1. Methodologies for an Industrial Production Index: a study by simulation Daniel Mota Instituto Nacional de Estatística, Portugal www.ine.pt, daniel.mota@ine.pt

2. Objectives... Motivation is assessing methodologies for building up an IPI: technologies and data collection have been greatly facilitated and improved. Main goal is to identify the best method (if there is one) Secondary goals are to investigate which methods promote data reduction and diminished response burden Finally, analyse potential discrepancies due to the use of “lagged” samples

3. Stylised facts In a dynamic sector, with more births than deaths, the sample index will underestimate the true index In a shrinking sector, the sample index will usually overestimate the true index in case the deaths are taken off the sample In a dynamic sector, with births and deaths, but a stable trend of production, the index will normally be consistent with the true index These assertions are independent of the method used to calculate the IPI index

4. Methodological issues Index is of a Laspeyres type (all formulae in the paper) Fixed weights vs variable weights in sample indices: weights in this context should always refer to the base year, then, weights should be fixed within a fixed sample and variable within re-samples However, this is not the end of the story for weights: under stringent circumstances, weights must be fixed. Also, working simultaneously with indices based on the universe and based on samples will lead to the coexistence of different kinds of weights in one type of index (more technical details in the paper) Fixed sample vs “rotating” samples (both approaches were tested) When using “rotating” samples, chaining becomes an issue: two methods to chain indices were tried out – chaining in December and chaining by yearly averages

5. Simulation methodology Data for the universe are generated: 8 sectors with distinct behaviours comprising a total of circa 50000 firms/products for 7 years Quantities were generated by a mild stochastic growth rule: Prices follow an almost AR process, with rho following a normal distribution of mean 1,2 and variance 0,4: Weights are relatively stable for most sectors (there is a clear growth of importance of one sector with a correspondent decrease of importance in another sector – sector 1 goes from 31 to 26% weight while sector 2 increases its importance from 19 to 27%) 2 approaches: immediate access to perfect information vs a real life environment

6. Methods Fixed samples and “rotating” samples Samples chosen either by decreasing turnover (standing for 85, 50 and 35% of total turnover) or by random processes (20% of the universe) If yearly samples, chaining is either done by yearly growth averages or in December in the usual way This leads to 14 distinct methods tested Symbols: 85, 50, 35 and ale (short for random) For fixed samples – f and v stand for fixed and variable weights For “rotating” samples – d and a stand for chaining in December or by yearly averages

7. Methods (table) Fixed sample (constant for 5 years) Rotating sample 85Fixed weightsVariable weightsChaining in December Yearly chaining 50Fixed weightsVariable weightsChaining in December Yearly chaining 35Fixed weightsVariable weightsChaining in December Yearly chaining ale (random)Chaining in December Yearly chaining

8. Results (contemporaneous samples)

11. Results (lagging samples)

14. Results (synthesis) √ mean squared error of indices (contemporaneous sample) 85f50f35f85v50v35v85d50d35dale20d85a50a35aale20a indices3,592,131,562,891,350,911,402,573,420,273,304,795,700,97 yoy rates1,651,321,241,280,920,880,480,891,180,171,141,651,940,40 ratio to best9,547,637,187,415,335,072,775,146,811,006,579,5311,222,32 √ mean squared error of indices (lagging sample) 85f50f35f85v50v35v85d50d35dale20d85a50a35aale20a indices5,074,644,285,054,644,314,112,802,214,813,321,781,094,18 yoy rates1,971,831,721,941,811,711,561,110,911,791,280,820,661,55 ratio to best3,012,802,632,972,762,602,381,691,402,741,961,261,002,37

15. Solutions Universe is usually known at y + ½ and sample for y + 2 is then based on the universe of y (y being the base year) The reference census must be made available sooner; nowadays there are powerful technological tools to help in this respect Calculating ratios of births over deaths may be used to correct the “representativity” of the current sample A possible solution (not yet fully studied in a real-life context) would be to publish “provisional” indices that would be updated with the growth ratio of previous year, combined with the re-sampling mentioned in the previous bullet The problems we set to solve in the beginning are more severe the more dynamic is the industry. In relatively stable environments, the problems are mild and opting for the method described with contemporaneous samples seems safe

16. Solutions (2) More “straightforward” solutions consist of using a bundle of methods e.g. for dynamic sectors (many births, independent of deaths), choose 35a For stable sectors (not many births or deaths), choose 85f For shrinking sectors (many deaths), opt for 35f This solution is dependent on the classification of the behaviour of each sector (which is usually known with a lag, although the behaviour of a sector tends to be somewhat predictable)

17. Conclusion The simulation is based on a big universe, with real-life characteristics and was repeated a number of times – therefore, results presented and corresponding conclusions are robust (to these factors) Lagging samples, in a dynamic world, stand as the biggest problem for statisticians In a dynamic environment, there are no clear best methods but there are some ways to mitigate the problems inherent to that condition In a relatively stable environment, the best method is clearly the one based on yearly samples chained in December and a second best is the same method but with yearly chaining In a rigid environment, a fixed sample is the best method, whatever the sub-method (either turnover or random)