Various CPI Aggregation Schemes: Empirical Study of Israeli Data

1. Various CPI Aggregation Schemes: Empirical Study of Israeli Data Yoel Finkel, Victoria Roshal Central Bureau of Statistics, Israel Presented at 10th Meeting of the Ottawa Group on Price Indices - October, 2007

2. CPI – a measure of inflation… for whom? • CPI – average of products or households? Does the average basket, based on population expenditure shares, represent every household in the country? • CPI used for indexation in social agreements: should there be only one, or several group-specific indexes? • If there is one index, how should one weigh the households, in order to fit the framework of social welfare?

3. Possible consequences of the aggregation problem • Misleading conclusions about the growth of inequality from one year to the next (Crawford&Smith, 2002). • Failure to correctly adjust the changes in the cost of living across households. • Distortion of the distribution of income. • Serious fiscal implication for government budgets (Lieu, Chang and Chang, 2004).

4. Research Specifications: • Aim: • to analyze the differences in the inflation rates experienced by different households in Israel • to evaluate the extent of dispersion in inflation rates in the years with different levels of inflation • to explore the differences between annual and monthly inflation • Data: • Monthly CPI indices of goods at the elementary aggregate level (fourth level) of commodity aggregation. • Expenditure shares data from the Household Expenditure Survey (HES) for 2002. • Time period: January 1990 - December 2005.

5. Limitations of the research • The household expenditure shares are fixed for 2002. • It is unlikely that a household would keep its consumption pattern unchanged for 16 years. • In addition, during the years 1990-2005 Israel passed through several periods of economic growth and depressions, which inevitably affected supply and demand. • Asymmetrical changes in prices have probably affected the expenditures (depending on the elasticities) • There is no possibility to measure the exact changes in prices for each household as the sample is designed for the average household or consumer unit. • The results obtained in other countries and periods could differ.

6. Methodology: Household-specific inflation rate price index for item stratum j at time t (b = base period) aggregate expenditure share of goods category j in the base period (base=2002)

7. Methodology: Aggregate Inflation where • Shn is the share of household h’s total expenditures devoted to good n, • Pn is the market price relative for good n, • wh is the weight given to the individual index for household h in computing average.

8. Various aggregation schemes • Plutocratic approach: weigh households according to their share of total expenditure (the present approach). • Democratic approach: weigh households equally. • Social Welfare approach: weigh households according to social preferences over the welfare function (Finkel 2007). Use the properties of the Extended Gini to emphasize different parts of the income/expenditure distribution (Lerman & Yitzhaki 1994, Wodon & Yitzhaki 2002, Yitzhaki 2003).

9. Analysis of Annual Inflation (annual average price indices)

10. Relationship between the Level of Inflation and its Dispersion (standard deviation)

11. Annual Inflation Rates Using Various Weighting Schemes

12. Annual Inflation Rates (percents) 1991-2005, using various weighting schemes

13. Average rate of inflation by group (1991-2005)

14. Number of years when a group experienced higher-than-average or lower-than-average inflation, by group (selected groups only)

15. Number of years when a group experienced higher-than-average or lower-than-average inflation, by group (selected groups only)

16. Annual inflation rates 1991-2005 ( 15 yr. avg.), by various definitions of deciles

17. Sources of heterogeneity: Different Consumption Patterns For total population, lowest and highest expenditure deciles

18. Sources of heterogeneity: Different Consumption Patterns For total population, lowest and highest income deciles

19. Sources of Heterogeneity: Evaluation of the Price Index, by Consumption Group

20. The relationship between the absolute mean inflation rate and the standard deviation, by low and high inflation rates

21. Monthly Inflation Rates by Socio-economic Group • Pensioners: suffered higher-than-average inflation rate for 85% of the periods of high inflation (>1%) • Lowest Expenditure Decile: higher-than-average inflation in 83% of high inflation periods • Non-owners of housing: 75% of the high inflation months. • 10 or less years of schooling: 69%.

22. Summary • In periods of low inflation, there is little difference in inflation rates obtained by different weighting schemes. • During high-inflation years, democratic and “social emphasized” weighting methods produced higher inflation rates. • On a monthly basis, these results are not as straightforward. • The “most suffering” groups from plutocratic weighting are pensioners, renters and those belonging to the lowest expenditure decile (there is some degree of overlap between these groups).

23. Other Conclusions • Aggregation is an important issue when a CPI is used for indexation. • Analysis of inflation according to different weighting schemes can also fall under the category of “quality of indices” and sensitivity analysis. Further Research: • Analysis of price (change) differentials in consumption of socio-economic groups is needed • Formal framework for deriving base period weights for different weighting schemes, suitable for NSI CPI construction (Finkel 2007)