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Imagined Problems in Computing Wealth Disparities

A rejoinder to K G K Subba Rao's comment on the paper on wealth disparities (EPW, September 22) responds to Rao's specific criticisms and further, addresses other shortcomings in the all-India debt and investment surveys.


Imagined Problems in Computing Wealth Disparities

Arjun Jayadev, Sripad Motiram, Vamsi Vakulabharanam

list N as the number of sample observations as we do in our tables, and if as Subba Rao puts it, “it is not clear what the aggregates against the bottom row indicate”, communication with us would have sufficed to clear this up. His misunderstanding in the next sentences regarding

A rejoinder to K G K Subba Rao’s comment on the paper on wealth disparities (EPW, September 22) responds to Rao’s specific criticisms and further, addresses other shortcomings in the all-India debt and investment surveys.

Arjun Jayadev ( is at the University of Massachusetts, Boston, US; Sripad Motiram is at Dalhousie University, Halifax, Canada and Vamsi Vakulabharanam is at Queens College, City University of New York, US.

Economic & Political Weekly december 22, 2007

e welcome K G K Subba Rao’s feedback on our paper ‘Patterns of Wealth Disparities in India during the Liberalisation Era’ (Economic & Political Weekly, September 22, 2007) in his discussion ‘Inconsistencies in Patterns of Wealth Disparities’ (Economic & Political Weekly, November 24, 2007). As we show below, Subba Rao, in his critique, has made several errors by reading our numbers incorrectly, and has pointed to issues that we ourselves have remarked upon in our paper. We use this opportunity to go beyond his criticism, to talk about shortcomings in the National Sample Survey Organisation’s (NSSO) all-India debt and investment surveys (AIDIS), which need to be rectified so that economists can analyse wealth related issues more effectively.

1 Response to Specific Criticisms

In his discussion paper Subba Rao points to several alleged inconsistencies in our paper. Several of the criticisms he provides are simply wrong and based on a faulty reading of the data and the tables presented in our paper and the NSSO report. This is especially so in his first section ‘Discrepancies in Data’.

Subba Rao presents two completely inconsistent figures, in Table 1 in his paper. He misreads the number of observations in our Table 1 (3,01,658 sample individuals in the overall economy, 2,00,179 sample individuals in the rural sector and 1,01,479 sample individuals in the urban sector for 1991 for example) to mean the average value of per capita assets in each sector. He then compares this number (number of individuals in each sector) to the average household wealth (in rupees) in each sector published in the NSSO report, and finds unsurprisingly that these do not match (if it did, this would indeed be miraculous). It is standard practice to the ratio of urban to rural assets certainly stems directly from this basic error.

Similarly, the discrepancy in Tables 2 and 3 that he points to between our asset structure and that of the NSSO report is possibly from misunderstanding the variables that our paper and the NSSO report measure. At the outset, we should repeat what we have said several times in our paper – we look at household per capita asset holdings. This is a fact that Subba Rao is well aware of since he points this out at both the beginning and the end of the paper, and we indeed remark upon this as a central feature of our paper. The NSSO, on the other hand, reports results at the household level for AIDIS. These are different concepts. Our figures in Table 2 are average household per capita assets disaggregated by the main categories of holdings for rural and urban areas. In other words, we take the value of landholdings in a household, divide it by the total assets in a household, and assign this value to each individual in the household as the proportion of total assets held as land by that individual. We then calculate the average of this figure across the population. For example, the average of this figure for rural individuals is 48.6 per cent for land holdings as in our Table 2. The NSSO on the other hand, utilises household means. Just to illustrate how this might change averages, consider a population with two rural households A and B, weighted equally in the population with the same wealth. Households A and B have one and two members, respectively. Household A has 50 per cent of assets in land and 50 per cent in buildings. Household B has 0 per cent of its assets in land and 100 per cent in buildings. The average landholding proportion per household is then 25 per cent = (50 per cent + 0 per cent)/2. The average landholding proportion per person is 16.6 per cent = (50 per cent + 0 per cent + 0 per cent)/3. There is


no reason a priori to assume that the actual values between two measures, one based on household averages and one based on household per capita averages will ever coincide and hence, we are not surprised that if one compares these different measures one will observe differing values.

