)
-1.52
(0.51)
-0.11
(0.34)
-0.02
(0.04)
0.04
(0.04)
-0.02
(0.05)
0.19
(0.09)
-0.02
(0.02)
-0.09
(0.06)
-0.07
(0.24)
-0.72
(0.39)
-0.12
(0.04)
0.02
(0.03)
0.13
(0.07)
-0.07
(0.14)
-0.02
(0.03)
-0.03
(0.09)
-0.02
(0.08)
-0.41
(0.12)
-0.34
(0.08)
-0.09
(0.02)
0.04
(0.18)
0.04
(0.32)
0.24
(0.08)
-0.49
(0.22)
0.92
(0.52)
0.71
(0.53)
-0.21
(0.13)
-0.97
(0.08)
RURAL
Wheat
Rice
Dairy
Meat
Oils &
Fats
Sugar
Other
Food
NonFood
URBAN
Wheat
Rice
Dairy
Meat
Oils &
Fats
Sugar
Other
Food
NonFood
Note: The rows refer to the good being affected, and the columns to the price being changed. Hence, row
2, column 7 for the rural sector estimates that a 1% increase in the price of other food will increase the
quantity of rice purchased by 0.38% The figures in parentheses are standard errors.
26
impressive when compared with critical values that take account of sample size; the
Schwartztest has criticalvalues of 135.0 and 135.6respectively,which are comfortably
larger than the test statisticshere. More convincingperhaps is the extent to which the
results in Table 6 overcomethe problemsin Table 5. For wheat, rice, dairy produce,
and to a large extent meat, the results are very close to those in the previous table.
However,for oils and fats and for sugar, where the previous estimateswere quite crossprice elasticitiesin Table 5 in these two imprecise,the estimateschangea great deal, and
are now much more preciselyestimated. Further, the several large columns no longer
appear in the symmetry-constrainedestimates. This is exactly what we had hoped that
the impositionof symmetrywould accomplish,and the results are a good indicationof
the usefulnessof evenvery simpletheoryin supplementingrelativelyuninformativedata.
The own-priceelasticitiesare very similar in the two tables, and those for sugar
and oils are still impreciselyestimated;symmetrycannothelp here. In the rural sector,
the own-price elasticity of sugar is positive, but the standard error is large. The
estimatesin the non-food row should be treated rather more seriouslythan those in the
non-foodcolumn. Sincethe budgetshares of the eightgoods add to unity, we have data
on the share of non-food, and the estimatesof the effects of food prices on non-foods
have essentiallythe same status as the estimatesof the effects of food prices on foods.
However, there are no unit value data for non-food, so that the estimatesof the effects
of the non-foodprice on foods are determinedby the theoreticalrestrictions,rather than
by the data. The standarderrors in the last columntend to reflectthis imprecision,and
these elasticitiesshould not be treated too seriously. There are several importantcrossprice elasticitiesthat survive the impositionof symmetry. There are well-determined
substitutioneffects betweenrice and wheat, betweenrice and meat, rice and sugar, and
betweenrice and oils, and there is a significantnegativeeffect, only some of which is
an income effect, between wheat and meat. These cross-priceeffects appear in both
urban and rural samples, and we feel that a good deal of credence should be given to
them.
27
The Analysis of Tax and Price Reform
This section looks at the implicationsof the estimates for the analysis of a
number of possible price reforms in Pakistan. The general procedure is the standard
one, of looking at the distributionalconsequencesof price changes,together with their
effectson economicefficiency,and trying to identifydirectionsof price reformthat can
improve efficiencywithout deleteriousdistributionalconsequences,or which can meet
stated distributionalaims of protectingthe poor, but withoutavoidableefficiencycosts.
For reasonsthat willbecome apparent,the policyoptionsthat we examineare somewhat
artificial ones, but the effects that they illustrate would be important in any more
thoroughgoinganalysis. We are also concernednot to use the results of the previous
sections mechanically, but instead to identify those implications for policy that are
credible and robust, and downweightthose that may be due to samplingvariability, or
are otherwisedoubtful.
The theory of price and tax reform in developing countriesis well-developed
in the literature, see for examplethe introductorychaptersin Newberyand Stern (1987),
and the survey paper by Dreze and Stern (1987). These principleshave been appliedto
tax reform in Pakistan by Ahmad and Stern (1990, 1991), and we shall follow the
general frameworkof that article, if not the details. In the standard case, where there
are no quality effects, and everyonefaces the same price, the analysisruns as follows.
Supposethat there is a proposal to increase the consumertax on good i. The (local)
consequencesof this changecan be assessedby lookingat the derivativesof consumer
welfare witli respect to the change, together with the effects on government revenue.
The compensation required by agent h for tax-induced price change Api is qhAp,. But
we are typically not indifferentas between different gainers and losers, particularly in
LDCs where there are very limited instrumentsfor redistribution, so these individual
compensationsmust be weightedaccording to weights ah that are proportional to the
social marginalvalues of income to each agent. The social cost of the tax increase is
therefore given by the derivative
aW =
ati
hOhqh
(35)
The tax change will also have an effect on governmentrevenue, directly through the
additional taxes raised on the good, and indirectly through the own- and cross-price
28
substitutioneffects that are induced by the price increase. If R is total government
revenue, then the revenuederivativeis givenby
8R
_ = ES q,h+
ati.
'
Lt-
aqkh36
kat,
(36)
The ratio of (35) to (36), typically denoted A,, measures the costliness of raising
additionalrevenuethroughgood i. If N.is large, additionalunits of revenueare obtained
at high socialcost, as wouldhappen,for example,if the good is heavilytaxed, is highly
price elastic, and most heavily consumedby the poor. By contrast, goods with low )
values are attractivecandidatesfor raising revenue.
