EXTENSION OF FGT MEASURES

CHAPTER SIX

6.0 EXTENSION OF FGT MEASURES

In view of the above, I proceed to explore how to customize the FGT measures ^In addressing my concerns highlighted above.

I thus customise theFGT thus,

1 n

(A _ a)a

FGTassets = -

LA;

^I

N ^;=1 A

where N is the sample size, A is the asset poverty line, a; is the value of asset holding of household i, Ais an indicator variable taking value one if a; <A and zero otherwise, and a is a parameter reflecting the weight placed on the severity of poverty. Po (i.e., a = 0) yields the headcount asset poverty ratio - share of a population falling below the asset poverty line - while PI and P2 yield the asset poverty gap - the money metric measure of the average asset bundle transfer needed to bring all poor households up to the asset poverty line - and the squared poverty gap, a more distributionally-sensitive indicator of severe asset poverty. The assumption here is that we are, firstly, able to define an asset threshold, secondly, value it and thirdly, come up with an asset poverty line against which a household is considered poor if it falls below that threshold.

1 N

(1 ^_i)a

FGTincome=

-LA; __

^I

N ;=1 1

where N is the sample size, I is the income poverty line, a; is the income of household i, A is an indicator variable taking value one if i; < I and zero otherwise, and a is a parameter reflecting the weight placed on the severity of poverty. Po (i.e., a =0) yields the headcount income poverty ratio - share of a population falling below the income poverty line - while P^I and P2 yield the income poverty gap - the money metric measure of the average financial transfer needed to bring all poor households up to the

income poverty line - and the squared poverty gap, a more distributionally-sensitive indicator of severe poverty.

Merely adding :FGTincome + FGTassets wi11lead to double counting as some people may be asset poor but income rich and vice versa. Thus it is prudent to combine the value of a household's asset bundle and income to yield a combined threshold based on them. This is of particular interest at this point in this thesis especially with regard to the relationship between assets and income. Would a person's status change under the following circumstances:

*

if only assets are taken into account as a measure of standard of living/poverty?

*

if only income is taken into consideration as a measure of standard of living?

*

ifboth assets and income are taken into account as a standard of living?

Thus, the FGT extensions given above and those to follow, attempt to address some of these issues. Those that follow are intended to determine whether people are asset poor or income poor or both? Also because most people think that wealth equals assets minus debt that is taken into account by deducing a FGTNetworth. People may be asset rich and temporarily income poor due to a shock. Thus, these are compulsions underlying our quest for tools that address such cases. This is also related to the debate about inequality.

In other words, to what extent do people also relate relative poverty to assets? Hence, the need for an asset gini coefficient.

1 N [

(A

+

I) - (a

ⁱ +ii

)J

^a

FGTAsset-Income = -

L;L ( )

N i+l A+I

where N is the sample size, A+I is the asset-income poverty line, ai +ii is the asset- income value of household i, Ais an indicator variable taking value one if a_i+ii< A+I

poverty. Po (i.e., a = 0) yields the headcount asset-income poverty ratio - share of a population falling below the asset-income poverty line - while PI and Pzyield the asset- income poverty gap - the money metric measure of the average asset-income transfer needed to bring all poor households up to the asset-income poverty line - and the squared poverty gap, a more distributionally-sensitive indicator of severe asset-income poverty.

The addition of the value of assets and income of a household yields the household's asset-income value. The asset-income poverty line is a summation of the asset poverty and the income poverty lines. Thus, this measure considers the poor on both scores, i.e. of assets and income, in the determination of their poverty status. These transformations enable us not only to look at the asset threshold from various perspectives, but also open up possibilities of deducing an FGT (networth). Networth can be equated to value of an asset bundle plus income less debt/liabilities.

FGT =

~ ~

^'J

((A+l)-(a; +i;

-DebtJJa

Networth N

f;f

^{Ai (A+}

¹⁾

where N is the sample size, A+I is the asset-income poverty line; a; +ii - Debt; is the networth of household i, A. is an indicator variable taking value one if a_i +i; - Debt;<

A+I and zero otherwise, and a is a parameter reflecting the weight placed on the severity of poverty. Po (i.e., a = 0) yields the headcount networth poverty ratio - share of a population falling below the asset-income poverty line - while PI and Pz ^{yield the} networth poverty gap - the money metric measure of the average asset-income transfer needed to bring all poor households up to the asset-income poverty line - and the squared poverty gap, a more distributionally-sensitive indicator of severe poverty. (In this case (A + I) assumes zero debt. This can find justification on the assumption that debt is not good for the poor).

Transformation of the gini coefficient

Recall the Gini coefficient is:

Gini = (2*covariance (Y, F(Y»)/mean(Y) where Y is income and F(Y) is the cumulative distribution of total household income in the sample (i.e. F(Y) = fey 1), ... J(yn» where f(yi) is equal to the rank of yi divided by the number of observations (n).

In the above Gini formula, mean (Y) can be replaced by mean asset bundle (A) and F(A) being the cumulative distribution of total value of assets in the sample, F(A) =

f(a,), ... J(an) to derive an Asset Gini coefficient. This will help to identify the skewness in the community with respect to assets and thereby reflect the asset inequality landscape in that community.