The math behind GDP back series which took away India's best growth year

A day after prime minister Narendra Modi-led government announced a downward revision of gross domestic product (GDP) growth numbers under the United Progressive Alliance (UPA) government by using the new methodology, the finance minister Arun Jaitley and Niti-Aayog vice chairman Rajiv Kumar staunchly defended the findings of the Central Statistics Office (CSO).

In separate responses earlier in the day, Jaitley and Kumar both said that the CSO has used the same methodology for preparing the back-series estimates for the years 2004-05 to 2010-11 that it has been following since it shifted to the new base (2011-12) three years ago.

"The new GDP series was announced in 2015 with 2011-12 as the base year. At that time, they had revised the series from 2012-13 onwards. Since then, all GDP data, whether quarterly or annual, have been based on the new series. This new series is globally more comparable as it takes into account a far greater representation of the Indian economy and is more reflective of the real state of Indian economy. When it was released, it revised the last two years of the UPA government (2012-13 and 2013-14). Curiously, at that time, the revision had made the GDP grow upwards. So, there was an improvement which was shown on the same basis of the last two years. At that time, it was welcomed by the people in the then government. They said, the new GDP series have proven that they did not mismanage the economy," said Jaitley, adding that it was in continuation of the same exercise that the new series have been made applicable from 2004-05 now.

"The series have been revised based on the applicability of the data. The formula remains the same. Based on the same yardstick, the earlier years of UPA has been revised downwards. So you gain in some years, you lose in some. Data is realistic, it is not fictional. So what was welcomed by UPA in 2015 is now criticised in 2018 because it got revised downwards. CSO is a completely credible organisation and it maintains an arm's length distance from the finance ministry," Jaitley elaborated.

Meanwhile, Rajiv Kumar said that the CSO has done "an amazingly technically competent exercise". "Having seen it in a huge depth along with 10 of the top leading statisticians of the country, who came for two round tables, three things have become clear. One, it's just a myth to say that India is decoupled from global economy. We have been impacted, we were impacted (which is the reason for the downward revision). Second, breaching the 8 per cent GDP growth ceiling is not easy. We have to try much harder. We need to take the reforms at the level where it matters. The third one is that we need to invest hugely on modernising our statistical system. This realisation I hope should be reflected in the budget," Kumar said.

The CSO, in its release, also points out that by and large the same methodology was used to arrive at the GDP growth estimates for previous years. However, it said that in certain cases, "owing to the limitations of the availability of data, either splicing method or ratios observed in the estimates in base year 2011-12 have been applied".

Splicing method (OCED definition: In an index number it may become necessary at certain times to make provision for the appearance of new items or the disappearance of items previously in use, e.g. in price index numbers, when commodities go off the market. The method of affecting the change is known as splicing) has been applied for preparing the estimates in construction sector entirely and applied partially in agriculture and allied sectors, gas, trade, repair, hotels and restaurants, real estate, ownership of dwelling and professional services, public administration and defence and other services.

The details of the methodology that was followed after lengthy deliberations with the Advisory Committee on National Accounts Statistics (ACNAS) on the availability of data and the various approaches for estimation of the back-series at the sectoral level are as follows:

Methodology for compiling back-series estimates:

1. Agriculture and allied sectors: For the back-series of crop, livestock, forestry and fisheries sectors; output and input have been recalculated as per the methodology adopted for the 2011-12 series. For most of the items, in constructing back-series at constant prices, the price vectors for 2004-05 have been replaced by 2011-12 price vectors. Production figures have been updated using revised rates and ratios. For the current price estimates, only production has been updated. For forestry subsector, the rates/ratio(s) of 2011-12 series have been used. For certain items namely, repair and maintenance, GVA of Government Irrigation System etc., back-series have been worked out using splicing method.

2. Mining & quarrying: The Mining sector covers fuel minerals, metallic minerals, non-metallic minerals and minor minerals. The back-series estimates for the mining sector have been derived as sum of GVA of NDE, PC, and HH. The NDE segment of the GVA estimates of coal, petroleum & natural gas has been obtained from the annual reports of the NDEs. The PC segment of the GVA estimates of coal and petroleum & natural gas has been estimated using the share of the private sector of the respective minerals in the past years since separate estimation for this segment was not feasible using the MCA-21 database. For other minerals (salt evaporated, other metallic & non-metallic minerals and minor minerals), the estimates of GVA in the new series have been obtained by splicing the old series GVA estimates separately for each category. The GVA estimates have then been adjusted for FISIM. The mineral-wise allocation has been done using the data from IBM for the past years. The constant price estimation procedure for the back-series has been the same as that of the 2011-12 series, i.e. using WPI for Coal and Petroleum & NG and Implicit Price Deflator (IPD) using IBM data for other minerals.