As written, equations(35) and (36) take no accountof distortionselsewherein
the economy, nor of the resource allocationeffects of tax changesthat will typically
result if prices do not reflect opportunitycosts. To take accountof these effects, write
the consumerprice pi as s1+ti, where, for the moment, si is interpretedas a base price
that is unaffectedby the tax change. Sincethe tax changedoes not alter the total amount
spent by consumers, (36) can be rewritten as
-a3R
a
Eq
(37)
so that the tax cost ratios A,become
vh
Oh
qhh38
fa.qh
Sh
Lk
(38)
at
Under appropriate(but non-trivial)assumptions,Dreze and Stern (1987)show that (38)
has an attractivealternativeinterpretationthat allowsa substantialgeneralizationover the
pure revenuefocus of (35) and (36). In particular,if actualtaxes are ignored,the vector
s is taken as a vector of shadow prices, i.e. prices that reflect the relative social
opportunitycosts of the goods, so that the vector t is a vector of shadowtax rates, then
(38) capturesall of the effectsof the tax changesthroughthe general equilibriumsystem,
and is therefore of quite general applicability. Indeed, the denominator of (38)
representsminus the resourcecosts, i.e. the resourcebenefitsof the tax increase, while
29
its numeratoris, as before, the welfarecost, so that the \-'s are simplycost-benefitratios
at the "right," i.e. shadowprices.
The implementationof (38) requires the consumptionof the various commodities, which we have from the survey, the price derivatives, which have been
estimatedin Section 1, social incomeweights, which are discussedbelow, and shadow
prices. Ahmad, Coadyand Stern (1988)have estimateda completeset of shadowprices
for Pakistanbased on an 86 x 86 input output table for 1976, and Ahmad and Stern
(1990, 1991)use these shadowprices in their tax reform experiments. However, these
prices embodya very large numberof assumptions,aboutshadowprices for land, labor,
and assets, as well as, most crucially, judgments about which goods are tradeable
(further divided into importablesand exportables) and which goods are non-traded.
These assumptions all have a role in determining the shadow prices, and while the
procedure itself is unimpeachable,the use of the prices for the current exercise makes
it very difficult to isolate the role played in the reform proposals by the different
elementsin the story. Instead, we shall work with an illustrativeset of shadow prices
for our eight goods. These prices are illustrativein the sense that they do not claim to
take into account all the ingredientsthat should ideally be included in shadowprices.
However, they are based on the current Pakistan situation, and help us see how
importantfeaturesof that situationenter into the analysisof price reform.
The crucial commoditiesare wheat, rice and sugar. Rice and sugar sell at
internalpricesthat are substantiallylower than their world pricesat the officialexchange
rate. Accordingto the PakistanEconomicSurvey, Governmentof Pakistan(annual),the
border price for both rice and wheat was approximately40% above the world prices in
the mid-80's. Both are tradeablegoods, and for both we work with accountingratios
(shadow prices divided by consumer prices) of 1.4. In the case of sugar, there is a
heavilyprotecteddomesticsugar refining industry,and the border price of refined sugar
is some 60% of the domesticprice. Oils and fats are also protectedby a complexsystem
of taxes and subsidies with the result that the border price is perhaps 95% of the
domesticprice. For the other four goods in the system, we shall work with accounting
ratios of unity. Althoughthere are tariffs and taxes on many non-food items, which
wouldcall for accountingratiosless thanunity, manyother items are non-traded,so that
their shadowprices depend on the shadowprice or conversionfactor for labor, which,
given the pricing of wheat and rice, is likely greater than unity. Our experimentsare
therefore conductedunder the suppositionthat the ratio of shadowprices to consumer
30
pricesfor the eight goods(wheat,rice, dairy, meat, oils and fats, sugar, otherfood, nonfood) are given by the vector (1.4, 1.4, 1.0, 1.0, 0.95, 0.6, 1.0, 1.0).
It is important to be precise about the policy experiments that are being
considered,and aboutthose that are not. The instrumentsthat are beingconsideredhere
are instrumentsthat increase or decrease the consumerprice of the good, as would be
the case, for example, if there were a value added tax, or if the good were being
importedover a tariff. Such instrumentsmay be availablein Pakistan for sugar or for
oils. However,to the extent that the rice and wheatsubsidiesare maintainedby export
taxes, the experimentsdescribed here do not correspondto what would happen if the
export tax were changed. An increase in an export tax increases consumerwelfare at
the sametime as it increasesgovernmentrevenue, so that if only these two effects were
considered,as is the case in (35) and (36), it would pay to increasethe tax indefinitely.
Of course, export taxes are limited by the supply responses of farmers, as well as by
internationaldemand when the country has some monopolypower, as is the case for
Pakistan with basmati. An export tax is an instrumentthat alters not only consumer
prices but also producerprices, and it cannotbe analyzedwithoutlooking at the supply
responses. The calculationshere, which look only at the demandside, correspondto a
differenthypotheticalexperiment,in which producerand consumerprices are separated.
This would supposethat the governmentprocures the total output of rice and wheat at
one set of prices, that it sells the commoditieseither to foreignersat world prices, or to
domestic consumersat a third set of prices. It is the consequencesof changingthese
domesticprices than can be examinedusing the apparatusdescribed above. Of course,
these are very artificialexperiments,which would not be feasible in practice. Farmers
who grow wheat cannot be charged one price for consumptionand paid another for
procurement. However, more realistic policies will have the same effects as those
describedhere, plus additionaleffects that work throughthe supplyside. What we have
to say here is only a part of the story, but it is a part that has to be understood if good
policy decisionsare to be made.
