Poverty is caused by low productivity. Reducing poverty involves raising productivity- which includes reducing risk- e.g. risk of unemployment or a penurious old age- and improving health and wealth creation and altering the terms of trade the country faces. It also involves changing what people do and how they do it. This is based on 'mimetic' effects. Some get richer faster and this drives emulation by others. So income distribution worsens though poverty has fallen. Leftists had always understood that Markets could lift people very rapidly out of poverty whereas Socialist policies could cause absolute deprivation to increase. Thus they needed to find a way to measure poverty which would show the country as suffering more poverty just when the opposite was starting to happen.
Sen, in his seminal 1976 paper, conjured up some absurd stipulations or 'axioms' in order to justify this type of mis-measurement. If the percentage of the poor had fallen from twenty five percent to ten percent because fifteen percent had managed to shift from subsistence agriculture to working in factories, instead of saying poverty has fallen by 15 per cent, Sen gives us a formula which multiplies the actual poverty rate- which is ten percent- by a higher figure which is supposed to track income distribution. Thus we can say, though only ten percent of the population is now poor, poverty has risen from twenty five percent to thirty percent because Neo-Liberalism is very evil and rapes poor people so as to enrich a tiny plutocracy. Sadly, since Sen was stupid, his poverty index could be easily manipulated to make any sort of claim. Thus, it would have been useful to supporters of dictators like Indira Gandhi to prove poverty had fallen so far in India that Americans wanted desperately to immigrate to India.
Sen wrote-
IN THE MEASUREMENT of poverty two distinct problems must be faced, viz., (i) identifying the poor among the total population, and (ii) constructing an index of poverty using the available information on the poor.
No. To measure something you need an 'operationalized' definition of it. Thus in measuring dick sizes you need to define dick as the organ men pee out off. You would also need to specify that they be flaccid or erect depending on your purpose. Since dick size is a sensitive subject you may need to give assurances of anonymity to the sample population. Thus though a person may find out as a result of the published findings that he has a below average dick size, still, he can't be identified as having this trait provided he keeps this trousers on. True, if you are trying to find out who has the biggest or smallest dick in a country, you may look at observable traits which correlate with dick size. However, measuring poverty isn't about finding the poorest people and then measuring their dick out of force of habit.
To measure poverty you need to define a poverty line and find out how many fall below it, though nobody really cares if you just make that shit up. You never need to 'identify poor people'. You have a sample and get relevant information about that sample. You may find that perhaps the 'poverty line' isn't high enough but that is a separate matter. What matters is making a little extra cash by padding your expenses on this gig. I mean nobody really gets hurt if you steal from a Charity- right?
The former problem involves the choice of a criterion of poverty
No. It is an arbitrary definition which may be income related or based on the basket of goods consumed. In practice, this meant that countries with a public distribution system said everybody, except 'refuseniks' and 'social parasites', was getting the basic ration and so poverty was non-existent. By contrast, Capitalist America was quietly starving to death just as Prophet Marx foretold. A proper Poverty Index would prove this beyond doubt, peradventure or infirmity of suspicion.
Alternatively you may simply assume that any agriculturist or agricultural labourer who owns less than a given amount of land is poor. Here you focus on low productivity and deduce poverty exists where it is likely to obtain. The utility of this approach is that it dovetails with poverty removal thanks to population transfer to higher productivity employment.
(e.g., the selection of a "poverty line" in terms of real income per head), and then ascertaining those who satisfy that criterion (e.g., fall below the "poverty line") and those who do not.
We don't know 'real income per head' for the poorest. We may know who and how many are receiving certain transfers or benefits in kind- e.g. attendance at soup kitchens. Here, poverty reduction is motivated by a desire to keep a lid on this type of expenditure. Encouraging emigration may be a solution.
In the literature on poverty significant contributions have been made in tackling this problem (see, for example. Rowntree [27], Weisbrod [41], Townsend [39], and Atkinson [I]), but relatively little work has been done on problem (ii)
because, if there are markets or a rationing system with 'repressed inflation', the aggregation has already been done and is represented by the threshold real income or basket of goods. In subsistence economies, what matters is how much land the peasant has.
