Consumer Mistakes and Advertising: The Case of Mortgage Refinancing

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Consumer Mistakes and Advertising: The Case of Mortgage Refinancing Serafin Grundl and You Suk Kim 2017-067 Please cite this paper as: Grundl, Serafin and You Suk Kim (2017). “Consumer Mistakes and Advertising: The Case of Mortgage Refinancing,” Finance and Economics Discussion Series 2017-067. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2017.067. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Consumer Mistakes and Advertising: The Case of Mortgage Refinancing Serafin Grundl and You Suk Kim∗ May 5, 2017 Abstract Doesadvertisinghelpconsumerstofindtheproductstheyneedorpushthemtobuyproducts they don’t need? In this paper, we study the effects of advertising on consumer mistakes andquantifytheresultingeffectonconsumerwelfareinthemarketformortgagerefinancing. Mortgage borrowers frequently make costly refinancing mistakes by either refinancing when they should wait, or by waiting when they should refinance. We assemble a novel data set thatcombinesaborrower’sexposuretodirectmailrefinanceadvertisingandtheirsubsequent refinancing decisions. Even though on average borrowers would lose approximately $500 by refinancing,theaveragemonthlyexposureof0.23refinancingadvertisementsreducestheexpected net present value of mortgage payments on average by $13, because borrowers who shouldrefinancearetargetedbyadvertisersandmoreresponsivetoadvertising. Acounterfactual advertising policy that redirects all advertising to borrowers who should refinance would increasethegaininborrowerwelfareto$45. JELCodes: M37,G21,D14 Keywords: Advertising,Mistakes,Mortgage,Refinancing ∗Board of Governors of the Federal Reserve System, serafin.j.grundl@frb.gov, you.kim@frb.gov. We thank Richard Rosen, John Driscoll and Naoki Aizawa for comments that helped to improve the paper. Pete Jacobsen and Meher Islam provided outstanding research assistance. We thank Caitlin Hesser for editing. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the staff, by the BoardofGovernors,orbytheFederalReserveBanks. 1

1 Introduction Consumers are susceptible to making mistakes, and firms engage in various activities that can either encourage or prevent consumer mistakes, which has important policy implications. On the onehand,firmsexploitthebehavioralbiasesofconsumerstosellthemproductstheydon’tneedor tosellthemoverpricedproducts. AkerlofandShiller(2015)arguethatsuchactivitiesareacentral part of free market economies. Examples include shrouding (Gabaix and Laibson (2006)), credit contracts with back-loaded repayment schedules (Heidhues and Koszegi (2010)), or conditioning offers on consumer naivete (Heidhues and Koszegi (2016)). Policies that restrict or regulate such activities, for example the CARD Act or the Qualified Mortgage Rule, can therefore be beneficial forconsumerswhoaresusceptibletomakingmistakes. Ontheotherhand,firmshaveanincentive to help consumers if they fail to buy products they do need, for example by providing information or by educating them about the benefits of a product. Hence, policies that restrict such activities can be harmful for consumers who are susceptible to making mistakes. Instead, policy makers shouldfacilitatesuchactivities. Advertising is an important firm activity that can either encourage or prevent consumer mistakes. Some view advertising as an attempt to sell consumers products they don’t need and others view it as helping consumers to find the products they do need. In the theoretical advertising literature the former view is loosely associated with models of deceptive advertising and models of persuasive advertising, whereas the latter view is associated with models of informative advertising.1 In many markets advertising has both roles at the same time, so the net effect of advertising onconsumerwelfarethroughmistakesisunclear. In this paper, we estimate the effect of advertising on consumer mistakes and quantify the resultingneteffectonconsumerwelfareinthemarketformortgagerefinancing. Inourtheoretical frameworktheeffectofadvertisingonconsumerwelfarethroughitsimpactonconsumermistakes depends on three determinants. First, the composition of consumers, which determines how much the average consumer gains or loses from buying the product. Second, targeting and intensity of advertising, which determines whether and how much advertisers target those consumers who stand to gain the most from buying the product. Third, differential responsiveness, i.e., whether consumerswhostandtogainmorefrombuyingtheproductaremoreresponsivetoadvertising. We quantify the importance of these three factors empirically in the market for mortgage advertising andinvestigatethepotentialimpactofimprovedtargetinginacounterfactualexperiment. The effect of advertising on consumer mistakes and the resulting net effect on consumer welfare has not been studied empirically before. There are two important reasons for the scarcity of 1Ozga(1960),Stigler(1961a),Telser(1964),Nelson(1970,1974)andGrossmanandShapiro(1984)arereferences oninformativeadvertising. Braithwaite(1928),Robinson(1933)orKaldor(1950)areearlyreferencesonpersuasive advertisingandGlaeserandUjhelyi(2010)isarecentreferenceondeceptiveadvertising. 2

empiricalwork. First,formanyproductsadvertisingislikelytoaffectnotonlytheprobabilitythat aconsumerbuysaproductbutalsotheutilitytheconsumergetsfromconsumingtheproduct. For example, because advertising increases the prestige associated with the product. Second, even in marketsinwhichadvertisingaffectsonlytheprobabilityofpurchasebutnottheconsumptionutility,thereisusuallynoobjectivemeasureofconsumptionutilitybecauseitdependsonunobserved tastes. Therefore consumer mistakes cannot be detected and quantified in choice data, because manychoicescanberationalizedbyunobservedtastes. Wearguethattherefisettingallowsustodetectandquantifymistakesinchoicedataandtherefore serves as a laboratory to study the effect of advertising on consumer mistakes empirically.2 First,advertisingisunlikelytoaffecttheconsumptionutilityaborrowergetsfromrefinancingbecause refi loans are not consumed there are no prestige effects in refi advertising. Second, the net present value of mortgage payments is an objective measure of the benefit of refinancing. Thereforerefimistakescanbedetectedandquantifiedinchoicedata. This has been recognized in the growing literature on refi mistakes (Agarwal, Rosen, and Yao (2015), Keys, Pope, and Pope (2016), Andersen, Campbell, Nielsen, and Ramadorai (2017)).3 Borrowers frequently make costly refinancing mistakes. If a borrower refinances her fixed rate mortgage, she can take advantage of a lower mortgage rate, but she must pay a refinancing cost. If the market mortgage rate falls sufficiently far below the borrower’s mortgage rate, it reaches a trigger point where it becomes optimal to exercise the refinancing option. Some borrowers refinance their mortgage prematurely, before the optimal trigger rate is reached. Other inattentive borrowers refinance too late or not at all. Such refinance mistakes can be very costly because for mosthouseholdstheirmortgageisthelargestliability.4 Refiadvertisingcanhelpinattentiveborrowerswhoshouldrefinancebutfailtotakeadvantage of lower interest rates by informing them. However, refi ads can also be deceptive. Lenders commonly advertise the projected reduction in monthly mortgage payments without pointing out that this reduction is partly achieved through an extension of the loan term, rather than through a reduction of the interest rate. Such ads have the potential to convince borrowers who should wait torefinanceprematurely. 2Followingtheterminologyintheliteratureon“refinancingmistakes”,werefertodecisionsas“mistakes”wheneveranalternativedecisionyieldsahigherexpectedpayoff,ifweconditiononallrelevantinformation-whetherthis informationwasavailabletothedecisionmakerornot. Suchdecisionsarenotalwayscalledmistakes. Forexample, suchdecisionscanbeoptimalinmodelsofrationalinattentionormodelsofcostlyreasoning(e.g. Andersen,Campbell, Nielsen, andRamadorai(2017)). However, webelievethatsuchreinterpretationsof“mistakes”donotneedto changetheinterpretationofourresults. Arationallyinattentiveborrowerforexample,whofailstotakeadvantageof lowerinterestrates,wouldstillbenefitfromadvertisingthatdrawsherattention.Arationallyinattentiveborrowerwho shouldnotrefinancemightbeharmedbyadvertisingthatdrawsherattentionevenifshedoesnotrefinance,however. 3SeealsoGreenandLaCour-Little(1999),Schwartz(2006)andCampbell(2006). 4ForexampleKeys,Pope,andPope(2016)estimatethatthemedianlossamonghouseholdswhofailtorefinance whentheinterestratereachestheoptimaltriggerrateis$11,500. 3