Before calculatingthe results, we need to adapt the basic modelof tax reform
to a world where people pay differentprices, and where qualityas well as quantity is an
object of choice. The simplestassumption,and that adoptedhere, is that taxes on each
good are ad valorem, so that the tax paid is a constantproportionof price, so that the
tax per kilo is higher for higher priced varieties, as well as at locationswhere rice is
more expensive. It is easy to thinkof cases wherethis is not true, where taxes are fixed
31
at rates per quintal, and where transport marginsare the same irrespectiveof the total
value of the load. Nevertheless,the assumptionyields substantialsimplifications,as we
shallsee. If the tax rate on goodi is T., thenthetax paidby consumerh on good i iSr ihqih
where jh = vh/(l +T.) is the ex-tax unit value. Hence, the compensationpayable for an
increase A7i is vphq"
A7i so that the numeratorof the X,ratio (35) is replaced by
2Y=ihSOhvPqP
(xhlnh)exw
=ih
(39)
where we have adoptedthe standardpractice that the social weight given to additional
incomefor h is proportionalto the level ofper capita householdexpenditure,x/n, raised
to the power of -e, for some e > 0. A value of e of unity impliesthat additionalincome
is twice as valuable to someone with half the income, with higher values implying a
greater focus on the poor, and lower values less. Socialwelfare accountingis done for
individuals, not households, but (39) is nevertheless correct under the inevitable
assumption that household consumptionlevels are equally shared among household
members.
To derive the revenueeffectsof changesin Tj,ithelps to decomposeunit value
into the product of pi and quality, ui. Revenueraised from consumerh, R^, is then
Rh
=
T jhh p
(40)
where ph is the ex-tax price faced by the consumer. We can then differentiatewith
respect to T,, rememberingto take into accountthe shading of qualities in response to
price, and using the facts that
apih
p;
Dln;=i
aTi
i+
alnpj
(41)
it is possibleto show that
?
a,r,
=
1
k
1F+7k - r
x"(6ki-6kiwi")
(42)
which can be evaluatedgiven actualor shadowtax rates, the data from the survey, and
the estimatesof the parameters. One final formula will be useful. Definethe aggregate
budget shares, the shares of each expenditurein aggregateconsumers' expenditure,by
32
EiXhW
Eh
h
Xh
and the "socially representative"budgetshares by
=
Yh
(x hln ) -exhw
(44)
xh
h
The cost-benefitratios A,are the ratios of (39) to (42) and can be written
Wi' /)W
I+
+
ii
I +Ti.
1t
J
+
Tk Oi
kg
Ei
1+TW
(45)
The numerator of (45) is a pure distributionalmeasure for good i; it can be interpreted
as the relative shares of the market representativeindividual(the representativeagent)
and the socially representative individual, whose income is lower the higher is the
inequalityaversionparameter e. This measureis modifiedby the action of the terms in
the denominator. The first of these (apart from 1) is the tax factor multipliedby the
elasticity of expenditureon good i with respectto its price, quality and quantity effects
taken together, see equation(15)above. This term measuresthe own-pricedistortionary
effect of the tax. If it is large and negative, as would be the case for a heavily taxed
price elastic good, the term will contributeto a large \,-ratio and would indicatethe
costlinessof raisingfurther revenueby that route. The last term is the sum of the tax
factors multipliedby the cross-priceelasticities,and captures the effectson other goods
of the change in the tax on good i, again with quantity and quality effects included.
From a theoreticalpoint of view, this decompositionis trivial, but when we look at the
results, it is useful to separatethe own-and cross-priceeffectssincethe former are likely
to be more reliablymeasuredthan the latter.
Table 7 shows the efficiency effects of raising taxes on each of the goods,
distinguishingbetweenthe terms in the denominatorof (45); these are calculatedfor the
rural sampleonly. The urban results are similar, and one sector is sufficientto illustrate
how the procedure works. The first columnshows the tax factors /(I +Ti) calculated
from the accountingratios discussedabove; these are the shadowtaxes calculatedfrom
comparisonof the world and domesticprices. Wheat and rice carry shadow subsidies,
oils and sugar, shadow taxes. The second columnshows the own-priceelasticitiesfor
33
Table 7: EfficiencyAspectsof Price Reform: Rural Sector
Tax Factor
eC,
Own
Cross
Total
-0.04
(0.03)
-0.17
(0.13)
-0.05
1.36
(0.08)
2.02
(0.14)
0.95
(0.02)
1.00
(0.12)
0.43
(0.16)
Wheat
-0.67
-0.61
Rice
-0.67
-1.80
Dairy
0.00
-1.01
0.40
(0.08)
1.20
(0.09)
0.0
Meat
0.00
-0.70
0.0
Oils
0.05
-1.67
-0.08
(0.02)
(0.02)
-0.00
(0.12)
-0.49
(0.16)
Sugar
0.29
0.05
Other Food
0.00
-0.41
0.01
(0.12)
0.0
-0.41
(0.16)
0.06
0.61
(0.19)
1.06
(0.06)
(0.06)
0.00
I_________I___
____
-0.75
0.00
(0.03)
1.00
(0.03)
Non-Food
___ ___
_
0.0
I________
__
Notes: The tax factor is the share of the shadow tax in the tax-inclusive price, ei,is the own-price elasticity
of quality times quantity, own and cross are the second and third terns in the denominator of (45), and total
is the denominator itself. Figures in parentheses are standard errors.
quantity and quality taken together. Becausethe quality effects are not large, these
elasticitiesare closeto those listed in Table 6, but they are conceptuallydistinct. Taxes
are ad valoremso that qualityshadingin responseto tax increasesdepressesrevenuejust
as do decreases in quantity. The third column shows the own-price distortions and
correspondsto the middle term in the denominatorof (45). Goods that bear no shadow
taxes do not appear in this column since there are no distortionaryeffects of small tax
increasesat zero tax rates. The large effects are on wheatand rice, with the latter much
larger because its own-priceelasticityis muchlarger. The standarderrors for both these
terms are small relative to their estimatedmagnitudes. By themselves,these own price
terms will generate small cost-benefitratios, particularly for rice. Subsidiesare being
paid, they are distortionary,particularlyfor rice, and it is desirableto reduce them, at
least from this limitedpoint of view.
