WPS4285
Policy ReseaRch WoRking PaPeR 4285
Poverty Analysis Using an International
Cross-Country Demand System
J. A. L. Cranfield
Paul V. Preckel
Thomas W. Hertel
The World Bank
Development Research Group
Trade Team
July 2007
Policy ReseaRch WoRking PaPeR 4285
Abstract
This paper proposes a new method for ex ante analysis reforms, where the poverty measures are derived using a
of the poverty impacts arising from policy reforms. unique poverty level of utility, rather than an income or
Three innovations underlie this approach. The first expenditure-based measure. They use these techniques
is the estimation of a global demand system using a with a demand system for food, other nondurables and
combination of micro-data from household surveys services estimated using a combination of 1996 ICP
and macro-data from the International Comparisons data set and national expenditure distribution data.
Project (ICP). Estimation is undertaken in a manner Calibration is demonstrated for three countries for which
that reconciles these two sources of information, household survey expenditure data are used during
explicitly recognizing that per capita national demands estimation--Indonesia, the Philippines and Thailand.
are an aggregation of the disaggregated, individual To show the usefulness of these calibrated models
household demands. The second innovation relates to a for policy analysis, the authors assess the effects of an
methodology for post-estimation calibration of the global assumed 5 percent food price rise as might be realized
demand system, giving rise to country-specific demand in the wake of a multilateral trade agreement. Results
systems and an associated expenditure function which, illustrate the important role of subsistence expenditures
when aggregated across the expenditure distribution, at lowest income levels, but of discretionary expenditure
reproduce observed per capita budget shares exactly. This at higher income levels. The welfare analysis underscores
leads to the third innovation, which is the establishment the relatively large impact of the price hike on poorer
of a unique poverty level of utility and an appropriately households, while a modified Foster-Greer-Thorbecke
modified set of Foster-Greer-Thorbecke poverty poverty measure shows that the 5 percent price rise
measures. With these tools in hand, the authors are able increases the incidence and intensity of poverty in all
to calculate the change in the head-count of poverty, three cases, although the specific effects vary considerably
poverty gap, and squared poverty gap arising from policy by country.
This paper--a product of the Trade Team, Development Research Group--is part of a larger effort in the group to
support poverty analysis and trade program. Copies of the paper are available free from the World Bank, 1818 H Street
NW, Washington, DC 20433. Please contact Paulina Flewitt, room MC3-333, telephone 202-473-2724, fax 202-522-
1159, email address pflewitt@worldbank.org. Policy Research Working Papers are also posted on the Web at http://econ.
worldbank.org. J. A. L. Cranfield may be contacted at jcranfie@uoguelph.ca. July 2007. (49 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
POVERTY ANALYSIS USING AN INTERNATIONAL CROSS-COUNTRY DEMAND
SYSTEM
J. A. L. Cranfield1, Paul V. Preckel2 & Thomas W. Hertel2
JEL Classification: D1, C4, I3
Keywords: Aggregation, consumer demands, expenditure distribution; poverty
1. Associate Professor and contact author, Department of Agricultural Economics and Business, University of
Guelph, Guelph, Ontario, Canada, N1G 2W1, Telephone: (519) 824-4120, Fax: (519) 767-1510, e-mail:
jcranfie@uoguelph.ca.
2. Professor, Department of Agricultural Economics, Purdue University, West Lafayette, Indiana, U.S.A., 47907.
Any errors or omissions remain the responsibility of the authors. The authors would like to thank Will Martin for his
continued support of our research. As well, the financial support of the Bank Netherlands Partnership Program of
the World Bank is gratefully acknowledged.
INTRODUCTION
Recent research into the evolution of the world distribution of income focuses on using a
combination of cross country and within country information to estimate the distribution of
income from an ex post perspective (Schultz 1998; Bourguignon and Morrisson 2002; Quah
2002; Sala-i-Martin 2002a, 2002b, 2006). These analyses have arrived at mixed results,
suggesting on the one hand no change, or slower growth, in the extent of poverty worldwide
(Bourguignon and Morrisson 2002) or falling poverty on the other hand (Sala-i-Martin 2006).
While useful from a historical perspective, such analyses do not permit us to predict how
inequality, and indeed poverty rates, might change in the future. This is particularly important
for analyzing the poverty impacts of trade policy changes, where the impact on low-income
households is likely to be very different from higher-income households.
Developing such a characterization of the poverty impacts of trade policy could be done
on a country-by-country basis wherein household expenditure survey data are employed to
approximate compensating variation as a budget share weighted average of price changes arising
from policy shocks (Chen and Ravallion 2003; Levinsohn et al. 2000). However, such an
approach does suffer from a number of weaknesses. Inconsistencies between national accounts
and household survey data (Sala-i-Martin 2006) renders results from household survey based
analysis suspect in making predictions about aggregate impacts. Moreover, considerable
difficulties arise in obtaining systematically comparably disaggregated expenditure information
from household surveys for a large number of countries. Even more substantial difficulties are
encountered when attempting to map these disaggregated expenditure patterns on particular
goods or services from household survey data to aggregate data, such as those contained in the
International Comparisons Project (ICP) particularly when many countries are involved.
Obtaining the price data needed to fully characterize preferences in terms of Engel and
substitution elasticities from household survey data is another problem. Lastly, the share-
weighted summation approach to approximating CV lacks theoretical rigor. Indeed the absence
of substitution effects can be quite problematic for large price changes (Friedman and Levinsohn
2002).1 All-in-all, it is often difficult to compare impacts across countries based on country-by-
1. More specifically, these authors find that incorporation of substitution effects dampens by 50% the welfare loss
from price increases following the Asian financial crisis.
1
country analyses which utilize survey data. In this regard, a theoretically rigorous,
internationally comparable analysis of the poverty impacts of international price changes should
be a welcome addition to the literature.
However, to date, most international demand studies have been done using only per
capita data which is of limited value to those interested in the distributional consequences of
policy reform. One exception is the recent work by Cranfield (1999) and Cranfield et al. (2004)
using maximum entropy and treating the per capita observation as an explicit aggregation over
households. This paper builds on that previous work and contributes a framework which enables
estimation of the future impact of poverty arising from exogenous policy shocks. It does so by
incorporating more disaggregated household survey data into an entropy-based estimation
procedure in which the demands for final goods and services at different points of the
expenditure distribution are estimated. This demand system, in turn, provides the basis for
analyzing the impact of a global food price increase of the sort anticipated by international trade
models in the wake of WTO reforms.
Recovery of disaggregate demands at each point of the national expenditure distribution
is achieved using a global demand system (i.e., a demand system with the same set of parameters
for each observation) which embodies more flexible income (expenditure) effects compared to
alternative demand systems. The value of the demand system is further enhanced via post-
estimation calibration of the parameters so that each country-specific demand system reproduces
observed per capita demands. The resulting country-specific, calibrated demand systems appear
to be well-suited to predicting expenditure patterns across the income spectrum in the three focus
countries in our study: Indonesia, Thailand and the Philippines. As such it provides a useful
vehicle for evaluating the welfare impacts of changes in consumer prices due to international
trade reforms.2
One of the great benefits of this approach to poverty analysis derives from the fact that
we are able to establish a unique poverty level of utility for each country. The poverty level of
utility is invariant to the international trade shock and resulting price changes and therefore
ideally suited for assessing the impact of a price change on the poverty level. This leads us to
2. Of course, one important limitation of the work in this paper is that we do not take into account factor earnings.
However, the approach to doing so is relatively straightforward, provided estimates of the earnings impacts are
2
define a modified Foster-Greer-Thorbecke (FGT) poverty measure useful in conducting ex ante
poverty analysis stemming from exogenous policy shocks. Specifically, since our approach
yields a single, calibrated expenditure function for the entire population in a country, we replace
the individual's expenditure level in the FGT measure with an expenditure function defined
across a price vector, calibrated demand parameters and the individual's level of utility. In a
similar vein, the threshold level of expenditure used in FGT is replaced with the expenditure
function defined across the same price vector, the same calibrated demand parameters, and the
poverty level of utility.
Use of the calibrated expenditure function and the poverty level of utility to define the
threshold level of expenditure is advantageous, as there is no ambiguity about how the threshold
level of expenditure in the modified FGT measure must change in the wake of policy reform. In
this framework, the threshold level of expenditure is that which is required to attain the initial
poverty level of utility, at the new prices. As such, it reflects optimal adjustments in demand, in
response to these price changes. Use of an explicit expenditure function in the FGT measure is
therefore a valuable innovation and clearly preferable to other income or expenditure-based
approaches, which rely on the indexation of a fixed bundle of goods and services to establish a
poverty line. In addition to being theoretically more satisfying, the expenditure function
approach lends itself to ease of use in the type of partial and general equilibrium modeling often
used for trade policy analysis.
This work draws together several recent strands of literature in consumer demand,
poverty and trade policy analysis. On the demand side, it represents another step in the long line
of literature related to estimation of international consumer demands (e.g. Theil and Clements
1987; Theil et al. 1989; Rimmer and Powell 1992; Cranfield et al. 2002; Seale et al. 2003). By
treating per capita national demands as the explicit aggregation of a distribution of demands
across the expenditure spectrum, it also adds to the literature which merges marco (i.e. per
capita) and micro (i.e. individual or household survey based) data for use in the analysis of
inequality and poverty (e.g. Ravallion and van de Walle 1991; Schultz 1998; Cranfield 1999;
Bourguignon and Morrisson 2002; Quah 2002; Sala-i-Martin 2002a, 2002b, 2006), thus allowing
us to look beyond the averages (see, for example, Ravallion 2006). This paper has especially
available. For an illustration of how this can be done, see the paper by Hertel et al. (2004).
3
strong ties to Sala-i-Martin (2002a, 2002b, 2006) in that we use per capita expenditure and
consumption data coupled with expenditure inequality data to recover an approximation to the
expenditure distribution and data sources directly linked to those that author has used in previous
work.3 However, we differ from Sala-i-Martin (2002a, 2002b, 2006) in that we are interested in
country-specific effects arising from policy shocks and we have the means to recover
information useful in welfare analysis. In particular, the demand system used here has an
explicit expenditure function which we use not only for welfare analysis, but also for poverty
analysis. Therefore, our poverty calculations are tied directly back to micro-theory and the
behaviour of economic agents; the value of this theoretically grounded approach to welfare and
poverty analysis has been highlighted previously in Ravallion (1998) and Neary (2004).
