Simultaneous or Sequential? Search Strategies in the U.S. Auto Insurance Industry

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Simultaneous or Sequential? Search Strategies in the U.S.

Auto Insurance Industry

Elisabeth Honka, Pradeep Chintagunta

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Elisabeth Honka, Pradeep Chintagunta (2017) Simultaneous or Sequential? Search Strategies in the U.S. Auto Insurance

Industry. Marketing Science 36(1):21-42. https://doi.org/10.1287/mksc.2016.0995

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MARKETING SCIENCE

Vol. 36, No. 1, January–February 2017, pp. 21–42

http://pubsonline.informs.org/journal/mksc/ ISSN 0732-2399 (print), ISSN 1526-548X (online)

Simultaneous or Sequential? Search Strategies in the

U.S. Auto Insurance Industry

Elisabeth Honka,

Pradeep Chintagunta

University of California Los Angeles, Los Angeles, California 90024;

Booth School of Business, University of Chicago,

Chicago, Illinois 60637

Contact:

[email protected] (EH); [email protected] (PC)

Received: April 29, 2014

Accepted: February 15, 2016

Published Online in Articles in Advance:

August 1, 2016

https://doi.org/10.1287/mksc.2016.0995

Abstract. We study the identiﬁcation of the search method consumers use when resolving

uncertainty in the prices of alternatives. We show that the search method—simultaneous

or sequential—is identiﬁed with data on consumers’ consideration sets (but not the

sequence of searches), prices for the considered alternatives and marketwide price dis-

tributions. We show that identiﬁcation comes from diﬀerences in the patterns of actual

prices in consumers’ consideration sets across search methods. We also provide a new

estimation approach for the sequential search model that uses such data. Using data on

consumer shopping behavior in the U.S. auto insurance industry that contain information

on consideration sets and choices, we ﬁnd that the pattern of actual prices in consumers’

consideration sets is consistent with consumers searching simultaneously. Via counterfac-

tuals we show that the consideration set and purchase market shares of the largest insur-

ance companies are overpredicted under the incorrect assumption of sequential search.

As the search method aﬀects consumers’ consideration sets, which in turn inﬂuence brand

choices, understanding the nature of consumer search and its implications for considera-

tion and choice is important from a managerial perspective.

History:

Russell Winer served as the senior editor and Chakravarthi Narasimhan served as associate

editor for this article.

Supplemental Material:

Data and the online appendix are available at https://doi.org/10.1287/

mksc.2016.0995.

Keywords:

consumer search

•

simultaneous search

•

sequential search

•

auto insurance industry

1. Introduction

Understanding the formation of consideration sets and

their subsequent implications for consumers’ prod-

uct choices has long been an area of interest to mar-

keters (e.g., Hauser and Wernerfelt 1990). Accordingly,

researchers have tried to understand how these sets

are formed (Hauser and Wernerfelt 1990) or have tried

to account for them when studying choice behavior

(Siddarth et al. 1995, Chiang et al. 1999, Mehta et al.

2003, Seiler 2013). In the latter case, even in the absence

of data on consideration sets, researchers have tried

to incorporate the notion of consideration sets via

functional form assumptions on consideration set and

choice probabilities. Explicitly accounting for the role

of consideration sets in consumers’ decision-making is

important from the perspective of correctly measuring

consumers’ brand preferences and their sensitivities

to marketing activities, as failure to do so could lead

to incorrect inferences regarding these market funda-

mentals. At the same time, research in economics has

shown that the process by which a consumer arrives

at his consideration set also has implications for these

parameters and consequently for ﬁrms operating in the

market.

The theoretical underpinnings of consideration set

formation are in the models of search.

A consumer

who engages in search is uncertain about some di-

mension(s) of the product or service, say, price, and

resolves this uncertainty by incurring a search cost.

In the search process, the consumer trades oﬀ the costs

incurred and beneﬁts accrued from the undertaking

to arrive at a consideration set for which he has com-

plete information. At this stage, the consumer is back

to the familiar choice situation of complete information

that has been extensively studied in the marketing lit-

erature (e.g., the brand choice literature using scanner

panel data). If a consumer incurs a marginal cost for

each product or service searched, then the number of

options the consumer ends up considering before mak-

ing a choice critically depends on the search strategy

the consumer uses.

In this paper, we look at situations in which con-

sumers are uncertain about price (but not the other

attributes of the product) and engage in costly search

to resolve this price uncertainty. We study two

search methods, namely, simultaneous and sequen-

tial search. Under a simultaneous search strategy, the

consumer samples a ﬁxed number of alternatives and

purchases the alternative with the lowest price (or

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

highest utility) in this set. The set of alternatives

searched is obtained by looking at the subset for which

the expected maximum utility net of search costs is

the highest among all possible subsets. A limitation

of the simultaneous search strategy is that it does not

take into account new information that the consumer

might obtain during the search process. So if the con-

sumer observes a very low price (or very high util-

ity) for an alternative early in the search process, the

beneﬁt from an additional search may be below the

marginal cost of that search. In a sequential search

strategy, on the other hand, the number of alternatives

searched is not ﬁxed, but is a random variable that

depends on the outcome of the search; this allows a

consumer to economize on information costs. In this

case, the consumer weighs the expected beneﬁts and

costs of gathering additional price information after

each new quote is obtained. If an acceptable price is

obtained early on, the expected gains from additional

searches are small and there is no need to pay the cost

of additional searches (see Baye et al. 2006).

Since in most instances researchers only observe

variation in prices or purchase outcomes, it is not pos-

sible to identify the search method with just these

data. Previous empirical research has circumvented

this challenge by explicitly assuming the type of search

that consumers engage in. For example, Mehta et al.

(2003), Pires (2015), and Muir et al. (2013) assume

that consumers search simultaneously, while Dahlby

and West (1986), Kim et al. (2010), and Chen and

Yao (2016) assume that consumers search sequen-

tially. In this paper, we focus on the case where con-

sumers engage in price search and the researcher

observes each consumer’s consideration set (but not

the sequence of searches), besides purchase outcomes,

prices, price distributions, and other characteristics.

We show that, under certain assumptions, the search

method is indeed identiﬁed by the price patterns in

consumers’ observed consideration sets. Diﬀerences in

price patterns emerge because in simultaneous search

consumers only use information on the expected

prices to decide which and how many companies

to search, whereas in sequential search consumers

continue searching and consider more alternatives

only when they receive high price draws for the ini-

tially considered alternatives. Our identiﬁcation strat-

egy holds for a broad range of settings that we discuss

in detail in Section 3.2.

Next, we examine the consequences of imposing an

incorrect search method assumption on the estimated

consumer preference and search cost parameters when

researchers have access to the above data. To accom-

plish this, we ﬁrst need an estimation approach for

the sequential search model where the researcher

has access to individual-level data on consideration

sets, purchases, and other characteristics, but not the

sequence of searches. We avoid having to enumer-

ate all possible search sequences by placing a small

set of restrictions on consumers’ utilities and reser-

vation utilities. These restrictions are derived from

Weitzman’s (1979) selection, stopping, and choice rules

and the insight that, in addition to Weitzman’s (1979)

rules, it must have been optimal for the consumer

not to stop searching and purchase earlier. Similar to

the simultaneous search model for which we apply

a simulated maximum likelihood estimation (SMLE)

approach suggested by Honka (2014), we propose an

SMLE-based approach for the sequential search model.

Using extensive simulations we are able to show that

incorrect assumptions on the search method could lead

to diﬀerent consideration sets and biased estimates of

preference parameters and search costs.

We provide an empirical application of our search

method identiﬁcation strategy and new sequential

search estimation approach in the context of the

U.S. auto insurance industry. Using data on con-

sumers’ consideration sets, purchases, prices, and

other characteristics, we ﬁrst ask: do households search

simultaneously or sequentially when shopping for

auto insurance price quotes? Since consumers in our

sample have been insured previously and coverage

levels tend not to change much, assuming that con-

sumers engage in price search is a reasonable assump-

tion in this context. We look for model-free evidence

of a search method taking the auto insurance industry-

speciﬁc practice of sending customers a renewal oﬀer

into account and then estimate the model parameters

under the assumptions of simultaneous and sequential

search. We ﬁnd both the model-free evidence and the

estimates to provide support for simultaneous search.

Our estimated search cost is $42. We then study via

counterfactuals how elasticities and market shares are

inﬂuenced by an incorrect assumption on the search

method. We ﬁnd that consideration set and purchase

market shares of the largest four insurance companies

are overpredicted under the incorrect assumption of

sequential search. We then assess the robustness of our

results to the presence of unobserved heterogeneity in

the search method and to assumptions required by our

estimation methods.

The main contributions of this paper are as follows.

First, we show both analytically and in simulations

that the search method consumers use is identiﬁed

by the price patterns in consumers’ consideration sets

for a very broad range of settings. Second, we pro-

vide a comparison of the consequences of assuming

simultaneous versus sequential search strategies on

the parameter estimates in contexts where the only

data available to researchers besides typically avail-

able choice data are information on consumers’ con-

sideration set compositions. These kinds of data are

becoming more widely available across a variety of

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

service businesses as well as from surveys conducted

by ﬁrms such as J.D. Power for a variety of categories

(e.g., automobile purchases, hotels, and retail banking).

Third, in providing such a comparison, we need to be

able to estimate model parameters under both search

method assumptions for these kinds of data. While

Honka (2014) provides an approach for simultaneous

search that we adopt here, we propose an estimation

approach under the sequential search assumption.

Finally, we quantify the eﬀects of assuming the incor-

rect search method on quantities that are typically of

interest to researchers such as elasticities and market

shares.

In the next section, we discuss the relevant litera-

ture. In Section 3, we introduce our model and dis-

cuss search method identiﬁcation. In Section 4, we

describe our estimation approaches and summarize

results from Monte Carlo studies. In Section 5, we

discuss our empirical application, and in Section 6,

we study a counterfactual. In Section 7, we check the

robustness of our results. We close our paper by dis-

cussing its limitations and future research opportuni-

ties and ﬁnally conclude.

2. Relevant Literature

The topic of consideration sets has seen much interest

in the marketing literature as it sits at the intersection

of economics (starting with the work of Stigler 1961,

who looks at the costs and beneﬁts of gathering infor-

mation on brands) and psychology (e.g., Miller 1956

notes the cognitive challenges of processing informa-

tion on all of the brands). In line with this basic idea,

several studies in marketing have approached the area

by looking at the costs and beneﬁts associated with

gathering information on brands (e.g., Ratchford 1980,

Shugan 1980, Hauser and Wernerfelt 1990, Roberts and

Lattin 1991, Mehta et al. 2003, etc.). Many aspects of

consideration sets have been investigated in the litera-

ture, including the beneﬁts to the prediction of choice

(e.g., Siddarth et al. 1995, Andrews and Srinivasan

1995, Bronnenberg and Vanhonacker 1996), greater

diagnostic insight into the choice process (e.g., Gensch

and Sooﬁ 1995), and understanding the antecedents

of consideration (DeSarbo and Jedidi 1995, Mitra and

Lynch 1996, DeSarbo et al. 1996). Roberts and Lattin

(1997), surveying the marketing literature on consid-

eration sets, highlight several potential areas of future

research, including understanding the dynamics of

consideration, similarity and diﬀerences in alternatives

included in the set, and other behavioral dimensions

of this phenomenon. Importantly, the authors also note

insightfully that since authors of several of the stud-

ies in the literature use only data on consumers’ ﬁnal

choices, i.e., “take no explicit measures of considera-

tion, they cannot address whether the consideration

stage of their model corresponds to a cognitive stage of

consideration in the consumer’s decision process, or if

it is just a statistical artifact of the data” (Roberts and

Lattin 1997, p. 407). In this paper, we try to understand

consumers’ consideration and choice by looking at data

from both of these stages in the choice process. Specif-

ically, using the literature from economics on search as

the underpinning of our empirical analysis, we investi-

gate the identiﬁcation of the search method as well as

the estimation of simultaneous and sequential models

of search behavior.

