PRICE SEARCH, CONSUMPTION INEQUALITY AND EXPENDITURE INEQUALITY OVER THE LIFE ‐CYCLE

• Author: Bulent Guler,Yavuz Arslan,Temel Taskin
• DOI: http://doi.org/10.1111/iere.12488
• Date: 01 February 2021
• Published date: 01 February 2021

INTERNATIONALECONOMIC REVIEW

Vol. 62, No. 1, February 2021 DOI: 10.1111/iere.12488

PRICE SEARCH, CONSUMPTION INEQUALITY AND EXPENDITURE

INEQUALITY OVER THE LIFE -CYCLE∗

By Yavuz Arslan, Bulent Guler, and Temel Taskin1

Bank for International Settlements, Switzerland; Indiana University, U.S.A.;

World Bank, U.S.A.

We differentiate consumption from expenditure by incorporating price search decision into an otherwise

standard life-cycle model. We f‌irst analytically show that, under very general conditions, poorer households

search more and pay lower prices compared to wealthier ones. As a result, consumption inequality is smaller

than expenditure inequality, and the gap between them increases over the life-cycle. Next, using a plausibly

calibrated model, we f‌ind that life-cycle increase in consumption inequality is about 30% lower than the in-

crease in expenditure inequality. Price search provides an insurance mechanism against income shocks and in-

creases the welfare of a newborn by 3.9%.

1. introduction

Most of the earlier literature that has studied the life-cycle dynamics of consumption

inequality implicitly assumed that consumption and expenditure are equivalent.2On the em-

pirical side, it has been common to use expenditure data to measure consumption. On the

theoretical side, the price of consumption was assumed to be 1. However, there is a growing

literature that documents a signif‌icant dispersion in prices paid for identical goods that implies

a difference between consumption and expenditure.3Our hypothesis is that to the extent that

prices paid covaries with age, wage, and wealth, consumption and expenditure will diverge

over the life-cycle.

∗Manuscript received March 2018; revised August 2020.

1We would like to thank Arpad Abraham, Mark Aguiar, Mark Bils,Yongsung Chang, Fatih Guvenen, TarikKara,

Fatih Karahan, Burhanettin Kuruscu, Cedric Okou, Serdar Ozkan, Fabrizio Perri, seminar participants at the Uni-

versity of Rochester, the European University Institute, the Central Bank of the Republic of Turkey, the Midwest

Macro Meeting in Bloomington, Indiana, the Society for Economic Dynamics Meeting in Istanbul, the Royal Eco-

nomic Society Meeting in London, and the Latin American Meeting of the Econometric Society in Santiago, Chile.

The authors acknowledge the Indiana University Pervasive Technology Institute for providing HPC resources that

have contributed to the research results reported within this article. All errors are our own. The views expressed here

are those of the authors and do not ref‌lect those of the World Bank or the Bank for International Settlements.Please

address correspondence to: Bulent Guler, Indiana University, 100 S. Woodlawn Ave, Bloomington, IN, 47405, USA.

Phone: +1-812-855-7791. E-mail: bguler@iu.edu.

2In this literature, studies usually estimate the life-cycle prof‌ile of inequality, and conclude that it rises around 30

log points over the life-cycle. A partial list of studies in this line of research includes Deaton and Paxson (1994), Blun-

dell and Preston (1998), Gourinchas and Parker (2002), Storesletten et al. (2004), Krueger and Perri (2006), Guvenen

(2007), Blundell et al. (2008), Kaplan and Violante (2010), Heathcote et al. (2014), and Aguiar and Bils (2015).

3Baye et al. (2006) provide a detailed survey of the dispersion in prices paid for identical goods. Aguiar and Hurst

(2007) show that richer people pay higher prices for identical goods in the United States. Also, they report that prices

paid for identical goods change over the life-cycle, which is a result of a change in price search due to a change in the

cost of time. Similar results are also shown by Kaplan and Menzio (2015). Using the U.S. data, Sorensen (2000) re-

ports a signif‌icant dispersion in prices paid for the same medicine. Dahlbay and West (1986) show that there is sub-

stantial price dispersion among automobile insurance companies in Canada. Pratt et al. (1979) document price disper-

sion for several categories of goods. Woodward and Hall (2012) f‌ind that mortgage borrowers loose at least $1,000 in

brokerage fees by visiting too few brokers. Kaplan and Menzio (2016) show that the existence of price search can re-

sult in self-fulf‌illing unemployment f‌luctuations.

