Voodoo of statistics and woes of growth rates

A WELL-KNOWN statistician once remarked: "Some people use statistics like a drunk uses a lamp post, more for support than for illumination". This is a good way of describing how statistics in the public arena have long since ceased to be just information about processes and events. They are for the most part used to buttress or refute an argument.

A good example of this is the ongoing debate on whether or not the reforms have made a difference to the growth of the Indian economy. The pro-reformists are very keen to show that liberalisation has indeed led to faster growth, while the sceptics must find a way to show that it has not. Let me add my own concoction to the your daily morning staple.

The trouble is that just as our heights vary from one to another the GDP growth rate too varies from year to year. Statistical methods provide various ways of summarising this variation to arrive at a single representative growth figure. A crucial assumption in all these methods is that the inherent growth rate is constant from year to year. The problem is in choosing a summary measure which best describes the pace of economic growth before and after reforms.

The `average' is probably the most intuitive statistical summary. But, the average (technically called the `mean') has the problem of being unduly pulled up or down by exceptionally large or small values in the data. You do not have this problem with average height because there are both exceptionally tall and short people in almost equal numbers - the two tend to cancel each other. But think of individual incomes. In our country there are many more exceptionally poor than exceptionally rich people. The 'average' income will then get pulled upward by the few rich individuals.

Exceptions aside, the objective is to find `typically' around what figure most people's incomes are. In this case, it is more appropriate to use another statistical device known as the 'median'. It is the middle value if you arrange all the income figures in an ascending order. For example, if five income figures in ascending order are (300, 320, 500, 575, 5000) then the median income is Rs. 500 while the mean income is Rs. 1339. The average here is obviously not the middle around which most of the income figures are, but the median is.

If you look at the year to year GDP growth figures you will find that there are a few years of exceptionally high or low growth rates. So, depending on how they fall in different periods they will exert their influence on the average. Defining the period for summarising the growth becomes an issue for this reason.

Most often analysts use a complex way to find the average annual growth for a period. Rather than looking at the year to year growth rates, they statistically draw (fit) a line or a curve through the graph of the GDP in each year. The line or the curve is fitted in such a way that it passes through the middle of the GDP graph. This line or the curve is assumed to be the one along which the economy is moving "up" over time. In the next step, the growth rate implied by the fitted line or curve - the `slope' - is taken as representative of the pace at which the economy is growing in this period. This is often referred to as the `trend growth rate' as the fitted line is taken as the inherent trend.

One can see that the growth rate arrived at depends wholly on how that trend/line is drawn. The problem is that this trend is commonly derived from the same principle as that of the average. I would like to call it the 'mean trend'. It has a sensitivity to exceptional values and periodisation that is similar to that of the average, though not to the same extent. An imaginative reader may now ask, ``Why don't you try a median based trend in that case?" Yes, I will.

Have a look at the graph for India's GDP in 1980-2000. There are two distinct periods when the GDP moved along a perceptibly consistent course: 1980-81 to 1987-88 and 1992-93 to 1999-00. Between these two periods there was no direction. GDP rose steeply in 1988-89, slowed down in the next two years, before flattening out in 1991-92. . One can see these years as constituting a third period of uneven GDP growth. This is the first tentative step in summarising the growth of the Indian economy during the period 1980-81 to 1999-00We can now try to summarise this abstraction numerically. The accompanying table presents the summary growth rates for these three periods obtained by the different methods discussed earlier.

The figures represent more or less the impression you have from the GDP graph. The slope of the GDP graph during the third period (post-reforms) is somewhat steeper than the first period (pre- reforms). Both the median and mean based growth rates indicate this. The middle period is a mixed bag but the graph definitely looks steeper than the first period initially before tappering off. The growth rates based on the two different trends differ for the middle period. Obviously, the very low growth in 1991-92 has created a problem for the mean trend based growth rate. I would prefer the median based growth rates as they are obviously less sensitive to the unusual years. On the whole, GDP growth in the post-reform period does seem to be higher than that in the 1980s. But the difference is not dramatic.

One can also argue that there is no analytical justification for seeing the middle period, 1998-1992, as a distinct period. It straddles both the pre- and post reform periods. If you include 1991-92 in the third phase the median trend growth rates for the two periods (middle without 1991-92 and the third one) still remain the same. However, the median trend for the first period extended to 1990-91 becomes 5.4 compared to 4.6 as in the table. Thus, no matter how you compute the median trend, the post-reform period saw an acceleration in growth of at least one percentage point, if not 1.8 percentage points or thereabouts. That is why I said growth in the post-reform period has been faster but the difference is not dramatic

One can raise questions regarding the need to statistically `test' for an increase or no change in the growth rates. Perhaps one can take up this issue on another occasion. Suffice to say here that the results of these tests are more inconclusive than usually presumed and a comparison of short periods poses a peculiar problem of its own. A caveat must also be added to my results. I have had to `splice' two different series of GDP data, one which ended in 1992-93 and another that began in 1993-94, which means making certain assumptions that may not be warranted.

You may now ask - Clever man, if the `median' is so useful why don't the government, the media and researchers use it more often? I am not saying that `median' is always the best measure . It is only one more tool to summarise information. The point is that you cannot summarise appropriately without looking at what you are summarising. This requires a dialogue with the data. The analysts instead seem to engage themselves in a monologue with pre-formulated answers. Again, you are going to ask - why do they do so? Well, you know the story of the QWERTY typewriter. Social habits are difficult to change.

Chandan Mukherjee

(Director of the Centre for Development Studies, Thiruvananthapuram)

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