Our paper is embedded in the literature on con-

sumer search. As this literature is extensive, we focus

only on recent eﬀorts to structurally estimate search

models or to identify the search method from data.

De los Santos et al. (2012) show that with data on

purchases, consideration sets, and the sequence of

searches, the search method consumers use is identi-

ﬁed for both homogeneous and diﬀerentiated goods.

In this paper, we focus on the situation where the

researcher observes only consideration sets and pur-

chases, but not the sequence of searches, i.e., the re-

searcher has less information, and show that even

in this case the search method is identiﬁed. Hong

and Shum (2006) develop methodologies to estimate

search costs under both simultaneous and sequential

search when only prices are observed. In this paper,

we are able to relax several of Hong and Shum’s

(2006) assumptions: For example, we allow goods to be

diﬀerentiated and price distributions to be company-

speciﬁc. Similar to Hong and Shum (2006), we are able

to compare search costs under the two assumptions on

search strategies. In a follow-up paper to Hong and

Shum (2006), Chen et al. (2007) develop nonparametric

likelihood ratio model selection tests that allow them to

test between simultaneous and sequential search mod-

els. Chen et al. (2007) do not ﬁnd signiﬁcant diﬀerences

between the simultaneous and sequential search mod-

els using the usual signiﬁcance levels in their empirical

application. Finally, this paper is also related to Honka

(2014). She quantiﬁes search and switching costs for

the U.S. auto insurance industry using the same data

we do in this paper. The simultaneous search model

presented here is similar to the one Honka (2014) uses.

3. Model and Search Method Identiﬁcation

3.1. Model

We present a general diﬀerentiated goods price search

model: Consumers know the distribution(s) of prices

in the market, but have to engage in costly search to

learn the speciﬁc price a company is going to charge

them. Given their search sets, consumers maximize

the utility of the purchased option. As standard in

the price search literature (see also Hong and Shum

2006, De los Santos et al. 2012, Honka 2014), we make

the following set of assumptions:

(a) prices are the

only source of uncertainty for the consumer that he

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

resolves through search; (b) consumers know the dis-

tribution of prices and have rational expectations for

these prices; (c) price draws are independent across

companies; (d) there is no learning about the price dis-

tribution from observing other variables (e.g., adver-

tising); (e) (search costs are suﬃciently low so that) all

consumers search at least once; and (f) consumers have

nonzero search costs. Furthermore, our model allows

for observed and unobserved heterogeneity in prefer-

ences and search costs.

More speciﬁcally, there are N consumers, indexed by

i  1, . . . , N, who purchase one of J brands, indexed by

j  1, . . . , J. Consumer i

s indirect utility for company j

is given by

 α

+ βp

+ X

γ + 

, (1)

where 

are independently and identically distributed

(i.i.d.) and observed by the consumer but not by

the researcher, α

are brand intercepts, and p

are

prices, which follow some well-deﬁned distribution

with mean µ

Without loss of generality, we assume

that β < 0. The term X

may contain other variables

that inﬂuence consumer utility. These variables can

be consumer-speciﬁc (e.g., demographics), company-

speciﬁc (e.g., advertising spending), or both. The

parameters to be estimated are α

, β, and γ.

3.1.1. Simultaneous Search. To decide on the set of

companies S

to obtain prices for, the consumer calcu-

lates the net beneﬁt of all possible search sets in terms

of their size and composition. A consumer’s net beneﬁt

of a searched set Γ

is given by the expected maximum

utility among the searched brands minus the cost of

 E

max

j∈S

− k · c

. (2)

Once a consumer has formed his consideration set and

learned the prices, all price uncertainty is resolved for

this set. Both the consumer and the researcher observe

prices. The consumer then picks the company with the

highest utility among the searched companies, i.e.,

m  arg max

j∈S

, (3)

where u

now includes the quoted prices for con-

sumer i by company j.

3.1.2. Sequential Search. We present a sequential

search model with recall. Weitzman (1979) showed that

it is optimal for a consumer to rank all companies

according to their reservation utilities in decreasing

order when deciding on the search sequence (selec-

tion rule). Reservation utility r

is the utility that

makes a consumer indiﬀerent between searching and

not searching



∫

∞

− r

) f (u

) du

. (4)

A consumer stops searching when the maximum util-

ity among the searched companies is larger than the

maximum reservation utility among the nonsearched

companies (stopping rule), i.e.,

max

j∈S

> max

. (5)

Finally, the choice rule states that the consumer

picks the company with the largest utility among the

searched ones

m  arg max

j∈S

. (6)

Thus, after receiving each price draw, the consumer

decides to either continue searching or to stop search-

ing and purchase from the set of searched compa-

nies. Note that, in contrast to the simultaneous search

model, the consideration and purchase stages are not

separate.

3.2. Search Method Identiﬁcation

We ﬁrst discuss the price patterns we would observe

under simultaneous and sequential search and then

describe circumstances under which these patterns are

distinct and those under which they are not; the latter

provides conditions under which the search method is

not identiﬁed.

We start out by discussing the data pattern that

characterizes the simultaneous search method. Recall

that prices follow some (potentially company-speciﬁc

and/or consumer-speciﬁc) distribution(s). Let usdeﬁne

Pr(p < µ

)  λ, i.e., the probability that a price draw

is below the expected price is λ. Furthermore, we

deﬁne event X  1 as a below-price-expectation price

draw and X  0 as an above-price-expectation price

draw. Recall that under simultaneous search the search

rule says that the consumer precommits to a search

set S

consisting of k

companies. Then we can calcu-

late the expected proportion of below-price-expectation

prices in a consumer’s consideration set of size k



m1





m1

E[X

] 

λk

 λ.

Thus, we expect λ percent of the price draws in con-

sumers’ consideration sets to be below and 1 − λ per-

cent to be above the expected price(s). The crucial

ingredients for identiﬁcation are that the researcher

observes the means of the price distributions µ

, the

actual prices in consumers’ consideration sets p

, and

the probability of a price draw being below its mean λ.

We now turn to sequential search and the data pat-

tern that is characteristic for this search method. We

present here the proof for diﬀerentiated goods with

consumer- and company-speciﬁc search costs and refer

the reader to Online Appendix B for detailed analyt-

ical proofs for both homogeneous and diﬀerentiated

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

goods. Recall that consumers have a utility function

as described in Equation (1), with β < 0 and 

∼ iid.

Consumers have search costs c

> 0 and make k

searches. The probability of getting a below-price-

expectation price draw is λ, i.e., P(p < µ

)  λ. Given

the assumptions for the price distributions, consumers’

utility also follows some well-deﬁned distribution with

mean µ

 α

+ βµ

+ X

γ + 

. Furthermore, since

P(p < µ

)  λ, it must be that P(u > µ

)  λ, i.e., a

below-price-expectation price draw always results in

an above-mean level of utility.

Using Weitzman’s (1979) selection rule, we know

that consumers order all alternatives in a decreasing

order of their reservation utilities r

. Consumers ﬁrst

search the alternative with the highest reservation util-

ity, then the alternative with the second highest reser-

vation utility, etc. To express the ranking according

to the reservation utilities r

, let us deﬁne r

i, t1

the company with the highest reservation utility for

consumer i, r

i, t2

as the company with the second

highest reservation utility for consumer i, etc. Using

Weitzman’s (1979) stopping rule, we know that con-

sumers stop searching when the maximum utility

among the searched alternatives is larger than the

maximum reservation utility among the nonsearched

companies. In the following, we characterize the pro-

portion of consumers who receive a price draw below

the expected price for the brands in their consideration

sets when these sets are of size one.

Before the ﬁrst search (denoted by “b1”) we clas-

sify consumers into one of two types—Type A and

Type B—with N  N

b1, A

+ N

b1, B

Type A (B) con-

sumers are those whose reservation utility of the

Figure 1. Consumers’ Decision Making During First Search Under Sequential Search

Stop

searching

(i)

Continue

searching

(ii)

Stop

searching

(iii)

Stop

searching

(vi)

Continue

searching

(iv)

Continue

searching

(v)

potentially second-to-be-searched company is smaller

(larger) than the expected utility of the company

searched ﬁrst, i.e., r

i, t2

< µ

i, t1

i, t2

≥ µ

i, t1

). Note

that according to Weitzman’s (1979) rule, consumers

can change their type, i.e., change from being Type B

to being Type A (but not vice versa!) as they move

from the ﬁrst to the second to the third search, etc.

In Figure 1, we characterize what happens to these con-

sumers after their ﬁrst search.

Consumers who stop searching after the ﬁrst search

include the following: (a) Type A consumers whose

realized utility in the ﬁrst search exceeds the expected

utility of the company searched ﬁrst and therefore, by

the deﬁnition of Type A consumers, is also larger than

the reservation utility of the company potentially to be

searched second (a fraction λ of Type A consumers);

(b) Type A consumers whose price draw is such that

the utility of the ﬁrst search at the realized price

draw is below the expected utility of the ﬁrst search

(the remaining fraction (1 − λ)) and whose reserva-

tion utility of the company potentially to be searched

second is nevertheless below the realized utility level

of the company searched ﬁrst (a further fraction

0 ≤ γ

≤ 1). This group represents a fraction (1− λ)γ

Type A consumers; and (c) Type B consumers who get

a low price draw and hence whose realized utility in

the ﬁrst search is larger than the expected utility of the

company searched ﬁrst (a fraction λ) and whose reser-

vation utility of the company potentially to be searched

second is below this realized level of utility of the com-

pany searched ﬁrst (a further fraction 0 < δ

≤ 1). This

group represents a fraction λδ

of Type B consumers.

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

Thus, the number of consumers who stop searching

after the ﬁrst search is N

 λN

b1, A

+ (1 − λ)γ

b1, A

λδ

b1, B

. Of these consumers, those in (a) and (c) are

the ones that get a below mean price draw. From this

we can compute the fraction of consumers that receive

a below mean price draw among those who only search

once as



λN

b1, A

+ λδ

b1, B

λN

b1, A

+ (1 − λ)γ

b1, A

+ λδ

b1, B

. (7)

In Online Appendix B, we show that this proportion

is always larger than λ for diﬀerentiated goods with

consumer- and company-speciﬁc search costs under

the necessary condition that we observe a positive

number of consumers in the data making more than

one search.

Suppose in the data we observe consumers making

k  1, . . . , K searches with K > 1, i.e., a setting in which

the search method is identiﬁed because we cannot get

the same price pattern under both simultaneous and

sequential search. We showed that, under simultane-

ous search, the proportion of below-price-expectation

price draws in consumers’ consideration sets is con-

stant and equals λ for all k. Under sequential search,

the proportion of below-price-expectation price draws

in consumers’ consideration sets of size one is always

larger than λ. Thus, with individual-level data on con-

sumers’ consideration sets on hand, the researcher

needs to look at the pattern of below-price-expectation

price draws among consumers searching once: If that

proportion equals λ, consumers are searching simulta-

neously. If that proportion is larger than λ, consumers

are searching sequentially.