The ideal data set to study the effect of refi advertising on borrower mistakes should provide information on advertising exposure of different mortgage borrowers and their subsequent refinancing decisions. However, such a data set is not readily available. With data on advertising throughmassmediasuchasTV,newspaperandradio,itisdifficulttoobservewhetheradvertising is seen by mortgage borrowers with different loan characteristics because the aggregate nature of themassadvertising.5 AlthoughMintelComperemedia(henceforth“Mintel”)collectsinformation on direct mail advertisements and characteristics of their recipients, the data set does not provide information about the recipients’ refinancing decisions. One common limitation of previous studies using the Mintel data is that the choice of the consumers who received direct-mail advertising couldnotbeobserved.6 Weovercomethedatalimitationbyassemblinganovelborrower-leveldatasetthatcombinesa borrower’sexposuretodirectmailrefinanceadvertisingandtheirsubsequentrefinancingdecisions. We merge the direct mail data from Mintel with borrower-level mortgage data from Credit Risk Insight Servicing McDash (CRISM), based on three common variables: a borrower’s zipcode, age and exact outstanding mortgage balance in a given month.7 Unlike more common loan-level data, the CRISM data allows us to observe when borrowers refinance their mortgage. Moreover, CRISM tracks important borrower characteristics such as the FICO score over time so we can focus on borrowers who are likely to qualify for a refi loan.8 Another important advantage of the data is that it allows us to capture the spillover effects of advertising, i.e. we estimate the effect of refi advertising on the overall probability of refinancing rather than only on the probability of refinancingwiththeadvertisinglender.9 Webeginbyformallylayingouthowadvertisingcanaffectborrowerwelfareinourframework, which imposes two important restrictions. First, we assume that refi advertising only affects the probability that the borrower refinances, but not the utility the borrower enjoys from refinancing. Second,weonlyconsiderthedirecteffectsofadvertisingonthepurchaseprobability,notequilibrium effects (e.g. on prices). In this framework, advertising affects borrower welfare only through its effect on the probability that borrowers make refi mistakes - either by refinancing prematurely or by failing to refinance when they should. We show that under these assumptions, the net effect of advertising on borrower welfare depends on three factors. First, differential responsiveness, i.e. whether borrowers who should refinance are more responsive to advertising, than those who 5ThemassadvertisingdataareusuallyavailablefromKantarMedia. 6Recent papers using the Mintel data include Han, Keys, and Li (2013), Ru and Schoar (2016), and Grodzicki (2015). 7CRISMcombinescreditbureaudatafromEquifaxmatchedtotheloan-levelMcDashloanservicingdata(formerly LenderProcessingService). 8Andersen, Campbell, Nielsen, and Ramadorai (2017) point out that studying refi mistakes with US data can be problematicbecausetheborrowercharacteristicsaretypicallyonlyobservedatthetimeoforigination. 9SeeSinkinsonandStarc(2015)andShapiro(2016)foradvertisingspillovers. 4

shouldn’t. Second,targetingandintensityofadvertising,whichdetermineswhetherandhowmuch advertisers target borrowers who should refinance. Third, borrower composition, i.e. how many borrowersshouldrefinanceandhowmanyshouldwait,andhowmuchcantheygainorloseifthey decidetorefinance. Tostudydifferentialresponsiveness,weestimatetheborrower’srefipolicyfunction. Wedivide the borrowers into those who should refinance and those who should wait following the literature on refi mistakes. To determine whether a borrower should refinance we follow the literature on refi mistakes and use the optimal refinancing policy proposed by Agarwal, Driscoll, and Laibson (2013). We find that advertising increases the refi probability for the small group of borrowers who should refinance by approximately 4 percentage points or roughly 25%, over the three quarters after receiving an refi ad. However, advertising has no significant effect on larger group of borrowers who should wait. These estimates suggest that refi advertising helps borrowers who shouldrefinancewithouthurtingborrowerswhoshouldwait. Endogeneity is a common concern in empirical studies of advertising. If advertisers use unobservable consumer characteristics to target consumers who are inherently more likely to buy the product regardless of advertising exposure, then the researcher would overstate the average effect of advertising. It is less clear if targeting based on unobservables would affect estimates of differential responsiveness and if yes, in which direction. In general we do not regard targeting based on unobservables as a major concern in our setting, because we observe many borrower characteristics, including information from a credit bureau, that is not observed by most advertisers.10 It canhoweverbeanimportantconcernforthoseadvertisersthathaveongoingrelationshipswiththe borrowerthroughotherlinesofbusiness(e.g. checkingaccounts),andthereforeobserveborrower characteristics that we do not observe. We address this concern by exploiting the fact that about one half of the advertisers are specialized mortgage firms such as Quicken Loans, which typically have no ongoing relationships with the borrowers, other than through the mortgage. We use advertising sent by specialized mortgage firms as an instrument for overall advertising, and our IV estimatesaresimilartothebaselineestimatesthattreatadvertisingasexogenous. To quantify the effect of refi advertising on borrower welfare, we measure borrower welfare as the expected net present value of mortgage payments. Even though the borrower composition is such that the average borrower would lose approximately $500 from refinancing, the average monthly exposure of 0.23 refi ads reduces the net present value of mortgage payments by $9- $13. This is due to differential responsiveness and targeting, i.e. borrowers who should refinance are more responsive to advertising and more likely to receive advertising. Without differential 10Itisworthnotingthatourestimatesoftheaverageeffectofadvertisingarerelativelysmallandinsomespecificationsnotstatisticallysignificantatconventionallevels. Thissuggeststhattheendogeneityconcernduetotargeting basedonunobservablesmightbelimited. 5

