Application of Regression Analyses to calculate Wholesale Price Index (WPI) – A case study
Statswork, a Unit of Guires Ltd., has worked with Voltas India’s premier air-conditioning company and a leading provider of engineering and back-up services. The Domestic Projects Group of Voltas contributes to nation-building through the execution of engineering projects for industry and infrastructure.
The Challenges
Voltas has approached for revalidation/validation of the data given by their client especially to validate their linking factor method in this case, the intercept and the slope value and the assumption of keeping April 2012 as constant. A general suggestion was to use Price indices of 2004-05 which was in effect till Mar.17. The New series 2011-12 came into effect from 1st April 2017. In order to maintain continuity in the time series data of the value of output, it is imperative to provide a linking factor, so that the new series, when released, may be compared with the outgoing one. The ministry of economic adviser recommends using a linking factor such that they are comparable. However, our client desires to use the Data of Price Indices of 2011-12 series from April 12 to March 2017 and keeping the intercept point as constant goes to refix the base indices using the formula of Y = a+ bX +€
The Voltas client has used three different methods to convert the base year 2004-05 to 2011-12. One is the ratio method and another one the client has used the Data of Price Indices of 2011-12 series from April 12 to March 2017 and keeping the intercept point as constant and refixed the base indices using the formula of The client has used slopthe e and intercept along with time to forecast the data 2004-05 using 2011-12 data. For analysing the time series data it ,must be emphaized that the past can effect the future, but not vice versa (Ostrom, 1990’ Velicer & Fava, 2003; Yanovitzky & VanLear, 2008). Therefore back-forcasting may not be the right method to chose for the objective being proposed.
Our Strategy
We have proposed complete revamping of the analyses based on the challenges. For the revalidation of statistical analyses, rather than using client data, the recent monthly (secondary) data were downloaded from the Office of the Economic Advisor site (2018). The Products chosen were Aluminium, Steel, Copper and Mineral Oil. The monthly data was available for both the old and new series. For the old series with base 2004-05, data were available from January 01 2005 to December 2012. However, the new series of WPI with base 2011-12 has however been provided from January 2013 to March 2017. Several considerations have to be addressed prior to the actual statistical analysis. They relate to the restriction that is imposed by the type of study, the number of samples necessary, characteristics of the data, and to the assumptions and methods of regression analysis. Based on the same regression method, we have rerun the analyses to predict the future using time series regression analyses method after considering multicollinearity.
Our Outcome and Impact
The base year of All-India WPI has been revised from 2004-05 to 2011-12 on 12 May 2017 to align it with the base year of other macroeconomic indicators like the Gross Domestic Product (GDP) and Index of Industrial Production (IIP). The revision entails not just shifting the base year to 2011-12 from 2004-05, but also changing the basket of commodities and assigning new weights to the commodities. Wholesale price index calculated with the 2011-12 base year does not include taxes in order to remove the impact of fiscal policy. This also brings the present WPI series closer to Producer Price Index, as is practised globally. Given that there are huge differences in the methodology, in order to compare the old with the new base series, the old series needs to be adjusted by some form of correction.
There are three commonly used methods for linking new series with old one. They are a) Arithmetic conversion method, b) Ratio method and c) Regression method
Arithmetic conversion method:In the arithmetic linking method the relationship between the indices in the old series (y) and those in the new series (x) us assumed to be linear =cx , where is the conversion factor given by y.
c=x, y and x being average values of the indices in the two series for the year chosen as the base period (12 months) of the new series (X=100)
Ratio method: The Month-wise ratio of new indices and old indices are worked out first, and then the average of ratios is taken as linking factors.
Regression method: The relationship is based on y=a+bx,
Where a and b would be so estimated that the sum of squares of deviations of the actual values of from the estimated values is minimum.
The linking factor derived from these three different formulae may vary and provide different estimates. In view of the conceptual and methodological difference between the 2004-05 and 2011-12 series, the estimate of a linking factor will vary depending on the type of method used. Therefore, the ministry of economic adviser recommends users free to choose any method as may be considered appropriate by them.