3.2.1. Discussion. The characteristic price patterns for

simultaneous and sequential search described above

hold for all models that satisfy the assumptions stated

at the beginning of Section 3.1. This includes (1) models

for homogeneous goods, (2) models for diﬀerentiated

products, (3) models that include unobserved hetero-

geneity in preferences and/or search costs, (4) mod-

els with correlations among preferences and search

costs, and (5) models with observed heterogeneity in

price distribution means µ

. On the other hand, we do

not ﬁnd the characteristic price patterns when there

is unobserved heterogeneity in the price distribution

means as the researcher would no longer be able to

judge whether a price draw is above or below the mean.

Note also that our identiﬁcation arguments here are

based on the ﬁrst moments of prices; in principle, there

could be identiﬁcation rules based on higher moments

as well. We leave this investigation for future research.

Next, we discuss the modeling assumptions stated

at the beginning of Section 3.1 and to what extent our

search method identiﬁcation results depend on them.

Recall that the assumptions are as follows: (a) prices are

the only source of uncertainty for the consumer that

he resolves through search; (b) consumers know the

distribution of prices and have rational expectations

for these prices; (c) price draws are independent across

companies; (d) there is no learning about the price dis-

tribution from observing other variables (e.g., adver-

tising); (e) (search costs are suﬃciently low so that) all

consumers search at least once; and (f) consumers have

nonzero search costs.

Assumptions (a) through (d) are standard in both

the theoretical and empirical literature on price search,

e.g., Stigler (1961), Weitzman (1979), Morgan and Man-

ning (1985), Mehta et al. (2003), Hong and Shum (2006),

Chen et al. (2007), Moraga-Gonzalez and Wildenbeest

(2008), De los Santos et al. (2012), Honka (2014), and

Honka et al. (2016). With regard to the rational expecta-

tions part of assumption (b), note that—just like almost

all previous literature on consumer search (barring

a few exceptions

)—we rely on the rational expecta-

tions assumption to prove search method identiﬁca-

tion. If (the researcher believes that) consumers do

not have rational price expectations or these rational

price expectations cannot be estimated from data, our

result for the characteristic price pattern under simul-

taneous search still holds. However, we are no longer

able to predict the characteristic pattern under sequen-

tial search.

Thus, the researcher is able to (visually

or statistically

) test the (stand-alone) assumption of

simultaneous search. If he is able to reject the null

hypothesis of simultaneous search, it means that con-

sumers do not search simultaneously. However, not

being able to reject the null hypothesis of simulta-

neous search does not imply that the researcher can

say anything about consumers (not) searching sequen-

tially; i.e., the results from any hypothesis test about

simultaneous search have no implications for whether

consumers search/do not search sequentially when

consumers have irrational price expectations.

With regard to assumption (e) that (search costs are

suﬃciently low so that) all consumers search at least

once, three approaches are common in the search liter-

ature to deal with consumers’ search/no-search deci-

sions: Researchers have assumed that (i) (search costs

are suﬃciently low so that) all consumers search at

least once (e.g., Reinganum 1979), (ii) the ﬁrst search

is free (e.g., Stiglitz 1987, Stahl 1989), and (iii) all con-

sumers use the same search method, but it is optimal

for some consumers to search/not to search depend-

ing on the level of their search costs (e.g., Janssen et al.

2005).

Throughout this paper, we use assumption (i)

for expository purposes. However, all of our results

hold across the three possible assumptions.

With regard to assumption (f) that consumers have

nonzero search costs, note that search costs have

to be only marginally larger than zero for search

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

method identiﬁcation to hold in all model speciﬁca-

tions (see Online Appendix B). When search costs

are exactly zero for some consumers or some com-

panies, our search method identiﬁcation results hold

for all homogeneous and diﬀerentiated goods mod-

els with constant (across consumers and companies),

consumer-speciﬁc, or company-speciﬁc search costs.

In this case, the necessary condition is that the distri-

bution of consideration set sizes has to have at least

two mass points (this is a straightforward generaliza-

tion of the necessary condition that a positive number

of consumers has to search more than once). Addi-

tionally, a suﬃcient but not necessary condition is

that consumers do not only search one or all compa-

nies in the market. We show this in detail in Online

Appendix C. Only to achieve search method iden-

tiﬁcation for (homogeneous or diﬀerentiated goods)

models with unobserved heterogeneity in search costs

across both consumers and companies, we need the

assumption that all consumers have nonzero search

costs.

Alternatively, if the researcher believes that the

assumption of nonzero search costs is not appropriate

in an empirical setting, search method identiﬁcation is

also given under the assumption that the search cost

distribution is continuous, i.e., has support, from 0 to a

positive number A > 0.

Again, this is only needed for

models with unobserved heterogeneity in search costs

across both consumers and companies. We provide

details on search method identiﬁcation when some

search costs are exactly zero in Online Appendix C.

4. Estimation

We now present estimation approaches for the simul-

taneous and sequential search models as described

in Section 3.1. Our goal is to present estimation

approaches that can be used for markets with any

number of alternatives. This is a challenge for the

estimation of a simultaneous search model that suf-

fers from the curse of dimensionality (Chiang et al.

1999, Kim et al. 2010). To overcome this challenge, we

use the theory developed by Chade and Smith (2005).

Their theory can only be used under two conditions:

(1) there is ﬁrst-order stochastic dominance among

the price distributions and (2) search costs cannot be

company-speciﬁc. We implement the ﬁrst condition by

assuming that the variances of the price distributions

are identical.

Note that these two assumptions are not

necessary for the sequential search model, but that we

nevertheless make them to keep everything other than

the search method consistent across the simultaneous

and sequential search models. Furthermore, our search

method identiﬁcation results do not rely on these two

assumptions as described in Section 3.2.

We start by pointing out the crucial diﬀerences

between what the consumer observes and what the

researcher observes: First, while the consumer knows

the distributions of prices in the market, the re-

searcher does not. Second, while the consumer knows

the sequence of searches, the researcher only par-

tially observes the sequence by observing which com-

panies are being searched and which ones are not

being searched. Third, in contrast to the consumer, the

researcher does not observe 

. To address the ﬁrst

issue that the researcher does not observe the price dis-

tributions, these distributions need to be inferred from

the data. In other words, the typical assumption of

rational expectations (e.g., Mehta et al. 2003, Hong and

Shum 2006, Moraga-Gonzalez and Wildenbeest 2008)

is that these distributions can be estimated from the

prices observed in the data. However, since the param-

eters of the distributions thus obtained are estimates,

the associated sampling error needs to be accounted

for when estimating the other parameters of the model

(see McFadden 1986).

4.1. Simultaneous Search

The estimation approach for the simultaneous search

model we present in this section is closely related to the

one developed in Honka (2014). The main diﬀerence

between the two models is that Honka (2014) assumes

that prices follow an Extreme Value (EV) type I distri-

bution, while we assume that prices follow a normal

distribution with p ∼ N(µ

, σ

). This change in distri-

butional assumption is driven by the desire to have

the same distributional assumption on prices under

both simultaneous and sequential search.

Given the

normal assumption for prices, the utility u

is a nor-

mally distributed random variable with mean µ



+ βµ

+ X

γ + 

and standard deviation σ  βσ

A consumer’s search decision under simultaneous

search depends on the expected indirect utilities (EIUs)

(Chade and Smith 2005). Consumer i

s EIUs where the

expectation is taken with respect to price are given by

E[u

]  α

+ βE[p

] + X

γ + 

. (8)

Consumer i observes these EIUs for every brand in

his market (including 

). To decide which companies

to search, consumer i ranks all companies according

to their EIUs (Chade and Smith 2005) and then picks

the top k companies to search. The term O

denotes

the set of top k companies consumer i ranked high-

est according to their EIUs. For example, O

contains

the company with the highest expected utility for con-

sumer i, O

contains the companies with the two high-

est expected utilities for consumer i, etc. To decide on

the number of companies k to obtain prices for, the con-

sumer calculates the net beneﬁt of all possible search

sets given the ranking of EIUs; i.e., if there are J com-

panies in the market, the consumer can choose among J

choice sets. A consumer’s beneﬁt of a searched set S

is given by the expected maximum utility among the

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

searched brands. The consumer picks the size of his

searched set S

that maximizes his net beneﬁt of search-

ing, denoted by Γ

, i.e., expected maximum utility

among the searched companies minus the cost of

 E

max

j∈O

− k · c. (9)

Recall that the researcher does not observe the exact

ranking according to the EIUs, but he observes the sets

of companies that the consumer considers and does not

consider. Honka (2014) has shown that this allows the

researcher to describe a consumer’s search set using

the following two conditions:

min

j∈S

(E[u

]) ≥ max

(E[u

]) ∩ Γ

≥ Γ

∀ k , k

; (10)

i.e., the minimum EIU among the searched brands is

larger than the maximum EIU among the nonsearched

brands and the net beneﬁt of the chosen searched set of

size k is larger than the net beneﬁt of any other search

set of size k

We account for the fact that the researcher does not

observe 

by assuming that 

has an EV type I dis-

tribution with location parameter 0 and scale param-

eter 1 and integrate over its distribution to obtain the

corresponding probabilities with which we can com-

pute the likelihood function. Then the probability that

a consumer picks a consideration set Υ is given by

iΥ | 

 P



min

j∈S

(E[u

]) ≥ max

(E[u

])∩Γ

≥ Γ

∀ k , k



(11)

Let us now turn to the purchase decision given consid-

eration. Let J be the base brand for consumer i. Then

the consumer’s choice probability conditional on his

consideration set is

ij | Υ, 

 P(u

≥ u

∀ j , j

, j, j

∈ S

). (12)

Note that there is a selection issue: Given a consumer’s

search decision, the 

do not follow an EV type I dis-

tribution, and the conditional choice probabilities do

not have a logit form.

In summary, the researcher estimates the price dis-

tributions, only partially observes the utility rankings,

and does not observe 

in the consumer’s utility func-

tion. Accounting for these diﬀerences compared to the

consumer, we derived an estimable model with the

consideration set probability given by Equation (11)

and the conditional purchase probability given by

Equation (12). We maximize the joint likelihood of

consideration set and purchase. The likelihood of our

model is given by

L 

i1

∫

+∞

−∞



l1

j1

iΥ | 

ij | Υ, 



f () d, (13)

where ϑ

indicates the chosen consideration set and δ

the company from which insurance is purchased. Nei-

ther the consideration set nor the conditional pur-

chase probability have a closed-form solution. Honka

(2014) describes how to estimate the simultaneous

search model under the assumption of EV type I

distributed prices in four steps in detail. Since our

assumption of normally distributed prices results in no

closed-form solution for the net beneﬁt of a searched

set Γ

, we need to add an additional step to the esti-

mation approach. Therefore, the simultaneous search

model under the assumption of normally distributed

prices is estimated the following way: First, we take Q

draws from 

for each consumer/company combina-

tion. Second (new step), for each 

draw, we take D

draws from the price distributions for each consumer/

company combination and calculate the expected max-

imum utility of a searched set as the average across

all D draws.

We repeat this step for each 

draw.

Third, for each 

draw, we calculate the smoothed

consideration and conditional purchase probabilities

using a multivariate scaled logistic cumulative dis-

tribution function (CDF) (Gumbel 1961) with scal-

ing parameters s

 · · ·  s

 5. Fourth, we average

the smoothed consideration and conditional purchase

probabilities across all 

draws. In the estimation, we

set D to 200 and Q to 100.