responsiveness, i.e. if all borrowers were equally responsive to advertising, the benefit would decrease to $0-$0.5. Without targeting, i.e. if all borrowers would receive the average amount of refiadvertising,thebenefitofadvertisingwoulddecreaseto$4-$11. Therelativelysmalldecrease inthebenefitofadvertisingiftargetingis“turnedoff”suggeststhattheobservedadvertisingpolicy isonlyslightlybetterthanuntargetedadvertising. This motivates our counterfactual experiment, in which we investigate the potential benefits of improved targeting. An advertising policy that redirects all advertising to those borrowers who should refinance, leaving the total amount of advertising (advertising intensity) unchanged, would increase the benefit of advertising from $9-$13 to $45-$50. Because borrowers who should refinance are more responsive to advertising than those who should wait, the responsiveness of the average ad recipient would be about 5 times larger in this counterfactual than under the observed advertisingpolicy. Therefore,advertiserswouldlikelyalsobebetteroffwithimprovedtargeting. What are the policy implications of these findings? First, even though most borrowers should not refinance, an advertising ban for refi loans would harm borrowers overall. Second, policies that allow advertisers to better target borrowers who should refinance could benefit borrowers and advertisers. However, the benefits of such a policy would have to be weighed against the privacy concern of borrowers. Conversely, our finding suggests that policies that are aimed at protecting theprivacyofconsumerscanmakeconsumersworseoffiftheytheymaketargetingmoredifficult. Literature This paper contributes to the literature on firm activities and consumer mistakes. Brown, Hossain, and Morgan (2010) and Chetty, Looney, and Kroft (2009) provide empirical evidencefromfieldexperimentsthatconsumersareinattentivetohiddenornonsalientattributesof products. Other papers have studied how the susceptibility of consumers to make mistakes affects firmincentivesandactivitiesanddocumentedthatfirmstargetunsophisticatedconsumers(e.g. Ru and Schoar (2016) and Seim, Vitorino, and Muir (2016)). This paper makes three contributions to this literature. First, we have an “objective” measure of consumer welfare and can therefore quantify the welfare impact of the activity. Second, we observe which consumers respond to the firm activity and can therefore study differential responsiveness. Third, we highlight that firm activitiescansometimeshelpconsumerstopreventmistakesratherthanencouragethem. Wealsocontributetotheempiricalliteratureonadvertising. Thereareveryfewpaperstryingto estimate the effect of advertising on consumer welfare.11 One strand of the empirical advertising literature tries to distinguish different models of advertising that posit different mechanisms by which advertising affects consumer decision making (e.g. Ackerberg (2001), Ackerberg (2003), Ching and Ishihara (2012) and Honka, Hortaçsu, and Vitorino (2016)). Different mechanisms 11Dubois,Griffith,andO’Connell(2016)isanexception. Theyrelyonastructuralmodelandquantifytheeffectof advertisingunderalternativeassumptionsaboutthemechanismbywhichadvertisingaffectsdecisionmaking. 6

by which advertising affects decision making are loosely related to the effect of advertising on consumer welfare. For example, it is natural to argue that advertising has a positive effect on consumer welfare if it is informative and a negative effect if it is deceptive.12 In this paper we measuredirectlyhowmuchborrowerswouldbenefitfromrefinancing,whichallowsustoestimate the effect of advertising on borrower welfare without even specifying possible mechanisms by whichadvertisingaffectsdecisionmaking.13 This paper contributes to the ongoing debate about targeted advertising. Some researchers have studied whether advertisers target consumers who are vulnerable.14 For example, Ru and Schoar (2016) find that credit card companies target less sophisticated households with directmail offers with teaser rates and back-loaded fees. Our contribution is that the refi setting allows us to study whether advertisers target consumers who should buy the product. Unlike targeting of vulnerable consumers such targeting can increase consumer surplus. However, the benefits of targetingmuststillbeweighedagainsttheprivacyconcernsofconsumers(seeGoldfarbandTucker (2011),Johnson(2013)andthesurveybyTucker(2012)). Hence,policymakersshouldrestrictthe accessofadvertiserstoinformationaboutthevulnerabilityofconsumers,butthereisatrade-offif similarrestrictionsapplytoinformationaboutwhichconsumersstandtogainfromadvertising. Recently,aliteratureonadvertisinginmarketsforconsumerfinancialproductshasemerged.15 The most closely related papers are Johnson, Meier, and Toubia (2015) and Gurun, Matvos, and Seru (2016), which study advertising in the mortgage market. Johnson, Meier, and Toubia (2015) present survey evidence that the failure of households to take up pre-approved HARP (Home Affordable Refinancing Program) offers can be explained with suspicion towards the motives of the financial institution. Gurun, Matvos, and Seru (2016) find that subprime lenders that advertise more are more expensive. There are several important differences between Gurun, Matvos, and Seru (2016) and our paper. First, we focus on prime borrowers who already have a mortgage and might want to refinance. Second, we focus on the decision whether to refinance, not on the choice ofthelender. Lastly,ourdataallowsustostudytheresponsivenessofborrowerstoadvertising. The remainder of this paper is structured as follows. Section 2 explains how how advertising can affect borrower welfare in our framework, how we measure borrower welfare empirically and how our theoretical framework relates to different models of advertising in the literature. Section 3 describes the data and presents summary statistics. In Section 4 we estimate the refi policy function and find that borrowers who should refinance are more responsive to advertising than 12However,thisisnotnecessarilythecaseaswediscussinsection2.3. 13Notice however that our framework rules out some mechanisms by which advertising affects decision making. FordetailsseethediscussionofthetheoreticaladvertisingliteratureattheendofSection2. 14SeeHeidhuesandKoszegi(2016)foratheoreticalcontribution. 15SeeHastings,Hortacsu,andSyverson(2013)foradvertisingofprivatizedpensionplans,AizawaandKim(2015) advertisinginhealthinsurance,Grodzicki(2015)forcreditcardadvertising,andHonka,Hortaçsu,andVitorino(2016) foradvertisingofbankaccounts. 7

borrowers who should wait. Section 5 quantifies the effect of advertising on borrower welfare, shows how improved targeting could increase the benefit from advertising, and discuss possible policyimplications. Section6concludes. 2 Advertising and Consumer Welfare 2.1 Theoretical Framework Consumer i decides whether to buy a product or to wait and potentially buy it later. Let x be a vector of relevant state variables. If the consumer buys the product she will experience utility U (x) and if she waitsU (x). U andU are unknown to the consumer because she does buy wait buy wait notknowallthebenefitstheproductmightprovideordrawbacksitmighthave. Forsomeproducts U andU arerealizedoveralongperiodoftimeandcandependonfuturestatesoftheworld. buy wait For example, if the consumer buys a refi loan U and U depend on the realization of future buy wait mortgagerates. (cid:2) (cid:3) The consumer’s expected utility from buying the product is u (x)=E U |x . Similarly, (cid:101)buy,i i buy u (x)=E [U |x]. The expectation operator E takes expectations using the consumer’s be- (cid:101)wait,i i wait i liefsg,aboutthebenefitsanddrawbacksoftheproduct. Consumerichoosestobuytheproductif (cid:101)i u (x)≥u (x)andwaitsotherwise. (cid:101)buy,i (cid:101)wait,i An important restriction embedded in this formulation is that after conditioning on x, differencesindecisionsacrossconsumersareonlyduetodifferencesinbeliefsg notduetodifferences (cid:101)i in preferences preferencesU (x) andU (x). Whether this is a plausible assumption depends buy wait whetherxislargeenough. Later,wewilldiscusstheplausibilityofthisassumptioninourmortgage setting. Theprobabilitythatarandomlydrawnconsumerwithstatevectorxbuystheproductisσ(x)= (cid:2) (cid:3) Pr u (x)≥u (x)|x . (cid:101)buy,i (cid:101)wait,i Mistakes We allow the consumer to make mistakes. Mistakes are due to incorrect beliefs g (cid:101)i (cid:2) (cid:3) aboutthebenefitsordrawbacksoftheproduct. Letu (x)=E U |x andu (x)=E[U |x] buy buy wait wait bethe“objective”expectedutilitiesassociatedwithbuyingandwaiting,wheretheexpectationsare taken using the “objective” belief g, which does not vary over consumers. Let σ∗ be the optimal decisionrule,whichisdefinedasσ∗(x)=1ifu (x)≥u (x)andσ∗(x)=0,otherwise. buy wait There are many reasons why consumer beliefs g might differ from g, not all of which are (cid:101)i commonly referred to as mistakes. For example, the beliefs can differ due to information frictions or rational inattention. In this paper we say that consumers make mistakes whenever σ differs from σ∗, even if the consumers maximize their subjective expected utility. This is consistent with 8