In the past, in order to maintain continuity in the time series data on the wholesale price index, the linking factor currently used by the government is geometric mean rather than arithmetic mean user earlier (the base year 2004-05 series). This is as per international best practice and similar to the practice adopted for the CPI. Data available for the overlapping period with the old base and new base indicate that the WPI inflation as per the new base is consistently lower than the same as per the old base. Several reasons are responsible for this outcome. The geometric mean itself has significantly moderated WPI inflation, besides other factors such as a change in the composition of the basket, weighting diagram, and so on. Moderation of WPI as per revised base has pushed up real GDP/GVA considerably during recent years.
Lessons Learned
Undertaking this work with Voltas allowed us to translate what we know about wholesale price index and regression into the context of pricing healthcare engineering projects. Here are a few suggestions for companies interested in using regression analyses to calculate the price index.
- Regression Analysis cannot be used to reflect the true level of price indices, and as such, they have to necessarily use the linking factor given by the ministry or the arithmetic conversion or weighted average.
- Bias or errors in the price index mainly due to use of imperfect indexing formula, change in the wholesale landscape, inappropriate quality adjustment, over recognition of quality change, failure to recognize quality change or new goods, or variation in existing goods, failure to include environmental improvements and the value of business services, poor representation of commodities,
- Secondly, the assumption of changes in the dependent variable based on a unit change in independent variables cannot be the common criterion and especially in this case since there are a variety of factors which go to decide the price indices released by the ministry.
- Although both regressors seek to explain the same dependent variable, they are neither measured nor can they be converted to, meaningfully common units of measurement both conceptually, methodologically and statistically. Especially, when there is a changing in the basket of commodities, increase no. of price quotations, 17 vegetables rather than 11, collect prices from more centres, to get better estimates. assigning new weights to the commodities does not include taxes in order to remove the impact of fiscal policy and many more changes between new and old series. This is precisely the point: Only when explanatory variables are on meaningfully common units of measurement is there a chance of comparison. If there is no common unit of measurement, there is no chance of meaningful comparison.
- Check what’s been proposed already. In this case, the Ministry has recommended using linking factor proposed by them. Especially item in the revised WPI is based on the net traded value of the item in the base year 2011-12. Secondly, item-level indices are being compiled based on statistically robust geometric mean as compared to Arithmetic mean used in the WPI 2004-05 series. However, it is extremely difficult to obtain the data in a timely fashion. A possible alternative is to apply the geometric mean method to the index calculation. As explained above, if it is assumed that expenditure shares do not change with relative price changes (i.e., the elasticity of substitution equals one), then the geometric mean index is equal to the theoretical price index. If the substitution effect is relatively small (i.e., the elasticity of substitution is smaller than one), the index will be biased downward. Taking these factors into account, the WPI using the geometric mean formula (WPI-UGM) applies the geometric mean method only at the lower level of aggregation–from “sample item” to “item class”–the level at which substitution between commodities seems more likely to occur. At the higher level of aggregation–from “item class” to “all items”–the arithmetic mean of the Laspeyres method is retained. This approach is based on the presumption that quantity changes are influenced not by relative prices of goods with little relevance to each other, but by relative prices of goods whose attributes are similar. For example, demand for instant coffee is not affected by changes in the relative price of passenger cars but is likely to be affected to some extent by changes in the relative price of regular coffee. Of course, the above approach is not applicable to all cases, since technological advances and other factors can trigger substitution even between commodity groups. Judging from the historical data, however, indexes partially adopting the geometric mean show less bias while indexes applying the geometric mean at all aggregation levels display a downward bias. Therefore, the newly published WPI presumably contains less downward bias than would have been the case if the geometric mean method had been applied at all aggregation levels.
The report is prepared by a Statswork R&D senior researcher who’s suitably qualified and approved by a director of research who has knowledge about economic indicators, especially wholesale pricing.