4.2. Sequential Search

Since we do not observe the sequence of searches,

we point out that observing a consumer’s considera-

tion set allows us to draw two conclusions based on

Weitzman’s (1979) rules: First, the minimum reserva-

tion utility among the searched companies has to be

larger than the maximum reservation utility among

the nonsearched companies (based on the selection

rule), i.e.,

min

j∈S

≥ max

. (14)

Otherwise, the consumer would have chosen to search

a diﬀerent set of companies. Second, the stopping and

choice rules in Equations (5) and (6) can be combined

to the following condition:

max

j∈S

≥ u

, max

, ∀ j

∈ S

\{ j}, (15)

i.e., that the maximum utility among the searched

companies is larger than any other utility among the

considered companies and the maximum reservation

utility among the nonconsidered companies.

Equations (14) and (15) are conditions that have to

hold based on Weitzman’s (1979) rules for optimal

behavior under sequential search and given the search

and purchase outcome that we observe in the data. At the

same time, it must also have been optimal for the con-

sumer not to stop searching and purchase earlier given

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

Weitzman’s (1979) rules. The challenge, as speciﬁed in

the second issue raised at the beginning of this section,

is that we do not observe the order in which the con-

sumer collected the price quotes. The critical realiza-

tion is that, given the parameter estimates, the observed

behavior must have a high probability of having been

optimal.

To illustrate, suppose a consumer searches three

companies. Then the parameter estimates also have to

satisfy the conditions under which it would have been

optimal for the consumer to continue searching after

his ﬁrst and second search. Formally, in the estimation,

given a set of estimates for the unknown parameters,

for each consumer i, let us rank all searched compa-

nies j according to their reservation utilities

(the “ˆ”

symbol refers to quantities computed at the current set

of estimates) where t  1, . . . , k indicates the rank of

a consumer’s reservation utility among the searched

companies. Note that t  1 (t  k) denotes the company

with the largest (smallest) reservation utility

. Fur-

thermore, rank all utilities of searched companies in

the same order as the reservation utilities; i.e.,

i, t1

denotes the utility for the company with the highest

reservation utility

it1

. Then, given the current parameter

estimates, the following conditions have to hold:

i, t1

it2

∩ max

t1, 2

i, t3

In other words, although the reservation utility of the

company with t  1 is larger than that with t  2 by def-

inition, the utility of the company with t  1 is smaller

than the reservation utility of the company with t  2,

thereby prompting the consumer to do a second search.

Similarly, the maximum utility from the (predicted)

ﬁrst and second search has to be smaller than the reser-

vation utility from the (predicted) third search, other-

wise the consumer would not have searched a third

time. Generally, for a consumer searching t  2, . . . , k

companies, the following set of conditions has to hold:

l2

max

t<l

itl

. (16)

To calculate a consumer’s reservation utilities, we fol-

low the approach suggested by Kim et al. (2010). The

additional estimation conditions as described in Equa-

tion (16) are necessary to correctly recover search costs.

These conditions impose restrictions on the utilities

and bound the search cost parameter from above.

Without these conditions, the search cost estimate is

biased upward. We describe the reason for this bias in

Section 5.4.2.

Since in the sequential search model, in contrast

to the simultaneous search model, there are no sep-

arate consideration and conditional purchase stages,

the probability of observing a consumer search a set

of companies Υ and purchase from company j under

sequential search is

ijΥ | 

 P



min

j∈S

≥ max

∩ max

j∈S

≥ u

, max

∩

l2

max

t<l

itl

∀ j

∈ S

\{ j}, t  2, . . . , k



. (17)

Then, the log-likelihood of the model is given by

L 

i1

∫

+∞

−∞

l1

j1

ijΥ | 

f () d, (18)

where y

indicates the chosen consideration set and

the purchased company. In principle, we can write out

all rankings of utilities and reservation utilities that sat-

isfy the conditions in Equation (17) and write the prob-

ability of observing a consumer’s search and purchase

behavior by calculating the sum of the probabilities of

all admissible rankings. The challenge with writing out

all utility and reservation utility rankings that satisfy

the conditions in Equation (17) is that their number

and complexity increases very quickly with the num-

ber of searches a consumer makes. Since, in our empir-

ical application, we observe consumers searching up to

10 times, this approach is not feasible. A second chal-

lenge is that, even if we wrote out all admissible rank-

ings of utilities and reservation utilities, the probability

as described in Equation (17) does not have a closed-

form solution. We use SMLE to estimate the sequential

search model as it allows us to overcome both chal-

lenges. SMLE does not solve the combinatorial prob-

lem, but it circumvents it by allowing us to estimate

the probability of observing a consumer search a set of

companies Υ and purchase from company j in Equa-

tion (17) without having to write out all admissible

rankings.

As in the estimation of the simultaneous search

model, we use a kernel-smoothed frequency simulator

(McFadden 1989) and smooth the probabilities using

a multivariate scaled logistic CDF (Gumbel 1961).

We describe the details of our estimation approach in

Online Appendix A. As we describe in the next section,

we have assessed the performance of our estimators

only in a simulation context. Evaluating the theoretical

properties of the estimators is left for future research;

here we appeal to the literature on simulation estima-

tors (see, e.g., Hajivassiliou 2000) to justify our choice

of estimation strategy.

4.3. Monte Carlo Simulations

We conduct a large set of simulation studies to illus-

trate search method identiﬁcation, demonstrate our

estimation approaches, and evaluate consequences on

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

estimates, model ﬁt, etc., of making incorrect assump-

tions for the search method, price distributions, and

the search costs in Online Appendix C. Here, we

brieﬂy summarize our results from these simulation

studies: First, the pattern of actual prices in considera-

tion sets identiﬁes the search method consumers use.

Next, our estimation approaches are able to recover

consumer preferences and search costs well when

the true data generating process is known. Further-

more, when the wrong search method assumption is

imposed in the estimation, true consumer preferences

and search costs are no longer recovered. Especially

the price and search cost coeﬃcients are biased down-

ward. We provide the intuition behind those down-

ward biases in Online Appendix D. We also show that

the model ﬁt under the incorrect assumption on the

search method is worse than the model ﬁt under the

correct assumption on the search method. We take

this as evidence that the ﬁt statistic is an additional

suggestive predictor of the correct search method.

Finally, making the correct assumption on the variance

of the price distributions and that search costs are not

company-speciﬁc is crucial to recover true consumer

preferences and search costs—especially for the simul-

taneous search model.

5. Empirical Application

We use data on consumer search and purchase behav-

ior for auto insurance from an insurance shopping

study conducted by a large marketing research com-

pany in 2006 and 2007. We observe which compa-

nies consumers collected price quotes from and which

companies consumers signed up with. This gives us

information on consumers’ consideration sets and pur-

chase decisions. In addition, we observe monthly

company-speciﬁc TV and radio advertising spending,

consumer- and company-speciﬁc advertising recall,

and quoted prices. We also have data on demographic

variables, psychographic factors, and observed con-

sumer attitudes toward insurance companies. As noted

before, since consumers in our sample have been

insured previously and coverage levels tend not to

change much, assuming that consumers engage in

price search and not in the search for other “attributes”

is a reasonable assumption in this context.

Table 1. Descriptive Statistics

Variable N Mean Std. dev. Minimum Maximum

Number of Price Quotes 945 2.96 1.38 1 10

Premium for 6-Month Policy 945 592.97 288.28 74 2,750

with Current Insurer

Number of Vehicles 945 1.58 0.64 1 3

Number of Drivers 945 1.64 0.59 1 4

Vehicle Year 945 2001.98 4.19 1960 2007

Respondent Age 945 45.23 12.94 20 84

Note. Prices are measured in dollars.

5.1. Data Description

Table 1 contains descriptive statistics of our data, and

Figure 2 shows a histogram of consumers’ considera-

tion set sizes. Consumers get, on average, 2.96 quotes

(including one from their previous insurer), with the

majority of consumers collecting two or three quotes

(see Figure 2). The average premium with the cur-

rent insurer is $592.97 (see Table 1). Table 2 compares

the mean characteristics for each respondent type (no

search/no switch, search/no switch, search/switch).

Consumers who neither search nor switch get, as

expected, only one quote—the one that their previ-

ous insurer sends to them. Consumers who search,

but decide not to switch collect 2.89 quotes on aver-

age, and consumers who search and switch gather 3.51

quotes. Consumers who neither search nor switch pay

the highest average premium ($660.13), followed by

consumers who search but decide to stay with their

previous insurer ($606.36). Consumers who search and

switch pay, on average, $551.44. For further details, we

refer the reader to Honka (2014) for a more detailed

description of our data.

5.2. Empirical Model

We assume consumers have rational expectations

about prices and estimate consumers’ price expecta-

tions using prices charged by previous insurers and a

large set of variables that determine insurance prices

such as demographics, drivers, cars, location, past

claims history, other insurance products, and coverage

choices.

We assume that prices follow a normal distri-

bution with the mean being a function of the variables

that determine insurance prices and a constant vari-

ance. The estimation results for the pricing regression

are shown in Table 3. We use the predicted prices from

this regression as price expectations in the main model

estimation. Note that within a consumer, the expected

prices across ﬁrms only vary because of the company-

speciﬁc ﬁxed eﬀects.

We refer the reader to Honka

(2014) for details on the price expectation estimation

process.

Consumer’s utility for auto insurance is given by

 α

+ β

adv

+β

ij, t−1

+ Z

γ + 

, (19)

where adv

denotes consumer- and company-speciﬁc

recalled advertising. It is calculated as an interaction

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

Figure 2. Consideration Set Sizes

12345678910

Consideration set size

% of consumers

eﬀect between consumer- and company-speciﬁc

advertising recall and company-speciﬁc advertising

spending. The term I

ij, t−1

is a dummy variable indi-

cating whether consumer i made a purchase from

the same company j as in time period t − 1, and Z

are observed psychographic factors. Collectively, I

ij, t−1

and Z

account for state-dependence and heterogene-

ity. With an average retention rate of about 70% in the

auto insurance industry, capturing consumer inertia

through β

is necessary to fully describe consumer

behavior in this market. Furthermore, we also control

for the following four psychographic factors denoted

by Z

: attitude toward auto insurance shopping and

switching, new technology adoption, proven reliability,

and out-of-box character. While the ﬁrst two variables

are consumer-speciﬁc, the last two variables (proven

reliability and out-of-box character) are both consumer-

and company-speciﬁc.

We chose to include these

four factors because Honka (2014) has shown that

they signiﬁcantly inﬂuence consumers’ utility for auto

insurance. Note that, under sequential search, the

eﬀects of consumer-speciﬁc variables in the utility

function cannot be identiﬁed (see discussion in Sec-

tion 5.4.2). We will therefore also explore the eﬀects of

these variables on search costs by making search costs

a function of the psychographic factors.

Table 2. Averages Across Customer Types

No search/ Search/ Search/

Variable No switch No switch Switch

Number of Respondents 56 586 303

Number of Price Quotes 1 2.89 3.51

Premium for 6-Month Policy 660.13 606.36 551.44

with Current Insurer

Number of Vehicles 1.61 1.60 1.54

Number of Drivers 1.73 1.65 1.60

Vehicle Year 2002.93 2001.86 2002.05

Respondent Age 42.17 46.90 42.35

Note. Prices are measured in dollars.