The next section presents a brief discussion of the demand system we estimate. The
empirical methods and data are then discussed. Results of the econometric estimation are then
presented, followed by development of the calibration scheme and subsequent results. The
calibrated demand systems are then used to evaluate the consumption-based poverty impacts of
international trade reforms. While this paper only performs these calculations for three countries
in Southeast Asia, Indonesia, Philippines and Thailand, the approach could be extended to
evaluating the poverty impacts of consumer price changes for all countries in the international
data set. This kind of comprehensive, econometrically-based analysis of the international poverty
impacts of trade reform has hitherto been missing from the literature.
AN IMPLICIT, DIRECTLY ADDITIVE DEMAND SYSTEM
The demand system used to characterize consumer preferences is an implicit, directly additive
demand system (nicknamed AIDADS). AIDADS is best characterized as a generalization of the
Linear Expenditure System (LES) which allows for non-linear Engel curves while maintaining a
parsimonious parameterization of consumer preferences. Rimmer and Powell (1996) developed
AIDADS4 based on Hanoch's (1975) seminal work on implicit additivity. Written in budget
3. Granted, Sala-i-Martin (2006) used per capita GDP and income inequality measures rather than expenditure
measures. Note, however, that use of expenditure data is consistent with the World Bank's approach to modeling
poverty issues.
4. AIDADS is in the family of demand systems satisfying Cooper and McLaren's (1992) conditions for effective
4
share form AIDADS appears as:
wi = pii + 1- i (1)
y i +i exp(u)
1+ exp(u) p
y
where wi is the ith good's budget share, p is a n vector of prices with typical element pi + , y +
is expenditure, i ,i , i are unknown parameters, is a n vector with typical element i , u is
utility and qi > i 0. In AIDADS, the following parametric restrictions are used to ensure
n n
well-behaved demands: 0 i,i 1 for all i, and i= i =1.
i=1 i=1
Further details on AIDADS can be found in Cranfield et al. (2002, 2004); however, a few
points are worthy of mention here. Firstly, as with the LES, AIDADS characterizes consumption
at the subsistence level using the parameters i which represent the quantity of good i required
for survival, and therefore not subject to discretionary adjustment. Estimation of the subsistence
quantities permits us to say something meaningful about consumers' behavioral response (or
rather the lack of it) at extremely low income levels.
While AIDADS and the LES share the subsistence parameters, AIDADS generalizes the
LES with a re-parameterization of the marginal expenditure share, such that the marginal
expenditure shares change with the level if expenditure. When i = i , AIDADS collapses to
the LES and the marginal expenditure share on good i is constant. The parameter i
characterizes the marginal expenditure shares on good i in the neighborhood of subsistence
income, whereas i describes the marginal budget share at extremely high levels of expenditure.
If i > i , then the marginal (and average) budget share falls with rising income. The opposite is
true wheni < i . From the point of view of characterizing consumption behavior at very low
income levels, this additional flexibility is very important, as the marginal expenditure shares of
the very poor are generally quite different from their counterparts evaluated at national, per
capita income levels.
global regularity (see Rimmer and Powell 1996 for details). AIDADS also has rank three (see Gorman 1980 and
Lewbel 1991 for further discussion on demand system rank).
5
EMPIRICAL METHODS & DATA
As the main purpose of this paper is to utilize an international, cross-country demand system for
poverty analysis, we do not focus on estimation methods per se. Indeed, the entropy-based
empirical methods used to recover the approximation to the distribution of expenditure, estimate
parameters of AIDADS and recover unobservable levels of consumption have been published
previously in Cranfield et al. (2004). However, since the present analysis incorporates a more
refined approach to the estimation problem, a technical appendix containing the empirical model
accompanies this paper.
Nevertheless, to contextualize the results, note that the empirical framework is developed
in a mathematical programming environment, wherein the underlying demand system parameters
and approximation to the distribution of expenditure are calculated. The numerical optimization
program minimizes an objective function composed of a concentrated log-likelihood function
and entropy function; the former allows for estimation of the demand system parameters, while
the latter enables recovery of the approximation to the distribution to expenditure. Constraints
are used to define the AIDADS demand system, associated parametric restrictions and regression
error terms, as well as the level of utility in the AIDADS model. Additional constraints are
included to ensure the recovered approximation to the expenditure distribution matches the
known moment conditions for expenditure and to ensure that the recovered disaggregate
demands aggregate back to the observed level of per capita demand.
As originally developed, maximum entropy methods provide a means to recover
unobservable information from an observable, but noisy signal or message. More recent usage,
however, has focused on recovery of unobservable information from observable statistics of an
underlying distribution. For example, if one observed the first j-moments of a random variable
and knew the support of the underlying distribution, one could use maximum entropy methods to
recover an approximation to the true distribution, such that the first j-moments of the
approximating distribution exactly match the observed moments, but reflects maximum
uncertainty with respect to the j+1 moments and beyond. Recovery of the approximating
distribution takes the form of a constrained optimization problem, wherein Shannon's measure of
uncertainty is maximized subject to constraints requiring the moments of the approximating
distribution to exactly match the known moments (see Jaynes 1957a, 1957b; Kapur and Kesavan
6
1992; or Golan et al. 1996 for further detail). However, the resulting first order conditions do
not have a closed-form solution, so numerical methods are used to solve the mathematical
programming problem computationally (see the technical appendix for details on this
mathematical programming model used in this study).
Our analysis uses price, per capita expenditure, and budget share data from a cross
section set of countries in the most recent (1996) International Comparisons Project (ICP). These
data are useful in analyzing international demand patterns as they are provided in identical units
(i.e., international dollars) and facilitate comparison of prices and quantities for disaggregate
commodities across countries.
The ICP data record final consumption of 26 goods and services in 114 countries, with
countries ranging in per capita expenditure from Malawi to the United States. In keeping with
the additive nature of AIDADS, the 26 goods and services are aggregated into three broad
aggregate goods: food (FOOD); other non-durables (ONONDUR); and services (SERVICES).
Because of the dynamic nature of decisions with respect to durable goods, and given the cross-
section nature of the data, durable goods have been omitted from this analysis. In other words,
we focus only on the allocation of expenditures across non-durables and services.5 Budget
shares are constructed by dividing nominal expenditure on each aggregate good by total nominal
expenditure. The price of each good equals the ratio of nominal expenditure for that good to real
expenditure for the same good. Total nominal expenditure per capita serves as the per capita
expenditure term in AIDADS. Table 1 provides summary statistics of the ICP data used for
estimation.
On the expenditure distribution side of the data base, quintiles and deciles, are obtained
from an updated release of Deninger and Squire's (1996) World Income Inequality Database
(WIID). Only expenditure or consumption based quintiles and deciles are used.6 Table 2 shows
5. Moreover, initial estimation of AIDADS with data that included durables resulted in an empirical model that
would not converge, nor would it converge after numerous attempts to resolve the issue (e.g. changing starting
points of the optimization program, changing the bounds on the choice variable set, etc).
6. The updated WIID is a compilation of Gini coefficients and quintile and decile data for various countries over
time.
7
the quintile and decile values, year of coverage, and measurement details.7 The household
survey data show the minimum, average and maximum value of expenditure for each percentile
of the population in the three focus countries. As these are rather voluminous, they are not
presented here. However, these data are drawn from household surveys for Indonesia (1993),
Thailand (1996) and Philippines (1999).8
ECONOMETRIC RESULTS
Estimated parameters of AIDADS are shown in Table 3. Beginning with the estimates of
subsistence quantities, i , note that the estimate for services is at its lower bound of zero, while
those for food and other non-durables are positive. The estimates of i suggest, as one might
expect, that food and other non-durables are a required part of the subsistence bundle of goods,
while services are not strictly required for survival. Premultiplying the i s by their respective,
country-specific, prices and summing over the three goods permits us to establish the cost of the
subsistence bundle. This survival level of expenditure on non-durables is equal to $14, $15 and
$26, respectively, for Indonesia, the Philippines and Thailand. The estimates of i upon which
these subsistence bundles are based reflect the level of real expenditure of the poorest household
in the sample, i.e. those households on the extreme lower end of the expenditure distribution (on
a global scale). Not surprisingly, these "survival" expenditures are drastically lower than poverty
7. The year of coverage often deviates from 1996, but usually by no more than five years, while quintiles are
measured in different units across countries (i.e., households versus individuals, gross versus net of taxes). Because
expenditure distributions tend to change slowly over time, the mismatch between years is assumed unimportant.
Due to the high correlation between expenditure, gross and net of taxes, and for households versus individuals, this
mismatch in the data is also assumed away.
8. One may wonder why these household survey data were not directly incorporated into the analysis. Sala-i-Martin
(2006) outlines three reasons why one should not use household survey means in such analysis. Albeit weak, his
first point is that the literature uses "...population-weighted distribution...", the implication being that comparison to
the literature requires use of data similar in nature. Second, and perhaps more persuasively, survey means have
poorly understood properties; the notion being that differences in survey methodologies and strategies results in
possible misleading summary statistics from household based surveys. Thirdly, surveys are not available for all
countries and all time periods. This latter point highlights the difficulties one might encounter in attempting to
estimate a global demand system using household based survey data. We would add to Sala-i-Martin's (2006) the
fact that not all surveys collect the information needed to estimate demand systems; some surveys do not (or cannot)
collect price data, while others only collect partial information on the household's consumption bundle, both of
which make it nearly impossible to estimate a useful demand system.
8
line(s) previously reported in the literature.9 The invariance of these subsistence purchases to
expenditure will have important implications for the overall behavior of consumption at the
lowest expenditure levels as will be shown below.
Next, turn to the two sets of parameters describing the behavior of marginal budget
shares. For FOOD, the estimated value of i indicates that, at subsistence expenditure levels, 73
percent of an additional dollar of expenditure is devoted to food, as opposed to18 percent for
other non-durables and just nine percent for services. This highlights the critical role of food in
the budget decisions of very poorest households. The estimates of i provide the target value
towards which the marginal budget share evolves as expenditure rises without bound. Not
surprisingly, this is zero for food at some point the household is satiated with respect to food
but over two-thirds for services; at extremely high expenditure levels slightly over two-thirds
each addition dollar of expenditure is allocated to services.