The cross terms in the next columnare typicallysmaller and, as expected,have
larger standarderrors. The large terms are for rice, for oils, and for sugar; all are
negative and all act so as to decrease the attractivenessof raising those prices. By
34
checkingback through the full matrix of price elasticities,it is possible to track down
the specific terms that are responsiblefor these total cross-priceeffects. For rice, the
interactionis with wheat. As we have seen, an increasein the price of rice is attractive
on own-priceefficiencygrounds,but it will also switch demandinto wheat, which itself
bears a subsidy, so that the attractionsof raisingthe price are (partially)reduced. The
oils and sugar terms are very similar; both are substitutesfor wheat and rice, so that
increasing either price generates demandsfor the rice and wheat subsidies which are
socially costly. In addition,increasesin the oils price generatea fall in the demand for
sugar, which bears a shadowtax, so that its opportunitycost is well below its price, an
effect which again makesit less attractiveto raise the prices of oils. The final column
in the Table presents the sum of both effects, plus one accordingto (45), together with
the estimatedstandarderror. Accordingto these, and recall that nothingyet has been
said aboutdistributionalissues, rice is the commoditywhoseprice should be raised, and
sugar and oils the commoditieswhoseprices shouldbe lowered. The wheatsubsidytoo
is distortionary,and there is an efficiencycasefor raisingthe price. The standarderrors
on the oils and sugar terms are relativelylarge, reflectingthe fact that they come from
cross-priceeffects, but they are not large enough to threaten the main thrust of these
conclusions.
Equity effects are incorporatedin Table 8 for a range of reasonablevalues of
the distributionalparameter e. The first panel correspondsto e= 0, so that there are no
distributionalconcerns,and the cost-benefitratios are simplythe reciprocalsof the last
column in Table 7. Rice is a good candidatefor a price increase, oils and fats for a
price decrease. As we move through the table to the right, the distributionaleffects
modify this picture to some extent. The "equity" columns in the table, which are the
relativebudgetshares of an increasinglypoor individualrelativeto the market representative individual,move away from luxuries and towards luxuries as the distributional
parameterincreases. Wheat, the basic staple, attractsa larger weightas we move down
the incomedistribution,as do oils and fats. Other food, which containspulses, has large
weights when e takes the extremevalue of 2. Wheat is a target for price increases on
efficiencygrounds,althoughnot as much so as rice, but the equity effectstend to make
it less attractive, and its X,-valuebecomesrelativelylarge as we moveto the right in the
table. However,for oils and fats, and to a lesser extent for sugar, which were the main
candidatesfor price decreases, the equity effects only strengthenthe conclusions. Oils
and fats in particular figure relativelyheavily in the budgets of low income consumers,
35
Table 8: Equity and Cost-BenefitRatios for Tax Increases
le=0
Wheat
Rice
Dairy
Meat
Oils
Sugar
Other Food
Non-Food
e=0.5
|
e=1.0
e=2.0
Equity
X
Equity
X
Equity
X
Equity
A
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.73
0.49
1.05
1.00
2.33
1.64
0.94
1.00
1.11
1.06
1.03
1.00
1.09
1.03
1.06
0.98
0.81
0.52
1.08
1.00
2.54
1.68
1.00
0.98
1.29
1.18
1.12
1.05
1.26
1.11
1.18
1.04
0.95
0.58
1.18
1.06
2.93
1.83
1.11
1.04
2.00
1.65
1.51
1.37
1.90
1.51
1.72
1.43
1.47
0.82
1.62
1.38
4.43
2.48
1.63
1.43
and reducingtheir price is desirablefor both equityand efficiencyreasons. Rice remains
the best candidatefor consumertax increases; it is not consumedby the very poor, and
its subsidyis the most distortionary.
In conclusion,let us emphasizeonce again that these policy implicationsdo not
apply directlyto the tax instrumentscurrentlyin use in Pakistan. Our findings suggest
that raising revenue from an increase in the price of rice to consumers would be
desirableon grounds of efficiencyand equity. But the main instrumentfor controlling
the price of rice is the export tax, a decrease in which would certainly increase the
consumerprice of rice, but it wouldalso decreasenot increasegovernmentrevenue, and
it would change supplies of rice, effects which we are in no positionto consider here.
Nevertheless,the fact that rice and wheat are substitutablefor one another in consumption, and that there are further substitutioneffectsbetweenrice, wheat, sugar and edible
oils, would have to be taken into account in a reform of any export taxes, just as they
are taken into account here. Indeed, perhaps the most useful lesson of the analysis in
this paper is how importantit is to measurethe way in which price changesaffect the
pattern of demand. The Pakistanisubstitutionpatterns betweenrice, wheat, sugar, and
edible oils are not consistentwith additivepreferencesand so cannotbe accommodated
within a model like the linear expendituresystem. In countrieswhere some prices are
far from opportunitycost, cross-priceeffectsof tax changeswill oftenbe more important
than the effects on the good itself, so that these effects must be measured in a flexible
way. Nor couldadditivepreferencesaccommodatethe pattern of total expenditureand
own-priceelasticitiesthat characterizedemandpatterns in Pakistan. Oils and fats are a
36
necessity, but have a high own-priceelasticity, so that the ratio of the own-price to
income elasticityis many times greater than for a rice, which has high own-priceand
income elasticities. Additive preferences require that this ratio be (approximately)
uniform over goods. Yet it is this ratio that is the principal determinant of how the
balancebetween equity and efficiencyought to be struck.