Sen is going to take an axiomatic approach to doing something which can't be done axiomatically. The data is imperfect. Ranking can't be done at all. Poor people don't fill out income tax returns. We don't know their income or income gap but can guess that their real income is lower than the poverty line because what they are doing is very low productivity- stuff like begging, prostitution, selling loose ciggies, wiping windshields at zebra crossings. More dissaving and transfers may play a role. Thus estimating the poverty head-count is empirical, sampling based, and ad hoc or arbitrary to some degree. For different purposes, one can have different estimates- e.g. a head count for extreme poverty, another for the 'emerging middle-class' which can finance a 'social minimum' through expenditure taxes, and so on and so forth.
with which this paper will be concerned. The most common procedure for handling problem (ii) seems to be simply to count the number of the poor
estimate it.
and check the percentage of the total population belonging to this category. This ratio, which we shall call the head-count ratio H, is obviously a very crude index.
It is not an index. It is merely an estimate of a type which may be useful enough in limited contexts.
An unchanged number of people below the "poverty line" may go with a sharp rise in the extent of the short-fall of income from the poverty line."
Only if the shape of the Income distribution changes- i.e. there is some structural change in the economy or there is an exogenous shock. Still, if you have a poverty line, you are welcome to have an extreme poverty line which captures a change of that sort.
The measure is also completely insensitive to the distribution of income among the poor.
So what? You can have plenty of different ratios. Once you have done some sampling or otherwise collected some data you can very cheaply do lots of different things with the same set of figures.
Suppose the Army has a minimum height requirement. Our College is asked how many of our students can be drafted immediately. We go through the records and say 'x number meet the height requirement'. The Navy however has a maximum weight requirement. We give them a different answer.
A pure transfer of income from the poorest poor to those who are better off will either keep H unchanged. or make it go down--~-surely a perverse response.
Not at all. Poverty has gone down though extreme poverty has risen. We may as well worry about the fact that average dick size fell after our College went co-educational. What matters is that dicks have some good reason to get enlarged.
Measure H thus violates both of the following axioms.
MONOTONICITY AXIOM: Ceteris paribus, a fall in income of a poor person must increase the poverty measure.
Why? The number of the poor hasn't changed. True, the extreme poverty head-count may have increased but that is a separate matter. Consider an economy where immigrants do the unskilled work. There is an exogenous shock- e.g. a fall in the price of the raw material the country exports- such that real income for the poor falls. Poverty may fall as the immigrants quit their jobs and leave the country. True, the people of the country may feel poorer because they are having to cook their own breakfast and look after their own kids- i.e. they are now more productive. But since there are now far fewer poor people, poverty has fallen.
TRANSFER AXIOM: a pure transfer from poor to rich must increase the measure.
This isn't true. The poor may be as stupid as shit. They send money to a rich pastor who says he can get them into Heaven. Has poverty increased? No. It's just that poor people are doing stupider shit than previously was the case.
. INCOME SHORT-FALL AND POVERTY Consider a community S of n people. The set of people
a set is only a set if it has a well defined extension.
with income no higher than x is called S(x).
We don't know exactly who is or isn't a member. Since there is no well defined extension, there is no set. All we have is an estimate based on some ad hoc assumptions.
If z is "the poverty line." i e., the level of income at which poverty begins, S(z) is the set of "the poor."
It is like the set of people who will die on a Tuesday. We have no access to that set. We can do nothing mathematical to it.
S(A) is the set of all, i.e., S. The income gap g , of any individual i is the difference between the poverty line z and their income . Obviously, g is nonnegative for the poor and negative for others. For any income configuration represented by an n-vector y. "the aggregate gap" Q(x) of the set S(x) of people with income no higher than x is a normalized weighted sum of the income gaps gi of everyone in S(s), using nonnegative weights ci(z, y).
What obvious mistake is Sen making here? The answer is that he is assuming everybody receives income. Some people, rich or poor may be living off savings or charity or other transfers. Moreover, some people may have income which has to be used to pay off debts or other obligations. Neglecting transfers is a great way to get to complain about how poverty has dramatically increased even if it continues to fall.