theterminologyusedintherefimistakeliterature. Lastly, define v(x)=σ(x)u (x)+[1−σ(x)]u (x). Hence, v measures the expected welbuy wait fareofaconsumercharacterizedbyx. Advertising We now consider the effect of advertising exposure a in this environment. With advertisingexposure,thewelfareofaconsumercharacterizedbyxisv(a,x)=σ(a,x)u (a,x)+ buy [1−σ(a,x)]u (a,x), and the effect of advertising exposure a on expected experience utility is wait δ(a,x)=v(a,x)−v(0,x). Generally,therearetwodirecteffectsofadvertisingonconsumerwelfarev.16 First,advertising can affect U and U , for example if advertising makes a product more prestigious. Second, buy wait advertisingcanchangeconsumerbeliefsg,forexampleifadvertisinginformstheconsumerabout (cid:101)i the benefits of a product. As we explain in more detail below, the first effect is associated with models of persuasive and complementary advertising whereas the second effect is associated with modelsofinformativeanddeceptiveadvertising. In the remainder of this paper we assume that advertising does not enter U and U and buy wait therefor does not affect u or u . We argue that this assumption is reasonable in the context of buy wait mortgagerefinancingbecauserefiloansarenotconsumedanditisunlikelythatthereare“prestige” effectsofrefiadvertising. ThreeDeterminantsofWelfareEffect Differential Responsiveness Under the assumption that advertising does not enterU and buy U ,δ canbeexpressedasfollows: wait (cid:2) (cid:3) δ(a,x) = [σ(a,x)−σ(0,x)] u (x)−u (x) . buy wait = ∆σ(a,x)∆u(x) It is clear that the effect of advertising on δ depends now solely on its effect on σ and thereby on the probability and severity of mistakes. If advertising has a large effect on σ for x such that u (x) ≥ u (x) and a small effect otherwise then advertising tends to help consumers. buy wait The effect of receiving advertising a on consumer welfare depends therefore on the differential in responsivenessofconsumerswhoshouldbuyandthosewhoshouldwait. 16We only consider the direct effects of advertising on consumer welfare, not potential equilibrium effects (e.g. pricechanges). 9

Targeting and Intensity of Advertising The expected effect of advertising on a consumer characterizedbyx is: ˆ E[δ(a,x)|x]= δ(a,x)dF(a|x). The distribution of advertising F conditional on x captures targeting and intensity of advertising. WesometimesrefertoF astheadvertisingpolicy. Whiletheintensityofadvertisingiscapturedby theunconditionalmeanofa,targetingdescribeshowthemeanvarieswithx. IfF hasalotofmass at 0 for consumers who should wait and a lot of mass at positive levels for consumers who should buy, then advertising tends to help consumers. Advertising intensity only affects the magnitude of E[δ(a,x)|x]whereastargetingalsoaffectsthesign. ConsumerComposition Lastly,wehavetointegrateoutxtocapturetheeffectofadvertising onallconsumers: ˆ E[δ(a,x)]= δ(a,x)dF(a|x)dG(x), (1) where G is the distribution of x, which captures that the overall effect of advertising on consumer welfare also depends on the composition of consumers, i.e. how many consumers should buy and how many borrowers should wait and how much they can gain or lose if they decide to buy due to advertising. Discussion Tounderstandwhetheradvertisingisbeneficialorharmfulallthreeofthesedeterminantshavetobetakenintoaccount. Forexample,itistemptingtobanadvertisingforaproductthat would harm the average potential buyer of the product. Examining equation (1), however, makes clearthatsuchabanmightharmconsumers,becausetheeffectsofdifferentialresponsivenessand targeting can dominate the effect of consumer composition. Similarly, if advertisers mostly target consumerswhowouldbeharmedbybuyingtheproduct,thiseffectcanbedominatedbytheeffect ofdifferentialresponsiveness. Later, we will try to quantify the contributions of differential responsiveness, targeting and consumer composition to the benefit of advertising E[δ(a,x)]. To quantify the importance of differential responsiveness we recalculate the benefit of advertising under a counterfactual σ(cid:48) such ´ that the average effect of advertising, ∆σ(a,x)dG(x) remains unchanged, but the effect of advertisingunderσ(cid:48) doesnotvarywithx. Toquantifytheimportanceoftargetingwerecalculatethe benefitofadvertisingunderacounterfactualtargetingpolicyF(cid:48) suchthattheadvertisingintensity, ´ adF(a|x)dG(x), remains unchanged but no longer varies with x. To quantify the importance ´ consumercompositionwecalculate ∆u(x)dG(x). 10

2.2 Empirical Implementation For most products, it is impossible to measure δ directly because the functions U and U buy wait are unknown.17 We argue that if the product is a refi loan, U and U can be measured by buy wait the NPV of mortgage payments if the borrower decides to refinance or wait, respectively. The crucial difference between the refi decision and other purchase decisions is that refi loans are not consumed,andrefinancingsimplyreplacesonepaymentstreamwithanotherpaymentstream. Hencewemeasureδ asfollows: (cid:2) (cid:3) δ(a,r,x) = [σ(a,r,x)−σ(0,r,x)] NPV (r,x;σ)−NPV (r,x;σ) wait refi = ∆σ(a,r,x)∆NPV(r,x;σ). (2) Herethevectorxcontainstheremainingprincipalbalance,theremainingloantermandtheinterest rate of the old mortgage and r denotes the current market mortgage rate.18 NPV (r,x;σ) denotes j the expected NPV for action j ∈{wait,refi} for a borrower characterized by state vector x when the current mortgage rate is r. Note that NPV (r,x;σ) depends on σ because the borrower can j refinance in the future. Importantly, NPV (r,x;σ) includes not only the interest and principal j payments but also today’s refinancing costs and potential future refinancing costs.19 NPV and refi NPV correspondto−u and−u inourtheoreticalframework. wait buy wait Weobservethevariablesinxinourdata. However,inadditiontotheobservablestatevariables, the NPVs likely depend on state variables that are not observable. For example, there could be unobserved differences in the “hassle costs” associated with refinancing. Moreover, there could be unobserved differences in time preferences, risk aversion or future moving propensity. It is likely that these unobservables can rationalize some of the apparent refinancing mistakes that we observe and that have been described in the literature on refi mistakes (e.g. Agarwal, Rosen, and Yao (2015) and Keys, Pope, and Pope (2016)).20 Later, we will discuss whether such unobserved heterogeneitycanaffectourestimatesofdifferentialresponsiveness. 17To estimate u (x)−u (x) we would typically follow a revealed preference approach and assume that conbuy wait sumersmakenomistakes. 18Weintroduceseparatenotationforthecurrentmortgageratebecausetheoptimalrefinancingpolicycanbecharacterizedbyatriggermortgagerate. 19WeprovidedetailsaboutthecalculationofNPV (r,x;σ)inSection5. j 20Johnson,Meier,andToubia(2015)havesurveymeasuresoftimepreferencesandriskaversionandfindthatthey cannot explain the failure of households to refinance their mortgage. They also have survey measures of the future moving propensity, which helps to rationalize some of the apparent refinancing mistakes. In one of our robustness checksweallowforheterogeneousmovingpropensitiesandfindsimilarestimatesofdifferentialresponsivenessasin thebaselineestimateswithauniformmovingpropensity. Wefindthatborrowerswhoshouldrefinancearemoreresponsivetoadvertising. Thissuggeststhatatleastsomeof these borrowers make mistakes or are inattentive and their failure to refinance despite low interest rates cannot be rationalizedbyunobservablessuchastimepreferences,riskaversionorfuturemovingpropensity. 11