3. Manufacturing: The back-series estimates of GVA for manufacturing have been compiled by summing up the estimates from ASI quasi corporate (i.e. proprietary, partnership, HUF etc.), Private Corporate (PC), Departmental Enterprises (DE), Non-Departmental Enterprises (NDE) and the unincorporated segments, separately for each compilation category. For the ASI-Quasi segment, the compilation category-wise GVA estimates have been computed from the ASI results for each year by taking into account only the non-corporate part of ASI. The estimates of GVA for the DE (including railways) segment have been compiled using splicing method. For the NDE segment, estimates have been computed by analysing the annual reports of the public sector companies using the methodology of the base year 2011-12. The same have been concorded compilation category-wise. Unincorporated segment has been back-casted using ASI pure quasi annual growth rates derived for the years 2010-11 to 2004-05, as followed in the new series. The PC segment has been derived by using the ASI private corporate growth rates (growth rates computed from ASI data of PC segment). The estimates at constant prices have been prepared by deflating compilation category-wise estimates by appropriate WPI

4. Electricity, gas, water supply and remediation (EGWR): The GVA back-series estimates have been compiled using data from General Government (GG), DE, NDE, PC and Households (HH). The estimates of GVA for the GG and DE segments have been back-casted using splicing. For the NDE segment, estimates have been computed by analysing the Annual Reports of the Public Sector Companies using the methodology of the base year 2011-12. The PC segment of the Electricity sector has been estimated using growth rates of the common companies over two consecutive years from CMIE data. For the PC segment of gas and water Supply, the ratio of PC to NDE of base year has been used for all the previous years. Further for PC and HH segments of Remediation and for the HH segment of water supply, splicing method has been adopted. For the Bio-Gas segment, there has been no methodological change in the new series. The constant price estimates for Electricity sector have been obtained using quantum index of Electricity. For the Gas sector, constant prices estimate of Bio-Gas has been compiled using splicing method. For the remaining Gas sector (other than Bio-Gas), quantum index has been used. For Water Supply sector, the GVA estimates at current prices have been deflated using Consumer Price Index (Industrial Workers) (CPI (IW)) to obtain the constant price estimates. For the remediation sector, both CPI (IW) and WPI have been used as deflators for the sewerage and the recycling segments respectively, as was applied in the base year 2011-12.

5. Construction: Back-series estimates of GVA for construction sector at current and constant prices have been estimated by splicing method.

6. Non-financial services sector: For Services Sector, mixed approach i.e. recalculation and splicing of GVA have been used. It has been tried to the extent possible that the same methodology, as that of 2011-12 series is applied to the back-series estimation also. The total GVA has been derived as the sum of GVA of GG, DE, NDE, PC and HH wherever applicable. As mentioned above, wherever data were available, recalculation method has been used. However, the back-series estimation has the following data limitations:

6.1. For preparing PC estimates in the 2004-05 series, either RBI data or NASCOMM or Labour Input was used for the estimation of GVA of various sectors. In the new series, MCA data has been used. As reliable and consistent data from MCA21 database are not available prior to 2011-12, the new base year ratios have been retained in some segments and splicing technique has been used for other segments of these sectors.

6.2. The 2011-12 series uses sector specific CPIs. For example, CPI (Education) is being used for Education industry estimates etc. The 2004-05 series used CPI (AL) and CPI (IW). The industry specific CPI (IW) has been used in back-series of 2011-12 as the sector specific CPIs used in 2011-12 series do not have such sector specific back-series.

6.3. The 2004-05 series used Gross Trading Income (GTI) index for Trade sector whereas the 2011-12 series uses sales tax index for Trade sector. Accordingly, sales tax index has been used in back-series of 2011-12.

6.4. The estimate of PC segment in telecommunication has been extrapolated with the help of minutes of usage in back-series of 2011-12. The indicator "no. of subscribers" was used in 2004-05 series. In the present series of 2011-12, telecommunication estimates at constant prices of private corporate are obtained by deflating with CPI (transport & communication). This is a deviation from current series practice. This has been done owing to non-availability of proper current price estimates of private corporate sector for back-series of 2011-12.

