How to measure welfare in multiple dimensions: the case of India

It is now widely agreed that welfare is a multidimensional concept.  That is, welfare does not reduce only to pecuniary consumption but encompasses different aspects of life relevant for assessing a person’s well-being.  We can mention, without exhausting all relevant dimensions: health, safety, education and quality of the environment.

Even though many economists now agree on this, it raises difficulties for anyone interested in measuring and/or comparing populations’ welfare.  Note that, ideally, assessing welfare in a country should take into account the distribution of these dimensions across people and not only their average or aggregate level.  It is precisely the kind of welfare assessment performed by Nicolas Gravel and Abhiroop Mukhopadhyay in their article “Is India better off today than 15 years ago?  A robust multidimensional answer”[1].

This paper provides a good example of a way for economists to overcome the obstacles related to multidimensional welfare assessment.

We would like to be able to compare two distributions of multiple variables (the different dimensions of welfare) over a population and make a judgment of the type “distribution A is better than distribution B”.  Better in what sense?

We may want to look at poverty. That is, we set a level for each variable that is considered as unacceptably low (we then obtain a list of poverty lines: one for each dimension).  We consider an individual as poor if she is under the poverty line in every dimension (this is a choice made by the authors).  Then, we may want to count, for instance, the number of poor people in each distribution and consider that the distribution with the least number of poor individuals is better.  The problem with this kind of judgments is that it depends heavily on the definition of the poverty line.  Two different poverty lines may lead to opposite assessments.

Let us illustrate this with an example, in which for the sake of simplicity, we evaluate welfare in only one dimension: consumption.  In the table below, we represent two populations (A and B), both composed of two individuals and we represent their daily consumption level.  Let us define a poverty line equal to $2, that is, any individual with a daily consumption smaller than $2 will be considered as poor.  With such a poverty line, no one is considered as poor in population A while individual B2 is poor.  In other words, we count more poor people in population B.  But let us consider another poverty line now.  Suppose we fix the poverty line at $4.  We now count 2 poor people in population A while there is still only one poor in population B.  As shown by this example, a welfare comparison based on a headcount of poor people in both populations may lead to opposite conclusions depending on the choice of the poverty line.

Here comes the idea of robustness.  If the analysis is sensitive to the choice of the poverty line, we may want to compare the two distributions in the fashion described above and repeat it for every list of poverty lines possible.  Then, we will deem distribution A to be better than distribution B only if it always contains less poor people no matter what list of poverty lines is used.  If this is the case, then the judgment that A is better than B will be “robust” to changes in the poverty line! This is precisely the idea that Nicolas Gravel and Abhiroop Mukhopadhyay develop in their paper.  They say, in such situations, that distribution A dominates distribution B for the Multidimensional Headcount Poverty criterion.  Coming back to our one-dimensional example, let us look at populations C and D’s daily consumption in the table below.  Clearly, no matter what poverty line is chosen, population D will contain more poor people than population C.

This simple example also illustrates the cost of performing robust analysis: a loss in discriminatory power.  Indeed, no robust ranking of population A and B could be made based on the One-Dimensional Headcount Poverty criterion; a ranking between A and B based on the latter criterion might differ depending on the choice of the poverty line.  Let us recall here that the Multidimensional Headcount Poverty dominance defined above involves lists of poverty lines; a list including one poverty line per dimension of well-being.  Therefore, the more dimensions one wants to include in the analysis, the more combinations or lists of poverty lines there are.  For one distribution to dominate another according to the Multidimensional Headcount Poverty criterion, it has to contain less poor people for any list of poverty lines.  In other words, the more dimensions one wants to include in the analysis, the less “likely” it becomes that two given distributions can be compared.  Obtaining Multidimensional Headcount Poverty dominance of one distribution over another becomes very difficult as the number of dimensions of well-being taken into account increases.

So, is India better off?

As recalled by Nicolas Gravel and Abhiroop Mukhopadyay, India’s economy (in per capita terms) has grown at an average rate of 3.5% a year over the last fifteen years.  It is therefore particularly interesting to apply to this country the kind of welfare assessment described above and obtain a robust answer to the question of whether welfare, considered in multiple dimensions, has increased in India over this period of time.

Nicolas Gravel and Abhiroop Mukhopadhyay consider, at three different points in times (1987, 1995 and 2002) the distribution of four dimensions of well-being: real consumption, literacy rate, under 5 mortality and violent crime rates.

Using statistical inference, they come to the conclusion that India is better off in 2002 than it was in 1987 according to the Multidimensional Headcount poverty criterion.  The authors emphasize that this is a strong result given that Multidimensional Headcount poverty dominance is difficult to obtain in four dimensions.

In other words, whatever list of poverty lines is considered (even very implausible ones), the number of people, in India, that are poor in every of the four dimensions mentioned above has decreased between 1987 and 2002.  That poverty has decreased in India over the last 15 years therefore seems to be a pretty… robust claim!

[1] Nicolas Gravel & Abhiroop Mukhopadhyay, 2010. “Is India better off today than 15 years ago?  A robust multidimensional answer.” Journal of Economic Inequality,  Springer, vol. 8(2), pages 173-195, June.

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