The value of the marginal budget shares, fitted budget shares and Engel elasticities for all
three goods, calculated at the means of the data, are presented in Table 4. As expected, when
evaluated at the means of the data, the marginal budget share for food is low (0.068), while that
for services is large (about 0.6). This highlights the danger of using the more restrictive LES
specification when one is interested in the behavior of households in poverty. By restricting the
marginal budget share to be constant, the LES is likely to understate the marginal budget share
on food at the subsistence level by a full order of magnitude (0.73 versus 0.068 at mean prices
and expenditure).
Ideally, we would like to be able to compare the recovered and observed budget shares
across the expenditure spectrum. However, in our experience, attempts to do so are tenuous at
best. In particular, there is an inherent discordance between the ICP data and the household
survey data. Firstly, the definition of specific goods and services differs. Secondly, the data
collection methods differ; ICP builds on the national accounts, while the household data are
based on surveys implemented using a sampling approach. (Sala-i-Martin (2006) devotes
considerable discussion to these issues.) As such, any comparison between actual budget shares
9. For instance, Ravallion et al. (1991) conclude that $23 per month (in 1985 PPP units), or $276 per annum, is a
reasonable lower bound to the poverty line.
9
from the household surveys and recovered budget shares tends to be dominated by differences in
the measurement of disaggregated spending, and as such, is not terribly informative. Moreover,
our primary interest lies in how one might use the recovered shares to undertake policy analysis.
As foreshadowed above, the first step in this regard is a post-estimation calibration scheme
which turns a global demand system into national demand systems. We turn attention next to
this scheme.
POST-ESTIMATION CALIBRATION
While it is a useful analytical construct, the assumption of globally common preferences and the
subsequent invariance of the AIDADS parameters across countries is problematic for policy
analysis. And so, as is commonly done with micro-simulation analysis, it is useful to have a
strategy for post-estimation calibration, in which the international demand system is
"nationalized" by forcing the calibrated system to pass through the observed per capita
expenditure levels. In this context post-estimation calibration of AIDADS is achieved by first
rescaling i and i , and then re-computing a value of . However, in keeping with our focus on
internationally comparable measures of poverty, we do not alter the subsistence quantities, i ,
which we assume to be a function of human needs and, as such, is invariant across regions.
Our calibration scheme works as follows. First, given that the subsistence parameters are
invariant across countries, the subsistence shares (i.e. price times i divided by expenditure) are
known and constant. Thus, it makes sense to parse the AIDADS equation in share form into two
components a subsistence share and a discretionary share (the latter could also be referred to as
the super-numeracy share). We then calculate the fitted discretionary budget shares at per capita
expenditure as:
^it = ^i +^i exp(ut)( py
1- t^) , (2)
1+ exp(ut ) t
where ^i and ^i are estimated values, ^ is the vector of estimated subsistence quantities, and
ut is the value of utility arising from choice of the optimal consumption bundle at the per capita
level of expenditure, yt . The calculated value of ^it is simply the value of the discretionary
10
budget share at the per capita level of expenditure, calculated using the estimated values of
AIDADS parameters.
Next, add the estimation residuals for the ith equation in the tth observation back to ^it to
obtain "observed" discretionary budget shares as follows:
it = ^it + wit -w^it
( ) (3)
where wit is the per capita budget share, wit is the fitted value of the budget share evaluated at
^
the per capita level of expenditure, calculated using the econometrically estimated value of the
AIDADS parameters. Here, the regression errors (stated in terms of budget shares) are added
back into the discretionary portion of AIDADS. Doing so assumes that all of the regression
error is attributable to an imperfectly observable discretionary budget share.
The next step in the calibration scheme is to adjust the original estimates of i and i
with the ratio of fitted to "observed" discretionary budget shares as follows: it = ^i ^it it and
~
~
it = i ^it it . Finally, normalize the values of it and it to ensure they sum to unity:
~ ~ ~
Cit = it~ ~ and Cit = it~ ~ , where the superscript "C" denotes the parameters have
j jt j jt
been calibrated. These country specific, calibrated values of i and i are then fixed and used
in calibrating utility and the parameter by solving a non-linear system of equations for each
country. This system contains the defining equation of utility for AIDADS and the AIDADS
system with quantities fixed at their observed per capita consumption levels, but evaluated at the
per capita level of expenditure.10 Hence, each country for which post-estimation calibration is
undertaken has its own values of i , i and . These calibrated parameters have the desirable
property that reproduce the observed per capita national budget share at the per capita level of
expenditure.11 Moreover, this calibration scheme results in a calibrated set of budget shares
10. This normalization is required, as integration of the calibrated demand system back to an underlying dual
function requires a constant of integration. Adjusting accordingly provides such normalization.
11. The only potential problem with this procedure occurs if the actual consumption level for a given good is not
larger than the subsistence level. This suggests that it may be of interest to constrain the subsistence levels to be
strictly less than the lowest level of observed consumption.
11
across all expenditure levels within each country's expenditure distribution.
Table 5 shows the estimated and calibrated values of the AIDADS model. Recall that the
subsistence parameters, i , are assumed to be invariant internationally and are not calibrated. In
light of the subsequent trade policy experiment which we will explore, we focus our attention
here on the behavior of food expenditures across the expenditure spectrum. In this regard, note
that since the original estimate of i for food is zero, then so too are the calibrated values of i .
However, relative to its value in the estimated international demand system, the calibrated value
of i has increased for Indonesia and the Philippines, but fallen for Thailand. The calibrated
values of have also changed relative to original estimate, with Indonesia's and Thailand's
calibrated values being smaller than that estimated for all countries, while the calibrated value
of is larger for the Philippines.
These calibrated values are not terribly useful in conveying the impact of calibration.
Instead it is more instructive to compare the recovered and calibrated budget shares for food
across the expenditure distribution in the three focus countries. Figures 1, 2, and 3 plot, among
other things, the recovered and calibrated budget shares for food across the income spectrum.
For Indonesia (Figure 1), the calibrated food expenditure shares now pass through the per capita
based budget share (depicted by a blue diamond), and vary only slightly from the recovered
shares. Specifically, the calibrated shares are rotated in a clockwise manner around the per
capita based budget share. Relative to the recovered shares, this means the calibrated shares are
larger than the recovered shares at low expenditure levels, while the reverse is true at high
expenditure levels. However, the difference between the calibrated and recovered shares is
slight, which makes this rotation difficult to observe.
These figures also plot the horizontal line corresponding to the calibrated value of i (for
the respective focus country) and we can see that i lies well above all of the calibrated budget
shares even for the poorest household. This is because i is a measure of the limiting
behaviour of marginal expenditures as total expenditure approaches our estimate of subsistence
expenditure. As the poorest household in the expenditure distribution for Indonesia has an
expenditure level well above the subsistence expenditure at local (i.e. Indonesian) prices, this
difference is not surprising. Since Engel's law suggests the marginal budget share for food falls
12
as expenditure grows, it is hardly surprising that the calibrated per capita budget share for food is
well below the limiting behaviour given by i .
Figures 1 3 also plot the break-down of the calibrated budget shares into the
subsistence ( pii y ) and discretionary shares ((i +i exp u ) (1+exp u )(1-p y) ),
( ) ( )
respectively. This permits us to examine how these individual components adjust to changes in
expenditure level, thereby decomposing changes in the overall budget share. Comparing the
subsistence and discretionary shares for food in Indonesia, we see that the majority of the change
in food's budget share is driven by discretionary expenditure. As the subsistence share has
expenditure in the denominator, this share falls with rising expenditures; for Indonesia, this
means that as expenditure approaches the level of the wealthiest household, the subsistence share
becomes nearly zero.
Somewhat different results are obtained for the Philippines, where calibrated shares differ
a bit more from the recovered shares (see Figure 2). Here, the calibrated shares have shifted
upwards relative to the recovered shares in order to pass through the observed national per capita
budget share. Moreover, the difference between the recovered and calibrated shares grows as one
progresses upwards through the Philippines' expenditure distribution. Calibrated food budget
shares are very close to the calibrated value of i for the Philippines (the horizontal line in
figure 2), suggesting that total expenditure on non-durable goods and services by the poorest
household in the Philippine's recovered expenditure distribution is closer to subsistence
expenditure (at local prices) than in Indonesia. The subsistence share of food at the subsistence
level of expenditure is much higher in The Philippines than in Indonesia -- approximately 16
percent of total non-durable expenditure in the poorest household. As with Indonesia, it falls
towards zero at the highest expenditure levels. It is also interesting to note that the behaviour of
the discretionary shares across the expenditure spectrum is rather different from Indonesia.
Discretionary shares for food in the Philippines initially rise with expenditure, thereupon
reaching a maximum, before beginning to fall after about 5.2 on the log expenditure scale. As
with Indonesia, food's budget share is almost entirely accounted for by discretionary
expenditures on food at high levels of expenditure.
13
For Thailand the difference between calibrated and recovered shares is much more
pronounced (Figure 3). As required, Thailand's calibrated food budget shares pass through the
per capita based budget share for food. Moreover, the calibrated shares have shifted down,
relative to the recovered shares, in near parallel fashion. Also note that the gap between the
calibrated value of i for food and the food budget share for the poorest household in Thailand's
expenditure distribution is even more pronounced than in Indonesia. And, as with Indonesia, the
subsistence shares and calibrated discretionary shares fall as expenditure increases, with the
discretionary share accounting for a larger portion of food's budget share as one moves up the
expenditure distribution.
What should be clear from the preceding discussion is that our calibration strategy does
not affect the subsistence shares. Calibration only plays a role in changing the location and
shape of the discretionary shares; it does so by altering the values of i , i and , and the
subsequent value of utility when the utility function is evaluated, subject to the budget
constraint, using the calibrated parameters. For the particular estimates presented above, only
the term (i +i exp u ) (1+exp u ) is altered, and that drives the changes in the discretionary
( ) ( )
share. It is important to recognize, however, that any exogenous policy shock to either prices or
expenditure (income) levels will alter both the subsistence and discretionary shares. For
instance, a price increase arising from trade liberalization would increase the subsistence share
for food, but may increase or decrease the discretionary share. The latter is qualified as the price
increase will decrease the (1-p component of the discretionary share but increase the
y)
(i +i exp u ) (1+exp u ) component (recall that the value of i for food is zero); depending
( ) ( )
on the size of these changes, the discretionary share may increase or decrease. As such, it is
difficult to say a priori if food's share of expenditure will rise or fall in the wake of a price hike.