In section 4 we estimate σ to see whether advertising exposure brings σ closer to an optimal refi policy function σ∗. A borrower would refinance under σ∗ if and only if ∆NPV(r,x;σ∗)≥0. This optimal policy can be characterized by a trigger rate r∗(x) such that a borrower refinances if r ≤ r∗(x) and waits otherwise. Define d(r,x) ≡ r∗(x)−r, i.e. d is the difference between the optimal trigger rate and the current mortgage rate. In our responsiveness estimates we let the effectofadvertisingvarywithd(r,x). Ifadvertisinghasalargereffectforlarged,thenadvertising exposurebringsσ closertoσ∗(a,r,x)=1{d(r,x)≥0}. To calculate r∗(x) we rely on the model of Agarwal, Driscoll, and Laibson (2013) (henceforth ADL). ADL make some simplifying assumptions to obtain a closed form solution for r∗ and demonstrate that their trigger rate closely approximates policies that are computed numerically withoutrelyingonsuchsimplifyingassumptions. Werefertotheoptimaltriggerrateproposedby ADL as r∗ (x) and define d (r,x)≡r∗ (x)−r. The ADL trigger rate is also used by Agar- ADL ADL ADL wal, Rosen, and Yao (2015) and Keys, Pope, and Pope (2016) to quantify refinancing mistakes.21 The expression for r∗ can be found in Appendix A. In the remainder of this paper we say that a ADL borrower“shouldrefinance”ifthemarketmortgagerateisbelowtheADLtriggerrateandthatthe borrower“shouldwait”otherwise. 2.3 Theoretical Advertising Literature Before we proceed to describing the data, we discuss how models of informative, deceptive, persuasive and complementary advertising can be interpreted in our framework.22 Readers who are notinterestedintherelationshiptothetheoreticaladvertisingliteraturecanjumpdirectlytosection 3. In models of informative and deceptive advertising, advertising affects decision making by changing the beliefs of consumers rather than by changing their utility function. In the context of our framework, this means that informative and deceptive advertising affect g and thereby u (cid:101)i (cid:101)buy andu andσ,butnotu andu . (cid:101)wait buy wait In models of informative advertising, advertising helps consumers to make more informed decisions. Important references include Marshall (1919), Stigler (1961b), Butters (1977) and Grossman and Shapiro (1984). The informative view suggests that advertising moves g closer to g and (cid:101)i therefore advertising tends to help consumers make better decisions. However, this is not necessarily the case. For example, suppose g is a belief about future interest rates and the fixed cost (cid:101)i 21Conceptually,thereisa“modelfree”alternativetostudyrefinancingmistakesbysimplycomparingtherealized streamsofmortgagepaymentsofborrowerswhorefinancedandthosewhodidnot.Inpractice,however,thisapproach wouldrequiredataoveraverylongtimeperiodtoensurethattherealizedpathofmortgageratesapproximatesrational expectations. Forexample,themortgageratesweredecreasingoverthefirsthalfofoursampleperiodsothemistakes ofborrowerswhofailedtorefinanceduringthistimeappeared“right”expost. 22SeetheexcellentsurveysbyBagwell(2007)andRenault(2015)formoredetaileddiscussionofthesemodels. 12

of refinancing. We could construct a g that deviates substantially from g such that the resulting (cid:101)i u andu areclosetou andu andtheconsumerthereforemakesapproximatelyoptimal (cid:101)buy (cid:101)wait buy wait decisions. This would be the case if the consumer has overly optimistic beliefs about the interest rate,butoverlypessimisticbeliefsaboutthefixedcostofrefinancingandthesetwobiasesapproximately offset each other. If informative advertising corrects the consumer’s belief about interest rates,butnotthebeliefaboutthefixedcostofrefinancing,itwouldmoveg closertog,butwould (cid:101)i leadtoworsedecisions. Morerecently,aliteratureondeceptiveadvertisinghasemerged,whichstressesthatadvertising can distort decision making because it informs consumers only selectively and tries to affect how the information is perceived.23 Deceptive advertising might move g further away from g, which (cid:101)i suggests that it leads to worse decisions. However, this is not necessarily the case, because we havearguedabovethatbeliefsthatarefurtherfromgcanleadtobetterdecisions. In models of persuasive and complementary advertising, advertising affects consumer preferences. Persuasive advertising changes consumer preferences, whereas complementary advertising entersasanargumentinastableutilityfunction. Persuasive advertising can be interpreted in two ways with different welfare implications. Under the first interpretation the pre-advertising preferences are the consumer’s true preferences and the relevant standard for consumer welfare whereas the post-advertising preferences explain the consumer’s choices, which can therefore be distorted. This distortionary interpretation goes back to Braithwaite (1928). In the context of our framework, the distortionary interpretation says that advertising affects u and u and thereby σ, but not u and u . Hence, the distortionary (cid:101)buy (cid:101)wait buy wait interpretation of persuasive advertising can be regarded as “reduced form” of models of informativeandespeciallymodelsofdeceptiveadvertisingwithoutspecifyingconsumerbeliefsg. Under (cid:101)i the second interpretation, the post-advertising preferences are the relevant standard for consumer 23AkerlofandShiller(2015)(“AdvertisingasStorytelling”)emphasizethisaspect: “... It’snotjustthatweacquire new’information’;wechangeourpointofviewandinterpretinformationinnewways. Importantly,theseevolutions of our thoughts mean that our opinions, and the decisions that are based on them, may be quite inconsistent. These descriptions of human thinking as narrative, or like narrative — so that it will not naturally, inevitably, be consistent—gives a role for advertising.” On the role of advertisers they write: “...advertisers are supposed to enhance the salesofthecompaniesthathirethem,evenifthosesalesreduceconsumers’wellbeing.” SeealsoKaldor(1950):“Asameansofsupplyinginformationitmaybearguedthatadvertisingislargelybiasedand deficient. Quiteapartfromthemakingofdeliberatelyfakedclaimsaboutproductswhichlegislationandprofessional etiquettehaveneversucceededinsuppressing,theinformationsuppliedinadvertisementsisgenerallybiased,inthat itconcentratesonparticularfeaturestotheexclusionofothers;makesnomentionofalternativesourcesofsupply;and itattemptstoinfluencethebehavioroftheconsumer,notsomuchbyenablinghimtoplanmoreintelligentlythrough givingmoreinformation,butbyforcingasmallamountofinformationthroughitssheerprominencetotheforeground ofconsciousness.” Nelson (1974) who develops models a model informative advertising discusses deceptive advertising informally. Recently, formal models of deceptive advertising have been studied by Glaeser and Ujhelyi (2010), Hattori and Higashida(2012),HattoriandHigashida(2014),Corts(2014),Piccolo,Tedeschi,Ursino,etal.(2015),Piccolo,Tedeschi, andUrsino(2015)andRhodesandWilson(2015). 13