It is common practice in the auto insurance indus-

try that consumers receive a renewal oﬀer about one

month before their policy is set to expire. We view

this renewal oﬀer as a “free” ﬁrst search since the con-

sumer does not have to exert any eﬀort to receive the

price quote. Furthermore, we assume that a consumer

knows the price his previous insurer is going to charge

him to renew his insurance policy before making the

decision (not) to search other companies. Finally, we

assume the search set S

contains all companies the

consumer actively searches and the consumer’s consid-

eration set C

contains all searched companies and the

previous insurer, i.e., C

 S

∪ { j

ij, t−1

5.3. Model-Free Evidence of Search Method

It is important to recognize that the (free) price quotes

from previous insurance providers constitute a setting

in the auto insurance industry that is nonstandard for

consumer search models and speciﬁc to this indus-

try. This is so because consumers do not “optimally”

(under the rules of optimal consumer search) choose

the company from which they get the ﬁrst price quote,

but it is always their previous insurance provider.

If consumers were able to optimally choose which com-

pany to search ﬁrst, they might or might not ﬁrst search

their previous insurance provider. This nonstandard

setting, i.e., the fact that the ﬁrst search might or might

not be optimal, needs to be taken into account when

identifying the search method consumers use when

searching for prices of auto insurance policies. In gen-

eral, the search method is not identiﬁed in such a non-

standard setting without an additional assumption.

Therefore, we make the additional assumption that

consumers would have chosen to always include their

previous provider in their consideration set (simul-

taneous search) or ﬁrst search their previous insur-

ance provider (if they could make that decision under

sequential search). In the latter case, the price quote

from their previous insurance provider is an optimal

ﬁrst search for consumers. The advantage of this par-

ticular assumption is that we can empirically test its

appropriateness in our data. This is due to the particu-

lar pattern in our data and might not be possible with

other data.

5.3.1. Pattern Under Simultaneous Search. Let us

start out by discussing the pattern of actual prices in

consumers’ consideration sets that is expected under

simultaneous search when consumers ﬁrst receive

price quotes from their previous insurers and then

decide optimally whether and which company(ies) to

search in addition. The price quotes from the previous

insurance providers inﬂuence consumers’ decisions to

search beyond the previous insurer price quotes. Note

that in the best case scenario, i.e., when consumers

optimally choose which companies to search, the pro-

portion of below-expectation actual prices among con-

sumers searching once is λ. When the ﬁrst price quotes

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

Table 3. Price Distribution

Variable Estimate Std. error Variable Estimate Std. error

Constant 2.2886

∗∗

(0.7624) 21st Century 0.2374 (0.5118)

Male −0.2063 (0.1574) AIG 0.4593 (0.4107)

Married −0.8474

∗∗

(0.2718) Allstate −0.1791 (0.3049)

Divorced/Separated −0.1308 (0.2635) American Family −0.6157 (0.5088)

Widowed 0.3808 (0.7642) Erie −1.3207

∗∗∗

(0.5062)

Domestic Partnership −0.1202 (0.3344) Farmers −0.3980 (0.3936)

Age −0.0224

∗∗∗

(0.0065) Geico −1.0452

∗∗∗

(0.2972)

Driver under 25 Years 1.0810

∗∗

(0.3316) GMAC 0.6378 (0.6153)

Two Vehicles 2.0683

∗∗∗

(0.1986) Hartford −0.7291 (0.4461)

Three Vehicles 4.1097

∗∗∗

(0.3031) Liberty Mutual 0.3033 (0.3907)

Two Drivers 0.3489 (0.2683) Mercury 0.2958 (0.5137)

Three Drivers 2.0738

∗∗∗

(0.4954) MetLife 0.9811 (0.5057)

Four Drivers 1.3158 (0.9044) Nationwide −0.4867 (0.3926)

Medium City Suburb 0.0366 (0.2498) Progressive −0.1205 (0.3162)

Large City Suburb 0.6730

∗∗

(0.2491) Safeco 0.2390 (0.5773)

Urban Area 1.0057

∗∗∗

(0.2776) Travelers 0.7033 (0.4416)

Home Owner Insurance −0.1854 (0.1720) Chosen Coverage Yes

with Current Insurer State Yes

Other Insurance −0.2136 (0.1746) Make × Class Yes

with Current Insurer

Two or More Accidents 2.7329

∗∗∗

(0.4659)

Two or More Tickets 1.2601

∗∗∗

(0.3656)

Model Age −0.0566

∗∗

(0.0182) R

0.72

Note. Prices are measured in $100.

∗∗

p < 0.01;

∗∗∗

p < 0.001.

do not come from companies that are optimal to be

searched for consumers, we expect the proportion

of below-price-expectation actual prices among con-

sumers who do not search beyond the previous insurer

quote to be equal to or larger than the probability of

getting a below-price-expectation price draw, λ. Intu-

itively speaking, this is the case because price quotes

from “worse” than the optimal companies need to be

lower than those from the optimal companies to pre-

vent a consumer from searching further.

To summarize, under simultaneous search, if it were

optimal for consumers to request price quotes from

their previous insurance providers (if consumers can

freely make that decision), the proportion of below-

price-expectation actual prices among consumers who

do not search beyond the previous insurers’ price

quotes would equal the probability of getting a

below-price-expectation price draw, λ. If it were not

optimal for consumers to ﬁrst request price quotes

from their previous insurance providers (if consumers

can freely make that decision), the proportion of below-

price-expectation actual prices among consumers who

do not search beyond the previous insurers’ price

quotes would be larger than the probability of getting

a below-price-expectation price draw, λ.

Conditional on the decision to search beyond the

price quotes from the previous insurers, if consumers

search simultaneously, the proportion of below-price-

expectation actual prices in consumers’ search sets, i.e.,

consideration sets minus the price quote from the pre-

vious insurance provider, should equal the probability

of getting a below-price-expectation price draw, λ.

5.3.2. Pattern Under Sequential Search. Under se-

quential search, even if the ﬁrst price quotes do not

come from companies consumers would have opti-

mally chosen, consumers nevertheless react to the

ﬁrst price quotes under the rules of optimal sequen-

tial search, i.e., they stop searching when the price

is “low enough” and continue searching when

the price is “too high.”

The exact proportion of

below-price-expectation actual prices among con-

sumers who do not search beyond previous insurers’

price quotes will depend on the arrival process of the

ﬁrst price quotes, consumer preferences, etc. However,

similar to the situation under simultaneous search, it

is easy to recognize that the proportion of below-price-

expectation actual prices among consumers who do

not search beyond the previous insurers’ price quotes

will be larger than or, at the limit, equal to the pro-

portion of below-price-expectation actual prices under

optimal sequential search, i.e., when consumers opti-

mally pick the companies to be searched ﬁrst, among

consumers searching once.

5.3.3. Patterns in Our Data. Suppose a researcher has

data from the auto insurance industry in which he

observes that the proportion of below-price-expec-

tation actual prices among consumers who do not

search beyond the previous insurers’ price quotes is

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

Table 4. Proportion of Below-Expectation Prices

Percentage of below-expectation prices in search sets of size

1 2 3 4 5 6 7 8 9

48.49 40.54 48.87 49.28 57.50 33.33 52 .38 37.50 44.44

(2.74) (3.15) (4.60) (6.02) (10.09) (17.82) (20.39) (48.41) (49.69)

Note. Standard errors are in parentheses.

larger than the probability of getting a below-price-

expectation price draw. Then the researcher cannot

distinguish between (a) consumers searching simulta-

neously and getting a “nonoptimal” ﬁrst price quote

and (b) consumers searching sequentially (whether

they get an “optimal” or “nonoptimal” ﬁrst price

quote). Thus, the search method is not identiﬁed.

Now suppose a researcher has data from the auto

insurance industry in which he observes that the

proportion of below-price-expectation actual prices

among consumers who do not search beyond the pre-

vious insurers’ price quotes equals the probability of

getting a below-price-expectation price draw. Such an

empirical data pattern can only arise when consumers

search simultaneously and getting a price quote from

the previous insurance provider is “optimal.” In such

a case, we have found support for our additional

assumption that the price quotes from the previous

insurance providers represent an optimal search for

consumers and that consumers search simultaneously.

In our data, we observe the proportion of below-

price-expectation actual prices among consumers who

stop searching after the previous insurer quotes to be

0.48, and we cannot reject the null hypothesis that

this proportion equals 0.5 at p < 0.05.

This result

suggests that consumers would search their previ-

ous insurance providers and not diﬀerent companies

if they could freely choose. To put it diﬀerently, this

result suggests that our additional assumption for the

empirical context of the auto insurance industry that

consumers would have searched their previous insur-

ance providers if they could make that decision is sup-

ported by (model-free) patterns in the data.

Next, we calculate the proportions of below-price-

expectation actual prices in consumers’ search sets,

i.e., consideration sets less the price quotes from

the previous insurance providers, and the results are

shown in Table 4. Note that we have less than 10 obser-

vations for each of the search sets of sizes 6, 7, 8, and 9,

and less than 30 observations for the search sets of

size 5. Thus, we implement the chi-square test below

twice: once using all search set sizes and once using

search set sizes for which we have more than 30 obser-

vations, i.e., search sets of sizes 1 to 4.

Visually, the proportion of below-price-expectation

actual prices in consumers’ search sets is around 0.5

(with some variation across search set sizes). We con-

ducted t-tests (one for each search set size) and were

not able to reject the null hypothesis that the propor-

tion of below-price-expectation actual prices is 0.5 for

all search set sizes with the exception of the search

set of size 2 at p < 0.05. Then, additionally, we also

tested the null hypothesis that the proportion of below-

price-expectation actual prices in search sets of size 1 is

the same as the proportion of below-price-expectation

actual prices in search sets of size 2. We were not

able to reject that null hypothesis at p < 0.05. Last,

we ﬁrst implemented a chi-square test that tested the

null hypothesis that all proportions of below-price-

expectation actual prices across the diﬀerent search

sets of sizes 1–9 are equal. Then, we also implemented

a chi-square test that tested the null hypothesis that the

proportions of below-price-expectation actual prices

across search sets of sizes 1–4 are equal. We were not

able to reject the null hypotheses that all proportions

are equal, in both chi-square tests at p < 0.05. Thus we

conclude that the pattern is consistent with consumers

searching simultaneously.

To summarize, the search method consumers use

can only be identiﬁed in an empirical context such

as the one described for the auto insurance industry

if we make the additional assumption that it would

have been optimal for consumers to search their pre-

vious insurance providers (if consumers could make

that decision). We ﬁnd empirical support for this

assumption in our data. Furthermore, we ﬁnd that

the patterns in our data show that consumers search

simultaneously.

5.4. Model Parameter Identiﬁcation

5.4.1. Under Simultaneous Search. We provide a

brief summary of the discussion of identiﬁcation of

the model parameters under simultaneous search and

refer the reader to Honka (2014) for more details. The

identiﬁcation of the parameters capturing diﬀerences

in brand intercepts and other variables that vary across

companies such as advertising spending is standard as

in a conditional choice model. These parameters also

play a role in consumers’ consideration set decisions.

The size of a consumer’s consideration set will help

pin down search costs. We can only identify a range

of search costs as it is utility-maximizing for all con-

sumers with search costs in that range to search a

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

speciﬁc number of times. Beyond the fact that a con-

sumer’s search cost lies within a range that rationalizes

searching a speciﬁc number of times, the variation in

our data does not identify a point estimate for search

costs. The search cost point estimate will be identiﬁed

by the functional form of the utility function and the

distributional assumption on the unobserved part of

the utility.

Recall that we assume that the ﬁrst search is free.

