The Perils of Using Seasonally Unadjusted Data
Many observers have used a flawed reading of the recent GDP figures to jump to the unwarranted conclusion that the Indian economy was unaffected by the note ban. While the government reveled at this unexpected positive spin, opponents apparently have been reduced to gnashing their teeth and muttering darkly about statistical skulduggery.
The true situation is a bit different. As we have already reported, seasonal adjustment would have shown that the quarterly growth rate has actually declined substantially in Q3, Seasonal adjustment is a commonly used statistical procedure and it has been considered essential practice for more than 50 years by most government statistical agencies around the world.
In our last post we reported preliminary results from applying a crude moving average based adjustment procedure to GDP growth. In this post we update our results by applying the X12-ARIMA procedure to GDP growth rates, using software provided by Eurostat. This seasonally adjusted data shows that the Q3 decline in GDP growth was sharp, and in line with forecasts made by leading economists.
The Necessity Of Seasonal Adjustment
A lot of macroeconomic aggregate data is seasonal, that is, they vary significantly with the time of the year. For example, we can clearly see this regular seasonal variation in the following chart of privately owned housing starts in the US. Most macro aggregates for the Indian economy, including GDP, are also highly seasonal, as the chart in our last post on this topic showed.
Any analysis of the short term movements of such a series has to take seasonality into account. Since monthly or quarterly changes are driven by both cyclical or one-time events, and also by seasonal variation, the effect of business cycles or one-off events like the note ban can only be studied after the seasonal movement has been eliminated from the data. For instance, the agriculture component of Q3 GDP jumped 70% in Q3. We may think that this means that agriculture did very well, until we find out that Q3 GDP rose 67% in 2015-16 and 74% in 2014-15 and even higher in earlier years. For another example consider government consumption expenditures. They fell 16% in Q3 of 2016-17. However, Q3 government expenditures were actually higher than in previous years when they declined 19%.
The usual way to take care of seasonal variation is a statistical procedure called “seasonal adjustment” that was devised by U.S. economists some 50 years ago. See here for a description. Variants of this X11 procedure and also another ARIMA based procedure are in wide use around the world, and most statistical agencies and central banks publish seasonally adjusted macroeconomic data. For instance, here is the seasonal adjustment procedure followed by the Australian Bureau of Statistics. Indeed, seasonal adjustment has become so standard that the US publishes only seasonally adjusted quarterly GDP.
Why Using Year Over Year Changes Is Not Enough
Unfortunately, seasonal adjustment has still not been adopted by the CSO in India and they only publish unadjusted data. The usual procedure in India is to eliminate seasonality by calculating year over year changes, i.e., changes relative to the month or quarter a year ago. All economic analysis is carried out using YoY changes and most observers seem to be perfectly happy to do so.
The fact that the most sophisticated statistical agencies in the world, like the US Bureau of Economic Analysis, Statistics Canada and Eurostat have spent a lot of resources to find good seasonal adjustment procedures, and do not use YoY changes to eliminate seasonality, should tell us that using YoY changes is not sufficiently and we do need seasonal adjustment. YoY calculations aggregate changes over 12 months or 4 quarters, and smear out the shorter term movement. For instance, if we know just that Q3 GDP has increased 7% from last year’s Q3, we don’t know if it started slow and then accelerated, or if it started strong and then slowed. And when we want to know the short term dynamics, such as whether a recession started last quarter, or how much a sudden currency ban has hurt the economy, then we cannot afford to smear out the monthly and quarterly changes in this way. YoY changes are inadequate there and we need to seasonally adjust the data and then look at monthly or quarterly changes.
Rudrani Bhattacharya, Radhika Pandey, Ila Patnaik, and Ajay Shah, from the National Institute of Public Finance and Policy in Delhi, published a study last year exploring the use of seasonal adjustment for Indian macroeconomic time series. In a blog post about their findings they write
The analysis of macroeconomic data using year-on-year growth rate suffers from serious problems. Each value for the year-on-year growth of a monthly series is the sum of twelve previous month-on-month changes. When we compare June 2015 to June 2014, we are looking back at the entire year and not at June 2015 or May 2015. To know what is happening in May 2015 or June 2015, we need to look at month-on-month changes. However, most of the time, these are obscured by seasonality.
Seasonal adjustment removes the seasonality, permits the computation of point-on-point growth rates, and thus allows us to know what is going on in the economy in the latest data. As an example, Bhattacharya et. al., 2008, show how our understanding of inflation in India is improved by using seasonally adjusted data, and how this could have improved the conduct of monetary policy.
The NIPFP researchers applied a seasonal adjustment procedure from the commercial econometric software Eviews to four series: industrial production, exports, consumer prices and wholesale prices and found that this improved the performance of these data. Their study is also an excellent introduction to the details of seasonal adjustment procedures.
The Decline in Seasonally Adjusted 2016-17 Q3 GDP
In this section we report the result of applying the X12-ARIMA seasonal adjustment procedure to quarterly GDP growth rates of Indian GDP using the DEMETRA+ free software provided by Eurostat. Since the current version of GDP has data only going back to 2011-12, we have extended the series backward to 2004-05 by using the data from the earlier series.
The chart from the seasonal adjustment procedure is shown below. In the top panel, the black line is the original series, the blue line is the seasonally adjusted series and the red line is the trend component. The section at the right is the ARIMA forecast of the original, adjusted and trend series. The bottom panel shows the seasonal (blue) and irregular (purple) components of the series.
The table below the annualised growth rates of various components of quarterly GDP growth during the past four quarters. The first column is the original unadjusted series, the second is the adjusted series, the next three are the decomposition into trend, seasonal and irregular components. The last four rows are from the ARIMA forecast. This forecast suggests a four quarter growth of about 5.5% starting in Q3 2016-17.
|Q4 2016-17 (f)||23.2%||6.9%||6.8%||15.6%|
|Q1 2017-18 (f)||-12.0%||7.2%||7.2%||-18.2%|
|Q2 2017-18 (f)||5.7%||6.2%||5.9%||-0.5%|
|Q3 2017-18 (f)||8.7%||3.3%||3.7%||5.2%|
The adjusted data shows that growth was high in Q4 of 2015-16, and held up in Q1 and Q2 of 2016-17, but fell sharply in Q3. The average annualised growth during the Q4, Q1 and Q2 quarters was about 7.7%, but fell to only 1.7% in Q3. The decline in quarterly (not annualized) growth was about 2.5%, close to our estimate for first round losses from the note ban. Jean Drèze’s comparison of the note ban to the shooting at the tyres of a car running at high speed seems entirely apt.