In practice we don't just look at Income but divide it by the number of dependents while also taking account of Wealth or capacity to borrow. Thus, once we have a headcount figure, we make adjustments based on common sense. If a 'baby boom' cohort of young people are taking on debt to stay in college, the headline count is misleading. In the UK there was also the problem of students (who received grants during term-time) 'signing on' during holidays. Thus all sorts of adjustments were made in an ad hoc manner.
As for Sen's axiomatic approach, it fell at the first hurdle by adopting false axioms and then mis-specifying the relevant mathematical model.
The specification will depend on a set of axioms to be proposed presently.
Sadly, if fiscal policy changes when the index changes, there is an impredicativity problem and thus no actual sets or functions exist. Sen's formula is nonsense. Alternatively, measuring poverty has no effect on the real world. But, in that case, why take up so depressing a hobby?
It should, however, be noted at this stage that the form is very general indeed,
It is meaningless. The poverty line either has zero fiscal effect, in which case it would be pointless to compute it, or else there are a number of possible Gini and other coefficients associated with it. Thus, there is impredicativity and no non-arbitrary solution.
In particular no requirement of additive separability has been imposed.
Which is why the thing is nonsense.
The index of poverty P of a given income configuration y - is defined to be the maximal value of the aggregate gap Q(x) for all x: (3) P = max, Q(x). Since the weights t., are all nonnegative. it is obvious from (1) and (2) that: P= Q(z).
In which case nobody is living off savings or transfers- i.e. they don't exist in the real world. The poverty line is meaningless or arbitrary.
That is, the index of poverty P of a community is given by the value of the weighted aggregate gap of the poor in that community.
Only if there is no dissaving, transfers and the 'poverty line' is exogenously given. Yet, for 'frictional' reasons, there must be some dissaving and transfers. Basically, you are adding a 'frictional' component to the head-count. What this means is that if a person falls below the poverty line and has some volatility of earnings (which is why they have some saving and dissaving or inter-group transfers) then though the number of poor hasn't changed, still you are inflating the head-count ratio. This is a type of double counting.
3. RELATIVE DEPRIVATION AND INTERPERSONAL COMPARABILITY In line with the motivation of the transfer axiom, it may be reasonable to require that if a person is accepted to be worse off then the weight c, on the income short-fall of the worse-off person i should be greater.
Very true. If I am accepted to be shorter than you, then greater and greater weight should be placed on my relative shortness till everybody agrees I am actually a dwarf though six foot one in height.
AXIOM E (of Relative Equity): If the individual welfare functions were cardinal, interpersonally fully comparable and identical for all persons,
which they can be by arbitrary stipulation
and furthermore if the Benthamite additive utilitarian form of social welfare were accepted, then it would be natural to relate Axiom E to the marginal utility of income of person i.
but this may be increasing for the poor. Marginal utility may only diminish for the rich. That still wouldn't be an argument for redistribution because the rich may prefer to migrate to where they are merely middle class and get better public services for their tax dollar.
But in this paper the utilitarian approach is not taken; nor are the assumptions of cardinality and full interpersonal comparability made. Individual welfare is taken to be ordinally measurable and level comparable.
By arbitrary stipulation. We don't know what will or won't give us welfare. Generally we act out of habit or do what smart people are doing.
The poverty line is about income which is measurable and cardinal in nature. Why bring in ordinality? It is irrelevant.
There is agreement on who is worse off than whom, e.g., "poor i is worse off than wealthy j," but no agreement on the values of the welfare differences is required.
But that agreement turns out to be wrong. There was a time when I appeared better off than my neighbour who was on the dole and smoked dope. But he was writing code which made him very wealthy.
While Axiom E can be justified on grounds of a strictly concave interpersonally comparable cardinal welfare function, that is not the only possible justification. The idea that a greater value should be attached to an increase in income (or reduction of short-fall) of a poorer person than that of a relatively richer person can also spring from considerations of interpersonal equity.
But this is like saying I'm a dwarf just because you are taller than me. It is a different matter if you will pay me a lot of money for calling me a dwarf. But just exaggerating my shortness without compensating me in any way is the opposite of 'interpersonal equity'. Still, we understand that virtue signallers want to say 'If the CEO got a bonus this proves that the custodial staff are having to submit to sodomy in return for a crust of stale bread.'
' The appeal of Axiom E is, I believe, much wider than that which can be obtained from an exclusive reliance on utilitarianism and diminishing marginal utility.