welfare and therefore advertising is not distorting the choices. In the context of our framework, (cid:0) (cid:1) the non-distortionary interpretation says that advertising changes U ,U and therefore has buy wait (cid:0) (cid:1) (cid:0) (cid:1) similareffectson u ,u and u ,u . (cid:101)buy (cid:101)wait buy wait Lastly, in models of complementary advertising, advertising enters as an argument in a stable utility function (Stigler and Becker (1977), Nichols (1985) and Becker and Murphy (1993)). For example,thesemodelscancapturetheprestigeeffectsofadvertising. Inourframework,thismeans (cid:0) (cid:1) that complementary advertising enters as an argument in U ,U and therefore therefore has buy wait (cid:0) (cid:1) (cid:0) (cid:1) similar effects on u ,u and u ,u . Hence, complementary advertising is similar to (cid:101)buy (cid:101)wait buy wait thethenon-distortionaryinterpretationofpersuasiveadvertising. We assume that refi advertising does not enter U and U . Hence, we rule out models of buy wait complementaryadvertisingandthenondistortionaryinterpretationsofpersuasiveadvertising. Our frameworkisconsistentwithmodelsofinformativeanddeceptiveadvertising. Itisalsoconsistent with thedistortionary interpretationof persuasive advertising,which can beregarded as areduced form of models of informative and especially deceptive advertising without specifying consumer beliefsg. (cid:101)i It is plausible that models of informative and deceptive advertising apply to refi advertising. On the one hand, refi advertising reminds borrowers of their refi option and perhaps of the current mortgage rate. On the other hand, refi advertising can often be considered to be deceptive. For example, refi ads often advertise the reduction in monthly payments without explaining that this reduction is partly achieved through term extension rather than through a reduction of the interest rate.24 3 Data Data Description To quantify the effect of advertising on borrower welfare and to determine the importance of differential responsiveness, targeting and borrower composition is challenging because available data sets do not contain the necessary information. Existing data sets do not provideinformationaboutrefinancingbehavior,borrowerandloancharacteristics,andadvertising exposure at the borrower level. Data on mortgage loans and mortgage borrowers do not contain information about a borrower’s exposure to refinance advertising, and data on advertising do not containinformationaboutaborrower’srefinancingbehavior. Typical loan-level mortgage data sets, such as McDash loan servicing data (formerly Lender ProcessingService),onlyprovideinformationaboutloancharacteristics. Loan-leveldataalonedo 24TheFTCwarnsconsumersspecificallyaboutdeceptivemortgageadvertisingandexplains“WhattheAdsSay” and“WhattheAdsDon’tSay”(http://www.consumer.ftc.gov/articles/0087-deceptive-mortgage-ads). UndertheConsumerFinancialProtectionActtheConsumerFinancialProtectionBureau(CFPB)isauthorizedtotakeactionagainst deceptivelendingacts. 14

not allow us to determine whether a loan was refinanced or prepaid for a different reason, because theyonlytrackloans,notborrowers. Moreover,theMcDashdatacontainaborrower’screditscore at loan origination, but not her updated credit score, which is one of the important characteristics that determine whether the borrower would qualify for a refi loan. Borrower-level panel data from Credit Risk Insight Servicing McDash (CRISM) combines credit bureau data from Equifax and the loan-level McDash data. Therefore it provides information about a borrower’s updated credit score and whether a borrower prepaid a loan to refinance. However, the CRISM data only provideinformationaboutborrowerandloancharacteristicsandrefinancingbehaviorbutnotabout advertisingexposure. Although data on mass advertising such as TV, newspaper and radio advertising is readily available, it is not suitable for this study because we want to link borrower-level advertising exposure, to borrower and loan characteristics and to subsequent refinancing behavior. Therefore, the direct-mail advertising data from Mintel Comperemedia (henceforth Mintel) is more suitable forthisstudy.25 Themainlimitationofdirect-mailadvertisingdataisthattherecipient’spurchase behavioristypicallynotobserved. We obtain information on borrower and loan characteristics, refinancing behavior and advertising exposure at the borrower level, by merging the CRISM and Mintel data sets. We are able to match a borrower in the Mintel and her record in CRISM based on the three common variables containedinbothdatasets: aborrower’sage,zipcodeandexactoutstandingmortgageloanbalance in a given month.26 We consider a match successful only when two observations in the two data setshaveexactlyidenticalvalues. Ourfinalsampleconsistsof12,435borrower-monthpairsfrom2009to2015forwhichweobserveadvertisingexposure. All borrowershaveafixed-rate mortgage. We excludeborrowerswith FICO scores below 620 and borrowers with loan-to-value ratios above 0.8.27 These borrowers are excludedbecausetheymightnotqualifyforarefiloan,andwedonotwanttoconfuseineligibility torefinancewithrefimistakes. Summary Statistics Table 1 shows summary statistics for two groups of borrowers depending onvaluesofr∗ (x)−r. Recall,thatwerefertoborrowerswithr∗ (x)<rasthosewho“should ADL ADL wait”andborrowerswithr∗ (x)≥r tothosewho“shouldrefinance”. ADL Thevariablesaredividedintofivegroups. Thefirstgroupofvariablesaredummyvariablesthat indicate whether the borrower refinanced. If a borrower decides to refinance, it can take several 25Recent studies using the Mintel data include Han, Keys, and Li (2015), Ru and Schoar (2016) and Grodzicki (2015). 26OurversionoftheMinteldatasetismergedtocreditbureaudatafromTransUnionandthereforecontainsinformationabouttheoutstandingmortgageloanbalance. 27We approximate a borrower’s updated house value using the house value at loan origination and a county-level housepriceindexprovidedbyCoreLogic. 15

months before the refi loan is closed and several additional months before we observe that the borrower has refinanced in the data. “Refinanced within n Quarters” is a dummy variable that equalstooneifaborrowerrefinanceswithinnquartersafterwemeasuretheadvertisingexposure. Notethatthesevariablesareequaltooneifaborrowerrefinanceswithanymortgagelender,notjust with the advertising lender. Hence, our estimates incorporate the spillover effects of advertising, which is important if we want to study the effects of advertising on consumer welfare, rather than theprofitabilityofadvertising. Thetableshowsthatborrowerswhoshouldrefinance,dorefinance atapproximatelytwicetherateasborrowerswhoshouldwait. However,8%oftheborrowerswho should wait refinance within three quarters and 85% of the borrowers who should refinance fail to doso. The second group of variables contains two measures of advertising exposure. The first measurecountsalldirect-mailadvertising. Aborrowerreceives0.23direct-mailrefinancepiecesinthe previous month on average. In other words, a borrower receives approximately one piece of refi advertising every four months. Moreover, borrowers who should refinance receive 50% more advertisingthanthosewhoshouldwait,whichsuggeststhatadvertiserstargetborrowerswhoshould refinance. However, notice that there are 10,941 borrowers who should wait and only 1,494 borrowers who should refinance. Consequently, about 83% of all refi ads are sent to borrowers who should wait.28 The second measure of advertising exposure count only direct mail refi advertising that is sent by specialized mortgage companies such as Quicken Loans, as opposed to depository institutionssuchasWellsFargo. Specializedmortgagefirmsaccountforapproximatelyabout50% ofthetotal. 28Thefractionofallrefiadssenttothosewhoshouldwaitcanbecalculatedasfollows: 0.83= 0.22∗10941 . 0.22∗10941+0.33∗1492 16

