Chapter 2 Literature Review
2.2 Issues on poverty lines
2.2.2 Kakwani-Sajaia method
The method introduced by Kakwani and Sajaia (hereafter Kakwani-Sajaia) differs in emphasis and underlying assumptions from Ravallion-Bidani. To overcome the conflict between
specificity and consistency, Kakwani-Sajaia proposed an eclectic approach that considers both criteria in poverty line estimation. This approach applies consumer theory in deriving
based on the assumption that the consumer’s utility level is a monotonic increasing function of the calorie costs. People with different consumption patterns would have different calorie costs. Thus, allowing for different consumption patterns would be possible by fixing the calorie cost in order to maintain the same utility level.
The average price of the ith food in the whole country is estimated from the following equation: ij N j j i a p p
∑
= = 1 (2.5)where pij is the average market price for ith food in jth region; and aj is the population share of
jth region. Below is the formula for the regional spatial price indices with the spatial price
index of 100 for the country, used as the base. ] / [ 100 i ij i j s p p P = ×
∑
(2.6)where si denotes the share of ith food in basket of n food. Translating to the Malaysian
context, the food poverty line, FLinehj is the amount of money needed to purchase the total
calorie requirement if the food cost is RMcalhj.
FLinehj = Calreqh * RMcalhj * Pj (2.7)
where Calreqh is per capita calorie requirement of household h; RMcalhj is the calorie cost of
the hth household in jth region, in Malaysia currency (Ringgit Malaysia); and Pj denotes the
regional spatial price indices. Kakwani-Sajaia suggested the use of the bottom quintile as the reference group to represent the poor household. This is represented by the hth household in
jth region.
Now follows the most contentious part of poverty line estimation. Kakwani-Sajaia (2004) used the minimum total expenditure required by a consumer to enjoy a given level of utility at a given price vector. Figure 2.1 illustrates the concept. It shows that the food and total
expenditure functions are increasing functions of the utility level. The distance BC is the food poverty line (bf). B gives the utility level UZ that is consistent with the food poverty line. The
non-food poverty line is shown by the distance CD which is derived from the standard
F Food expenditure function bf E D C A B Total expenditure function X G H UZ* UZ Expenditure Utility level UM Figure 2.1 Non-food poverty line derivation
Note. X denotes the Malaysian official method, 2005.
Source. Modified from Kakwani-Sajaia (2004).
The lower bound poverty line proposed by Ravallion-Bidani is determined by where the total expenditure equals the food poverty line, and all non-food expenditure is viewed as essential. By contrast, Ravallion-Bidani’s non-food poverty line is displayed by EF, which is smaller than CD proposed by Kakwani-Sajaia. Kakwani-Sajaia argued that the non-food poverty line proposed by Ravallion-Bidani is not consistent with the standard utility theory. The non-food poverty line EF corresponds to the utility level UZ* but the food poverty line corresponds to
the utility level UZ. This indicates that the food and non-food poverty lines do not imply the
same level of consumer utility.
The Malaysian government estimated the non-food poverty line by modifying the lower bound approach proposed by Ravallion (1998). The non-food poverty line was based on the expenditures of households whose total expenditure was 20 percent higher than the food poverty line. This non-food poverty line was chosen in order to obtain a sample size sufficient for estimation; the figure of 20 percent can thus be seen as arbitrary. This can also be
illustrated in Figure 2.1. The distance XG is the total poverty line estimated by the government. GH denotes the non-food poverty line which is higher than the lower bound proposed by Ravallion but still lower than Kakwani’s consumer theory approach. Applying Kakwani-Sajaia’s argument, the non-food poverty line estimated by the government
corresponds to the utility level UM, whereas the food poverty line corresponds to the utility
level UZ. The food and non-food poverty lines also do not imply the same level of consumer
In estimating the non-food poverty lines, the non-food expenditure are household’s actual expenditure on items which includes clothing and footwear; housing, water, electricity and gas; furnishing and household equipment; health; transport; communication; education and personal goods. The average non-food expenditure was similar to the non-parametric upper bound poverty line proposed by Ravallion (1998) where the households’ per capita food expenditure is equal to per capita food poverty line.
As the food poverty line depends on the calorie requirement of the household, it varies between households and regions. Kakwani-Sajaia introduced the food welfare index which takes the value of 100 when per capita food expenditure is equivalent to the per capita food poverty line. Households whose food welfare index lies between 95 and 105 are chosen to estimate the average non-food poverty line. The per capita non-food expenditure on the items mentioned above for these selected households will represent the average per capita non-food poverty line for different reference groups. The food welfare ratio is a ratio of the households’ actual food expenditure to the households’ respective food poverty line, multiplied by 100 shown below:
Fwelh = FExph / Flineh * 100 (2.8)
MNFPLnj =
Ψ ∈ h
average (MNFPLhnj)…n=1,.., 8. (2.9)
where MNFPLnj denotes the average expenditure on all non-food items by region and area;
and ψ is a set of household whose 90≤ Fwelh≥110.
Next, the non-food poverty line derived below takes into consideration of the economies of scale in household consumption.
NFPLhnj = κ*MNFPLnj * HSh(θn-1) (2.10)
where θn is the economy of scale for non-food items; HSh is the size of the hth household; and
κ denotes the parameter to scale up all the non-food items (so that the mean of NFPLhnj
across households is equal to MNFPLnj).
The total per capita non-food poverty line for the hth household is given as follows:
NfLineh =
∑
= N n hnj NFPL 1 (2.11)Finally, the total poverty line is derived as follows:
where FLineh and NfLineh denote the food and non-food poverty lines, respectively.