A very clever economist friend, Debraj Ray, sadly lost to India for US academe, had two superb observations on compound interest rates. The first was that most people don’t have a natural feel for exponents or compound growth rates. For instance, until the recent downturn in India’s quarterly growth rate, newspapers were replete with assertions of how India could easily achieve 10 per cent real GDP (gross domestic product) growth, and then sustain it for the next 15 years. When you told the enthusiasts that 10 per cent growth over 15 years would imply more than a four-fold increase in real GDP, you saw incredulity followed by one of two reactions: either a choice of a lower growth rate, or sinewy nationalist stuff such as “Why not?”

Ray’s second observation was that it took something like a hyperinflation for people to instinctively grasp the power of compounding. If prices rose for a fairly long time at 10 per cent per week (that, by the way, translates to 14,104 per cent per year), everyone in the country, however innumerate, would be able to accurately anticipate what prices would be in the coming week. Ray was in Brazil during its last period of hyperinflation, and had seen taxi drivers, maids and slum children getting naturally adept at applying the compound interest.

This brings me to our present bout of price rise. With point-to-point WPI (Wholesale Price Index) inflation having dipped from 12.63 per cent on 9 August 2008 to 12.1 per cent on 30 August, many civil servants and commentators are talking of the certainty of inflation coming down to single digit by the end of the fiscal year. These assertions are based on two premises: first, that key prices will be either coming down rapidly, or not increasing at the same extent as before; and second, that the ‘base-effect’ is coming into play.

The first assertion is easily understood. The second needs explaining. What it means is that so long as the numerator decreases, or doesn’t increase too much, a rising denominator — reflecting the price hikes of the past — will necessarily bring down the rate of growth of prices, or inflation. These days, this magical, quasi-academic term ‘base-effect’ is really making the rounds. Ask most people who read this magazine or the pink papers as to why WPI inflation should come down, and you get the profound answer, “Because of the base-effect.”

So, here’s a bit of investigation. In India, point-to-point inflation is the percentage growth of the WPI between any week and the corresponding period 52 weeks ago. Therefore, irrespective of what the WPI will be on 28 March 2009 (the last date for recording prices in 2008-09), the denominator, or base, will be the WPI of 52 weeks earlier, namely that of 29 March 2008. On that date, the all-commodity WPI was 226. It is useful to keep this number in mind for the following four scenarios:

If WPI inflation for 2008-09 is to actually close at 8 per cent, then the all-commodity WPI has to be 244 on 28 March 2009. It was 240.8 on 30 August 2008. In other words, it cannot increase by more than 1.4 per cent between 30 August 2008 and 28 March 2009. At a time when we are facing over 12 per cent inflation, do you seriously expect it to drop to 1.4 per cent over the remaining period, so that we end up with 8 per cent at the end of the fiscal year? I don’t.

If inflation for 2008-09 is to end at 9 per cent, the WPI has to be 246.3 on 28 March 2009. By the same logic, WPI cannot increase by more than 2.3 per cent between 30 August 2008 and 28 March 2009. Again, a very tough call, that requires some serious fall in prices in the coming months.

For 2008-09 inflation to close at 10 per cent, the WPI must be 248.6 on 28 March 2009. That translates to a ‘going-forward’ inflation of 3.2 per cent between 30 August 2008 and end-March 2009.

And for 2008-09 inflation to close at 11 per cent, the WPI must be 250.9 on 28 March 2009 — or a ‘going-forward’ inflation of 4.2 per cent between 30 August 2008 and end-March 2009.

My take is that unless there is a spectacular fall in prices in the coming months, we won’t see 8 per cent point-to-point inflation by end-March 2009. It is more likely to be around 10-10.5 per cent — falling, but still in double digits. The moral of this story: Be hopeful, by all means. But don’t ignore the data.
 

Thanks to my colleague, Deepti Prasad, for the data.
 
Published: Business Standard, September 2008