7. Financial services: In financial corporations, the constant price estimates are prepared by volume extrapolation. The volume parameters used in base 2011-12 and the back-series for the years 2004-05 to 2010-11 have been the same. The main deflator, namely, index based on implicit price deflator of non-financial sector (unadjusted for FISIM) has been used in both the current series as well as for the back-series for the years 2004-05 to 2010-11. The methodology followed for preparing current price estimates in base 2011-12 has been followed for preparing the back-series for the years 2004-05 to 2010-11 as well. The two main differences in base 2011-12 have been in computing the GVA of the central bank (Reserve Bank of India) using cost method and the FISIM using the reference rate (RR) method for commercial banks and other financial intermediaries. Further, the methodology for estimating GVA of unorganised financial sector has been revised. Stock exchanges, stock broking companies and asset management companies have been brought under the coverage of financial corporations. These computations, for the current price estimates of back-series 2004-05 to 2010-11 have been done, subject to a few data limitations described hereafter:

7.1. The overall lending rate, deposit rate and reference rate, separately for each year, have been computed using data for each year, released by the RBI for different groups of commercial banks. This data for RRBs and cooperative banks was not available. Therefore, ratio of new FISIM/old FISIM as derived for the commercial banks has been applied on old FISIM of RRBs and cooperative banks to estimate the new FISIM of RRBs and cooperative banks,

7.2. For the private NBFIs, ratio of new FISIM/old FISIM derived for base year 2011-12 has been applied on old FISIM for years 2004-05 to 2010-11 to estimate the new FISIM. This has been adjusted further to take care of the difference in output in base year due to receipt of updated data of private NBFIs for the base year and thereafter.

7.3. Data on stock exchange, stock broking companies, asset management companies (SE+SB+AMC) and regulatory authorities were not available for earlier years. The ratios of GVA for these subsectors to GVA of remaining subsectors (within the financial corporations) have been computed for the years 2011-12 and 2012-13. Average of these ratios has been applied on the estimated GVA of remaining sub-sectors, to arrive at the GVA of SE+SB+AMC and regulatory authorities for the back-series.

8. Public administration and defence: There has been no change in the estimation process for public administration and defence. The difference in the estimates in the new series are due to improved coverage of local bodies and autonomous institutions. For this component, the back-series estimates have been prepared using splicing method.

9. Net taxes: As per SNA 2008, in 2011-12 series, Taxes have been reclassified into Product, Production and Income & Wealth Taxes instead of Direct and Indirect Taxes. Similarly, Subsidies have been reclassified into Product and Production subsidies. As per latest classification, Customs, Excise, Sales tax, Service tax and other indirect taxes like electricity tax, taxes on passengers and goods, taxes on vehicles etc. are part of product taxes. Taxes were reclassified based on the component-wise information available in previous series, to the extent possible. A few components where past data was not separately available, splicing method has been applied to arrive at component-wise back-series estimates of product and production taxes. Current price estimates of production subsidies were first computed by adding production subsidies of NDEs and imputed subsidies of DEs. The total subsidies net of the production subsidies gave the product subsidies for the years 2004-05 to 2011-12 in line with new series. Splicing procedure was then adopted to get the backseries estimates of subsidies in current prices. For constant prices estimates, as in 2011-12 series, volume extrapolation method has been used for product taxes and deflation method has been used for product subsidies. Expenditure Aggregates

10. GFCE: The estimates of Government Final Consumption Expenditure (GFCE) at current prices for the years prior to 2011-12 have been arrived at by splicing and the constant prices estimates have been arrived at by deflating the current prices using appropriate indices.

11. PFCE: The estimates of Private Final Consumption Expenditure (PFCE) for the years prior to 2011-12 both at current and constant price have been arrived at by using splicing technique.

12. Exports & Imports: The estimates of Exports and Imports for the back-series at current prices were taken as published in NAS 2014 and the constant price estimates have been arrived at using splicing.

13. GCF and Savings: In the new series 2011-12, GFCF comprises of four broad categories of assets as per SNA-2008 - (i) Dwellings, Other Buildings & Structures (DOBS) (ii) Machinery & Equipment (ME) (iii) Cultivated Biological Resources (CBR) and (iv) Intellectual Property Products (IPP). In 2011-12 series, for estimation of change in stocks of inventories, the book values of stocks for the corporations have been revalued using suitable WPIs. Expenditure of households on valuables has been included as savings in the form of physical assets of households in the new series. Back-series estimates of GFCF have been compiled using splicing technique as is done for construction assets, which accounts for about 57% of GFCF. Further, Institution-wise splicing was done for compiling back-series estimates of GFCF. The total GFCF is distributed on the basis of share of each asset in total GFCF for the year 2011-12. Similar treatment has been adopted in compilation of back-series estimates of Change in Stocks, Valuables and Savings.