Consumer Choice, Ination, and Welfare�y

Sephorah Manginz r Ayushi Bajajx

November 30, 2020

Abstract

We introduce consumer choice into a search-theoretic model of monetary exchange. In contrast to standard search models featuring bilateral meetings, consumers can meet multiple sellers and choose a seller with whom to trade. Consumer choice is inuenced by random utility shocks that are private infor- mation for consumers. Prices and quantities traded are determined in compet- itive search equilibrium. We nd that consumer choice increases the welfare cost of ination. In our baseline calibration, the welfare cost of 10% ination is more than twice as high with choice: 1.5% of consumption versus 0.6% without choice. At the same time, consumer choice alleviates the ine¢ ciency at the Friedman rule by reducing the dispersion of utility shocks for chosen goods, thus diminishing the extent of private information. In our baseline calibration, the welfare loss at the Friedman rule (compared to the e¢ cient allocation) is only 0.16% of consumption with choice versus 0.45% without choice.

JEL codes: D82, E31, E40, E50, E52

Keywords: Money; Ination; Choice; Directed search; Competitive search

�We are particularly grateful to Guillaume Rocheteau and Randy Wright for especially useful feedback. We also thank Michael Choi, Lucas Herrenbrueck, Janet Jiang, and Mario Silva for useful comments, as well as seminar participants at U.C. Irvine and Simon Fraser University, and conference participants at the Bank of Canada Summer Workshop on Money, Banking, and Payments.

yAuthor names are listed in random order. zCorresponding author. Research School of Economics, The Australian National University, HW

Arndt Building 25A, Kingsley Place, Acton ACT 2601. Email: sephorah.mangin@anu.edu.au. xDepartment of Economics, Monash University. Email: ayushi.bajaj@monash.edu.

1 Introduction

Consumer choice is an important feature of monetary exchange. When consumers

purchase goods, they typically choose from a number of goods that are available

simultaneously from a range of competing sellers. Choice is often idiosyncratic: dif-

ferent consumers might make di¤erent choices when faced with the same range of

goods, and the same consumer might make di¤erent choices at di¤erent points in

time. Discrete choice models with random utility shocks have been used extensively

to study these kinds of choices in the large literature following Anderson, De Palma,

and Thisse (1992), but these models do not feature monetary exchange.

Search-theoretic models have become the standard way of modelling the micro-

foundations of monetary exchange, as surveyed in Lagos, Rocheteau, and Wright

(2017). However, meetings are typically one-on-one (or bilateral) in these models:

each buyer meets at most one seller during a single period of time. While many pa-

pers have incorporated random utility shocks or match-specic preference shocks into

the process of monetary exchange, such as Lagos and Rocheteau (2005), these shocks

typically inuence only the quantities traded and the payments not the choice of

seller because meetings are bilateral. In this way, there is no genuine role for what

we call consumer choice, i.e. buyerschoice of seller.

To show that choice matters for monetary policy, we consider a classic application

of search-theoretic models of money: estimating the welfare cost of ination. While

we might expect that greater choice would increase welfare, the e¤ect of choice on

the welfare cost of ination is not clear. This paper asks the question: how does

consumer choice a¤ect the welfare cost of ination? Our answer is that greater choice

signicantly increases the welfare cost of ination. As a result, economies with greater

choice may be more sensitive to the e¤ects of lower levels of ination.

To provide our answer to this question, we develop a search-theoretic model of

money that features consumer choice. In particular, we build on the framework of

Rocheteau and Wright (2005), hereafter denoted RW, for two reasons. First, it shares

the convenience of the Lagos and Wright (2005) structure, i.e. alternating centralized

and decentralized markets. Second, it features endogenous seller entry, which will

turn out to be a crucial feature in our environment with choice of sellers.

We focus on competitive search equilibrium. Buyers and sellers choose to enter

submarkets in which terms of trade, or contracts, are posted by market makers. After

1

entering a submarket, buyers and sellers commit to trading at the terms posted in

that submarket. Within each submarket, there are search frictions that govern how

buyers and sellers meet. Competitive search is a natural alternative to bargaining

in the environment we consider because buyers can meet multiple sellers within a

single meeting. At the same time, it is a natural benchmark for welfare analysis since

competitive search is often used to decentralize the constrained e¢ cient allocation in

search-theoretic environments, as discussed in Wright, Kircher, Julien, and Guerrieri

(2020). Moreover, since the cost of ination is generally much lower when prices are

determined by competitive search instead of bargaining, our estimates of the welfare

cost of ination are conservative and can be interpreted as lower bounds.

Our model has two main features that are necessary for consumer choice. First,

search frictions within submarkets are modelled using a random meeting technology

that featuresmany-on-one meetings (sometimes calledmultilateral meetings). During

any given period of time, each seller meets exactly one buyer, but a buyer may meet

possibly many sellers. In particular, a buyer can meet either no sellers, one seller, or

more than one sellers, but they can trade with only one seller in each period.

Second, buyersutility from consumption depends on both the quantity of goods

consumed and their (idiosyncratic) seller-specic utility. After a meeting takes place,

the buyer draws an i.i.d. preference or utility shock for each seller they meet and

then chooses to purchase from the seller that maximizes their net utility. Sellers

cannot observe buyersutility shocks; they are private information for the buyer. We

sometimes refer to the realization of a shock as the goods quality, but it is really

perceived quality (or suitability) since it is an idiosyncratic tasteshock. What is

important is that these seller-specic shocks determine each buyers choice of seller.

These two features jointly imply that consumers have the opportunity to choose

which goods to purchase among those o¤ered by sellers. An important consequence

of consumer choice is that the distribution of utility shocks of chosen goods is en-

dogenous and depends on the seller-buyer ratio. As a result, the average quality of a

chosen good and the expected trade surplus (or match surplus) depends directly on

the seller-buyer ratio. A larger number of sellers per buyer means that buyers have

both a greater meeting probability plus greater choice among sellers, which increases

the average quality of the goods that are actually chosen by buyers.

After choosing a seller with whom to trade, buyers choose which quantity of the

good to purchase and make the corresponding payment. We focus on incentive-

2

compatible direct revelation mechanisms that induce buyers to reveal their private

information to their chosen seller. In equilibrium, there is only one active submarket

and sellers o¤er the same non-linear price schedule that species both the quantity

traded and the payment in real dollars for any given realization of the buyers utility

shock. Equilibria may be either full trade (all meetings result in trade) or partial

trade (not all meetings result in trade). Within any meeting, buyers may spend all

of their money, some of their money, or none.

In terms of e¢ ciency, there are two margins: an extensive margin (seller entry)

and an intensive margin (quantity traded). With consumer choice, the extensive

margin has two components since seller entry directly a¤ects both the number of

trades and the expected trade surplus. There may be ine¢ ciencies on both the

intensive and extensive margins. In particular, outside the Friedman rule, there are

various possibilities for ranges of underconsumption and overconsumption relative to

the e¢ cient quantity, and there may be either under-entry or over-entry of sellers. In

general, the Friedman rule does not deliver e¢ ciency along either the extensive or

intensive margin. First, there is underconsumption of all goods. Second, there may be

either under-entry, over-entry, or e¢ cient entry of sellers at the Friedman rule. These

ine¢ ciencies at the Friedman rule are due to the presence of private information.

After presenting our key analytic results, we quantify the e¤ect of consumer choice

on the welfare cost of ination. We calibrate the model to match data from Lucas

and Nicolini (2015) on money demand in the U.S. from 1915-2008. In order to isolate

the e¤ect of consumer choice, we also calibrate an alterna