Wye City Group Meeting on Rural Development and
Agricultural Household Income
Measuring under-nourishment : comparative analysis
between parametric and non-parametric methods based on
Burkina Faso agricultural survey
FAO Head-Quarters, Rome, Italy
11-12 June 2009
Moussa Kabore, Statistician
TARGET
Measuring undernourishment is necessary for the
monitoring Millennium Development Goals, in
particular the objective n°1: “reduce by half the
proportion of people suffering from hunger”. At subnational level, it enables:

To carry out a cartography of food insecurity,

To monitor food insecurity in time,



To identify the most vulnerable groups within a
country,
To identify the causes of food insecurity,
To evaluate the impact of policies and projects, in order
to improve the decisions taken on the matter.
Several methods are used to determine the
phenomenon. They are based on data sources of
different nature.
 The idea of this paper is not to make an exhaustive
inventory on the methods for estimating food insecurity
but to do a comparative analysis on the two main
methods used:



the parametric method based on food balance sheets and the
distribution of food consumption in the population, used by FAO
at national level,
the non-parametric method based on the FGT index (FOSTER,
GREER and THORBECKE) and household survey micro-data,
which was developed for the measurement of the incidence of
monetary poverty and that we adapted for the measurement of
the incidence of undernourishment.
 The
aim is to seek a possible convergence
between the two methods in order to enable
national statistical systems to regularly calculate
the incidence of food insecurity at sub-national
level depending on the nature of available data.
 We
will initially describe the two methods before
estimating the incidence of food insecurity with
each method.
 Data
used is related to rural area households
survey (National annual crop sample survey
data). We will then propose an estimation method
taking urban areas into account.
DESCRIPTION OF PARAMETRIC METHOD

The method is based on the distribution of per caput
energy food consumption. This distribution is assumed
to be log-normal. Practically, the incidence of
undernourishment is estimated in the following way:
P (U)  P(xr )  xr f(x) dx Fx(r )
L
l
L
Where:
 P (U) represents the proportion underfed population on
total population,
 X is food energy consumption per individual,
 rl is the minimum energy requirement and
 F (X) is the food density function within the population.
In the literature, we assume that F follows the
lognormal law.
DESCRIPTION OF PARAMETRIC
METHOD

Its implementation requires the knowledge of two
distribution statistics :


the average per capita energy food consumption
and the standard deviation of its distribution.
Per capita food consumption is derived from
national food balance sheets or from data from
household surveys.
 Standard deviation estimates require necessarily
households expenditures or food consumption
survey data.


However, its use at sub-national level requires
the knowledge of these parameters for each
regional entity, which can be difficult to obtain.
DESCRIPTION OF THE NONPARAMETRIC METHOD
It is based on the FGT index function which is described in the
following way:
q
1  Z  Yi 
P   

N i 1  Z 

Z : food consumption poverty line (in Kcal),
 Yi : energy consumed by the ith individual,
 q : number of individuals in the population considered as
undernourished,
 N : total number of the population, and
 α that is a parameter (α = 0 in our case).

 This
FGT method is usually applied to calculate
the incidence of monetary poverty (see paper content for
mathematical purpose) ;
 The implementation of this method necessarily
requires data from Household Expenditure or
Food Consumption surveys.
 Food consumption poverty line (Z) is derived
from FAO food consumption table that is
applied on each sample household member
taking account its demographic characteristics;
 Food energy consumption per individual (Yi) is
obtained in each household by dividing total
food intake with the household population size;
 Each household member is assumed to be
undernourished if Yi < Z
DATA PRESENTATION


In the Burkina Faso context, farmer unit and rural household unit are
the same (and 97% are crop producer).
Data used for this paper come from national annual crop survey
(Enquête permanente agricole) for 2006 and 2007. This survey is a PPS
sample design into two degrees (706 Village unit and 4000 farmer unit).