We wish further to note that we are not even sure (once again) whether the figures Subba Rao is using are conceptually the same as the ones that we report, leaving aside the issue of household versus per capita averages. The figures in the NSSO reports that he cites are labeled “percentage share of different components of assets in the total value of assets for each occupational category” [NSSO 2005], while we consider the average proportion of total assets held by an individual in a particular component.

When we examine average landholding proportion per household from the NSS unit level data in order to compare it with the published household level figure that Subba Rao points to, we find substantial differences with respect to the published figures for all categories from the NSSO table (for example, the average share of landholdings in total assets is 47.4 per cent in the rural sector in 2002 using the unit level CD while the percentage share of landholdings in total assets for the rural sector is 63.2 per cent in 2002). We suspect that the NSSO figure being reported is conceptually different and is the sum total value of the components as a proportion of sum total assets in the sector. That is, for example, the sum total value of land held by all households in the rural sector divided by the sum total of total assets held by households in the rural sector. This is an entirely different conceptualisation. The first figure (ours) tells what proportion of total assets of the average individual is held as a given component. The second figure tells one what is the proportion of all assets held by the sector in a given component. In fact, a cursory check of the unit level data appears to confirm this for the rural sector but we can only speculate as to the methodology employed by the NSSO, and so we cannot be certain if this is the case.

Just to reiterate the same point, Table 3 in our list of tables is the percentage of all individuals who have positive assets in each category. Since Subba Rao does not tell us which figures we are in conflict with, we can only speculate but we are reasonably sure that since the NSS reports figures at the household level, Subba Rao is once again comparing apples and oranges.

We have little to respond to in the section on estimates of net worth and debt since we are in agreement with many of the sentiments and comments (the importance of gold, the difficulties with regard to the underreporting of land and so on, the complexity of getting accurate pictures of household wealth, etc). None of the comments in the section are criticisms of our paper and a particularly useful suggestion made is to provide a figure for dead-weight indebtedness, which we will certainly do in future papers.

In the last section ‘Double Deflation’, Subba Rao suggests that our paper is “contaminated” by two deflations. First, it must be noted that there is only one deflation procedure. Calculating figures at a per capita level as opposed to a household level does not constitute deflating the figures. Indeed, virtually all estimates of poverty and inequality that use the individual as the unit of reference rely on similar procedures. Moreover, as we note, it is important to treat the individual as the unit of reference, since welfare ultimately resides in individuals and not in households.

Use of Price Indices

The more relevant criticism is of our use of consumer price indices (CPI) as deflators. We were and are aware of the problems associated with the use of the CPI, since different assets require different price deflators, especially if, as in the case of durables, the asset becomes cheaper overtime. This is an old and abiding problem with comparing wealth distributions across time. In fact in our paper, we explicitly draw attention to the literature on this and note that it is only because no appropriate wealth deflators are available that we utilise CPI (“given the absence of explicit wealth based deflators [Vaidyanathan 1993], in order to make real comparisons between wealth holdings at two different points in time, consumption based deflators need to be used” p 3855). One should therefore, read our figures as meaning the average value of assets in 1991 and 2002 after discounting for the loss of the purchasing power of the rupee between 1991 and 2002. They should not be understood to mean real values in the sense of keeping the specific price of each asset constant in each year of the series. Subba Rao makes another error in saying that this problem carries over to the calculation of real gains in financial assets since the CPI is appropriate to calculate real gains in financial assets. The real rate of interest on a financial asset after all is the nominal rate of interest less inflation (which can be measured by the CPI).

In the very last paragraph, Subba Rao asks whether one will need to sample the wealthiest with probability 1 to make the survey accurate. Our response is that a census is certainly more accurate than a survey but we were not suggesting that this be done! In fact, our point is a totally uncontroversial one. Wealth is usually highly unequally distributed. It is also widely accepted by many practitioners that given this fact, if over-sampling of the very wealthy does not take place, summary figures are likely to be biased. For example, Subramanian and Jayaraj (2006) note that adding the wealth of the 178 richest households from the Business Standard survey of the richest Indian households in 2002 to the 2002 all-India debt and investment survey data increases the asset share of the richest 1 per cent from 15.72 per cent to 17.77 per cent.

There are many statisticians and economists who have considered novel ways to over-sample the wealthy. Kennickell (2006), for example proposes using a combination of population stratification and prediction from tax returns to compensate for the loss in the sample of the wealthiest households. We do not suppose that every methodology proposed is appropriate for the Indian context, but we do believe that this is an issue to be addressed and adequately dealt with by the concerned statisticians.