The base brand intercept is identiﬁed from the con-

sumer’s decision to search or not to search beyond

the free ﬁrst search. Intuitively speaking, the free ﬁrst

search assumption creates a “fall-back option” similar

to the outside option and allows us to identify the base

brand intercept. So while the search cost estimate is

pinned down by the average number of searches, the

base brand intercept is identiﬁed by the search or no

search decision (beyond the free ﬁrst search). This also

means that if there was a “ﬁxed” component of the

search cost that did not vary by the number of searches,

this ﬁxed cost would not be separately identiﬁed from

the base brand intercept mean.

Consumer-speciﬁc variables that do not vary across

companies are identiﬁed by consumers with certain

characteristics searching more or less than others. For

example, suppose older consumers search less than

younger consumers. Then—given that the search cost

coeﬃcient is identiﬁed by the average number of

searches across all consumers—older consumers must

have a smaller beneﬁt of searching, i.e., a lower util-

ity for insurance, than younger consumers. Thus, we

would expect a negative coeﬃcient for age in the utility

function. It is important to recognize that this argu-

ment only holds under the assumption of identical

search costs across consumers. Alternatively, we could

allow the consumer-speciﬁc variables to shift search

costs instead of the utility.

5.4.2. Under Sequential Search. In the sequential

search model, the parameters capturing diﬀerences in

brand intercepts and variables that vary across compa-

nies such as advertising spending are identiﬁed from

the conditions on the utilities and reservation utilities,

i.e., Equations (4)–(6).

Search costs are identiﬁed from Weitzman’s (1979)

stopping rule (Equation (5)). They are not identiﬁed

from the search rule, as it only imposes a relative

ranking on the reservation utilities. Recall that the

reservation utility is the utility that makes a consumer

indiﬀerent between searching and not searching. If

there is a unique solution for Equation (4), as has been

shown by previous research (e.g., Kim et al. 2010), and

search costs are not company-speciﬁc as we assume in

our empirical model, then the relative ranking of the

reservation utilities will not change when search costs

equally increase or decrease for all companies. Thus,

search costs are not identiﬁed from Weitzman’s (1979)

search rule. Search costs are also not identiﬁed from

Weitzman’s (1979) choice rule (Equation (6)), as search

costs do not enter it. Search costs are identiﬁed by

the stopping rule only as it describes the relationship

between utilities and reservation utilities.

Previous research (e.g., Kim et al. 2010) has shown

that reservation utilities decrease when search costs

increase. Thus, as search costs increase, the stopping

rule demanding that the maximum utility among the

searched companies is larger than the maximum reser-

vation utility among the nonsearched companies is sat-

isﬁed earlier and consumers stop searching earlier. This

is the mechanism behind the intuitive result that higher

search costs make consumers search less. The num-

ber of searches a consumer makes identiﬁes a range of

search costs as it is utility-maximizing for a consumer

with search costs in that range to search a speciﬁc num-

ber of times. For example, suppose it is optimal for a

consumer to search once if his search costs lie between

two and three, twice if his search costs lie between one

and two, and three times if his search costs lie between

zero and one. Then, by observing the consumer stop

after the second search, we know that his search cost

must be at least one, but we do not know whether his

search costs are one, two, or three. Thus, imposing the

stopping rule as shown in Equation (5) on the observed

consideration set only puts a lower bound on the search

cost estimate, as it only requires that search costs must

have been larger than a lower bound to make the con-

sumer stop searching. As a consequence, if only the

stopping rule on the observed consideration set is used

in the estimation, the search cost estimate exhibits an

upward bias. This is the upward bias on the search cost

estimate we described in Section 4.2.

By imposing the conditions that, given the current

estimates, it must have been optimal for the consumer

to continue searching (Equation (16)), we impose an

upper bound on the search cost estimate that elim-

inates the previously described upward bias of the

search cost estimate and allows us to recover the true

values. The intuition here is that if the search costs had

been higher, the consumer would not have continued

searching. Beyond that a consumer’s search cost lies

within this range, which rationalizes stopping after a

speciﬁc number of searches (but not earlier), the vari-

ation in our data does not identify a point estimate

for search costs. The search cost point estimate will be

identiﬁed by the functional form of the utility function

and the distributional assumption on the unobserved

part of the utility (as in the case of the simultaneous

search model).

The base brand intercept—as in the simultaneous

search model—is identiﬁed by a consumer’s decision

to search or not to search more than once given our

assumption that the ﬁrst search is free. Thus, observing

a proportion of consumers to only search once (and

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

“pay” no search costs) is crucial in identifying the base

brand intercept. As in the simultaneous search model,

if there was a “ﬁxed” component of the search cost that

did not vary by the number of searches, this ﬁxed cost

would not be separately identiﬁed from the base brand

intercept mean.

By contrast to the simultaneous search model, vari-

ables in the utility function that do not vary across

companies, i.e., are consumer-speciﬁc, are not identi-

ﬁed in the sequential search model. The eﬀects of these

consumer-speciﬁc variables are not identiﬁed from the

choice or search rules as adding a constant to all utili-

ties or reservation utilities does not change the relative

rankings among the utilities or reservation utilities,

respectively. The eﬀects of these consumer-speciﬁc

variables are also not identiﬁed from the stopping rule

as adding a constant to the utility function does not

aﬀect the relationship between utilities and reserva-

tion utilities, i.e., whether a speciﬁc utility or a spe-

ciﬁc reservation utility is larger. The intuition behind

this result is the following: Based on Kim et al. (2010),

we know that a reservation utility in our model can

be calculated as the sum of expected utility (expecta-

tion taken with respect to price) and a constant that

depends on search costs, the price coeﬃcient, and the

standard deviation of the price distribution. Thus, for

the same company j, any diﬀerence in utility for com-

pany j and reservation utility for company j comes

from the diﬀerence in expected and actual price. For

diﬀerent companies, any diﬀerence in utility for com-

pany j and reservation utility for company j

comes

from the diﬀerence in actual price for company j

and expected price for company j

and diﬀerences in

company-speciﬁc observed variables. Thus, variables

that do not vary across companies do not aﬀect the

relationship between utilities and reservation utilities

and are not identiﬁed from the stopping rule.

The lack of identiﬁcation of the eﬀects of variables

that do not vary by alternative in the utility function

in the sequential search method raises the issue of

how to introduce demographic characteristics in mod-

els of search. For the simultaneous search model, these

variables can be introduced either directly in the util-

ity function or as shifters of search costs across con-

sumers. For the sequential search model, only the latter

operationalization is feasible. In the robustness checks

(Section 7.1), we explore the consequences of introduc-

ing demographics—either in the utility function or in

the search cost.

5.5. Estimation and Results

We need to adapt the estimation of both the simulta-

neous and the sequential search model compared to

the ones shown in Section 4 to reﬂect a speciﬁc setting

of the auto insurance industry, namely, that consumers

know the prices their previous insurance providers

are going to charge them. For the simultaneous search

model, we refer the reader to Honka (2014) for the esti-

mation details. For the sequential search model, we

refer the reader to Online Appendix E.

As described in Section 4, we need to make the

assumption of ﬁrst-order stochastic dominance among

the price distributions to use Chade and Smith (2005)

and Honka (2014) to estimate the simultaneous search

model. We do so by assuming that the variances of the

company-speciﬁc price distributions are identical. We

tested the appropriateness of this assumption in two

ways: First, we conducted a Bartlett test to test whether

the company-speciﬁc variances of the price residuals

from our pricing regression are equal. We were not able

to reject the null hypothesis that all company-speciﬁc

price residual variances are identical. Second, we esti-

mated the normal distribution of prices by making the

variance parameter a function of company ﬁxed eﬀects

in addition to the mean parameter being a function

of consumer demographics, insurance policy charac-

teristics, and company ﬁxed eﬀects. None of the ﬁrm

ﬁxed eﬀects on the variance parameter was signiﬁcant.

We conclude that the assumption of identical price

variances is appropriate in our context.

Column (i) in Table 5 shows the results under the

assumption that all consumers search simultaneously,

and column (ii) shows the results under the assump-

tion that all consumers search sequentially. The simul-

taneous search model ﬁts the data better than the

sequential search model. As discussed in Section 4.3,

the model ﬁt is an additional predictor of the search

method consumers use. Furthermore, both the search

cost and the price coeﬃcient estimates under sequen-

tial search are very small. As outlined in Online

Appendix D, when the true data generating process

is simultaneous search but a sequential search model

is estimated, we expect both the search cost and the

price coeﬃcient estimate to be severely biased down-

ward. Together with the model-free evidence from the

previous section that also indicated that consumers

search simultaneously, we ﬁnd consistent evidence of

simultaneous search being the search method con-

sumers use when shopping for auto insurance. Given

this overwhelming evidence, we treat simultaneous

search as the actual search method consumers use

when shopping for auto insurance in the following

sections. Our search cost estimate per search is $42.09.

Note that the search cost estimate under simultaneous

search is similar to the one ($41.81) found by Honka

(2014) using the same data and the same model (Model

0 in her paper). The small diﬀerence in search cost esti-

mates can be explained by the diﬀerent assumption on

the price distributions noted previously. Dahlby and

West (1986) ﬁnd search costs to range from $131 to $570

(adjusted for inﬂation and converted from Canadian

dollars) for auto insurance. We attribute these higher

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

Table 5. Results

Search method

(i) (ii)

Simultaneous search Sequential search

Estimate Std. error Estimate Std. error

Brand preferences

21st Century −1.7019

∗∗∗

(0.2047) 0.3814

∗∗

(0.1449)

AIG −1.1634

∗∗∗

(0.2005) 0.8831

∗∗∗

(0.1223)

Allstate −1.5772

∗∗∗

(0.2241) 0.8214

∗∗∗

(0.1612)

American Family −1.5522

∗∗∗

(0.2204) 0.9392

∗∗∗

(0.1631)

Erie −1.8607

∗∗∗

(0.2164) 0.7687

∗∗∗

(0.1584)

Farmers −1.8135

∗∗∗

(0.2064) 0.6096

∗∗∗

(0.1384)

Geico −2.1390

∗∗∗

(0.2762) 0.0801 (0.1649)

GMAC −1.7801

∗∗∗

(0.3297) 0.7602

∗∗∗

(0.1455)

Hartford −1.6454

∗∗∗

(0.1879) 0.5208

∗∗∗

(0.1238)

Liberty Mutual −1.5790

∗∗∗

(0.2023) 0.1565 (0.1541)

Mercury −1.8209

∗∗∗

(0.2427) 0.3002 (0.2401)

MetLife −1.5956

∗∗∗

(0.2369) 0.4384

∗∗

(0.1467)

Nationwide −1.9770

∗∗∗

(0.1951) 1.0862

∗∗∗

(0.1318)

Progressive −1.4661

∗∗∗

(0.2173) −0.0955 (0.0500)

Safeco −2.1445

∗∗∗

(0.2422) 0.3894

∗∗

(0.1242)

State Farm −1.5930

∗∗∗

(0.2172) 0.9673

∗∗∗

(0.1455)

Travelers −1.5936

∗∗∗

(0.1952) 0.8484

∗∗∗

(0.1340)

Other parameters

Price −0.4479

∗∗∗

(0.0446) −0.0683

∗∗∗

(0.0029)

Recalled advertising 0.1279

∗∗

(0.0491) 0.1303

∗∗∗

(0.0119)

Inertia 0.7172

∗∗∗

(0.0745) 0.6274

∗∗∗

(0.0361)

Search cost 0.1885

∗∗∗

(0.0445) 0.0005

∗∗∗

(0.0001)

Psychographic factors

Attitude toward auto insurance

shopping and switching −0.4075

∗∗

(0.1419)

New technology adoption −0.1604 (0.1413)

Proven reliability 0.3431

∗∗∗

(0.0556) 0.0100 (0.0226)

Out-of-box character 0.1436

∗∗

(0.0527) 0.0723

∗∗

(0.0263)

Log-likelihood −3,079.12 −4,571.58

Akaike information criterion 6,208.24 9,193.16

Bayesian information criterion 6,346.85 9,331.77

Note. Prices are measured in $100.

