 Now, what can we say about what has been happening to inequality in the distribution of consumption expenditure in India? There is a certain received story, and I'll present you with a summary version of this received story in the words of an economist called Bhala. So the use of the word sick is very much in order here. I'm simply quoting him. He says, far from India having a problem with non-inclusive growth, China, it is likely the case that the Indian model of growth has delivered relatively much more to the poor, get respirables than China. Often in the polemical debate about poverty and policy and the poverty of policy, the facts, unfortunately, become irrelevant. What is revealing is that, to date, there has been little variation in real inequality in India. While comparative data needs to be explored, it is likely the case that this near-constancy is unusual, given the buzz of the conventional wisdom that inequality increases with growth and or that Indian inequality has sharply worsened. Now, this is much of a piece with what people like Alualia, Jagdish Bhagwati, Tien Srinivasan have said, although their statements are on the whole and not surprisingly somewhat more guarded than Pallas. But the general thrust of the evaluation of inequality in India is that it's nothing to be alarmed about. And where poverty is concerned, money metric poverty is concerned, the general consensus is that there have been dramatic declines in money metric poverty. I think both of these judgments are very strongly suspect. The issue relating to poverty is obviously not a part of this talk, so I will not deal with it. But what can we say about the source of these sorts of judgments which have been made about inequality in India? What I will do is to concentrate on two issues, of which the second is the one that I'll spend a larger amount of time on, which might explain why we get the sorts of results that we do. First is the use of the database. You see, as I told you, we have six points of time separated, one from the other by five years, because the National Sample Survey thick data, as they are called, are produced sequentially, once every five years. Now the data for the year 2000 and 1999-2000, rather, by now there is a fair consensus on the view that these data are virtually unusable. And this has had to do with the fact that the recall periods for the survey in 1999-2000 were drastically changed from the recall periods that were employed earlier, which were usually 30-day recall periods. The 1999-2000 data employed a seven-day recall period, a 30-day recall period, and for certain elements of consumption that which is largely specialized in by the rich, was a 365-day recall period. And the 30-day recall period was eventually contaminated by both the seven-day recall period, which resulted in an overestimation of the consumption of the poor, and the 365-day recall period, which resulted in an underestimation of the consumption of the rich, with the result that inequality in the distribution of consumption expenditure overall in the year 1999-2000 severely bucked the trend, which was observed earlier. So if you're going to employ the 1999-2000 data as part of a six-point data set, then that's going to unduly influence your results. So there is a strong case for actually omitting that here, and that's what we do in our paper. Now, by way of an aside, in doing poverty analysis, many people have observed that the national sample survey estimates of mean consumption have been much lower than the national account statistics mean consumption estimates. And in fact, there has been an increasing divergence between the two estimates. Now, many people engaged in poverty analysis, as it happens, Bhalla is one of them, have strongly argued in favor of employing their national account statistics source as the appropriate data source, that has a higher mean. Now, the ordinary rules of stochastic dominance will ensure that when you have a given distribution, which is yielded by the national sample survey data, which are then inflated by a higher mean, you're going to have a lower level of poverty, and one which displays an increasingly dramatic declining trend. But it was discovered subsequently that the underestimation in the NSS data, vis-a-vis the national account statistics data, was generally at the upper end of the distribution, which really is irrelevant for poverty computations. So it would be quite inappropriate, completely inadmissible, in fact, to do this sort of prorating exercise, whereby you simply employ the national sample survey distribution and scale it up by a factor, which is given by the ratio of the national account statistics to the national sample survey mean. So there's a small irony which is involved here, which I'll come to in a moment. So if you want to display pleasing trends of poverty decline, this is a good way of doing it. The only thing is that it's completely uncalled for, and there are good reasons why you ought not to do it. But what's also true is that the national sample survey data on consumption expenditure display a very small rate of growth in per capita consumption expenditure compared to the NAS and compared to what we know to be the case. So if we are really seeking to capture growth, then there might well be a case or actually resorting to this sort of adjustment by scaling up the national sample survey distribution by a factor given by the ratios of the two means. Unfortunately, what happens when you do that is that it tells a story about inequality, which is not very complementary. If you happen to measure inequality in a manner which I will argue you ought to be doing. And that brings me to the second point. So I'm done with the data part of it, and I've taken care of the data part by simply dropping the objectionable year 1999-2000 from the data set. Now the second major issue has to do with the protocols of inequality measurement. All of the analyses which I've spoken of can find themselves to what's called a relative measure of inequality, such as the Gini coefficient. Now a relative measure of inequality is simply a measure which satisfies what is called the scale invariance property, which simply requires that if all incomes in a given income distribution are scaled up or down by a given factor, then inequality ought not to be seen to have changed. So that's what scale invariance is about. Now consider a simple 2% distribution, which is order. Please don't lock the time for this. Yeah, here we go. Supposing you have a distribution 1, 100, which goes up to 2, 105. Now for any scale invariant inequality index, inequality will be seen to have declined substantially. In the second case, we should be the first. Because look at what's happening. The richer person's income is increasing by just 5% in the transition from the first distribution to the second, while the poorer person's income is increasing by as much as 100%. But what is also true is that out of the total increase in income, it's 107. This is 101. Out of the 6 rupees increase in income in the transition from this vector to this, as much as 5 out of 6 have gone to the richer person and just 1 rupee is accrued to the poorer person. In other words, when you employ a scale invariant inequality measure, then you allow the base levels of incomes to play a very substantial role in determining what you would or would not see as being inclusive in growth. Now this has been a very intriguing problem for me. It's not as if I'm talking about an issue which has not been known. As far as I can tell, it was flagged as far away as 1969 by Serge Christophe Combe. And then he revisited this topic again in 1973 and 1976, and then I believe he gave up because nobody seemed