Of even greater importance is how such a price shock might affect the poorest households and
hence the incidence of poverty. In the tradition of micro-simulation, we turn next to an
exploration of these questions by simulating the impacts of a five percent global food price rise
using the calibrated demand system. We will focus particular attention on the resulting changes
in consumer demand and poverty.
14
POVERTY IMPACTS OF A GLOBAL FOOD PRICE RISE
There has been considerable interest recently in the potential impacts of multilateral trade
liberalization on poverty in developing countries. The clear consensus is that agricultural reforms
in the rich countries will cause world farm and food prices to rise, as farm subsidies are
eliminated and rich country border protection is reduced (Beghin et al.; Cline; Anderson and
Martin). Moreover, recent proposals for the exemption of so-called Special Products from tariff
cuts in developing countries would mean that the world price rises would not be offset by tariff
cuts for many staple food products. In addition, the G-33 proposal for a Special Safeguard
Mechanism could permit substantial tariff rises in the face of import surges. In short, there is a
strong likelihood that food prices will rise in developing countries, following a successful
conclusion of the Doha Development Agenda. Regardless of its origin, a food price rise may be
expected to benefit agricultural producers in the developing world, while hurting consumers. The
net outcome is therefore ambiguous (Hertel and Winters 2005). Providing a comprehensive
analysis of the trade/poverty debate is beyond the scope of this paper. However, the framework
developed here offers an important improvement in the way the consumption impacts of such a
price hike are evaluated. Instead of simply assuming that the poor consume the national per
capita bundle of goods and services (Cline 2004) or that they consume only food (Anderson et
al. 2006), we a now in a position to assess the differential impact of a food price increase across
the entire expenditure (income) spectrum.
For illustrative purposes, we apply a five percent increase in the price of food and
examine its impact on the demand for food and household welfare within each focus country.
The change in welfare at the new prices is then used to assess the impact on a modified FGT
measure of poverty. Traditionally, the FGT measure is defined as:
N
P = N -1 (1- yn
z )(yn z)
n=1
where {0,1,2}12, N is the number of observations (i.e. households), yn is the nth household's
expenditure, z is a poverty line threshold level of expenditure and (yn z) is an indicator
12. To avoid confusion with a parameter of AIDADS, we use as the subscript to the FGT measure (i.e., P )
rather than the traditional .
15
function assuming a value of unity if the condition is true, and zero otherwise. P0 measures the
proportion of people in the population who are at or below the poverty line threshold, P1 is the
poverty gap (i.e., the per capita expenditure short fall of those in poverty, expressed as a share of
the poverty line threshold level of expenditure), and P2 is a poverty measure which "...is
sensitive to distribution among the poor" (Deaton 2000, p.147). In some respects, P2 could be
viewed as akin to a partial Herfindahl index. It is a partial measure because it only reflects the
concentration of expenditure amongst the poor.
For purposes of this paper, we redefine P as:
N e(p,un))
~
P = N - 1( 1- (4)
e(p,u)
~ (un u)
n=1
where e(p,un) is the calibrated AIDADS expenditure function evaluated at the price vector p
~ ~
and calibrated utility for the nth household (un ), while e(p,u) is the calibrated AIDADS
~
expenditure function evaluated using the price vector p and the poverty level of utility, u .
~
When p is set equal to the base price vector, e(p,un) and e(p,u) measure household
~ ~ ~
expenditure on non-durables and the poverty level of expenditure, respectively, before the price
shock. When p is set equal to the shocked price vector, the post-shock levels of expenditure as
~
well as cost of attaining the poverty level of utility at the new prices are obtained. Note that
while the poverty level of expenditure, e p,u , changes, the poverty level of utility is invariant to
(~ )
the price shock. The use of utility in the indicator function is advantageous as utility will vary
with expenditure and prices, and consumer demands at the poverty line are free to change as
well.
A natural question to next ask is how one establishes the poverty level of utility. We use
two approaches to establishing the poverty level of utility. The first approach assumes one has a
poverty level of expenditure. In this case, country specific poverty levels of utility can be
calculated by maximizing the AIDADS utility function, using the calibrated AIDADS
parameters, subject to the budget constraint evaluated at local prices and the poverty level of
expenditure. The resulting solution will include the optimal consumption bundle at the poverty
16
level of expenditure and local prices, but also the poverty level of utility (i.e. the utility of the
consumption bundle purchased at local prices with the poverty level of expenditure). The
advantage of such an approach is that the resulting poverty levels of utility (across countries)
reflect inter-country price level differences that otherwise would not be accounted for if one used
a poverty level of expenditure only. We use this approach to calculate poverty levels of utility
associated with one and two dollar a day poverty thresholds; specifically, we use a one dollar a
day poverty level of expenditure (i.e. $365 per annum) in calculating the poverty level of utility
for Indonesia and the Philippines, and the two dollar a day (i.e. $730 per annum) threshold for
Thailand.13 The one and two dollar a day poverty thresholds of expenditure are employed in
order to have some measure of consistency with the second way in which a poverty level of
utility can be established.
In particular, the World Bank's World Development Indicators (WDI) provides national
poverty rates (NPRs), defined as the proportion of national populations which fall below
nationally defined poverty levels. These percentages are 15.7, 36.8 and 13.0 percent in
Indonesia, the Philippines and Thailand, respectively. Using the recovered approximation to the
expenditure distribution and its support, it is easy to determine the poverty level of utility and
expenditure. The share of a country's population is summed until the cumulative sum just
exceeds the national level of poverty. The utility level of the household group just below the
point at which the cumulative sum just exceeds the NPR is the poverty level of utility. We can
then map back from that household group to the expenditure level consistent with these NPR
based thresholds; these values are $331 for Indonesia, $343 for the Philippines and $629 for
Thailand. Moreover, it should now be clear why we choose the one dollar a day poverty level of
expenditure for Indonesia and the Philippines, and two dollars a day for Thailand in our first
approach to defining the poverty level of utility; doing so makes the analysis based on the two
poverty level of utility approaches more comparable in terms of poverty level of expenditure.
13. The one and two dollar a day poverty lines have been the subject of some discussion in the literature. Sala-i-
Martin (2006) notes that the World Bank's definition of the poverty line was stated as $1.02 per day (in 1985 prices)
in 1990, but at $1.08 (in 1993 prices) in 2000. The issue is what base year is used to define the poverty line, and the
extent of price inflation since that base year was established. Nevertheless, as our approach could accommodate any
poverty line, we do not address whether one ought to use one dollar a day, $1.02 per day or $1.08 per day, and focus
instead on how one might use the approach with any particular poverty line definition.
17
The average percent change in demand for food when the price of food increases by five
percent ranges from -3.8 percent for Thailand to -4.1 percent of the Philippines. To better
illustrate these reductions in demand for food across the focus countries, Figure 4 shows the
level of demand for food in the focus countries before and after the price shock. Price shock
induced reductions in quantity demanded vary not only across focus countries, but also across
expenditure levels within each focus country. For instance, Indonesia, the Philippines and
Thailand have per capita non-durable expenditure levels of $655, $763 and $1,454, respectively,
based the 1996 ICP data base. Figure 4 shows that Thailand (a wealthier country compared to
Indonesia and the Philippines) generally has smaller changes in the quantity of food demanded,
regardless of where one is located in the expenditure distribution. Changes in demand for food
in Indonesia and the Philippines are larger compared to Thailand, but also reflect considerable
within-country variation.
To better illustrate what is driving the changes in demand arising from the five percent
increase in price, Figure 5 plots the uncompensated price elasticity for food in the Philippines
and its components based on the calibrated demand system. These components include the
expenditure (Engel) elasticity, budget share, the negative of the product of the share and Engel
elasticity and the compensated price elasticity (i.e. the components of the Slutsky equation are
plotted across the expenditure spectrum). What is clear is that the expenditure effect (i.e. the
negative of the Engel elasticity times the budget share) dominates the compensated price effect,
and is the most significant driver of changes in the uncompensated price elasticity. Moreover,
the uncompensated own-price elasticity for food becomes more inelastic as expenditure grows.
Consequently, the relative change in demand falls as expenditure grows due to the decline in
both the budget share and Engel elasticity. However, because the level of demand increases
from low to high expenditure levels, these smaller relative changes in demand actually translate
into larger absolute changes in demand at higher expenditure levels (Figure 4).
To relate the price shock impact back to the fundamental parameters of AIDADS, figures
6, 7 and 8 show the breakdown of the change in food's budget share into the change in the
subsistence share and the change in the discretionary share spent on food, across expenditure
levels in the focus countries. Recall that the subsistence share will rise for any price shock,
whereas the discretionary share may increase or decrease, depending on the size of change in
18
(1-p y) versus i (1+exp(u)) (where we have reflected the fact that i is zero in the
calibrated demand system). Further insight can be gained by noting that when i equals zero (as
is the case for food), the impact of a price change on the discretionary share can be expressed as:
jt^ ^ tu
= 1+exp(ut ){
^i p)
t -i }. (5).
it
p -i +(1- yt 1+exp(ut ) it p
Since i (1+exp ut ) is positive, the sign of (5) depends on the two terms within the brackets
( )
{}, but since put it is negative, the term in {} can be either positive or negative.
In Indonesia (see figure 6), the change in food's budget share initially increases as
expenditure increases, reaches a maximum and then declines. As is evident in the figure, the
change in the subsistence share becomes smaller as one progresses through the expenditure
levels, while the change in the discretionary share increases from a very small level, to a
maximum and then declines. The latter effect suggests that 6.8 on the natural log of expenditure
scale is the critical point after which the reduction in (1-p arising from the price increase
y)
overwhelms the increase in i (1+exp u ) and the change in the overall budget share for food
( )
begins to drop. As is clear from figure 6, the change in the subsistence share dominates at low
expenditure levels, as associated points in figure 6 lie above those representing the change in the
discretionary budget share for food. However, the change in overall food budget share is
dominated by the change in discretionary share at higher expenditure levels.
The change in food's budget share for the Philippines (figure 7) is somewhat different;
specifically, the share initially falls, reaches a local minimum, rises to a maximum and then falls
again. This wave pattern of adjustment reflects two competing sets of changes. On the one
hand, the change in the subsistence share falls through the entire range of expenditure (as
expected). On the other hand, the change in the discretionary budget share is initially negative,
but increases, becomes positive, reaches a maximum and then begins to fall. Based on this, we
may conclude that at low levels of expenditure, the role of the subsistence parameter for food
overwhelms the positive effect of the second term in brackets in equation 5.