∗∗

p < 0.01;

∗∗∗

p < 0.001.

search costs to the data used by Dahlby and West (1986)

having been collected partially in rural Canada in the

1970s, where the density of agents was lower, and to the

introductions of calling centers and the Internet, which

signiﬁcantly lowered consumer search costs. For Medi-

gap insurance, Lin and Wildenbeest (2015) estimate

median search cost per insurer to be $30. We conclude

that our search cost estimate is in line with search cost

estimates found by previous literature in the same and

related categories.

6. Eﬀects of an Incorrect Assumption on

the Search Method

Most previous empirical research on consumer search

has made an assumption of the search method con-

sumers use (e.g., Mehta et al. 2003, Kim et al. 2010,

Seiler 2013). In this counterfactual, we investigate the

eﬀects of an incorrect search method assumption on

predicted quantities that are typically of interest to

researchers such as elasticities, consideration set, and

purchase market shares. To do so, we use the results

from Table 5 and predict search cost elasticities, con-

sideration set, and purchase market shares under the

correct assumption of simultaneous search and the

incorrect assumption of sequential search.

6.1. Search Cost Elasticities

We predict the percentage change in companies’ con-

sideration and purchase market shares due to a 10%

decrease in search costs using simulation methods.

Note that the search cost elasticity for purchase across

all companies (in terms of number of purchased poli-

cies) is zero in the auto insurance market because

consumers are required to have auto insurance. Thus,

the total number of purchased auto insurance policies

does not vary with search costs. The company-speciﬁc

search cost elasticities for purchase can be both positive

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

and negative. Two eﬀects determine search cost elastic-

ities: First, some companies are hurt by a decrease in

search costs because a consumer searches more compa-

nies due to the lower search costs, there is more compe-

tition within this consumer’s consideration set, and the

company no longer gets chosen by the consumer. Sec-

ond, some companies beneﬁt from a decrease in search

costs as a consumer decides to search more companies

due to the decrease in search costs and the company

newly gets searched and purchased. All companies

encounter both eﬀects when search costs decrease, and

the net eﬀect determines whether the company-speciﬁc

search cost elasticity is positive or negative. Our search

cost elasticity estimates need to be interpreted in light

of this trade-oﬀ for each company.

Under the correct simultaneous search assumption,

a 10% (50%) decrease in search costs results in a

4.03% (29.31%) increase in the average number of

actively searched companies, i.e., excluding the free

quote from the previous insurance provider, while

under the incorrect assumption of sequential search,

a 10% (50%) decrease in search costs results in a 1.89%

(13.08%) increase in the average number of actively

searched companies. Thus, the eﬀects of a decrease

in search costs are underestimated in terms of the

number of actively searched companies under the

incorrect assumption on the search method. Table 6

shows percentage changes in the consideration and

purchase market shares due to a 10% decrease in

search costs. Columns (i) and (iii) display the results

under the correct assumption of simultaneous search,

while columns (ii) and (iv) display the results under

the incorrect assumption of sequential search. First,

the predicted changes in both the consideration set

and purchase shares under the incorrect assumption

of sequential search are smaller than those under the

correct assumption of simultaneous search. This is

expected, as the number of active searches increases

by only 1.89% under sequential search, which means

that only very few companies are newly added to con-

sumers’ consideration sets and thus their purchase

decisions stay largely the same. Second, the predicted

changes, especially in consideration set shares, can be

diﬀerent in terms of direction and magnitude under

the correct and incorrect assumption on the search

method. For example, while the consideration set

shares for 21st Century, Progressive, and Travelers are

rather similar, the consideration set shares for Amer-

ican Family, Hartford, and Liberty Mutual are quite

diﬀerent.

6.2. Consideration Set and Purchase

Market Shares

Table 7 shows the predicted consideration set and pur-

chase market shares under both assumptions on the

search methods. Note that consideration set and pur-

chase market shares can be over- or underpredicted

Table 6. Search Cost Elasticities Due to a 10% Decrease in

Search Costs

(i) (ii) (iii) (iv)

Consideration set shares Purchase market shares

Company Sim. search Seq. search Sim. search Seq. search

21st Century 0.14 0.13 0.47 0.00

(0.08) (0.03) (0.11) (0.02)

AIG −0.12 0.02 0.10 0.00

(0.10) (0.03) (0.08) (0.02)

Allstate −0.10 −0.04 0.31 0.00

(0.03) (0.03) (0.06) (0.02)

American Family −0.26 0.15 0.24 0 .00

(0.23) (0.05) (0.16) (0.03)

Erie −0.02 0.02 0.05 0.00

(0.10) (0.05) (0.10) (0.04)

Farmers −0.13 −0.04 0.14 0.00

(0.10) (0.03) (0.06) (0.03)

Geico −0 .25 −0.16 −0.03 0.00

(0.05) (0.04) (0.07) (0.03)

GMAC 0.15 0.23 −0.27 0.00

(0.10) (0.03) (0.06) (0.02)

Hartford −0.09 0.10 0.10 0.00

(0.19) (0.04) (0.12) (0.04)

Liberty Mutual 0.41 0.07 0.32 0.00

(0.14) (0.03) (0.13) (0.03)

Mercury 0.26 0.17 −0.17 0.00

(0.12) (0.04) (0.10) (0.02)

MetLife 0.19 0.12 −0.01 0.00

(0.11) (0.04) (0.11) (0.03)

Nationwide 0.07 0.00 0.02 0 .00

(0.06) (0.03) (0.12) (0.02)

Progressive −0.07 −0.12 −0.25 0.00

(0.09) (0.04) (0.04) (0.03)

Safeco 0.42 0.14 −0.12 0.00

(0.06) (0.03) (0.12) (0.02)

State Farm 0.08 0.00 −0.48 0.00

(0.13) (0.04) (0.16) (0.03)

Travelers −0.05 −0.08 −0.10 0.00

(0.09) (0.04) (0.08) (0.03)

Note. Bootstrapped standard errors are in parentheses.

under the incorrect assumption of sequential search.

With the exception of 21st Century the direction of the

over- or underprediction is directionally the same for

consideration set and purchase market shares. Compa-

nies with the largest overpredictions of their purchase

market shares (in percent) under sequential search are

AIG, Allstate, and Progressive. Note that the purchase

market shares of the four largest insurance companies

(Allstate, Geico, Progressive, and State Farm) are being

overpredicted under sequential search. Companies

with the largest underpredictions of their purchase

market shares (in percent) under sequential search are

GMAC, Hartford, Mercury, and Safeco. The substantial

diﬀerences in these shares across search methods for

some of the brands in the data suggest that the choice

of a search strategy in a given empirical application can

have a large impact on predicted shares. This under-

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

Table 7. Consideration Set and Purchase Market Share Predictions

(i) (ii) (iii) (iv)

Consideration set composition Purchase market shares

Company Sim. search Seq. search Sim. search Seq. search

21st Century 5.10 4.53 4.26 4.35

(0.63) (0.32) (0.60) (0.32)

AIG 7.89 7.99 6.91 8.07

(0.55) (0.72) (0.57) (0.78)

Allstate 9.03 9.62 8.12 9.78

(0.85) (0.11) (0.85) (0.09)

American Family 2.69 2.29 2.57 2.26

(0.39) (0.14) (0.40) (0.14)

Erie 3.15 3.13 3.13 3.12

(0.44) (0.27) (0.45) (0.27)

Farmers 6.31 6.98 6.09 6.99

(0.72) (0.37) (0.73) (0.39)

Geico 10.26 10.85 10.66 11.20

(0.65) (0.65) (0.68) (0.66)

GMAC 3.84 3.12 3.71 2.97

(0.55) (0.96) (0.56) (1.00)

Hartford 8.04 6.78 8 .16 6.67

(1.53) (0.55) (1.61) (0.57)

Liberty Mutual 5.87 5.39 5.92 5.32

(0.84) (0.47) (0.90) (0.48)

Mercury 2.93 2.38 2.94 2.34

(0.51) (0.26) (0.57) (0.25)

MetLife 4.04 3.81 4.04 3.70

(0.60) (1.77) (0.67) (1.81)

Nationwide 5.62 5.16 5.83 5.00

(0.40) (0.38) (0.45) (0.39)

Progressive 9.97 12.32 11.04 12.77

(0.50) (0.70) (0.54) (0.72)

Safeco 3.18 2.73 3.34 2.58

(0.73) (0.61) (0.80) (0.64)

State Farm 7.55 8.58 8.45 8.69

(0.57) (0.56) (0.62) (0.59)

Travelers 4.54 4.34 4.81 4.19

(0.32) (0.17) (0.34) (0.19)

Notes. Consideration set and purchase market shares are shown in percentages. Bootstrapped stan-

dard errors are in parentheses.

scores the importance of an approach to identify the

search method in such applications.

7. Robustness Checks

7.1. Alternative Model Speciﬁcations

We check the robustness of our empirical results by

estimating four alternative model speciﬁcations. As

discussed in Section 5.4.2, the eﬀects of variables that

do not change across companies such as two of the

psychographics factors are not identiﬁed in the util-

ity function under sequential search. We therefore

estimate a simultaneous and sequential search model

where those psychographics factors enter through

consumers’ search costs instead of consumers’ util-

ity function. While not reported here, we ﬁnd that

for the simultaneous search model the estimates and

the log-likelihood are very similar to column (i) in

Table 5. For the sequential search model, we ﬁnd that,

while the inclusion of the two psychographics fac-

tors increases the log-likelihood (as to be expected),

the log-likelihood of the model under simultaneous

search remains larger. Other parameter estimates for

the sequential search model remain very similar to col-

umn (ii) in Table 5.

The sequential search model is also more ﬂexible

in that the assumption of ﬁrst-order stochastic domi-

nance among the price distributions is not necessary

for estimation. Thus, we estimate the sequential search

model using company-speciﬁc price variances. While

not reported here, we ﬁnd neither the parameter esti-

mates nor the log-likelihood to change much com-

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

pared to column (ii) in Table 5. This is likely due

to the company-speciﬁc price variances being simi-

lar in the empirical data. Finally, we also estimate a

sequential search model with company-speciﬁc price

variances and consumer-speciﬁc psychographic factors

entering the model through search costs. While we ﬁnd

the log-likelihood to increase, this increase is due to

the inclusion of additional psychographic factors. Fur-

thermore, we ﬁnd that the log-likelihood of this most

ﬂexible sequential search model is still much smaller

than the one of the less ﬂexible simultaneous search

model (column (i) in Table 5). We conclude that our

results are robust to alternative model speciﬁcations

and that simultaneous search is the appropriate model-

ing assumption to describe consumer shopping behav-

ior in the auto insurance industry.

7.2. Unobserved Heterogeneity

In the empirical application, heterogeneity across con-

sumers is captured via observable characteristics such

as psychographic factors as well as lagged choice (a la

Guadagni and Little 1983). One concern could be the

presence of unobserved heterogeneity in preferences,

search costs, and search method. Given the nature of

our survey data, accounting for unobserved hetero-

geneity would typically not be possible. However, we

have access to variables that could aﬀect the search

method such as credit scores, but that are unlikely

to directly aﬀect the utility of the alternatives.