The survey questionnaire enables to set a balance between supplies and
utilizations of each product used by each household member between
October of the year n-1 to September of year N.
In each household, quantity data are collected directly per product and
per member who manipulated the food product (available from own
production, sale, purchase, gift..) during the 12 last month. More
specifically: crop production, opening and closing stock data come from
direct observation.

On supply, the following data are collected for each product, each
member : Production, Purchase, Gifts, Initial Stock.

In Utilizations the following are collected: Sale, Closing Stock, Gifts.

ESTIMATION OF ENERGY
AVAILABILITY



Food product balances at household level are used to
deduct food consumption.
Food energy conversion table (FAO, 1996) is used to convert
physical quantities into food energy. Per capita food energy
consumption is calculated by simple ratio between total energy
consumed in the household with the household size.
The consumption deduced from this data source cannot be used
to measure food energy intake for each member (ex. Children
who did not produce or buy products but are consumers). But in
the absence of an investigation on individual consumption, we
use average energy consumption in the household as proxy
which in any case improves the analysis of undernourishment.
RESULTS
FOOD CONSUMPTION NORMALITY TEST IN RURAL AREA
0
.2
.4
.6
.8
Le kernel density estimation in STATA is used to generate the distribution of food
consumption
5
6
7
lcon
8
9
The test concludes to the normality of
data distribution.
Distribution parameters
Mean: 2704 kcal.
(It can be also obtained from the food
balance)
deviation : 1320 kcal
Kernel density estimate
Normal density
Skewness/Kurtosis tests for Normality with ln(consotete)
------- joint -----Variable | Pr(Skewness)
Pr(Kurtosis)
chi2(2) Prob>chi2
-------------+------------------------------------------------------lncon |
0.000
0.000
402.09
0.0000
Where the Skewness value is egal to -1969.805
0
.5
Density
1
1.5
After applying the procedure of Skewness value (K) annulations we obtain this
new distribution of ln(contete-K) :
7.5
8
8.5
ln(contetef+1969.805)
9
9.5
Kernel density estimate
Normal density
Variable |
Obs
Weight
Mean
Std. Dev.
Min
Max
------------- +----------------------------------------------------------------lncon0 | 3843 11141964.5 8.410604 0.280089 7.659576 9.090232
ESTIMATION OF MINIMUM REQUIRED
ENERGY (MRE)
 The
minimum required energy is estimated in the
following way:
 rl = Σ ij (MRE ij * P ij )
 MREij = minimum required food energy per person
per day by age and sex (from FAO table)
 Pij = population structure by age and sex (from
demographic questionnaire of agricultural annual survey)
 we
obtain:
rl =2102 Kcal/pers/day in rural
Application of the parametric method assume the normality of data
distribution
ESTIMATION OF NDERNOURISHMENT
USING PARAMETRIC METHOD
Food consumption (X) is distributed as log-normal law
N(2704 ; 1320)
 P(X < rl) =F((rl-2704)/ 1320) = 0,324
 F is the log-normal density function.

Result: 32,4% of the rural population were under
feed in 2006
ESTIMATE OF UNDERNOURISHMENT
USING NON-PARAMETRIC METHOD
 We
calculate average energy consumption per
capita for each household from the data of the
investigation.
 Each household (and each member) is classified as
undernourished if the average per caput food
consumption is less than the minimum required
energy (2102 Kcal/pers/day).
 The characteristic of the household is attributed
to each member.
Result : 35,7% of rural population are
classified undernourished in 2006.
CONCLUSION

The non- parametric method can be applied on households
data from national agricultural survey;

The results obtained seem close to the parametric method but
the tests statistics of convergence must continue;



The non- parametric method based on data from national crop
and food security surveys enhance estimation quality by
avoiding price effect encountered in data from household
expenditure survey ;
Agricultural survey in Burkina Faso and some Sahelian
countries is conducted every year, which allows the annual
calculation of this indicator;
The non- parametric method allows cross-analysis of
household undernourishment status with other socioeconomic variables and the ability to monitor MDG at sub
national level.
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