Figure 8 illustrates that results are also different for Thailand, where the change in food's
budget share arising from the five percent food price rise is positive, but decreasing in
expenditure. However, as before, the change in food's share in the total non-durables budget
19
reflects a diminishing role of the subsistence expenditure, and variable role for discretionary
expenditure. In particular, the latter increases, reaches a maximum and then decreases as
expenditure grows, while the subsistence share falls as expenditure grows.
Three points emerge from this analysis. First, the change in quantity of food demanded,
as a result of the price shock, is larger for households with higher expenditure levels. Second,
food's share of total expenditure increases with the price increase (as one might naturally
expect). Lastly, the change in food's budget share is dominated by changes in subsistence
expenditure shares at low income levels, but changes in discretionary expenditure shares at
higher income levels.
Recognize too that the increase in food price erodes a household's purchasing power.
The impact of this purchasing power change is captured in figure 9, which shows the
compensating variation (CV) associated with the shock to food price calculated using the
calibrated AIDADS expenditure function. As expected given a price increase, and regardless of
the focus country, CV increases as expenditure increases. However, when CV is expressed as a
percent of initial expenditure, as shown in figure 10, it is clear that the price shock has a much
larger relative impact on poorer households than on wealthier households.
Table 6 summarizes the impact of the price shock on the modified FGT poverty measures
developed here. Across all focus countries, and regardless of how the poverty level of utility is
established, the FGT poverty measures increase with a five percent increase in the price of food.
In percentage terms, the increase in P is greatest in Indonesia, followed by Thailand and then
the Philippines. And, while the size of the percent change varies across the approaches to
establishing the poverty level of utility, the magnitudes of these changes are generally the same
(except for P1 in Thailand). Nevertheless, results suggest that the five percent food price
increase generates a greater incidence and intensity of poverty in Indonesia than in Thailand or
the Philippines. The larger percent changes in P0 and P1 in Indonesia drive the greater incidence
of poverty, while the larger percent in P2 drive the greater intensity of poverty.
SUMMARY AND CONCLUSIONS
As has been recently pointed out by Sala-i-Martin, there are fundamental inconsistencies
between household survey data and national accounts data. This complicates the measurement of
20
poverty, as well as the assessment of changes in poverty due to (e.g.) trade reforms. In response
to this problem, the present paper has developed a means by which one can recover an
approximation to the distribution of expenditure, estimate parameters of a demand system and
recover unobservable levels of consumption in a manner that replicates the means by which
aggregate economic data are collected, namely, as the sum of disaggregate expenditure and
demand levels. The proposed approach takes advantage both of international cross-section data,
as well as data from household expenditure surveys. In so doing, it provides an effective vehicle
for analyzing the poverty impacts of national price shocks.
The central feature of our approach involves the recovery of demands for goods and
services across the expenditure distribution within a set of countries in a manner which is
consistent with the national accounts. Specifically, we calibrate the underlying global demand
system parameters to in order to replicate observed per capita levels of demand. Consequently,
our approach allows for analysis, not only at the per capita level, but also analysis of the impact
of policies on the distribution of welfare measures across individuals within the population. This
approach also leads us to a redefinition of the widely used Foster-Greer-Thorbecke poverty
measure in terms of the poverty level of utility. This has the great advantage of permitting
consumption patterns at the poverty line to change as a function of relative prices, thereby
resulting in an improved estimate of the impact of price changes on the cost of living at the
poverty line.
In order to illustrate how this approach can be used for poverty analysis, we examine the
impact of a five percent rise in the world price of food, as a consequence of rich country trade
reforms. This is a topic that has received considerable attention recently. However, these studies
have not been able to come to grips with the differential consumption impacts of this price
increase across the income spectrum, within a theoretically consistent framework. We analyze
these differential impacts in considerable detail, decomposing the households' responses into
subsistence and discretionary components. At the lowest expenditure levels, the impact of higher
food prices on subsistence expenditures dominates the change in total food expenditures.
However, this changes as one moves to higher expenditure levels, giving rise non-monotonic
changes in food expenditure shares across the income spectrum. Not surprisingly, the food price
increase has an adverse impact on consumers in the countries examined, with the largest welfare
21
losses felt by the poorest households in the Philippines. At the same time, the five percent food
price rise increases the incidence and intensity of poverty in the focus countries considered here
(i.e. the Philippines, Indonesia and Thailand). In percentage terms, these poverty increases are
larges for Indonesia, followed by Thailand and the Philippines.
While our partial equilibrium analysis does not account for the impact of higher world
food prices on household incomes, the framework that we outline here could be readily
incorporated into a general equilibrium model aimed at assessing the poverty impacts of trade
reforms. Indeed, such a step would enhance the credibility of such analyses, which are often
viewed as being overly simplistic in their treatment of household expenditures.
22
Table 1. ICP Data Summary Statistics
FOOD ONONDUR SERVICE
Budget shares
Mean 0.368 0.244 0.388
Standard deviation 0.029 0.005 0.021
Prices
Mean 0.634 0.601 0.520
Standard deviation 0.074 0.226 0.198
Per capita expenditure (`000 of international dollars)
Mean 48.97
Standard deviation 4292.68
23
24
Type E E E E E E C E E E E E E E C C C C C C C C C C C
Year 1995 1995 1997 1996 1994 1993 1991 1995 1999 1997 1993 1994 1998 1992 1996 1996 1996 1996 2000 1997 1996 1995 1997 1994 1997
10
22.80 39.69 31.18 24.15 40.62 23.69 38.80 33.31 44.8 43.99 22.32
9
Values
Values 15.12 15.62 14.96 15.36 16.71 14.62 16.70 16.50 14.6 15.76 14.40
8 Quintile Decile 12.54 11.12 11.48 12.36 11.39 12.19 11.85 11.83 10.1 10.77 11.95
and and
7
10.64 8.53 9.34 10.55 8.58 10.58 8.96 9.60 7.8 8.17 10.42
Available Available
Class 6 are are 9.11 6.79 7.93 9.16 6.74 9.31 6.89 7.82 6.3 6.32 9.33
1
Data Data
5
Expenditure 49.7 43.77 44.4 42.3 50.2 39.3 43.40 40.9 46.6 52.8 39.21 47.7 47.5 46.1 8.06 5.48 6.91 8.01 5.37 8.16 5.41 6.41 5.2 4.94 8.36
Decile
Estimation Quintile
for 4
used whichrof 21.3 22.01 21.1 23.1 20.9 22.9 22.60 23 21.3 21.9 22.42 21.6 21.5 21.6 whichrof 7.02 4.51 5.96 6.89 4.18 7.19 4.20 5.32 4.2 3.87 7.45
3
14.2 15.87 15.5 16.4 14.2 17.4 15.70 16.6 14.8 13.6 16.98 14.8 14.7 15.3 6.01 3.71 5.09 5.82 3.19 6.15 3.24 4.17 3.3 2.93 6.50
Measures
2 Observations
Observations 9.4 11.44 11.4 11.5 9.7 12.9 11.60 12.2 10.6 8.1 12.88 10.2 10.2 10.9 5.02 2.88 4.21 4.69 2.17 5.00 2.44 3.09 2.4 2.08 5.44
Quintile
1
and 5.4 6.91 7.6 6.7 5 7.5 6.70 7.3 6.5 3.6 8.50 5.8 6.1 6.1 3.68 1.68 2.93 3.01 1.07 3.10 1.51 1.96 1.2 1.17 3.83
Decile
2. a enista ne niae roone d'Ivoir
Table Country Ecuador Estonia Jordan Kazakhstan Kenya Korea Mauritius Mongolia Morocco Panam Poland Turkey Turkm n Yem Albania Arm Bangladesh Belarus Bolivia Bulgaria Cam Cote Egypt Guinea Hungary
25
C C C C C C C C C C C C C E C C C C C C C C C C expenditure
on
1996 1997 1996 1996 1997 1997 1994 1998 1997 1996 1996 1997 1997 1996 1994 1993 1995 1999 1993 1995 2001 1998 1996 1995 based
are
37.04 33.35 22.25 26.65 26.16 33.48 42.20 40.60 28.09 38.94 37.98 37.36 32.59 38.97 37.43 17.92 31.58 26.72 37.47 32.32 32.56 30.05 44.25 67.44 data
the
18.35 15.99 14.41 14.99 15.49 16.30 15.96 16.06 16.37 14.54 15.96 11.90 16.00 17.42 14.05 13.90 14.61 14.86 15.98 15.19 16.54 15.41 15.47 9.92
whether
12.42 11.52 12.16 12.07 12.56 12.19 11.27 11.12 12.86 10.63 11.40 9.49 11.74 12.47 10.40 12.04 11.15 11.78 11.38 11.83 12.36 11.64 10.54 6.41
denotes
9.12 9.18 10.63 10.23 10.38 9.43 8.58 8.52 10.45 8.49 8.80 8.19 9.50 9.64 8.42 10.85 9.18 9.98 8.87 9.54 9.95 9.43 7.97 4.67 Type
ented;
7.01 7.58 9.38 8.75 8.91 7.63 6.70 6.80 8.58 6.96 7.05 7.25 7.96 7.32 7.11 9.78 7.82 8.74 7.16 8.02 8.16 8.03 6.29 3.58 empl
im
was
5.34 6.40 8.42 7.64 7.55 6.32 5.21 5.42 7.11 5.89 5.72 6.51 6.65 5.47 6.15 8.87 6.82 7.75 5.84 6.83 6.67 6.88 5.00 2.76
survey
4.13 5.38 7.47 6.61 6.54 5.22 3.98 4.39 5.97 4.90 4.69 5.86 5.48 3.94 5.37 8.05 5.97 6.77 4.76 5.74 5.41 5.98 3.95 2.10
underlying
3.19 4.55 6.36 5.57 5.44 4.23 2.91 3.43 4.84 4.09 3.78 5.26 4.46 2.49 4.59 7.26 5.23 5.72 3.82 4.75 4.17 5.19 3.06 1.54
the
2.22 3.68 5.26 4.52 4.36 3.23 2.05 2.42 3.72 3.33 2.91 4.58 3.40 1.53 3.77 6.40 4.42 4.67 2.91 3.62 2.90 4.33 2.22 1.05 which
in
year (C)
1.16 2.37 3.66 2.96 2.60 1.96 1.15 1.24 2.01 2.24 1.71 3.58 2.21 0.76 2.71 4.93 3.24 2.99 1.80 2.16 1.29 3.05 1.25 0.53 the
ption
denotes
icaa consum
Lanka bia babwe
Year or
Jam Kyrgyz Latvia Lithuania Macedonia Madagascar Mali Mexico Moldova Nepal Nigeria Pakistan Peru Russia Senegal Slovakia Sri Tajikistan Tanzania Ukraine Uzbekistan Vietnam Zam Zim 1. (E)
Table 3. Estimated AIDADS parameters
FOOD ONONDUR SERVICE
0.730 0.181 0.090
0.000 0.311 0.689
0.346 0.039 0.000
2.783
Table 4. Marginal budget shares, fitted budget shares and Engel elasticities, evaluated at
the means of the data.
