Tyranny of numbers

This is a question that many people are asking,  some wishing the answer were in the affirmative, but the truth is that with current data this question is not easy to answer.  The data we have (thanks to the good work at the Statistical Center of Iran) helps us identify the poor in 2004, the year before Mr. Ahmadinejad took office, but do not tell us what happened to these people three years later.  For this we would need panel data, that SCI used to collect, but stopped after 2003 for lack of funding (and interest on the part of researchers).

The question that we can answer with the data that we do have (Household Expenditures and Income Surveys–HEIS, for short) is whether the proportion of those poor has changed since 2004.   This is the question that several researchers, including the study that I noted in my earlier post, have asked and tried to answer.  To answer this we need to compare the distributions of per capita expenditures over time.  This appears straightforward enough, but it involves an important, and often controversial, assumption about where to place the poverty line in different years.  The assumption most often made is to take one poverty line for a given year and calculate what it would buy in other years.  As an example, let us take our poverty lines for 2007 from this study that I mentioned in my previous post (about 34600 rials per day for urban and 14800 rials  for rural individuals–a rather large gap).  How much these sums of money would be wroth in 2004? 

One obvious way to make this calculation is to use the Consumer Price Index (CPI) to deflate the 2007 figures to 2004 prices.  These would be 23,500 rials for an urban and 10,100 rials for a rural person.  (By the way, the poverty lines for 2004 used in the same study are lower than these numbers–about 20,000 rials for urban and 8500 rials for rural persons– which biases the results toward rising poverty.)  But then some may object to the accuracy or even relevance of the CPI for the poor on the grounds that the basket bought by poor and non-poor consumers are not the same.  There are problems with the CPI but none so serious as to render it worthless for such a purpose.  (Those who routinely claim that the real rate of inflation is twice what Iran’s Central Bank reports do not know about the power of compounding–in 15 years the actual price level would be about ten times the official level!).  One can always do sensitivity analysis by trying different inflation rates, and even different inflation rates for people at different levels of income.

When comparing poverty over short period of time,  such as we do here, where the poverty line is drawn is of much less significance than getting the deflator right. Most of the time the change in poverty is not sensitive to which poverty line one adopts.  To see this, consider the curve that yields the poverty rate for various poverty lines, which is the cumulative distribution function (CDF).  For Iran this curve often shifts is a parallel fashion from one year to the next, even though the distribution of income may change in between.  Let us for the moment assume that the inflation rate, which reflects the basket of goods bought by the average consumer, accurately measures the inflation experienced by the poor.       

Figures 1a and 1b compare the CDF of per capita urban and rural expenditures for 2004 and 2007 using HEIS data files.  The vertical axis is the proportion of people below a certain level of per capita expenditures measured in 2007 rials. The two vertical lines are, respectively, poverty lines corresponding to the so-called $2 per day standard ($3 per day in 2007, applied to both rural and urban areas) and the much higher calorie-based line standard adopted by Iranian researchers I have mentioned.  By eyeballing the graphs, it is easy to convince yourself that no matter where the poverty line is drawn the share of people in poverty is lower in 2007 compared to 2004.  In particular, the lower (international) and the higher lines (taken from the aforementioned study) give the same result for change in poverty. The shift in the CDF in urban areas is larger, meaning that improvements in expenditures were greater in urban than rural areas.

Figures 1a and 1b.  The cumulative distributions of per capita expenditures in 2007 rials

The only way to get the result that poverty rate has increased during 2004-07 from these data is to use an inflation rate for the poor which is higher than the rich.  Unfortunately, for those who wish to believe such as result, there is little evidence that the price of the basket consumed by the poor has increased faster than for the rich.   In the next post I will show why working with the unstable relation between calorie and expenditures is not a good way to analyse the trend in poverty.