With

information on these variables, we can appeal to a

discrete-heterogeneity concomitant variable approach

(see, e.g., Dayton and Macready 1988) to distinguish

those who search sequentially (consumers with high

credit scores) from those who search simultaneously

(consumers with low credit scores). We estimate such

a two-segment concomitant variable latent class model

(Kamakura and Russell 1989) where one class of con-

sumers searches simultaneously and the other class of

consumers searches sequentially. While not reported

here, we ﬁnd that the size of the simultaneously search-

ing consumer segment is 0.88, and that the model

estimates are very similar to the ones from model (i)

in Table 5. Search costs are estimated to be $42.11.

We therefore conclude that our results are robust to

this form of unobserved heterogeneity in the data.

8. Limitations and Future Research

There are several limitations to our research. First,

we assume that consumers have rational expectations

about prices. A model that has information on con-

sumer price expectations or is able to recover them

would enable researchers to test the hypothesis of ratio-

nal price expectations and compare it with other price

expectation formation theories. A related issue in our

empirical context is that we have access only to cross-

sectional data from 945 survey respondents. To recover

the price expectations for these consumers, we need to

make a speciﬁc functional form assumption on the rela-

tionship between prices and consumer characteristics.

Having access to more data would free us from having

to make this assumption. Second, our search method

identiﬁcation strategy for the case where there is unob-

served heterogeneity in search costs across consumers

and companies relies on the nonveriﬁable assumption

that all consumers have positive search costs. It will

be a fruitful avenue for future research to come up

with a search method identiﬁcation strategy that does

not make this assumption. Third, our model implicitly

assumes that consumers make one and only one deci-

sion about the search method they want to use (and the

number of quotes they are going to collect under simul-

taneous search) before starting any search activity. In

reality, consumers might go through multiple search

stages. For example, a consumer might initially decide

to collect two price quotes searching simultaneously

and then, after learning about the two prices, decide to

search sequentially, stop after three price quotes, and

make a purchase. Developing such a multistage search

model is left for future research. To carry out such anal-

yses, however, researchers need to be equipped with

more detailed data than those used in this paper. At the

same time, the data we use are increasingly becoming

available; the approaches proposed in this paper there-

fore allow us to make progress on answering important

questions regarding the magnitudes of search costs

and consequences of assumptions made in estimating

models of search.

Fourth, our goal in this paper is to present search

models that can be used in markets with any num-

ber of companies. To estimate the simultaneous search

model in markets with a lot of alternatives, we have

to assume that search costs are not company-speciﬁc.

Note that this limitation has no implications for our

search method identiﬁcation strategy and that it can be

overcome in markets with few alternatives by using a

choice model approach a la Mehta et al. (2003). Finally,

following the standard search literature, our model

assumes that consumers search to resolve uncertainty

about a single product characteristic, i.e., price. Yet in

many contexts, consumers might search to learn about

two or more product characteristics. For example, con-

sumers might search to learn about coverage options

and prices in the auto insurance industry. We leave it

for future research to develop a model that allows con-

sumers to search for multiple product characteristics.

9. Conclusion

In this paper, we explore whether the search method

consumers use can be deduced in data where con-

sumer purchases and consideration sets, but not the

sequence of searches, are observed. We show ana-

lytically that the search method is nonparametrically

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

identiﬁed in those kind of data. Under simultaneous

search, the average proportion of below-expectation

price draws is constant across all consideration set

sizes and equals the probability of getting a below-

price-expectation price draw, while under sequen-

tial search, the proportion of below-expectation price

draws among consumers searching once is larger than

the probability of getting a below-price-expectation

price draw.

We suggest a new estimation approach for the se-

quential search model where the researcher has access

to individual-level data on consideration sets, pur-

chases, and other characteristics, but not the sequence

of searches. Our SMLE approach is able to over-

come the challenge of the researcher not knowing the

sequence of searches.

We apply our model and estimation approach to

data from the U.S. auto insurance industry and ﬁnd

consumers to search simultaneously with search costs

of about $42. Using our estimates, we predict consid-

eration set and purchase market shares under both

search methods. We ﬁnd consideration and purchase

market shares of the largest insurance companies to

be overpredicted under the incorrect assumption of

sequential search.

Acknowledgments

The authors thank Bart Bronnenberg; Jean-Pierre Dubé;

Ken Hendricks; Ali Hortaçsu; Jean-François Houde; Stephan

Seiler; Maria Ana Vitorino; Matthĳs Wildenbeest; the par-

ticipants of the 2012 Marketing Science Conference, 2012

INFORMS Annual Meeting, 11th International Industrial

Organization Conference, 9th Invitational Choice Sympo-

sium, 2013 Quantitative Marketing and Economics Confer-

ence, 2014 Econometric Society Meeting, and 2015 NBER

Industrial Organization Winter Meeting; and seminar par-

ticipants at the Yale School of Management, University of

Minnesota, University of Maryland, University of Miami,

Harvard Business School, Temple University, Texas A&M

University, University of California San Diego, Dartmouth

College, University of Kansas, Indian School of Business,

UCLA, Chinese University of Hong Kong, University of

Michigan, and Southern Methodist University for their

comments. The authors are grateful to an anonymous com-

pany for providing them with the data. The feedback from

two reviewers, an associate editor, and the senior editor is

also gratefully acknowledged. The usual disclaimer applies.

Endnotes

Note that we use the terms “consideration set” and “search set”

interchangeably in Sections 1–4 of this paper. Starting with our

empirical application in Section 5, we introduce a distinction be-

tween both terms.

A search cost is an information “cost” borne by a consumer to

acquire information about a ﬁrm—usually in the form of time and

eﬀort required to obtain such information. It does not have to be a

monetary cost.

We discuss these assumptions and the extent to which our search

method identiﬁcation approach relies on them in Section 3.2.1.

While we do not model the supply side in this paper, our demand

model is consistent with several general equilibrium models that

result in price uncertainty and consumer search, e.g., a pure strat-

egy equilibrium where consumers do not know company costs,

which translates into uncertainty about prices (Benabou 1993), or

a mixed strategy equilibrium model where companies randomize

prices (Burdett and Judd 1983).

We present the most general model with consumer- and company-

speciﬁc price distribution means. This includes simpler settings

where the price distribution means are company-speciﬁc, consumer-

speciﬁc, or marketwide.

For expositional purposes, we show β and γ without any sub-

scripts. They can be added when appropriate.

Note that our search method identiﬁcation proof does not rely on

the existence of both types of consumers, as we discuss in detail in

Online Appendix B.

Exceptions are, for example, Rothschild (1974), De los Santos et al.

(2015), and Matsumoto and Spence (2014).

Details about the characteristic patterns under simultaneous and

sequential search when consumers’ price expectations are not ratio-

nal are available from the authors on request.

Based on our discussion in Section 3.2, the researcher can test

the null hypothesis of simultaneous search either through K t-tests

that the proportion of below-(true) price-expectation price draws

in consumers’ consideration sets equals λ and/or through a chi-

squared test for the proportion of below-(true) price-expectation

price draws being constant across consideration set sizes.

Note that for assumption (ii), i.e., that the ﬁrst search is free,

assumption (f), i.e., that consumers have nonzero search costs, still

applies. In that case, it applies to all searches beyond the free ﬁrst

search.

Details are available from the authors on request.

We discuss in detail and provide an example of why the assump-

tion of nonzero search costs is necessary in this case in Case 5 in

Online Appendix C.

Note that we do not require the search cost distribution to be

continuous over its full range. We only require it to be continu-

ous over the interval 0 to A > 0. Our search method identiﬁcation

goes through when a search cost distribution has support, e.g.,

from 0 to A and from B to C with C ≥ B > A > 0.

We study the eﬀects of the equal price variance and identical

search costs assumptions for both simultaneous and sequential

search models in simulation studies in Online Appendix D.

Note that in markets with few alternatives, i.e., markets where the

curse of dimensionality is not severe, one could use a choice-model

approach to estimate the simultaneous search model (for details,

see Mehta et al. 2003, Honka 2014). In that case, the assumptions of

ﬁrst-order stochastic dominance among the price distributions and

that search costs are not company-speciﬁc are not necessary.

We chose the assumption of normally distributed prices instead

of EV type I distributed prices for both simultaneous and sequential

search models since it allows us to use the approach suggested

by Kim et al. (2010) to calculate the reservation utilities under

sequential search. The Kim et al. (2010) estimation approach for the

reservation utilities cannot be used when prices follow an EV type I

distribution.

Note that we hold the set of D draws from the price distributions

constant within an estimation. We also hold it constant across all

50 replications in the Monte Carlo simulations.

The ﬁt statistic is only a suggestive predictor of the correct search

method since simulations cannot cover the entire space of variables,

parameters, and all possible functional forms of utilities.

Note that Honka (2014) conducted extensive checks to ensure

that using prices charged by previous insurers is a valid approach

Honka and Chintagunta: Search Strategies in the U.S. Auto Insurance Industry

to estimating the marketwide distributions of insurance prices and

does not suﬀer from a selection bias.

Note that because of the size of our data, we are not able to

include company-speciﬁc eﬀects of demographic variables in con-

sumers’ price expectations.

Details on these psychographic factors and summary statistics of

the items that constitute them are available from the authors on

request.

The technical reason for the necessity of an additional assumption

is as follows: If consumers do not optimally choose the company to

search ﬁrst, we cannot derive a general mathematical representation

of the proportion of below-price-expectation actual prices among

consumers who do not search beyond the ﬁrst quote without addi-

tional information/data or other additional assumptions—neither

under simultaneous nor sequential search (we provide details why

this is the case in Sections 5.3.1 and 5.3.2).

This applies to diﬀerentiated goods. We view and model auto

insurance as a diﬀerentiated good.

Consumers stop searching and purchase when the maximum

reservation utility among the searched companies is larger than the

maximum reservation utility among the nonsearched companies

(Weitzman 1979).

Note that the necessary condition that we observe consumers to

search more than once is satisﬁed in our data.

Recall that insurance prices depend on consumer and policy char-

acteristics. In estimating the distribution of prices, we account for

this by making the expected price a function of these consumer

and policy characteristics. Thus, when calculating the proportion of

below-expectation prices, we compare actual prices in consumers’

consideration sets to consumer- and company-speciﬁc expected

prices.

We calculate search costs in dollars by dividing the search cost

coeﬃcient c by the price coeﬃcient β

We also estimated a sequential search model in which search

costs are a function of company-speciﬁc advertising spending in the

month prior to the consumer’s insurance purchase. While advertis-

ing spending signiﬁcantly decreases search costs, the log-likelihood

of such a sequential search model remains worse than the log-

likelihood of the simultaneous search model reported in column (i)

in Table 5. Note that we cannot estimate such a model under simul-

taneous search, as search costs cannot be company-speciﬁc in our

estimation approach (Chade and Smith 2005).

Morgan and Manning (1985) ﬁnd that using simultaneous search

is more eﬃcient for consumers when prices need to be gathered

quickly. Chade and Smith (2006) and Kircher (2009) ﬁnd that using

simultaneous search is more eﬃcient for consumers when the other

side of the market might reject the consumer. Variables that translate

into these two factors in the auto insurance market are potentially

the timing of the price search process (close to the policy expiration

date or weeks in advance), tickets and accidents in the past, and

low credit scores.

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