Table 1: Summary Statistics. Column (1) shows the mean for borrowers who should wait according to the optimal trigger rate by ADL; column (2) shows borrowers who should refinance; and column (3) shows the unconditional mean. The first group of variables shows how many households refinanced in the subsequent quarters. The second group contains two measures of advertising exposure. First, the total number of direct mail refi ads a household received in the previous month. Second, the number of refi ads from nonbanks. The third group are the variables in x that determine the optimal trigger rate r∗ (x), and the prevailing rate mortgage rate r. The ADL fourth group is the optimal trigger rate r∗ (x) proposed by ADL, the difference between the op- ADL timal trigger rate and the available mortgage rate d (r,x)=r∗ (x)−r, and a dummy variable ADL ADL d (r,x)≥0, which indicates whether the borrower should refinance based on the ADL model. ADL Lastly, the fifth group contains other controls. We exclude borrowers with loan to value ratios above0.8orFICOscoresbelow620. ShouldWait ShouldRefinance Total Group1: RefiBehavior Refinancedwithin1Quarter 0.03 0.06 0.03 Refinancedwithin2Quarters 0.05 0.11 0.06 Refinancedwithin3Quarters 0.08 0.16 0.09 Refinancedwithin4Quarters 0.11 0.20 0.12 Group2: AdvertisingExposure DirectMailAdvertising(DMA) 0.22 0.33 0.23 DMA:Nonbanks 0.11 0.22 0.13 Group3: xandr RemainingPrincipalBalance(in$1,000) 106.07 124.04 108.22 RemainingTerm(inMonths) 225.34 258.92 229.37 RateofCurrentMortgage(in%) 5.14 6.74 5.33 MarketFRMRate(in%) 4.29 3.97 4.25 Group4: OptimalRefiPolicy OptimalTriggerRate(in%) 2.51 4.65 2.77 OptimalTriggerRate-MarketRate(in%) -1.78 0.69 -1.49 ShouldRefinance 0.00 1.00 0.12 Group5: Controls MortgageInquiries(Past3Months) 0.06 0.10 0.06 FICOScore 774.90 751.27 772.06 LTVRatio 0.47 0.55 0.48 Income(in$1,000) 80.83 75.95 80.25 Age 54.33 54.85 54.39 Observations 10943 1492 12435 FractionofTotal 88% 12% 100% The third group of variables contains x and r. The optimal trigger rate r∗ (x) depends on ADL the remaining principal balance, the remaining mortgage term, and the interest rate of the current mortgage. It is increasing in all three of these state variables. It is increasing in the remaining 17

principal, because the interest savings are proportional to the principal but part of the refinancing costsarefixed. Itincreasingintheremainingloantermbecauseiftheremainingloantermisshort the borrower has to pay the high mortgage rate on the old loan only for a short period of time. Naturally, it is also increasing in the interest rate of the old mortgage. Consequently, borrowers who should refinance have higher remaining balances, longer remaining loan terms and higher interestratesontheircurrentmortgage. Theavailablemortgageratei,istheaveragemortgagerate for 30 year fixed rate mortgages provided by the St. Louis Fed.29 Unsurprisingly, borrowers who shouldrefinancefacelowermortgagerates. The fourth group of variables are generated using the optimal refinancing model by ADL, the optimaltriggerrater∗ (x),thegapbetweentheoptimaltriggerrateandthemarketrated (r,x) ADL ADL and an indicator called “Should Refinance” ford (r,x)≥0. If it is not optimal for the borrower ADL torefinanceatanypositiveinterestratebasedontheADLmodel,wesetr∗ (x)tozero.30 While ADL the market rate is about one percentage point below the rate of the current mortgage on average, it is about 1.5 percentage points above the optimal trigger rate. Indeed, only 12 percent of the borrowers should refinance according to the ADL trigger rate. The optimal trigger rate is 2.51 percent on average for borrowers who should wait and 4.65 percent for borrowers who should refinance. Thefifthgroupincludesadditionalcontrolsthatmightaffectaborrower’srefinancingbehavior. Thenumberofmortgageinquiriesrecordedbythecreditbureauinthepreviousthreemonthscould capture whether a borrower is already looking for a refi loan. Borrowers who are already looking for a refi loan are more likely to refinance regardless of advertising exposure. In addition, we also consider the FICO score, the LTV ratio, income and age because they can determine whether a borrowerqualifiesforamortgage. Table 2 splits the sample further. It shows borrowers who should wait in columns (1) and (2) and borrowers who should refinance in columns (3) and (4). Within each group of borrowers, it compares borrowers who did not receive advertising (columns (1) and (3)) with borrowers who receivedadvertising(columns(2)and(4)). Forborrowerswhoshouldwait,advertisingappearsto have a small effect on the probability of refinancing. The probability that the borrower refinances withintwo,threeorfourquartersisonepercentagepointhigherforborrowerswhoreceivedadvertising,andthereisnodifferenceintheprobabilityofrefinancingwithinonequarter. Forborrowers whoshouldrefinance,however,advertisingappearstohavealargereffectontheprobabilityofrefinancing. Therefiprobabilityisbetweenfourandfivepercentagepointshigherforborrowerswho receivedadvertisingoverahorizonoftwo,threeorfourquartersandtwopercentagepointshigher 29Thedataisavailableathttps://fred.stlouisfed.org/series/MORTGAGE30US.Inarobustnesscheck,weallowdifferentborrowerstohaveaccesstodifferentinterestratestoaccountforpossibledifferencesindefaultriskormortgage shoppingcosts. 30Thisisthecasefor8.5%ofallobservations. 18