FOOD ONONDUR SERVICE
Marginal budget share 0.068 0.298 0.633
Fitted budget share 0.259 0.264 0.476
Engel Elasticity 0.263 1.129 1.329
Table 5. Estimated and Calibrated AIDADS Parameters
FOOD ONONDUR SERVICE
Estimated 0.730 0.181 0.090
Indonesia-calibrated 0.738 0.164 0.098
Philippines-calibrated 0.731 0.226 0.043
Thailand-calibrated 0.589 0.244 0.166
Estimated 0.000 0.311 0.689
Indonesia-calibrated 0.000 0.271 0.729
Philippines-calibrated 0.000 0.540 0.460
Thailand-calibrated 0.000 0.247 0.753
Estimated 0.346 0.039 0.000
Indonesia 0.346 0.039 0.000
Philippines 0.346 0.039 0.000
Thailand 0.346 0.039 0.000
Estimated 2.783
Indonesia 2.740
Philippines 3.127
Thailand 2.358
26
Table 6. Foster-Greer-Thorbecke P measures of poverty (percentage change in
parentheses)
WDI One/two dollars a day
Base Shock Base Shock
Indonesiaa
P0 15.93 17.04 20.74 22.59
(6.98) (8.93)
P1 2.79 3.19 4.24 4.73
(14.14) (11.68)
P2 0.69 0.82 1.19 1.37
(18.96) (15.42)
Philippinesa
P0 37.03 38.15 39.26 40.37
(3.00) (2.83)
P1 14.36 15.05 15.79 16.51
(4.84) (4.51)
P2 7.21 7.65 8.13 8.60
(6.16) (5.78)
Thailandb
P0 13.33 14.07 20.00 21.11
(5.56) (5.56)
P1 2.23 2.48 4.23 4.57
(11.10) (7.92)
P2 0.52 0.59 1.22 1.35
(15.20) (10.67)
a. Based a one dollar a day poverty level of expenditure
b. Based a two dollar a day poverty level of expenditure
27
28
share
at
capi
per
alu
ctA phalA
78
reut
share
expendi
of ed onaryi
log brati ret
ralu sc
Cal Di Indonesia.
for
Nat
shares
share budget
rede ncee food
st
Recov Subsi
calibrated
and
56 Recovered
8 7 6 5 4 3 2 1 0
0. 0. 0. e0. rahs te0. gduB 0. 0. 0. 1.
Figure
29
phalA
er
sha
onaryi
scret
Di
78
share
reut ence
st
expendi Subsi
of
log Philippines.
ralu the
share
Nat at for
capi
shares
per
alu
ctA budget
food
d
te
ra
libaC calibrated
and
rede
456 Recovered
8 7 6 5 4 3 2 1 0
0. 0. 0. e0. rahs te0. gduB 0. 0. 0. Recov 2.
Figure
30
share
at
8
capi
per
alutcA phalA
reut
share
expendi
of ed onaryi
log brati ret
ralu sc Thailand.
Cal Di
for
Nat
shares
share budget
ce
en food
ered st
Recov Subsi
calibrated
and
67 Recovered
7 6 5 4 3 2 1 0
0. 0. 0. erah0. s tegdu0. B 0. 0. 3.
Figure
a 31
thiw
5.
and
scenario
88
case
base
5.
hailandT- hailandT- the
se ocked under
77 Ba Sh
country,
reu
focus
5.
pendit ch
ea model.
ex
of Philippines-
log
66 Philippines- thiniw AIDADS
ralu
Nat Base Shocked
5. distributions calibrated
the
nesia using
55 ndoI- expenditure
ndonesiaI- across calculated
5. Base Shocked food price,
for to
shock
44 Demand
20)stinu fo16 sderdnu12 h( dednamed ytitnauQ
8 4 0 4.
percent
Figure five
32
.58
calibrated
the
8 on
based
.57
7 ncompensatedU components,
its
and
e
tur
.56 pendi
ex ompensatedC Philippines
of
ogl le the
in
6 al
e*Eng food
aturN for
Shar-
.55 e
elasticity
Shar
5 el demand
Eng
n-price
ow
.54
4
1 0 Uncompensated
0.8 0.6 0.4yticitsale/erah-0 S
0.2 2. 4. 6. 8. -1 system.
-0 -0 -0 5.
Figure demand
33
price
percent
share
ni fivea
from
Change
arising
78 share
Indonesia
uret onaryi in
scret food
di
expendi ni for
of
ogl angehC share
ural
Nat budget
share total
ence and
st
subsi
ni
discretionary
Change
subsistence,
in
56
0
005 Change
0. 0045 004 003 002 001
0. 0. 0035
er0. ahs tegdub0. ni egnahC0.
0. 0025 0. 0015 0. 0005
0. 6:
Figure increase.
34
percent
8 fivea
share
ni from
arising
Change
7 share Philippines
the
reut onaryi in
scret food
di
expendi ni for
of
ogl
ralu angehC share
budget
Nat
share total
ence and
st
subsi
ni
discretionary
Change
subsistence,
in
456
01 0
Change
0. 008 006 004 002 002 004 006
0. 0. 0. 0. 0.- 0.- 0.- 7:
erahs tegdub ni egnahC increase.
Figure price
35
price
percent
share
ni fivea
8
from
Change
arising
share
reut Thailand
onaryi in
scret food
di
expendi ni for
of
ogl
ralu angehC share
Nat budget
share total
ence and
st
subsi
ni
discretionary
Change
subsistence,
in
67
0
0045 004 0035 003 0025 002 0015 001 Change
0. 0. 0. erahs tegdub ni egnah0.C
0. 0. 0. 0. 0005
0. 8:
Figure increase.
36
.58
8
.57
7 nd
e
tur ilaahT price.
.56 food
pendi nes in
ex
of ppiil
6 oglla Phi increase
a
aturN percent
.55 Indonesi five
the
from
5
arising
.54 variation
4
0
0.8 0.7 0.6 0.5)srall0.4 od0.3 0.2 0.1 Compensating
9.
fo sderdnuh( noitairav gnitasnepmoC
Figure
37
.58
.
8
expenditure
of
.57
percenta
as
7
andl price
e
tur haiT
food
.56 in
pendi nes
ex
of ppiil
increase
ogl Phi
6 al a
aturN ercentp
five
.55 Indonesi the
from
5 arising
variation
.54
4 Compensating
8% erutidnepxe6% fo tnec5%rep a sa4% noitair3%av gnita2% snepm1%oC
7% 0% 10.
Figure
REFERENCES
Anderson, K., Martin, W., 2006. Agricultural Trade Reform and the Doha Development Agenda.
Palgrave-Macmillan, New York.
Anderson, K., Martin, W., van der Mensbrugghe, D., 2006. Global Impacts of the Doha
Scenarios on Poverty. In Hertel, T., Winters, L. (Eds), Poverty and the WTO: Impacts of
the Doha Development Agenda: Palgrave-Macmillan, New York.
Bourguignon, F., Morrisson, C., 2002. Inequality among World Citizens: 1820-1992. The
American Economic Review (92), 727-744.
Chen, S., Ravallion, M., 2003. Welfare Impacts of China's Accession to the WTO. In
Bhattasali,
D. , Li, S., Martin, W. (Eds), China and the WTO: Accession, Policy Reform, and
Poverty Reduction Strategies. Oxford University Press, Oxford.
Cline, W., 2004. Trade Policy and Global Poverty. Institute for International Economics,
Washington, D.C.
Cooper, R., McLaren, K., 1992. An Empirically Oriented Demand System with Improved
Regularity Properties. Canadian Journal of Economics (25), 652-667.
Cranfield, J., 1999. Aggregating Non-Linear Consumer Demands A Maximum Entropy Approach.
Ph.D. Dissertation, Department of Agricultural Economics, Purdue University
Cranfield, J., Preckel, P., Eales, J. Hertel, T., 2002. Estimating Consumer Demands across the
Development Spectrum: Maximum Likelihood Estimates of an Implicit Direct Additivity
Model. Journal of Development Economics, (68): 289-307.
Cranfield, J., Preckel, P., Eales, J., Hertel, T., 2004. Simultaneous Estimation of an Implicit
Directly Additive Demand System and the Distribution of Expenditure An Application
of Maximum Entropy. Economic Modelling (21), 361-385.
Deaton, A., 2000. The Analysis of Household Surveys. The World Bank, Washington D.C.
Deninger, K., Squire, L., 1996. A New Data Set Measuring Income Inequality. The World
Bank
Economic Review (10), 565-591.
Foster, J., Greer, J., Thorbecke, E., 1984. A Class of Decomposable Poverty Measures.
Econometrica (52), 761-766.
38
Friedman, J., Levinsohn, J., 2002. The Distributional Impacts of Indonesia's Financial Crisis on
Household Welfare: A `Rapid Response' Methodology. World Bank Economic Review
(16), 397-423.
Golan, A., Judge, G., Miller, D., 1996. Maximum Entropy Econometrics: Robust Estimation
with Limited Data. John Wiley and Sons, New York.
Gorman, W., 1980. Some Engel Curves. In: Deaton, A. (Ed.) Essays in the Theory and
Measurement of Consumer Behaviour. Cambridge University Press, New York, pp. 7-30
Hanoch, G., 1975. Production and Demand Models with Direct of Indirect Implicit Additivity,
Econometrica (43), 395-419.
Hertel, T., Ivanic, M., Preckel, P., Cranfield, J., 2004. The Earnings Effect of Multilateral Trade
Liberalization: Implications for Poverty. World Bank Economic Review, (18), 205-236.
