Robert Martin

Division of Price and Index Number Research

FCSM 2021 Research and Policy Conference

November 4, 2021

Democratic Aggregation: Issues and Implications for Consumer Price Indexes

‹#› — U.S. Bureau of Labor Statistics • bls.gov

1

Outline

Introduction

Group Price Index Theory

Methods

Results

Discussion and Conclusion

‹#› — U.S. Bureau of Labor Statistics • bls.gov

Overview

Current Consumer Price Index (CPI) methodology geared to measure inflation from macroeconomic perspective

Prices and expenditure weights for a “representative consumer”

Budget shares matches the “average dollar” of expenditure

Different from inflation experienced by the average household?

Among other potential differences, like consumption vs. payments

Main finding: Aggregation differences are three times larger when using Tornqvist formula than when using modified Laspeyres (Lowe)

‹#› — U.S. Bureau of Labor Statistics • bls.gov

3

Selected Literature

Price index theory: Prais (1958), Pollak (1989), ILO/IMF/OECD/UNECE/Eurostat/World Bank (2004), Ley (2005)

Individual and subgroup heterogeneity: Garner, et. al. (1996), Cage, Garner, and Ruiz-Castillo (2002), McGranahan and Paulson (2005, Chicago Fed IBEX), Hobijn and Lagakos (2005), Hobijn, et. al. (2009), Jaravel (2018, 2021), Kaplan and Shulhofer-Wohl (2017), Cage, et. al. (2018)

Common finding: Plutocratic-Democratic gap tends to be small when using Lowe (a.k.a. modified Laspeyres) formula

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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Group Price Indexes

Standard price index formulas use market-level prices and expenditures (i.e., a “representative consumer”)

Formulas used by BLS

Lowe/modified Laspeyres: For CPI-U, fixed biennial weights

Tornqvist: For Chained CPI-U, updating monthly weights

These implicitly give more weight to households with higher expenditure

Democratic price indexes give equal weight to each household

Building blocks are household-specific price indexes

‹#› — U.S. Bureau of Labor Statistics • bls.gov

Household Price Indexes

Items ; households 

Time: months ; 

For Lowe:  is biennial weight reference period,  is pivot month

Quantities , prices 

Data limitation: assume households face common 

Expenditure shares 

For Lowe: 

For Tornqvist:  

‹#› — U.S. Bureau of Labor Statistics • bls.gov

6

Household Price Indexes (2)

Lowe: 

Tornqvist: ,  

In application,   and  represent elementary CPI for 211 items and 32 geographic areas

Household share of total expenditure

For Plut. Lowe: 

For Plut. Torn: 

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Democratic and Plutocratic Price Indexes
|             | Lowe | Tornqvist |
|-------------|------|-----------|
| Plutocratic |      |           |
| Democratic  |      |           |

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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The Plutocratic Gap

Gaps derive from differences in how price changes are weighted

Lowe Plut. Gap: 

Torn. Plut. Gap: 

 is the coeff. of var. of  across , captures use of arithmetic mean instead of geometric mean across 

Ley (2005): Gap determined by how spending patterns vary by household expenditure level and how they covary with price changes

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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Methods Overview

Using CPI elementary indexes, Consumer Expenditure Survey (CE) for second-stage aggregation weights

Key limitation: same elementary price indexes (211 items) used for each household. Only variation is by 32 geographic areas

CE = two independent surveys: Interview and Diary

For Tornqvist, the democratic average is over the one-month index links, which are then chained together as in C-CPI-U

For Lowe, to better mimic biennial weighting of CPI-U, using only households who completed four interviews 

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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Interview-Diary Matching

Interview households: Records for 3-12 months

Roughly 75% of CPI expenditures: most of Housing, Transportation, Medical Care, Education and Communication

Diary households: Records for 1-2 weeks

Roughly 25% of CPI expenditures: Most of Food and Beverages, Apparel. Significant portion of Recreation and Other Goods

For each Interview-month, select one Diary which has similar demographic characteristics, where similarity is based on predicted expenditures (similar to Hobijn, et. al. 2009)

‹#› — U.S. Bureau of Labor Statistics • bls.gov

Results

‹#› — U.S. Bureau of Labor Statistics • bls.gov

Indexes for the Urban Population
| Index                 | Estimate |
|-----------------------|----------|
| Plutocratic Lowe      | 2.055%   |
| Democratic Lowe       | 2.132%   |
| Difference, Lowe      | -0.077%  |
| Plutocratic Tornqvist | 1.831%   |
| Democratic Tornqvist  | 2.073%   |
| Difference, Tornqvist | -0.242%  |
| Official Indexes      |          |
| CPI-U (Lowe)          | 2.099%   |
| C-CPI-U (Torn.)       | 1.845%   |

Avg. 12 mo. Percent Change

(Dec. 2002-Dec. 2019)

Index Levels (Dec. 2001 = 1.0)

‹#› — U.S. Bureau of Labor Statistics • bls.gov

|         | P. Torn. | D. Torn | Diff    |
|---------|----------|---------|---------|
| 2001-04 | 1.910%   | 2.389%  | -0.479% |
| 2005-08 | 3.016%   | 3.508%  | -0.492% |
| 2009-12 | 1.540%   | 1.568%  | -0.028% |
| 2013-16 | 0.941%   | 0.959%  | -0.018% |
| 2017-19 | 1.679%   | 1.916%  | -0.237% |

Avg. 12 mo. % ch., Urban 

Gap in Tornqvist 12 mo. % ch., Urban 

Tornqvist Aggregation Differences Over Time

Note: Margins of error are preliminary and conditional on elementary item-area indexes.

