Sunday, June 28, 2009

Seasonality in Indian Inflation (WPI) Data

Indian inflation as measured by Wholesale Price Index (WPI) is released every week. 2 weeks back this number came out negative for the first time in 30 years. Though, WPI is indicating deflation; no one in India is concerned about it and this negative number is attributed to high base index. In India the inflation is actually calculated year-over-year (y-o-y), unlike other economies where inflation calculated as annualized month-over-month (m-o-m) change. Thus, the base index plays an important role in inflation calculation in India.

The problem with having a base index 1 year old is that the conditions may have changed, which makes y-o-y calculations misleading. Consider that last year oil was approaching $140 around July but is no longer the case today. Therefore, most countries prefer annualized m-o-m change. However, to annualize m-o-m data it is important to adjust the data for seasonality. Retail industry provides a to understand seasonality. In retail most of the sales happen in the last quarter (Q4) of the year (due to holiday shopping). Sales in Q3 and Q1 of next year will be considerably less than Q4. Thus without adjusting for seasonality it would be difficult understand the trend.

Now that we understand seasonality, the next question to consider is: Is there seasonality in Indian inflation data inflation (WPI) and whether we have seasonally adjusted data? The second question is easier to answer: there is no official (or unofficial that I am aware of) measure of seasonally adjusted data in India.

Office of the Economic Adviser, Ministry of Commerce and Industry, provides and maintains the WPI data. I downloaded the monthly WPI data from this site to figure out whether there is seasonality in the data.

Visual inspection of the plot gives no clue about the seasonality of the data. The trend is increase in the WPI throughout year except for 2008 when it ran up from under 220 to over 240 from Jan '08 to Aug '08. The chart clearly shows the impact that base year of 2008 has on y-o-y calculation. Since Feb '09 the data shows the same trend of gradual increase but since the base is increasing at a higher rate the inflation rate is actually decreasing!

Having hit a dead end with the visual method, I tried to see if there was any software available that could do the seasonal adjustment. I found x-12 Arima, which is used and maintained by US Census Bureau and used for official seasonal adjustment for all kinds of data. Moreover, this is also used by NZ and UK governments with some modifications. I tried making modification as identified in the NZ paper but did not get any meaningful differences from the default method. So to get the seasonally adjusted data I used the defaults for the program.

Now that I had adjusted data, calculating annualized inflation based on m-o-m changes was easy. However, using m-o-m made the inflation very volatile. So I decided to smooth it by averaging over a quarter (3-months) e.g. to calculate the inflation for May '09, I calculated m-o-m inflation for Mar '09, Apr '09 and May '09, took the average and multiplied the result by 12.
i.e. Annualized Seasonally Adjusted - 3 month average = [Average (Inflation current month + Inflation previous month + Inflation 2nd previous month)]*12.

The plot of seasonally adjusted data and y-o-y change in unadjusted data is provided below.

The chart clearly shows that seasonally adjusted inflation bottomed in Dec '08 and has been steadily going up since then. Therefore, now its easy to understand why the RBI (India's Central Bank) is not worried about deflation. It would be interesting to see RBI's policy looking at this data and see if they , however I could not find data on RBI's policy rate history.

The annual number, barring a price shock, is likely to remain negative for atleast couple of months. It would be interesting to see how the m-o-m data shapes out in the coming month. I believe it is important to keep an eye on this number. If the m-o-m data does not stabilize and continues in the same trajectory and RBI continues easy monetary policy then next year RBI may well be battling with inflation again.


  1. from where do i get the data that is released every week - sorry but i have just begun to study economics and am looking out for data sources.

  2. As I mentioned in my article go to to get the WPI data