Hertel, T., Winters, W., 2005. Poverty and the WTO: Impacts of the Doha Development Agenda.
The World Bank, Washington D.C.
Indonesia, 1993. SUSENAS: Indonesia's socio-economic survey. Biro Pusat Statistik, Jakarta,
Indonesia.
Jaynes, E., 1957a. Information Theory and Statistical Mechanics I. Physics Review. (106), 620-
630.
Jaynes, E., 1957b. Information Theory and Statistical Mechanics II. Physics Review. (108), 171-
190.
Kapur, J., Kesavan, H., 1992. Entropy Optimization Principals with Applications. Academic
Press, Boston.
Levinsohn, J., Berry, S., Friedman, J., 2000. Impacts of the Indonesian Economic Crisis: Price
Changes and the Poor. Presented at "Conference on Poverty and the International
Economy," Stockholm, October 20-21, subsequently published in M. Dooley and J.
Frankel, eds., Managing Currency Crises in Emerging Markets. Chicago: Univ. of
Chicago Press, 2003.
Lewbel, A., 1991. The Rank of Demand Systems: Theory and Nonparametric Estimation.
Econometrica (59), 711-730
Neary, J., 2004. Rationalizing the Penn World Table: True Multilateral Indices for International
Comparisons of Real Income. The American Economic Review, (94): 1411-1428.
39
Philippines, 1999. Annual poverty indicators survey. National Statistics Office, Manila,
Philippines.
Quah, D., 2002. One Third of the World's Growth and Inequality. Mimeo, London School of
Economics.
Ravallion, M., 1998. Poverty Lines in Theory and Practice. LSMS Working Paper 133, The
World Bank, Washington D.C.
Ravallion, M., 2006. Looking beyond the averages in the trade and poverty debate. World
Development. (34), 1374-1392.
Ravallion, M., van de Walle, D., 1991. The Impact on Poverty if Food Pricing Reforms: A
Welfare Analysis for Indonesia. Journal of Policy Modeling, (13): 281-299.
Ravallion, M., Datt, G. van de Walle, D., 1991. Quantifying Absolute Poverty in the Developing
World. Review of Income and Wealth, (37): 345-361.
Rimmer, M., Powell, A., 1992. Demand Patterns across the Development Spectrum: Estimates of
AIDADS. Working Paper #OP-75, IMPACT Project, Monash University.
Rimmer, M., Powell, A., 1996. An Implicitly Additive Demand System. Applied Economics,
(28), 1613-1622.
Sala-i-Martin, X., 2002a. The Disturbing "Rise" of Global Income Inequality. NBER Working
Paper 8904.
Sala-i-Martin, X., 2002b. The World Distribution of Income (Estimated From Individual
Country
Distributions). NBER Working Paper 8933.
Sala-i-Martin, X., 2006. The World Distribution of Income: Falling Poverty and...Convergance,
Period. Quarterly Journal of Economics (CXXI): 351-397.
Seale, J., Regmi, A., Bernstein, J., 2003. International Evidence on Food Consumption Patterns.
Technical Bulletin 1904, United States Department of Agriculture, Washington, DC.
Schultz, T., 1998. Inequality in the Distribution of Personal Income in the World: How it is
Changing and Why. Journal of Population Economics, (11): 307-344.
Thailand, 1996. Thailand Socio-Economic Survey, National Statistics Division, Thailand.
Theil, H., Clements, K., 1987. Applied Demand Analysis: Results from System-Wide
Approaches. Ballinger Publishing Company, Cambridge, Mass.
40
Theil, H., Chung, C., Seale, J., 1989. International Evidence on Consumption Patterns. In:
Rhodes, G., Fomby, T. (Eds.), Advances in Econometrics, Supplement 1. JAI Press,
London.
41
TECHNICAL APPENDIX FOR: POVERTY ANALYSIS USING AN INTERNATIONAL
CROSS-COUNTRY DEMAND SYSTEM
In what follows we outline the empirical model used our paper entitled "Poverty Analysis using
and International Cross-Country Demand System". This method allows for recovery of
expenditure distributions and household level demands using inequality measures, information
from household level surveys and per capita data. While somewhat specific to the available data,
the methodology may be readily modified to suit different contexts. Key to our approach is
availability of information on the distribution of expenditure. If summary statistics on the
distribution of expenditure are not available for a country, no attempt is made to recover an
expenditure distribution, nor household demands for that country. The demand system for those
countries simply relates per capita demand to prices and per capita expenditure. However, for
some observations, we have expenditures at the quintile, decile or percentile level. In these
instances, the model recovers an approximation to the expenditure distribution and household
demands at different points in each country's expenditure distribution. For purposes of this
paper, we focus our attention on three countries where percentile data are available to us
(Thailand, Indonesia and the Philippines). The percentiles are used to identify the support of the
recovered distribution of expenditure, and to recover the expenditure distributions in these focus
countries.
The set of observations (i.e., countries) is denoted by T, with t indexing individual
national observations. This set can be parsed into mutually exclusive and exhaustive subsets
based on whether expenditure distribution data are available and the nature of these inequality
data. Specifically, let TH denote the subset of observations for which percentiles are available,
TD the subset of observations for which deciles are available, TQ the subset of observations for
which quintiles are available and TN the subset of observations for which no distributional data
are available. Thus T = TH TD TQ TN .
When inequality information is available, the support of each country's expenditure
distribution is parsed into expenditure classes, indexed by c. The total number of classes
depends on the corresponding observation and the nature of the inequality data. If percentile
42
data are available, the support of the expenditure distribution is separated into percentiles,
denoted by the set CH. If deciles are available, the support of the expenditure distribution is
separated into ten expenditure classes, denoted by the set CD. If quintiles are available, the
support of the expenditure distribution is demarked into quintiles, denoted by the set CQ.
Further, each expenditure class is sub-divided into three expenditure levels, denoted by
l L = {1,2,3} (calculation of these expenditure levels is discussed later). Thus, for t TH , there
are initially three hundred points in the support of the recovered expenditure distribution (one
hundred expenditure classes, each containing three expenditure levels).14 For t TD , there are
thirty points in the support of the recovered expenditure distribution, while for t TQ , there are
fifteen points in the support of the recovered expenditure distribution. As such, the resolution of
the recovered expenditure varies by country and the nature of the distribution information that is
used. As previously noted, if no inequality information is available, then no attempt is made to
recover the distribution of expenditure.
The optimization problem underpinning the estimation framework takes the form of a
non-linear programming problem. The objective function consists of a term representing the
information recovery process and a term representing the concentrated log-likelihood function.
The measure of information recovery is the maximum entropy metric defined across shares of
each observation's population at each expenditure level in the respective expenditure
distribution. The objective function and choice variables of the problem are expressed as:
Max -+0.5×ln n-1
r 2
ii
i=1
i,i,i, , (A.1)
utcl, vti, tcl
where denotes the entropy component of the objective function and is expressed as
tcllntcl + tcllntcl + tcllntcl , and the tcl terms are the
tTH cCH lL tTD cCD lL tTQ cCQ lL
proportion of country t's total population with expenditure at the lth level of the cth expenditure
14 These three hundred points are trimmed to reflect the fact that survey based observations at extremely low and
high levels of household expenditure are unreliable sources of information, due mainly to the scant number of
observations at these extremes.
43
class. Note that by assumption, 0 < tcl <1. This entropy component is broken into three parts
to facilitate clarity of exposition. The first term is the entropy of the recovered expenditure
distribution for observations where percentile data are available. The second and third terms
measure the entropy of the recovered distributions for observations where deciles and quintiles
are available, respectively. As mentioned in the paper, the concentrated log-likelihood
component of the objective function enables estimation of the demand system parameters, while
the entropy measure enables recovery of the expenditure distribution via population weights at
each point of the expenditure distribution's support. Incorporating both elements in a single
objective function may seem odd; however, this is an important step in obtaining parameter
estimates and recovered expenditure distributions that are internally consistent with the data, and
with the other choice elements of the optimization problem.
The second part of the overall objective function represents a concentrated log-likelihood
function. The rii terms are the diagonal elements of R, which is an upper triangular matrix
resulting from the following Cholesky decomposition of the covariance matrix: ^ = Rt R , where
^ is the covariance matrix for the demand system being estimated. The relationship between
the residuals and elements of R can be defined by noting that each element in ^ must be the
T
same regardless of whether it is computed as T -1 v v or based on the matrix decomposition
it kt
t=1
of ^ , where vit are the residuals of the ith good's demand equation in the tth observation. As
such, the following constraint is included during estimation:
T n-1
T -1v (A.2)
itvjt = rkirkj i n, j n.
t=1 k=1
(Since AIDADS satisfies the adding up property of demand, the residuals must sum to zero, in
which case the covariance matrix is singular. Equation A.2 reflects this fact by dropping the last
equation's residual in the summation terms.)
One of the advantages of the entropy framework developed by Cranfield et al. (2004) is
that it enables recovery of a distribution of expenditure that exactly matches the known
inequality and expenditure moment information used during estimation. Furthermore, the
problem is structured such that the recovered population shares are also used to recover
44
unobserved budget shares for each good at each expenditure level in the distribution, such that
the weighted sum of the recovered budget shares (with population shares serving as weights)
equals the observed (per capita based) budget shares, up to a random error term. To see the logic
underlying this process, note that per capita demands can be defined as follows:
xit = Z -1 Z
z=1xitz , where z indexes individuals in country t, xitz is consumption of the ith good
by individual z in country t, and xit is per capita demand. Disaggregate demands are assumed to
be recoverable such that they add up to the observed level of per capita demand up to an error
term with known properties: xit = x +vit , where xitcl is demand for the ith good by a
c l tcl itcl
household at the lth expenditure level in the cth expenditure class of the tth observation's
expenditure distribution and vit is an independently distributed normal error term with mean
vector zero and finite covariance matrix. The inclusion of the random error term implicitly
assumes errors in aggregation. Moreover, the error terms included in the consumption adding-up
constraints are used to define the terms in the Cholesky factorization in the objective function.
As such, estimation via maximum likelihood minimizes these errors.