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© (2020) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of So-

cial and Economic Research Association

296 arslan, guler, and taskin

In order to quantify the signif‌icance of this price search channel, we use a standard life-

cycle model with incomplete markets and endogenous labor supply. We assume that house-

holds face idiosyncratic wage shocks. However, they can insure themselves against these

shocks through a risk-free asset and f‌lexible labor supply. Different from the standard models,

we also allow households to search for lower prices to mitigate the effects of adverse shocks.

When households search more, they pay less and consume more. However, they enjoy less

leisure due to their time constraint.

First, we analytically show that when labor supply is exogenous or zero, price search is a

decreasing function of wealth. When labor supply is endogenous, price search becomes neg-

atively correlated with wage. We then analyze the effect of price search on expenditure in-

equality and consumption inequality. The model allows us to get a closed-form expression for

the gap between expenditure inequality and consumption inequality. This gap crucially de-

pends on the return to price search technology, wage inequality, and the covariance of con-

sumption and wage, which are both positive and increasing over the life-cycle. This implies

that the gap between expenditure inequality and consumption inequality widens over the

life-cycle.

We calibrate the benchmark model to the U.S. economy to quantify the magnitude of the

difference between consumption and expenditure. Our results show that the increase in the

variance of consumption is 30% lower than the increase in the variance of expenditure over

the life-cycle. The rise in the covariance of wage and consumption over the life-cycle can ex-

plain about 85% of this difference. The rest is due to the rise in the variance of wages.

We show that the rise in the variance of prices and search effort implied by the model is

supported by data. We use A.C. Nielsen data and show that the variance of price paid is small

(compared to the variance of consumption and expenditure) and increases over the life-cycle,

as the model predicts. This data set does not have a perfectly comparable variable for the

search effort. Therefore, we use proxies, such as shopping frequencies, number of different

stores visited, trips per stores, and coupon usage. We show that the variances of all proxies in-

crease over the life-cycle.

Our f‌indings suggest that the link between average income and average consumption

growth is signif‌icantly weaker than the one between income and expenditure (Carroll and

Summers, 1989; Guvenen, 2007). The reason is that households with higher wage growth will

pay increasingly higher prices over their life-cycle. As a result, their expenditure will grow

faster than their consumption. In order to quantify the mechanism, we compare two groups

of households, one with a 1% higher annual wage growth rate than the benchmark economy

and the other with a 1% lower wage growth rate than the benchmark economy over the life-

cycle. We show that the difference between the average consumption differential at the age 65

is 15% lower than the expenditure differential.

In addition to its impact on consumption and expenditure, price search enables consumers

to insure themselves against stochastic income shocks. We follow the formulation of Blundell

et al. (2008) and Kaplan and Violante (2010), and quantify the partial insurance role of price

search by computing the consumption insurance coeff‌icients with respect to transitory and

persistent shocks. The computed insurance coeff‌icient of consumption for persistent shocks

is 29 percentage points higher in the model with price search compared to the one without

price search. The same coeff‌icient is 10 percentage points higher for transitory shocks. As sug-

gested by higher insurance coeff‌icients, price search improves the welfare of the households.

A comparison of the benchmark economy and the one with no price dispersion shows that

the newborn households gain 3.9% in consumption equivalent terms by choosing the bench-

mark economy.

Surprisingly, our results suggest that the availability of price search increases asset holdings

(by 14%). Absent any other mechanisms one would expect that, as price search improves in-

surance, it would reduce the need to hold a large amount of assets. However, price search

modif‌ies the return dynamics of the risk-free bond and transforms it into a more favorable

asset. Intuitively, a household would search more and pay lower prices when he/she receives