to be paying much attention to what he was saying. For the reasons that I've just explained, Combe referred to scale invariant inequality in diseases as the rightist measures. And he said that there is at least as much of a case for diagnosing invariance of an inequality measure in the presence of scale increases as of diagnosing invariance when there are equal absolute increases. So he says, and that is a property which he called translation invariance, simply requires that if you were to increase everybody's income, not by the same proportion but by the same absolute amount, then and only then will you say that inequality has remained unchanged. Now, are we aware of any translation invariant inequality in disease? Actually, this is done in stats 101. It's a measure called the standard deviation, the square of which is the variance. So this is an extremely well known translation invariant inequality index. Remember that given any vector x, if you were to multiply each person's income by lambda, then the standard deviation of the variance of this, sorry, is equal to lambda squared times the variance of x. So in other words, dispersion is not preserved by the standard deviation of change. Now, a very well known index of relative inequality is what's called the coefficient of variation, which is just the standard deviation deflated by the mean. So like any nice relative index of inequality, the coefficient of variation is mean independent, and you ensure that by simply deflating the standard deviation. Now, if in the presence of income growth, there is a problem of scale invariant in disease being rightist, and of translation invariant inequality in disease being leftist in the terminology of Combe, then is that not a case for measuring inequality in a manner which avoids the extreme values underlying both kinds of inequality in disease? The scale invariant and the translation invariant inequality in disease, which are also called relative and absolute indices. Is that a case for that? And the answer would seem to be obviously yes. And the class of inequality in disease, which fall between these two extremes, is what Combe called intermediate or centrist inequality measures, which satisfy this property. Namely, that if everybody's income were to increase by the same proportion, then you would count that as an increase in inequality. And if everybody's income were to increase by the same absolute amount, then you would count that as a decline in inequality. But to state it in the form of an invariance condition, this is what was done by an economist. Well, he's not an economist, he's a mathematician. It's always difficult to deal with a word which doesn't have any vowels in it. So I don't know how to pronounce this. Let's say, creature for the moment. I might well be wrong, but I'll call him creature. The method which he proposed was supposing you have a given increase in the mean income of a society. Take the first incremental rupee. And one half of it, you allocate in the proportions of the existing distribution. And the other half, you just allocate equally among all the people in the society. So you will get a new distribution from your initial distribution x to x1. And this requirement was, since you're giving equal weight to both relative and to absolute increases, you should declare x1 to be indifferent to x inequality-wise. And then start using x1 as your new base point. You go on to another vector x2, which consists of taking the second incremental rupee and dividing one half of that in the proportions of the existing x1 and one half equally. And so on down the line until you have exhausted the change in the mean income. And you come to some income y hat, which will obviously have the same mean as the terminal distribution y, which you were given at the outset. Now if y coincides with y hat, then you have an invariance condition which says, from a centrist point of view, that inequality in x is the same as inequality in y. So that is the Kirchner measure. He used a set of basic elementary axioms together with this requirement of invariance to characterize a class of inequality and disease, which were basically positive monotone transformations of a certain index, which I'll just call k, which turned out, as it happens, to be simply the product of the standard deviation and just the product of a relative measure and an absolute measure. So if I have still got a couple of minutes, I'll wind up. So this, I learned subsequently that apparently this is a very commonly employed descriptive measure of statistics. It's called the coefficient of difference, I believe. It's simply the variance divided by the mean. And this was pointed out to me by somebody else who had read an earlier version of my paper and has applied it to a problem in demography. And it's a particular salience in the context of the Poisson distribution because the value of this measure for the Poisson distribution is unity, so on. It's just a funny thing. But anyway, long and short of what I said is that if you get rid of the year 1999, 2000, and if you employ a centrist, not even necessarily an absolute measure of inequality, if you simply employ a centrist measure of inequality like the creature, then you get what you expect. The coefficient of variation does not display any trend line. The standard deviation displays an increasing trend, but you don't have to go as far as that. It can be reasonable and moderate in the value judgments which you make when you're measuring inequality. And even if you use the creature and X, you find that for India, the trend in inequality is a pronouncedly increasing one. And you get similar results when you resort to adjustment of the distribution to take account of the discrepancy between the natural sample survey and the natural account statistics. So by making certain, I think, absolutely essential adjustments to both the data and to the protocols of measurement, you would find that you end up corroborating the point of view which most people share through a process of casual observation and contrary to what the experts would have us believe. And for me to end on a slight note of advocacy, it's still not clear to me why we keep on using relative measures of inequality, unless it be that we are committed to the notion that the value of an inequality measure should not change with the units in which you measure an income. And it was more recently, in 2007, an economist called Chen showed that this is an unnecessarily demanding cardinal property of invariance and that you ought to be content with much weaker ordinal property, which demands not that the value of the inequality index should be invariant with respect to the units in which you measure the income, but there is a ranking of inequality distributions which ought to be invariant with respect to the units. So if x is greater than y, and if 20 seconds, and x prime and y prime are derived by scale transformations of x and y respectively, and if x is greater than y, inequality in x is greater than y, all you require is that inequality in x prime should be greater than inequality in y prime, not that the values should be the same. And the Kirchher Index, apart from a few other indices satisfy this property, this is also subgroup decomposed. So there is a good case for employing something like the Kirchher Index. And I say this with some measure of vigor, because we're plainly doing the wrong thing. I mean, you're not going to be interested in doing anything about either poverty or inequality if you don't diagnose the condition appropriately. And the bulk of a problem has come from a virtually willful and perverse insistence on getting things wrong. That's all. Thank you. Thank you very much.