37
References
Ahmad, S.E., and N.H. Stern, (1991), The theory and practice of tax reformfor
developingcountries,Cambridge. CambridgeUniversityPress.
Ahmad, S.E., and N.H. Stern, (1990), "Tax reform and shadowprices for Pakistan,"
OxfordEconomicPapers, 42, 135-159.
Ahmad, S.E., Coady, D., and N.H. Stern, (1988), "A completeset of shadowprices
for Pakistan:illustrationsfor 1975-6," PakistanDevelopmentReview, 27, 7-43.
Ahmad, S.E., Ludlow, S., and N.H. Stern, (1988), "Demand responsesin Pakistan: a
modificationof the linear expendituresystemfor 1976," PakistanDevelopment
Review, 27, 293-308.
Alderman,H., (1988), "Estimatesof consumerprice responsein Pakistanusing market
prices as data," PakistanDevelopmentReview, 27, 89-107.
Deaton, A.S., (1981), "Optimal taxation and the structure of preferences",
Econometrica,Vol. 49, pp. 1245-60.
Deaton, A.S., (1987a), "Econometricissues for tax design in developing countries,"
Chapter4 in Newbery and Stern (1987).
Deaton, A.S., (1987b), "Estimationof own- and cross-priceelasticitiesfrom survey
data," Journal of Econometrics,36, 7-30.
Deaton, A.S., (1988), "Quantity, quality, and spatial variation of price," American
EconomicReview, 78, 418-430.
Deaton, A.S., (1990), "Price elasticitiesfrom survey data: extensionsand Indonesian
results," Journal of Econometrics,44, 281-309.
Deaton,A.S., and J. Muellbauer,(1980a),"An almostideal demandsystem,"American
EconomicReview, 70, 312-326.
Deaton, A.S., and J. Muellbauer, (1980b), Economicsand consumerbehavior, New
York. CambridgeUniversityPress.
Dreze, J.P., and N.H. Stern, (1987), "The theory of cost-benefitanalysis," in A.
Auerbachand M. Feldstein,eds., Handbookof Public Economics,Amsterdam.
North-Holland.
Government of Pakistan, (annual), Pakistan Economic Survey, Islamabad. Ministry of
Finance.
Governmentof Pakistan, (monthly),Monthly StatisticalBulletin, Islamabad. Federal
Bureauof Statistics.
38
Newbery, D.M.G., and N.H. Stern, (1987), The theory of taxationfor developing
countries,Oxford. Oxford UniversityPress for The World Bank.
Schwartz, G., (1978), "Estimatingthe dimensionof a model," Annals of Statistics, 6,
461-464.
39
Appendix: AlternativeMethods of Estimation
The methodologyused in this paper, and describedin the Section2, is designed
to extract price and expenditureelasticitiesfrom survey data in the form in which they
are typically available. It allows for the possibilitiesthat there are village level fixed
effectsin demandpatterns, effectsthat may be correlatedwith average village incomes,
that unit values are not prices, and that there maybe non-independentmeasurementerror
in the reported unit value and quantitydata. Handlingthese various issuesimposescosts
in terms of relativecomplexity,and the questionarises as to whetherthere may be shortcuts that ignore some of the problems that are less serious in practice. In fact, the
calculationsin section 1 are not very difficultto carry out, and it is only the calculation
of the standard errors that requires careful and customizedprogramming. As always,
the heaviest work is in the preparation and cleaning of the basic data, not in the
calculationof the estimates.
This sectionhas two purposes. The first is to providesome alternativeestimates
that are calculatedusing standardregression methods,and examineshow much difference there is betweenthese and the methodologyof this paper. The second purpose is
to try out alternative data, not methodologies. We follow Alderman (1988) and
reestimatethe model using not the unit values from the survey, but the urban regional
price data that is independentlycollected by the Federal Bureau of Statistics and
published in the Monthly StatisticalBulletin. Householdsare matched to the survey
point that is geographicallyclosestto them, and assignedthe price for that area in the
quarter during which they were interviewed. The model is essentiallythe same as that
used in the paper, but the prices are genuineprices, not unit values. The disadvantage
of the method is that there are relatively few collectionpoints, and they are all urban,
so that they may provide only very poor indicationsof the prices facing the households
in the survey.
Note that the two sets of alternativeestimatesdo not have the same status. For
the modelsusing the alternativeprice data, we would like to obtain the same answersas
before, since there is nothing incorrect in using the alternativeprices, except for the
possible effectsof measurementerror. But if the issuesraised in Section2 are real, the
short-cutmethodologiesare essentiallyincorrectand they shouldgive different answers.
Of course, measurementerror, village taste differences, or quality effects may not be
very importantin a particular application,and the estimatesmay turn out to be similar.
40
This is no guaranteethat in other applicationsthe same wouldbe true, althoughit is to
some extentpossible to highlightthe sourcesof difference, and to be aware of situations
in which short-cuts wouldbe dangerous. Even so, the alternativeestimatesgivenhere
are only indicativeof the possibilities. A full understandingof the alternativeestimators
would require more analysisand Monte Carlo experimentationthan can be included in
this paper, althoughsee Deaton (1990)for some limited evidence.