Everybody who earns less than me is a rent-boy. If they didn't take it up the arse all the time how could they have gotten the money to buy a little stale bread? I often stay up nights thinking about their suffering while pleasuring myself.
Axiom E gives expression to a very mild requirement of equity.
viz everybody earning less than us is having to rent out their arse so as to eat stale bread.
Another axiom is now proposed, which incorporates Axiom E, but is substantially more demanding. AXIOM R (Ordinal Rank Weights): The weight ci(z,y) on the income gap of person i equals the rank order of i in the interpersonal welfare ordering of the poor. The method of constructing weights on the basis of rank orders is not new,
but no one was ever stupid enough to extend it to poverty studies. In some fields- e.g. top singer, top athlete etc- earnings follow a steep Power Law and rank order matters a lot. But the lowest income quartile will have a relatively flat, not a fat-tailed distribution.
In any case, the rank order of the poor is unknowable because we have no data on their real income. We just have a reasonable guess that it is below some particular level. Suppose poverty is defined as '5 purchasing-power adjusted dollars a day'. You have a figure for the population from census data or sampling and you have another figure for average family size and the total number of people employed in sectors where the average product of labour is sufficiently high and you proceed on that basis while making all sorts of ad hoc adjustments to do with remittances, dissaving etc.
Axiom R is taken as an axiom here, though it can be easily made a theorem derived from more primitive axioms.
which are bat shit crazy
There are essentially two ways of doing this. The first is to follow Borda in equidistanced cardinalization of an ordering.
The richest billionaire may be ten times richer than the second richest. But the poorest beggar won't be much poorer than the second poorest. This axiom is as stupid as shit. Essentially, an illicit assumption is made about how the population is distributed between the poverty line and the extreme poverty line. This is like saying if I am the shortest on the baseball team, I am obviously a dwarf.
If A, B, and C are ranked in that order in terms of their weights, and if there is no intermediate alternative between A and B, and none between B and C, "I say that the degree of superiority that this elector has given to A over B should be considered the same as the degree of superiority that he has accorded to B over C"
Which is fine if we are voting for who is the best singer or athlete because the star is miles ahead of the runner up.
We know from Axiom E that if i is worse off than j, then the weight on i's income gap should be greater than on j's income gap. Using Borda's procedure combined with appropriate normalization of the origin and the unit, we arrive at Axiom R. The second is to take a "relativist" view of poverty, viewing deprivation as an essentially relative concept (see Runciman .
The guy was a Viscount. Thus he knew all about poverty. Dukes and Earls kept sodomizing him in return for which he was given a stale crust of bread.
The lower a person is in the welfare scale, the greater his sense of poverty, and his welfare rank among others may be taken to indicate the weight to be placed on his income gap.8 Axiom R can be derived from this approach as well. We turn now to the relation between income and welfare, since Axioms E and R are in terms of welfare rankings, whereas the observed data are on income rankings. There are, of course, good reasons to think that sometimes a richer person may have lower welfare than a poorer person, e.g., if he is a cripple, and this may raise interesting issues of equity.
Wealthy cripples are being sodomized by Viscounts who can spare a crust or two of stale bread.
When dealing with a general measure of poverty for the community as a whole, however, it is not easy to bring such detailed considerations into the exercise. Axiom M proceeds on the cruder assumptions that a richer person is also better off. Furthermore, the individual welfare relation is taken to be a strict complete ordering to avoid some problems that arise with rank-order methods in the case of indifference. This last assumption is less arbitrary than it may at first seem.
It is not arbitrary, it is mad. If a complete ordering exists the person who has it is omniscient. She can cure cancer and achieve room temperature nuclear fusion. Only a moron would believe in so crazy an axiom.
. CRUDE INDICATORS AND NORMALIZATION In Section 1, references were made to two measures of poverty currently in use. The "head-count ratio" is the ratio of the number of people with income yi d z, to the total population size n: 'This can be axiomatized either in terms of the welfare rank of the person among the poor (as in Aiom R) or in terms of that among the entire population (see Axiom R* in Section 6 below).
So this means you have to have complete information about every member of society. Sampling won't do. Thus poor countries can't have a poverty index. This means nobody there is poor. Why are they being so mean about sending money to help starving Viscounts who are being incessantly sodomized by Dukes?
