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Empirical Economics

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07-08-2023

Heterogeneity in prices and inflation over the life cycle

Author: Toshiaki Shoji

Published in: Empirical Economics | Issue 2/2024

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Abstract

Using 1.7 million consumers’ purchasing records in Japan, this study constructs two types of price indexes at the consumer level. The first measures the relative price level of each consumer in a given time period (i.e., cross-sectional price-level comparison), while the other captures the change in prices between two different time periods for a given consumer (i.e., individual inflation rate). This study shows that these price indexes do not comove over the life cycle. In particular, older consumers who have retired pay higher prices for identical goods than working-age consumers, while facing the lower inflation rate. This difference in inflation rates stems from the fact that retired consumers tend to adjust their shopping baskets. Life-cycle variation in individual inflation rates is consistent with the argument that older consumers tend to increase the shopping frequency and search for low-priced goods.

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International Labor Organization (2004) describes indexation of these payments in more detail.

Argente and Lee (2020) use a similar method and examine inflation inequality across income groups during the Great Recession, while their cost-of-living index is obtained at the group level rather than the consumer level.

I exclude purchasing records for unprocessed food from the analysis, because the quantity information is inaccurate for these products (recording the number of packages rather than the amount).

Consumers have an incentive to obtain a member’s card, because many stores offer coupons when a member’s purchases reach a certain value.

The dataset does not cover other types of stores (e.g., convenience stores or drug stores). As suggested by Abe and Shiotani (2014), switching to these stores may explain part of the price differences across age groups.

In Appendix, Table 5 reports the number of observations by age group.

Based on the same dataset, LaPoint and Sakabe (2020) analyze the consumption response to public pension payments, while Shoji (2020) focuses on large swings in demand for storable goods before and after a consumption tax hike.

These inflation rates are calculated based on the so-called matched sample i.e., the set of goods purchased by a given consumer in both the base period and the current period. See Sect. 4 for formal definitions.

Precisely, Aguiar and Hurst perform some additional normalization to make the mean of this price index one.

As of 2012, the statutory retirement age in Japan was 60 years old, which was raised to 65 in April 2013. Although the dataset does not include each consumer’s employment status, it provides indirect evidence for the impact of retirement on shopping behavior. Specifically, in Appendix, Fig. 6 shows that the fraction of consumers visiting stores weekends only (Saturday and/or Sunday) has a gap between the working-age consumers (aged 20–59) and retired consumers (aged over 60).

Another possible interpretation is that retired consumers may spend much time on home production, rather than shopping.

Precisely, under the CES functional form, the weight is given by the logarithmic mean as used in Feenstra (1994). In this study, I use the Törnqvist weight to facilitate comparison with earlier studies that focus on the matched sample.

More specifically, Kaplan and Schulhofer-Wohl (2017) drop the observations of products purchased only in the base period or current period and calculate traditional price indexes such as Laspeyres, Paasche, and Fischer. The Laspeyres price index is \(\frac{\sum _{j\in I_{t-12}\cap I_{t}}p_{j}(t)q_{j}(t-12)}{\sum _{j\in I_{t-12}\cap I_{t}}p_{j}(t-12)q_{j}(t-12)}\), and other price indexes are obtained similarly. The counterpart in this study is given by Eq. (5), where I use the Törnqvist weight. As suggested by Diewert (1976), both the Fischer and Törnqvist price indexes provide the second-order approximation of the true cost of living.

Note that under the CES functional form, a consumer’s choice set completely corresponds to the set of goods purchased in practice. As noted by Feenstra (1994), in this setting zero consumption of a good means its price being infinite, so that this good is not available to the consumer.

I use alternative values for \(\sigma \) in Fig. 4 and check the robustness of the results.

An additional result presented in Fig. 3 is that inflation rates with shopping basket changes are higher than those without shopping basket changes for all age groups. This means that product-turnover effects (or sometimes called quality effects) generate the upward pressure on prices. This finding is consistent with the result of Abe et al. (2015), but is inconsistent with that of Ueda et al. (2019). Note that product turnover is defined at the store (or a group of stores) level in these studies, while it is defined at the consumer level in this study.

Although Japan introduced quantitative and qualitative easing in April 2013, increases in the inflation rate for food products (excluding unprocessed food) reported in the CPI were limited (from \(-\) 0.4% in January 2013 to 0.8% in December 2013).

There are two possible reasons for why the overall rate of change in the shopping frequency is negative. The first is that macroeconomic conditions changed for this period (2012–2013), so that consumers reduced their shopping frequency across the board. The other reason is that observing the fixed pairs of consumers and stores results in a decline in the measured frequency of shopping trips.

More specifically, in this estimation, I use the frequency of shopping trips as a proxy for shopping time, which may carry measurement error as discussed by Aguiar and Hurst (2007) and Nevo and Wong (2019). In such a case, age can be used as an instrument, based on the assumption that the opportunity cost of time varies over the life cycle and creates different shopping intensity across age groups.

Abe N, Shiotani K (2014) Who faces higher prices? An empirical analysis based on Japanese homescan data. Asian Econ Policy Rev 9:94–115CrossRef

Abe N, Enda T, Inakura N, Tonogi A (2015) Effects of new goods and product turnover on price indexes. RCESR discussion paper series No. DP15-2

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Feenstra RC (1994) New product varieties and the measurement of international prices. Am Econ Rev 84(1):157–177

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Kaplan G, Menzio G (2015) The morphology of price dispersion. Int Econ Rev 56(4):1165–1206CrossRef

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Kuroda H (2014) Toward overcoming deflation. In: Speech at the annual Tokyo conference hosted by the center on Japanese economy and business (CJEB). Columbia Business School

LaPoint C, Sakabe S (2020) Coming in at a trickle: the optimal frequency of public benefit payments. Working Paper

Nevo A, Wong A (2019) The elasticity of substitution between time and market goods: evidence from the great recession. Int Econ Rev 60(1):25–51CrossRef

Shoji T (2020) Liquidity constraints and a surge in storable goods demand: evidence from Japan. Working Paper

Ueda K, Watanabe K, Watanabe T (2019) Product turnover and the cost-of-living index: quality versus fashion effects. Am Econ J Macroecon 11(2):310–347CrossRef

Title: Heterogeneity in prices and inflation over the life cycle
Author: Toshiaki Shoji
Publication date: 07-08-2023
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 2/2024
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-023-02479-7

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