There are eightdifferent sets of estimatesin the columnsof Table Al. In order
to keep the comparisonsmanageable, we confine ourselves to the rural sector, and
present only the results for the total expenditureelasticityand the own-priceelasticity,
the former in the top of the table, and the latter in the bottom. The first columnrepeats
the results of Section2, and is taken from Table 5. The last two columns,to the right
of the double line, are the results from using the alternativeprice data, and will be
discussedbelow.
Columns (2) and (3) come from the followingspecification:
Inq, = C1+ aliInx+ol2iInn+
jin
Anv(A)
+ lyi.z+province and seasonal dummies + ui
where qi is the quantity purchased of good i, z is the same vector of household
demographicsused in the first-stageregression as in Section2, and the unit values are
includedon the right hand side as if they were prices. Equation (Al) is attractivein its
simplicity;the parametersare elasticities,and a doublelogarithmicregressionis perhaps
the simplestway to estimatethem. However,there are a numberof immediateproblems
of application. The most immediateis that householdswho do not purchase the good
must be excludedfrom the regression;the logarithmof zero does not exist. For the
analysisof tax reform, the exclusionof non-purchasinghouseholdsis undesirablesince
we are interestedin the effects of price changeon total or average demand, and we are
not concerned whether that change takes place at the intensiveor extensive margins.
From an econometricpoint of view, the exclusion of zero purchases also reduces the
sample size, particularlyif all the unit values are includedon the right hand side, since
in that case only those householdscan be included who are recorded as purchasingall
of the goods. This is a very severe restriction. Table 2 shows the fractions of
householdsbuying each good, but a much smaller fraction buy all of them and only
41
1,666 of the 9,119 rural householdsdo so. The regressionsin column(2) report results
from this very severely selectedsample, while in column (3), the selectionproblem is
lessenedby includingonly the own-priceon the right hand side, effectivelyassuminga
priori that the cross-priceterms are negligibleor at least, uncorrelated with the other
variables.
Columns (4) and (5) are obtainedfrom regressionsidenticalto (26) but with the
budget share as the dependent variable in place of the logarithmof the quantity. The
functionalform is thus essentiallythe sameas that used in Section2, but the regressions
are run directly withoutallowancefor village fixed effects, measurementerror, or any
distinctionbetweenunit value and price. Althoughall zero shares can now be included
on the left hand side, the selectionproblemrecurs through the unit values. Once again,
column (4) reports estimateson the restricted sampleof 1,666 householdswith all the
unit values included, and column (5) those estimateswith only the own unit value, so
that the selection fractions are those in Table 2. Finally, column (6) uses the same
model as columns(4) and (5), but all the data are averagedover each clusterprior to the
estimation. Included in the regressions are all those clusters where each good is
purchasedby at least one household;of the 757 rural clusters, 620 satisfy this condition.
This is the sameselectionthat is enforcedupon us in Section2.
There is another possible techniquewhich is not examinedhere, but which is
sometimes used and with which we experimentedearly in the research. One of the
problemsof estimatinga modelon the householddata comesfrom the potentialspurious
correlationbetweenmeasuredquantitiesand measuredunit values, a correlationthat can
be generatedby measurementerror in either or both. One possibilityis to replace the
individualunit value by the averageof all the unit values in the village; since prices are
the supposedto be the same for all householdsin the village, this is clearlylegitimate.
However, the procedure does not resolve the spurious correlationproblem, since the
village mean is still correlatedwith the individualunit valuesused to computeit. It can
therefore be modifiedone step further by using for each householdthe villagemean unit
value computedusing all unit values in the village except that of the household itself.
While this removes any spurious correlation between quantities and unit values, or
betweenshares and unit values, the "leave-out" mean, like the original mean, is still an
error-ridden estimate of the true and unobservable average village unit value.
Attenuationbias is therefore not removed. In the modelsused in Section2, where the
share is the dependentvariable,the spuriouscorrelationproblem is typicallyless serious
42
Table Al: AlternativeEstimatesof Total Expenditureand Price Elastcities
(Rural Pakistan 1984-85)
.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
TOTAL EXPENDITURE ELASTICITIES
Wheat
Rice
Dairy produce
Meat
Oils & Fats
Sugar
Other Food
0.37
0.68
1.05
1.10
0.42
0.86
0.59
0.31
0.63
0.68
0.91
0.44
0.72
0.57
0.28
0.66
0.85
0.98
0.37
0.79
0.64
0.48
0.70
0.81
1.04
0.44
0.76
0.66
0.35
0.61
0.92
1.05
0.42
0.82
0.70
0.34
1.03
1.03
1.35
0.38
1.22
0.81
0.44
0.85
1.12
1.32
0.43
0.95
0.74
0.38
0.91
0.99
1.48
0.42
1.12
0.89
-0.75
-1.07
-0.92
-0.45
-0.00
-0.59
-0.32
-0.93
-1.09
-0.94
-0.35
-0.89
-0.78
-0.54
-0.76
-1.37
-0.91
-0.31
+0.04
-0.31
-0.43
-0.89
-1.41
-0.91
-0.27
-0.65
-0.62
-0.64
-0.72
-1.94
-0.98
-0.71
-1.62
-0.22
-0.42
-1.16
-2.18
-1.02
-0.52
+2.88
+0.76
-0.91
-1.18
-2.25
-1.00
-0.60
+3.57
+0.82
-0.95
OWN-PRICE ELASTICITIES
Wheat
Rice
Dairy produce
Meat
Oils & Fats
Sugar
Other Food
-0.51
-1.59
-0.87
-0.57
-2.04
-0.07
-0.35
Notes: Column (1) was calculated using the methodology of Section 1, and the estimates are those in Table
V. Column (2) comes from a double logarithmic regression of Inq on Inx, the logarithms of the unit values
of all the goods, and the other variables. Column (3) is the same as (2), but only the "own" unit value is
included in the regression. Column (4) shows elasticities calculated from the results of regressing the shares
on Irx, all unit values, and the other variables, while (5) is the same as (4) but omitting all but the own unit
value. Column (5) is the same as regression (3), but uses cluster/village means for all variables. Columns
(6) and (7) correspond to columns (4) and (5) but use the urban prices from the Monthly Statistical Bulletin
in place of the unit values from the survey.
