1. Sensitivity of calculations of measures of inflation Peter Stoltze

2. 1.Introduction 2.Data 3.Methods i. Calculation measures of inflation ii. Resampling and jackknife estimation 4.Results 5.Conclusion Outline 2

3.  Inflation is used to describe the development in prices over time, and it can be measured by comparing prices for comparable goods at different points in time  To get an adequate measure, the comparison is based on a subset of relevant goods (a shopping cart)  Statistics Denmark (together with the consulting firm COWI) has compiled T2T (time-to-time) reports for a large number of countries outside the EU area, where the national figures for price development are deemed not fit for purpose… 1. Introduction 3

4.  Albania, Angola, Argentina, Armenia, Azerbaijan, Bangladesh, Barbados, Belarus, Benin, Bolivia, Bosnia and Herzegovina, Botswana, Brazil, Cameroon, Chad, Chile, China, Colombia, Congo, Costa Rica, Croatia, Cuba, Dominican Republic, East Timor, Ecuador, Egypt, El Salvador, Ecuador, Gabon, Georgia, Ghana, Guatemala, Guyana, Honduras, India, Indonesia, Ivory Coast, Jamaica, Jordan, Kazakhstan, Kenya, Kirghizstan, Korea, Kosovo, Laos, Malawi, Malaysia, Mali, Mexico, Micronesia, Montenegro, Mozambique, Namibia, New Caledonia, New Papua Guinea, Nicaragua, Nigeria, Uzbekistan, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Russia, Samoa, Saudi Arabia, Saudi Arabia, Singapore, South Sudan, Sri Lanka, Suriname, Syria, Tajikistan, Taiwan, Chad, Thailand, The Dominican Republic, Togo, Tonga, Trinidad & Tobago, Uganda, Ukraine, Uruguay, Venezuela, Vietnam, Zambia and Zimbabwe 1. Introduction 4

5.  Collection of data was done by actual visiting selected stores  Before this evaluation, the results compiled from the data set from Russia were seen as reliable (low undertainty)  The other three were seen as unreliable (high uncertainty) 2. Data 5 Country T1 [yyyy.mm] t2Inflation Botswana2006.052007.04-3.37 % Malawi2006.052007.041.27 % Russia2005.122006.053.32 % Saudi Arabia2006.052007.0417.04 %

6.  A rather large number of specific items (goods) were defined, each of which can be attributed to one of 57 defined item groups  Typically, prices for several items are collected from each visited shop (especially grocery stores) 2. Data 6 Country No. of prices (sets) No. items No. item groups No. shops Botswana260964332 Malawi3151034737 Russia5111275174 Saudi Arabia223572720

7.  Calculation measures of inflation  Resampling and jackknife estimation 3. Methods 7

8.  The basic calculation of the inflation i is done as  The inflation can be normalized (extrapolated) to cover a period of a certain length (typically 1 year)  The inflation could be calculated for all items using the basic formula, and one could then calculate a simple average, but the set-up here is a bit more complex… 3.1 Calculation measures of inflation 8

9.  First the inflation is calculated at the item level, because a certain item (good) can be sampled multiple times  Then the inflations at the item level are aggregated to the item group level using a geometric mean 3.1 Calculation measures of inflation 9

10.  The combined (or overall) inflation is calculated as a weighted mean at the item group level  However, rules for imputing missing values (see below) makes it difficult to set up a closed expression for the uncertainty of the overall inflation  At the item group level, missing values are imputed using weighted means of related item groups – however, some items groups are just left out of the calculation 3.1 Calculation measures of inflation 10

11. 3.2 Resampling and jackknife estimation 11

12. 3.2 Resampling and jackknife estimation 12

13. 3.2 Resampling and jackknife estimation 13

14. 3.2 Resampling and jackknife estimation 14

15.  A jackknife estimate is calculated from the pseudo inflations using a simple average  Calculating the variance of the jackknife estimate is also straight forward (akin standard error of mean) 3.2 Resampling and jackknife estimation 15

16. 3.2 Resampling and jackknife estimation 16

17.  At the item level the smallest pseudo inflation is calculated at 1,35 % and the largest is 4,61 % while all other are in the range [3.21; 3.89]  The parametric confidence intervals are more narrow than the non-parametric confidence interval 4. Results (Russia) 17 LevelniParametric c.i.Non-parametric c.i.MinMax Single observation5113.317[3.307; 3.326][3.288; 3.355]1.3514.607 Item1273.303[3.267; 3.339][3.197; 3.453]1.3263.737 Item group513.317[3.217; 3.418][2.482; 3.737]1.3264.353 Shop743.302[3.244; 3.359][3.105; 3.716]1.3263.737

18. 4. Results (Russia) 18

19. 4. Results (Russia) 19

20. 4. Results (Saudi Arabia) 20

21. LevelniParametric c.i.Non-parametric c.i.MinMax Botswana Single observation260-3,366[-3,384; -3,347][-3,586; -3,056]-4,094-2,169 Item96-3,348[-3,426; -3,271][-3,842; -2,491]-4,094-0,700 Item group43-3,292[-3,451; -3,132][-3,940; -2,541]-4,094-0,700 Shop32-3,270[-3,496; -3,043][-4,369; -0,700]-4,369-0,700 Malawi Single observation3151,274[1,267; 1,281][1,160; 1,394]0,8941,847 Item1031,276[1,244; 1,308][0,776; 1,712]0,6221,847 Item group471,260[1,197; 1,323][0,622; 1,629]0,4761,728 Shop371,298[1,224; 1,372][0,642; 1,847]0,6421,847 Saudi Arabia Single observation22317,042[16,970; 17,114][16,699; 17,715]12,61822,604 Item5717,062[16,666; 17,458][12,580; 19,819]10,94823,937 Item group2716,892[16,057; 17,727][10,948; 23,937]10,94823,937 Shop2017,129[15,954; 18,303][10,948; 23,937]10,94823,937 4. Results 21

22.  A suggestion to a method to evaluate the sensitivity of measures of inflations based on a composite calculation (including imputation at different levels of aggregation)  The calculated jackknife estimates are valid for scenarios where observations (or groups of observations) are left out one at a time  Other scenarios could be investigated along the same lines, but other techniques are required (e.g. non-exhaustive search using Monte Carlo) 5. Conclusions 22

23. 5. Conclusions 23