2 Issues on Wealth Data

We now turn to what we consider to be the more important issues that have been raised in this discussion. These are the

december 22, 2007 Economic & Political Weekly


following. First, how do we make survey data more representative of the wealth distribution in India? Second, what are the equivalence scales that we should deploy? The latter issue is relevant not merely for the analysis of wealth but also for consumption since the default equivalence scale is that all the members of the household (adults and children) are equally weighted (an assumption we believe that this needs revision).

We have discussed the first issue in section 2 of our paper, where we talk about the problems associated with the AIDIS data. Essentially, the three main problems are (i) underrepresentation of the wealthy; (ii) underreporting of wealth; and (iii) misvaluation of wealth.

The first problem can be corrected (at least to a certain extent) by over-sampling the wealthy and by using methods similar to the ones that we discussed above. The second problem is really an issue with survey design and administration – how do we design and administer a survey so that respondents are reasonably truthful? The third problem has to do with what prices and deflators should be used. On the issue of price deflators, given the need for making inter-temporal comparisons in the evaluation of various policies, the NSSO would certainly do well to begin providing in-depth and readily available deflators across a wide variety of goods and services so that comparisons can be made more effectively. This is something that will certainly be useful for comparing wealth distributions but also for many other endeavors. We hope that there is a discussion on these issues, so that even if these problems remain unsolved, a consensus might emerge, which can help both researchers and policymakers choose the best practice.

On the issue of equivalence scales, the use of a particular scale embodies certain assumptions about household behaviour and/or the socio-economic context within which households operate. For example, per capita analysis treats all individuals within the household (children, adults, the old, etc) as the same and ignores returns to scale within the household. On the contrary, completely ignoring household size makes its own underlying assumptions and has its own

Economic & Political Weekly december 22, 2007

problems. These issues have been discussed in the literature [for example, see Sierminska and Smeeding 2005] although we are not aware of any study focusing on the Indian context. Again, we think that there has to be some discussion in the Indian context on what the right assumptions are and thereby, what the right equivalence scale is. Apart from this, researchers can also examine the sensitivity of their conclusions and inferences to the choice of the equivalence scale. For example, one approach that has been used in the literature is to use Sεwhere S is the size of the household and ε is a parameter that takes various values reflecting returns to scale (ε=1 is the per capita approach). By experimenting with various values of ε, researchers can examine how sensitive their conclusions are to the choice of their equivalence scale.

3 Conclusions

To summarise then, although we are pleased by the attention paid to our paper by Subba Rao, and indeed thank him for spending the time to write this response, most of his critique is unfounded and derives from basically misunderstanding our figures and by making inaccurate comparisons based on differing methodologies.

There are nevertheless genuine issues that need to be addressed in the formulation and analysis of the AIDIS as we have and others have noted. The study of wealth and asset distribution is critically important for understanding the dynamics of an economy and researchers are handicapped to the extent that surveys have shortcomings. It is our hope and expectation that as more researchers engage with this topic, solutions to these issues will be found.


Jayadev, A, S Motiram and V Vakulabharanam (2007): ‘Patterns of Wealth Disparities in India during the Liberalisation Era’, Economic & Political Weekly, Vol 42, No 38, pp 3853-63.

Kennickell, A (2006): ‘The Role of Over-sampling of the Wealthy in the Survey of Consumer Finances’, mimeo, Federal Reserve Bank 2006, available at http://www.

National Sample Survey Organisation (NSSO) (2005): ‘Household Assets and Liabilities in India (as on June 30, 2002)’, Report No 500 (59/18.2/1).

Sierminska, E and T Smeeding (2005): ‘Measurement Issues: Equivalence Scales, Accounting Framework, and Reference Unit’, paper presented at the Luxembourg Wealth Study conference, Perugia, Italy, January 27-29.

Subba Rao, K G K (2007): ‘Inconsistencies in Patterns of Wealth Disparities’, Economic & Political Weekly, November 24, pp 78-79.

Subramanian, S and D Jayaraj (2006): ‘The Distribution of Household Wealth in India’, UNU WIDER Research Paper No 2006/116.

Vaidyanathan, A (1993): ‘Asset Holdings and Consumption of Rural Households in India: A Study of Spatial and Temporal Variations’, Agricultural Development Policy: Adjustments and Reorientation, Indian Society of Agricultural Economics, New Delhi and Oxford.

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