than the attenuationproblem. Computationusing the "leave-out" method is almost as
complicatedas the full-method, and so it has little to commend it, and we do not
examineit further.
Columns(7) and (8) in the table correspondto the sameregressionsas columns
(4) and (6), that is they use (26) with shares as dependentvariables, but the prices from
the urban centers are used in place of the unit values. Column (7) uses the individual
data, and column(8) the data averagedby cluster. There are no missingvaluesfor these
43
regressions, so that column (7) uses all 9,119 rural households,and column(8) all 757
rural clusters.
There are a variety of econometricissuesthat can account for the differences
in the columnsof Table Al. Columns (2) and (3) use a doublelogarithmicfunctional
form that is different from the share-logform of the other columns. Because of the
missingvalue (zero)problem, these regressionsare also estimatedon different samples
from the others, and the samples vary from commodityto commodity. Column (1)
obtainsits total expenditureelasticitiesfrom within-villageestimation,and so allowsfor
villagetaste differencesthat canbe correlatedwith villageincomeor villagedemographics. If these effectsare important,all the other estimateswillbe biased, since they pool
within and betweenvillage information. Columns(2) through (6) treat unit values as if
they were prices, and makeno allowancefor the effectsof qualitychoice on unit values.
All columnsexcept the first assumethat the total expenditureelasticity of expenditure
on eachgood is identicalto the total expenditureelasticityof quantity. Columns (1), (2)
and (3) measure the latter, and columns (4) through (8) the former. The last seven
columnsalso make no allowancefor measurementerror. In the last two columns,which
use the urban prices, the measurementerror has the standardeffects, of attenuatingthe
coefficienton the price, which in this context impliesthat the own-priceelasticitiesare
biased towardsminus one. For columns(2) through (6), the effectsof the measurement
error are more complicated. Given the way that unit values are measured, it is likely
that the reported logarithmsof each unit value, which is the logarithmof expenditure
minus the logarithm of quantity, will be spuriously negatively correlated with the
reported logarithm of quantity. For columns (2) and (3), this will generate an
attenuationbias towardszero on the price term, togetherwith a bias towards minus one
from the spurious correlation, and the net effect cannot be signed theoretically. For
columns(3) through (6), it is more likely that the measurementerrors of the dependent
variables,the shares, and the log unit values willbe uncorrelated,so that the attenuation
bias will dominate,and the own-priceelasticitieswill be biased towardsminus one. Of
course, all of these results supposethat the specificationin Section2 is correct, which
may or may not be the case. Even so, one cannotreversethe supposition,and treat any
of the other models as the correct specification. Although the assumptionsbehind
column (1) may be invalid,the problemsof measurementerror and qualityvariation are
real enough, and they are ignoredby the modelsin the other columns. Note too that all
44
results aboutbias are results about expectationsor probabilitylimits, and need not be
true for any one realization.
Begin with the upper panel of Table Al, which containsthe total expenditure
elasticities. Most of these are remarkablyrobust acrossthe differentmodels,presumably
becausethere is a great deal of variationin total expenditure,and the slope of the Engel
curve is very well-determinedand robust to a wide range of misspecifications. All of
the wheat expenditureelasticitiesare between 0.28 and 0.48. Given that there is a
quality elasticityof ten percent for wheat, see Table 4, column(1) gives an expenditure
elasticityof 0.48, which is close to the 0.44 estimatein column (7) using Alderman's
method. Apart from column(4), the other figures are too low. For rice, there is again
good agreementbetween column (1) plus the quality elasticityof 0.11 and column (7).
The other figures are not very different, althoughthe estimatesthat ignore the witlhinvillagevariance, columns(6) and (8), are clearlytoo high. Similar results applyto the
other expenditureelasticities. If the fourth row of Table 4 is addedto the first column
of Table Al, the results are close to those in Column(7), so that the two "defensible"
sets of estimates are in good agreement. Averaging over clusters in column (8)
sometimesmakes some difference,but is perhaps not of major importance. The biggest
deviation is in column (2), where the double logarithmicspecificationon the heavily
selected sample generates an elasticity for expenditureon dairy produce of 0.68,
comparedwith an estimatethat is greater than unity in the first column.