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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Contributions to Tornqvist Plutocratic Gap

Bars represent over items in the major group

By CPI Major Group (December 12 mo. log-change)

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15

Tornqvist Indexes for Subgroups

Average 12-month Percent Change

*Averages cover Dec. 2000 – Dec. 2019. Quintiles based on total CPI-eligible expenditures of CE Interview households in the index month

**Averages cover Jan. 2005 – Dec. 2019. Quintiles based before-tax income of CE Interview households in the prior year. CE started imputing missing income in 2004.

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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Expenditure Quintiles*

Income Quintiles**

Summary and Conclusions

Equally-weighting household has (on average) three times the impact when using the Tornqvist formula versus the Lowe

Similar results using only Interview expenditures or geo. mean across  

The gap is still small relative to overall dispersion in 

The Tornqvist gap has trended smaller over time, but has ticked up recently

Housing and Transportation are the most important categories in determining the gap

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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Future Research

This is work in progress, so comments are welcome

Ongoing: more practical approximations to democratic index (i.e., an average of indexes by expenditure quintile) 

Ongoing: impact of democratic aggregation on sampling variation

Long-term: missing “within-stratum” heterogeneity (e.g., in prices paid) is likely very important (Jaravel, 2021)

‹#› — U.S. Bureau of Labor Statistics • bls.gov

Thank you!Robert MartinDivision of Price and Index Number ResearchBureau of Labor Statisticsmartin.robert@bls.gov

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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References (1)

Cage, R. A., Garner, T. I., & Ruiz-Castillo, J. (2002). Constructing Household Specific Consumer Price Indexes: An Analysis of Different Techniques and Methods. Washington, DC: Bureau of Labor Statistics. Retrieved from https://www.bls.gov/osmr/research-papers/2002/pdf/ec020030.pdf

Cage, R. A., Klick, J., & Johnson, W. (2018). Population Subgroup Price Indexes: Evidence of Heterogeneity or Measurement Error? Meeting of the Group of Experts on Consumer Price Indexes, United Nations Economic Commission for Europe Geneva, Switzerland, May 7-9, 2018. https://www.unece.org/fileadmin/DAM/stats/documents/ece/ces/ge.22/2018/United_States.pdf.

Garner, T. I., Johnson, D. S., & Kokoski, M. F. (1996). An experimental Consumer Price Index for the poor. Monthly Labor Review, 32-42. Retrieved from https://www.bls.gov/opub/mlr/1996/09/art5full.pdf

Hobijn, B., & Lagakos, D. (2005). Inflation Inequality in the United States. Review of Income and Wealth, 51(4), 581-606.

Hobijn, B., Mayer, K., Stennis, C., & Topa, G. (2009). Household Inflation Experiences in the U.S.: A Comprehensive Approach. Working Paper 2009-19. Federal Reserve Bank of San Francisco.

ILO/IMF/OECD/UNECE/Eurostat/World Bank. (2004). Consumer Price Index Manual: Theory and Practice. (P. Hill, Ed.) Geneva: International Labor Organization.

‹#› — U.S. Bureau of Labor Statistics • bls.gov

References (2)

Jaravel, X. (2018). The Unequal Gains from Product Innovations: Evidence from the U.S. Retail Sector. The Quarterly Journal of Economics, 134.2, 715-783. Retrieved from https://doi.org/10.1093/qje/qjy031

Jaravel, X. (2021). Inflation Inequality: Measurement, Causes, and Policy Implications. The Annual Review of Economics 13.

Ley, E. (2005). Whose Inflation? A characterization of the CPI plutocratic gap. Oxford Economic Papers, 634-646.

Kaplan, G., & Schulhofer-Wohl, S. (2017). Inflation at the household level. Journal of Monetary Economics, 91, 19-38.

McGranahan, L., & Paulson, A. L. (2005). Constructing the Chicago Fed Income Based Economic Index-Consumer Price Index: Inflation Experiences by Demographic Group: 1983-2005, Working Paper 2005-20.

Pollak, R. A. (1989). The Theory of the Cost-of-Living Index. New York, NY: Oxford University Press.

Prais, S. J. (1958). Whose Cost of Living? The Review of Economic Studies, 26, 126-34.

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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