Both lead to essentially the same result if correspondingly normalized.
Both can lead to any crazy result you like because ex falso quodlibet- from false, foolish, nonsense any nonsense can be deduced.
Now for Sen's 'theorem' : For large numbers of the poor, the only poverty index satisfying Axioms R, M, and N is given by: (8) P = H (I + (1 -I)G), where G is the Gini coeflcient of the income distribution of the poor and H is the headcount ratio and I is the income gap
Notice that if everybody save one rich dude has a different nominal income falling short of the poverty line then G will be almost 1 and thus the poverty measure would be the head count measure. But the rich dude may be so rich that he can provide everybody with free food and housing and so forth. So this is actually a rich country- like some Gulf Emirates when I was young- though it may appear horrendously poor. Equally, a perfectly equal society where everybody starved would have a lower Poverty index than the head count ratio assuming everybody had some income but not enough.
INTERPRETATION AND VARIATIONS The poverty index proposed here turns out to have quite an easy interpretation.
Lying about how vast numbers of people are crushed by poverty in affluent countries is a great service to God and Man. True, people lose all respect for your profession if you tell stupid lies. Still, if you are a brown monkey then you may be declared the Mother Theresa of Economics.
The measure is made up of the head-count ratio H multiplied by the income-gap ratio I augmented by the Gini coefficient G of the distribution of income among the poor weighted by (1 -I), i.e., weighted by the ratio of the mean income of the poor to the poverty-line income level.
This means India can triumph over poverty by
1) reducing the poverty line which reduces H directly and also reduces I and therefore P
2) chasing away entrepreneurs which reduces G but which also makes the country actually poorer
However, the US and UK too could become as shitty as India by pretending poverty was rising and that the right way to tackle this was to kill the goose that lays the golden egg of enterprise in the name of equality. Sadly, voters in the West rebelled against such policies around the time Sen ran away from India with his best friend's wife.
One way of understanding its rationale is the following : I represents poverty as measured by the proportionate gap between the mean income of the poor and the poverty line income.
which is arbitrarily chosen.
It ignores distribution among the poor. and G provides this information.
No it doesn't. Anyway there is little point getting information about the exact difference in income among people who are below the income tax threshold.
In addition to the poverty gap of the mean income of the poor reflected in I, there is the "gap" arising from the unequal distribution of the mean income, which is reflected by the Gini coefficient G of that distribution multiplied by the mean income ratio. The income-gap measure thus augmented to take note of inequality among the poor, i.e., I + (1 - I)G, is normalized per poor person, and does not take note of the number of people below the poverty line, which could be minute or large. Multiplying [I + (1 -I)G]by the head-count ratio H now produces the composite measure P. While this is perhaps the easiest way of interpreting the poverty index P,it must be borne in mind that its justification lies in the axioms used to derive it.
They were all as stupid as fuck.
The multiplicative form chosen in Axiom N, though simple, is arbitrary. Axiom M, perhaps justifiable in the absence of detailed information on the poor, is objectionable when much is known about individual members of the group, e.g., that cripple Mr. A while richer than robust Mr. B is less well off in some sense
though he may be better off in some other sense
Finally, Axiom R follows Borda's procedure of cardinalizing an ordering by treating rank numbers as weights. This is, of course, also arbitrary, though frequently used in other contexts as the popularity of several variants of the rank order procedures of voting indicates. The justification can be either in terms of intensity of preference being surmised from rankings only by using a version of "insufficient reason" (following Borda), or in terms of an essentially relativist conception of poverty.
In which case why bother about it? Sexiness or Cuteness of Charm are 'relativist'. Poverty is about productivity. Boosting it makes everybody better off. The thing is substantive not relative.
Axiom R may not be acceptable to many since there is arbitrariness in making the weight on person i's income gap equal his poverty rank. Even with a gicen level of income, a person's poverty weight will go down if a richer poor becomes poorer than him. The advantages and defects of the rank-order system are clear enough.
They are irrelevant. It would be a waste of time to rank the poor. An article titled 'the ten richest men ranked in order of net worth' is clickbait. One titled 'ten poorest beggars ranked in order of smelliness' will attract few readers.
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