In the present analysis, these residuals are defined using an AIDADS based approach to
the consumption adding-up constraints:
piti + 1- i,tTN
yt i +i exp(ut) pytt
1+ exp(ut )
wit -vit = (A.3)
pit 1 i +i exp(utcl )
yt tcl
cCK lL i +
pit 1+ exp(utcl ) (ytcl -pt) i,tTK,K
where K = {H,D,Q} indexes the index used to delineate observations with different types of
inequality information and wit is the per capita budget share for the ith good in the tth
observation.. As mentioned, equation (A.3) serves to ensure that the recovered disaggregate
demands add-up to the observed per capita level, in expectation. Specifically, for each
observation, disaggregate demands at each expenditure level, ytcl , are assumed to add up to the
known level of economy wide demand with population fractions tcl used as weights. Note too
that the AIDADS model (stated in consumption level form) has been substituted in directly for
45
the unobservable disaggregate demands ( xitcl ). Hence, this constraint allows for estimation of
the AIDADS parameters.
As with traditional, maximum likelihood estimation of AIDADS (see, for example,
Cranfield et al. 2002), the defining equation of utility is also included in the scheme used here to
permit estimation of the levels of utility. As with equation (A.3), the constraints representing the
defining equation of utility differ according to the data that is available for the respective
observation. Equation (A.4) shows the set of utility function constraints:
n
1+exp(u
i
i=1 +i exp(ut )ln 1 i1++exp iexp(ut )
) (ut ) tTN
t pit (yt -pt)-ut
= . (A.4)
n
tTK,
i=1
1+exp(u
i+i exp(utcl)ln 1 i1++exp iexp(utcl )
) (utcl )
tcl pit (ytcl -pt)-utcl cCK ,l,K
Note first that the AIDADS model in levels form has been substituted into the defining equation
of utility (this is the term in the ln(·) ). As Cranfield et al. (2002) report, doing so greatly
facilitates estimation of AIDADS, and allows one to include the defining equation of utility for
AIDADS in implicit form. The first line of this constraint represents observations for which no
inequality data are available; as such, it is included using per capita expenditure and utility levels
for the "average" consumer in the respective observations. The last line in this constraint
represents utility functions for those observations for which inequality data are available. In the
latter instance, expenditure is indexed on the expenditure class and level, as is utility.
Equation (A.5) reflects the fact that the sum of the population fractions, tcl , across all
expenditure levels in each expenditure class in each observation must equal unity:
1/90 tTH,cCH
L
= /10 t TD,cCD . (A.5)
tcl 1
l=1
1 /5 t TQ,cCQ
By definition, when percentile data are available, the sum of tcl across levels in an expenditure
class must sum to 1/100. However, the focus countries' percentile data are drawn from
46
household survey data. Survey data such as these can be fraught with problems related to
observations at the extreme levels of expenditure. In particular, there tend to be fewer
observations at extremely low and high expenditure levels. Consequently, the tails of the
expenditure distribution may be difficult to accurately identify. To remedy potential problems
arising from the tails of the distributions, the lower and upper five percentiles are dropped during
estimation. As such, the population shares within each expenditure class must sum to 1/90.
However, in those cases where we work with deciles and quintiles, there is no such extreme
point problem and so the sum of tcl across expenditure levels within each class must sum to
1/10 and 1/5, respectively.
Since the recovered expenditure distributions are driven by known information (in this
case per capita expenditure and inequality information in the form of percentiles, deciles and
quintiles), it is important that the recovered expenditure distribution "give back" exactly what is
known. That is, the location and scale parameters of the recovered expenditure distribution
should exactly match the known location and scale parameters of the data. In this regard,
equation (A.6) defines an expenditure adding up condition for the recovered expenditure
distribution:
ytc 90 tTH,cCH
L DECILEtc yt t TD,cCD (A.6)
tclytcl =
l=1
QUINTILEtcyt tTQ,cCQ
where ytc is the observed average level of household expenditure in the cth expenditure class of
the tth observation, while DECILEtc and QUINTILEtc are the decile and quintile values for the
respective observation-expenditure class combinations. In observations where deciles or
quintiles are available, equation (A.6) requires the share-weighted sum of the expenditure levels
within an expenditure class to sum to the product of per capita expenditure and the class's
quintile or decile value (see Cranfield et al. 2004 for details). Stated another way, when
percentile data are available, the recovered expenditure distributions must add back to the
observed expenditure class means.
47
In addition to the constraints discussed above, the following bounds and constraints are
placed on the choice variables (either to prevent unbounded problems in the optimization
n n
program or arising from the need for theoretical consistency of AIDADS): i= i =1,
i=1 i=1
i [0,0.9] for all i, i [0,0.8]for all i, i [0,0.5] for all i, (-,), utN [-4,2],
utcl [-7,3]for all t TN ,c,l , vti [-1,1] for all i,t, tcl [10-9,-1] for all
t TK ,c,l,K H,D,Q , where is the product of the cardinality of the sets TK and L, and
{ }
yclt -pt for all t TN ,c,l , where >0 .15
In countries for which deciles and quintiles are available, the lower and upper bounds of
each expenditure class are calculated using the methods reported in Cranfield et al. (2004). In
particular, within each expenditure class, an expenditure level is placed at the conditional mean
of that expenditure class (i.e. expenditure at l=2 equals the conditional mean for that expenditure
class), and at one-third of the class's interval above and below the mid point to provide
expenditure levels at l=3 and l=1, respectively. For observations where percentile data are
available, the minimum and maximum bounds of the expenditure class is known. However,
applying the one-third rule as above resulted in an infeasible solution. As such, the lower bound
of each expenditure class for observations in the set TH are defined as yct - (y ) 2 ,
ct - yct
MIN
where yct is the average level of expenditure in the cth expenditure class of the tth observation,
and yctMIN is the minimum level of expenditure in the cth expenditure class of the tth observation.
The upper bound of each expenditure class is defined as yct + yct ( MAX - yct) 2 , where yct MAX is
the maximum level of expenditure in the cth expenditure class of the tth observation.
15 This value is set slightly above zero to ensure this constraint is not active in the optimal solution, which would
imply no discretionary expenditure.
48
REFERENCES
Cranfield, J., Preckel, P., Eales, J. Hertel, T., 2002. Estimating Consumer Demands across the
Development Spectrum: Maximum Likelihood Estimates of an Implicit Direct Additivity Model.
Journal of Development Economics, (68): 289-307.
Cranfield, J., Preckel, P., Eales, J., Hertel, T., 2004. Simultaneous Estimation of an Implicit
Directly Additive Demand System and the Distribution of Expenditure An Application of
Maximum Entropy. Economic Modelling, (21): 361-385.
49
Policy Research Working Paper Series
Title Author Date Contact for paper
WPS4263HIV/AIDSandSocialCapitalina AntonioC.David June2007 A.David
Cross-SectionofCountries 82842
WPS4264FinancingofthePrivateSectorin ConstantinosStephanou June2007 S.Coca
Mexico,200005:Evolution, EmanuelSalinasMuñoz 37474
Composition,andDeterminants
WPS4265TheStructureofImportTariffsinthe OleksandrShepotylo June2007 P.Flewitt
RussianFederation:200105 32724
WPS4266TheEconomicCommunityofWest SimpliceG.Zouhon-Bi June2007 S.Zouhon-Bi
AfricanStates:FiscalRevenue LyngeNielsen 82929
ImplicationsoftheProspective
EconomicPartnershipAgreement
withtheEuropeanUnion
WPS4267FinancialIntermediationinthe HeikoHesse June2007 G.Johnson
Pre-ConsolicatedBankingSectorin 34436
Nigeria
WPS4268PowertothePeople:Evidencefrom MartinaBjörkman June2007 I.Hafiz
aRandomizedFieldExperimentofa JakobSvensson 37851
Community-BasedMonitoringProject
inUganda
WPS4269ShadowSovereignRatingsfor DilipRatha June2007 N.Aliyeva
UnratedDevelopingCountries PrabalDe 80524
SanketMohapatra
WPS4270Jump-StartingSelf-Employment? RitaAlmeida June2007 A.Bonfield
EvidenceamongWelfareParticipants EmanuelaGalasso 31248
inArgentina
WPS4271Construction,Corruption,and CharlesKenny June2007 C.Kenny
DevelopingCountries 33540
WPS4272Migration,Remittances,Poverty, DavidMcKenzie July2007 M.Sasin
andHumanCapital:Conceptualand MarcinJ.Sasin 36877
EmpiricalChallenges
WPS4273RulesofOriginandtheWebofEast MiriamManchin July2007 L.Yeargin
AsianFreeTradeAgreements AnnetteO.Pelkmans-Balaoing 81553
WPS4274AreLaborRegulationsDriving MohammadAmin July2007 S.Narsiah
ComputerUsageinIndia'sRetail 88768
Stores?
WPS4275CanForeignLobbyingEnhance KishoreGawande July2007 V.Cornago
Development?TheCaseofTourism WilliamMaloney 84039
intheCaribbean GabrielV.MontesRojas
WPS4276HumanCapital,TradeLiberalization, TomKrebs July2007 V.Cornago
andIncomeRisk PravinKrishna 84039
WilliamMaloney
WPS4277ClimateChangeAdaptationinAfrica: SungnoNiggolSeo July2007 P.Kokila
AMicroeconomicAnalysisof RobertMendelsohn 33716
LivestockChoice
WPS4278EndogenousIrrigation:TheImpactof PradeepKurukulasuriya July2007 P.Kokila
ClimateChangeonFarmersin RobertMendelsohn 33716
Africa
WPS4279TheImpactofClimateChangeon SungnoNiggolSeo July2007 P.Kokila
LivestockManagementinAfrica: RobertMendelsohn 33716
AStructuralRicardianAnalysis
Policy Research Working Paper Series
Title Author Date Contact for paper
WPS4280 GovernanceMattersVI:Aggregate DanielKaufmann July2007 R.Bonfield
andIndividualGovernance: AartKraay 31248
Indicators,1996-2006 MassimoMastruzzi
WPS4281 CreditGrowthInEmergingEurope: SophieSirtaine July2007 S.Sirtaine
ACauseForStabilityConcerns? IliasSkamnelos 87006
WPS4282 AreCashTransfersMadetoWomen NorbertSchady July2007 I.Hafiz
SpentLikeOtherSourcesofIncome JoséRosero 37851
WPS4283 InnovationShortfalls WilliamMaloney July2007 V.Cornago
AndrésRodríguez-Clare 84039
WPS4284 CustomerMarketPowerandthe NeeltjeVanHoren July2007 M.Gamboa
ProvisionofTradeCredit: 34847
EvidencefromEasternEuropeand
CentralAsia