The price elasticitiesvary a good deal more. The price informationin the data,
althoughplentifulfor most goods, is less plentifulthan the informationon outlay, and
is less able to overcomethe variations in specification. As is to be expected, there is
most variability in estimateswhere there is least variabilityin the price, for edible oils
and fats, and to some extent for sugar. The estimatesusing the urban prices generate
positive price elasticities for these two goods, and the other methods show large
differences, especiallyfor sugar. We know from Section 2 and Table 5 that the price
elasticitiesof these two categories are estimated with large standard errors, and this
clearly appliesto the estimatesfrom the other modelstoo. However,the imprecisionis
often not apparent from the calculatedstandarderrors of these models, and several of
the estimatesin columns(2) through (8) would appear to be estimatedquite precisely,
if the regression results were to be treated seriously. It is difficult to draw any firm
conclusionsfrom the resultsfor the othercommodities. Theaveragingover clustersdoes
not seem to have very marked effects, perhaps because most of the price variation is
45
between rather than within villages. Rice appearsto be quite price elastic, whetherwe
use the unit valuesor the urban prices, althoughthe latter make it more so. It is perhaps
also difficult to believe that wheat, which is the staple food, has a price elasticity
(numerically)in excessof unity, although there may well be some substitutionbetween
wheat and rice. Dairy produce and meat have similar price elasticities in both
approaches,althoughfor otherfood, the estimatein column(I) is again smallerthan that
in Column (7). Apart from rice, where the effect is the other way, these results are
perhaps consistent with an attenuationbias towards minus one in column (7). The
doublelogarithmicspecificationin columns(3) and (4) does not seemto be very reliable,
and sometimesproduces markedly different answers dependingon whether the crossprice effects are included. The selectivity problems that are involved in making this
choiceseem to render this a very unsatisfactorymodelin practice. Columns(4) and (5),
which are the short-cut methods closest to column (1), produce the results that are
closest, except for the obvious problems with oils and fats and sugar. But these
specificationstoo suffer from the selectivity issue, albeit by less than the double
logarithmicformulation.
The estimationof price elasticitiesis not an easy task, and it is perhaps too
muchto expectthat there shouldbe simpleways of providinggood estimates. Some of
the short-cutmethodsproducereasonableestimatesfor some commodities,but there is
no guarantee that they would do so in other applications. In the absence of the full
analysisthere wouldbe no way of knowingwhetherthe approximationsare adequateor
catastrophic,and their use involvesthe analystin a numberof difficultand unsatisfactory
compromises. The full analysisin column (1) may not producethe right answer, but we
know that the other methods cannotdeliver it, and will provide acceptable approximations only if the problems they ignore happen not to be serious in a particular
application. The simplicitycomes at too high a price.
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LSMS Working Papers (continued)
No. 51
ChildAnthropometryin C6ted'Ivoire:Estimatesfrom Two Surveys,1985and 1986
No. 52
Public-PrivateSectorWageComparisonsandMoonlightingin DevelopingCountries:Evidence
from C6ted'Ivoireand Peru
No. 53
Socioeconomic
DeterminantsofFertilityin C6ted'Ivoire
No. 54
The Willingnessto Payfor Educationin DevelopingCountries:EvidencefromRuralPeru
No. 55
Rigiditedessalaires:Donne'esmicro6conomiques
et macroeconomiques
sur l'ajustementdu marche
du travaildans le secteurmoderne(in French only)
No. 56
ThePoorin Latin Americaduring Adjustment:A CaseStudy ofPeru
No.57
The SubstitutabilityofPublicand PrivateHealthCareforthe Treatmentof Childrenin Pakistan
No.58
Identifyingthe Poor:Is "Headship"a UsefulConcept?
No. 59
LaborMarketPerformance
as a DeterminantofMigration
No. 60
TheRelativeEffectivenessof Privateand PublicSchools:Evidencefrom Two DevelopingCountries
No. 61
LargeSampleDistributionof SeveralInequalityMeasures:WithApplicationto C6ted'lvoire
No. 62
TestingforSignificanceof PovertyDifferences:WithApplicationto C6ted'Ivoire
No. 63
Povertyand EconomicGrowth:With Applicationto C6ted'Ivoire
No. 64
Educationand Earningsin Peru'sInformalNonfarmFamilyEnterprises
No.65
Formaland InformalSectorWageDeterminationin UrbanLow-IncomeNeighborhoodsin Pakistan
No. 66
Testingfor LaborMarketDuality:ThePrivate WageSectorin C6ted'Ivoire
No.67
DoesEducationPay in theLaborMarket?TheLaborForceParticipation,Occupation,and Earnings
of PeruvianWomen
No. 68
TheCompositionand DistributionofIncomein C6ted'Ivoire
No.69
PriceElasticitiesfrom SurveyData:ExtensionsandIndonesianResults
No. 70
EfficientAllocationof Transfersto thePoor:TheProblemof UnobservedHouseholdIncome
No. 71
Investigatingthe DeterminantsofHouseholdWelfarein C6ted'Ivoire
No. 72
TheSelectivityofFertilityand the DeterminantsofHuman CapitalInvestments:Parametric
and SemiparametricEstimates
No. 73
ShadowWagesandPeasantFamilyLaborSupply:An EconometricApplicationto the PeruvianSierra
No. 74
TheAction of Human Resourcesand Povertyon One Another:What WeHaveYet to Learn
No. 75
The Distributionof Welfarein Ghana,1987-88
No. 76
Schooling,Skills,and the Returnsto GovernmentInvestment in Education:An ExplorationUsing
Datafrom Ghana
No.77
Workers'Benefitsfrom Bolivia'sEmergencySocialFund
No.78
Dual SelectionCriteriawith Multiple Alternatives: Migration,WorkStatus,and Wages
No. 79
GenderDifferencesin HouseholdResourceAllocations
No.80
TheHouseholdSurvey asa Toolfor PolicyChange: Lessonsfrom theJamaicanSurvey of Living
Conditions
No. 81
PatternsofAging in Thailandand Coted'Ivoire
No.82
DoesUndernutritionRespondtoIncomesand Prices?DominanceTestsfor Indonesia
No.83
Growthand RedistributionComponentsof Changesin PovertyMeasure: A Decomposition
with
Applicationsto BrazilandIndiain the 1980s
No.84
MeasuringIncomefromFamilyEnterpriseswith HouseholdSurveys
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