over a horizon of a single quarter. This suggests that borrowers who should refinance are more responsive to advertising. In the next section, we present responsiveness estimates that control for otherdeterminantsofrefinancingbehaviorandconfirmthissuggestiveevidence. 4 Differential Responsiveness Specification Inthissectionweestimatetherefinancingpolicyσ. Tofacilitatecomparisonswith specifications where we instrument for advertising, we estimate a linear probability model rather thananonlinearbinarychoicemodel: refinanced =β +β d (x,r)×a+β a+β d (x,r)+Zβ +ξ +ξ +ε. (3) 0 1 ADL 2 3 ADL Z c q The dependent variable is a dummy that is equal to one if a borrower refinances within the following three quarters.31 Recall that d (x,r) measures the gap between the optimal trigger rate ADL r∗ (x) and the market mortgage rate r. If the borrower follows the optimal ADL refi strategy, ADL she should exercise her refinancing option if d (x,r) is positive and wait if d (x,r) is neg- ADL ADL ative. The magnitude of d (x,r) tells us how far the borrower is in the exercise region or the ADL waiting region, respectively. The variable a is the number of refinance advertising mailings the borrower received in the previous month. The main coefficient of interest is β for the interaction 1 term d (x,r)×a. The variables in Z are included to control for borrower and loan character- ADL istics, which include the borrower’s age, current FICO score, current LTV ratio and the number of mortgage inquiries within the past three months.32 Recall that we exclude borrowers with a FICO score below 620 or LTV ratio above 0.8 because such borrowers might be ineligible for refinancing. In addition, we control for the FICO score and the LTV ratio account for the fact that it might be easier to qualify for a refi loan for borrowers with good credit scores and low LTV ratios. Moreover, the number of mortgage inquiries within the past three months is included in order to control for borrowers who have recently looked for a refinancing option. It is important to control for recent mortgage inquiries because lenders might target borrowers who are already in the market for refinancing and the estimated effects of advertising could therefore be driven by reversecausality. Lastly,weincludecountyandquarterfixedeffectsξ andξ .33 c q 31Laterweshowthatourresultsaresimilarifweconsiderrefinancingwithinone,twoorfourquartersinstead. 32Forasubsampleofborrowerswealsoobserveeducationandoccupationbutwefoundthesenottobeimportant forrefinancingbehavior. 33In more recent years the Mintel sample includes respondents who are panelists, whereas the sample was a repeatedcross-sectioninearlieryears. Thereforewealsoexperimentedwithspecificationswithborrowerfixedeffects. However, we only have within borrower-variation for some borrowers. These estimates therefore rely heavily on the functional form of the linear probability model and should be interpreted with caution. We also estimated specifications with county-quarter fixed effects, which suffer from a similar problem. The estimates of β in these two 1 19

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Endogeneity Identification of the effects of advertising on demand is challenging because of the possibility that advertisers target consumers who are inherently more likely to purchase an advertisedproduct. Ifanadvertiserhasmoreinformationthanresearchersaboutwhichconsumers are more or less likely to purchase the product, then advertising might be targeted at consumers with high demand for the product even after controlling for characteristics that are observed by the researchers. In this case, there is a concern about reserve causality: even if advertising has no effect on a consumer’s demand we would find a relationship between advertising and demand. Noticethatwhilethisreversecausalityconcernwouldleadtoanupwardbiasoftheoveralleffectof advertising, it is unclear whether β , which measures differential responsiveness, would be biased 1 and in which direction the bias would go. This is important, because we are more interested in differentialresponsivenessthantheaverageeffectofadvertising. In our setting, the concern about targeting based on unobserved borrower characteristics is less serious than in other settings, because we observe more information about borrowers than most lenders. Even if a lender has an existing relationship with a mortgage borrower through loan servicing, the information about the borrower is likely limited to her mortgage characteristics and paymentbehavior,whichwealsoobserve. Inaddition,wealsoobserveaborrower’supdatedFICO score, which contains information, not only about the payment behavior for the mortgage but also otheraccountssuchascreditcardsandautoloans.34 Aninstanceinwhichalendermayhavemoreinformationaboutaborrowerthanweobserveis whenthelenderhasanongoingrelationshipwiththeborrowerthroughotherproducts,forexample, checkingaccounts. Suchlendersmightbeabletoobservehowaborrower’sincomeorassetshave evolved over time. Because we observe a borrower’s annual income, the amount of information unobserved in our data is likely limited and we do not know whether using this information for targeted advertising would be legal. Nevertheless, this possibility still raises the issue of reverse causality. We address this reverse causality concern by using direct mailings by specialized mortgage companies as an instrumental variable for the total number of direct mailings . The idea is that lenders who likely have an additional ongoing relationship with the borrower are depository institutions, which usually have multiple lines of business. For example, banks like Wells Fargo offer numerous financial services to consumers such as checking and savings accounts, wealth management, etc. In contrast, most specialized mortgage companies, such as Quicken Loans, usually specificationsare0.0133and0.0146,whichissimilartoourbaselinespecification. 34Lenderscantargetborrowerswhoarelikelytorefinancebypurchasingalistofborroweraddressesfromcredit bureausthatsatisfycertainconditions. Forexample,lenderscanselectborrowerswhohavemortgageswithoutstandingbalancesandmonthlypaymentsabovecertainthresholds.Moreover,alendermightevenaskforalistofborrowers withapositivenumberofmortgageinquiresinthepastmonthstotargetadvertisingtothosewhoarealreadylooking forarefiloan. Asweobservethesevariables,thiskindoftargetingshouldnotcreateareversecausalityconcernfor ourestimates. 21

only have a mortgage origination and perhaps mortgage servicing business. Thus, these lenders are unlikely to have information about borrowers that we do not observe in our data As shown in Table1,directmailingsfromnonbanklendersmakeupslightlymorethanahalfofthetotaldirect mailingsreceivedinoursample. In the next section we present our results. The baseline estimates are from the OLS regression of equation (3), and we present IV estimates as a robustness check after discussing the baseline estimates. Results Table3showsthebaselineestimates. Thefirstcolumnpresentsestimateswithaspecificationwithouttheinteractiontermd (x,r)×a,whilethesecondcolumnpresentstheestimates ADL withthespecificationgiveninequation(3). Inthefirstcolumnwefindthattheeffectofadvertising ondemandissmallandbarelystatisticallysignificantonaverage. ThisisconsistentwithLewisand Rao (2015), who show that it is generally difficult to estimate the returns to advertising precisely. However,turningtothesecondcolumn,wefindthattheeffectofadvertisingisveryheterogeneous and depends on d (x,r). Borrowers who are further in the exercise region are more responsive ADL to advertising. If the market mortgage rate equals the trigger rate where it becomes optimal to refinance based on the ADL model, one piece of direct mail advertising increases the probability ofrefinancingby2.50percentagepointsorabout15%oftheunconditionalrefinancingprobability of those with d (x,r)≥0. If the market mortgage rate is one percentage point above the ADL ADL trigger rate, i.e. the borrower should wait, the effect decreases by 1.59 to 0.91 percentage points. Conversely, if the market mortgage rate is one percentage point below the ADL optimal trigger rate,i.e. theborrowershouldrefinance,theeffectincreasesby1.59to4.09percentagepoints. This result suggests that advertising is potentially beneficial for borrowers. The estimated heterogeneous effects of advertising will help to mitigate mistakes of those borrower who fail to take advantage of low interest rates. At the same time, advertising is unlikely to exacerbate mistakesofprematurerefinancingforthosewhowouldnotbenefitfromrefinancing. Asdiscussed in section 2, however, differential responsiveness is just one of the factors that determine the net effect of advertising on borrower welfare. Borrower welfare also depends on targeting and the compositionofborrowers,whichwewilltakeintoaccountinsection5. Our finding suggests that the recipients of refi ads respond more to the informative aspects of refi ads than to the deceptive aspects. In particular our finding is consistent with a model in which advertising increases the probability that borrowers are attentive. Inattentive borrowers fail to take advantage of lower mortgage rates because do not consider the possibility of refinancing. However, while models of informative advertising might be a more natural interpretation of the findings,wecannotrejectmodelsofdeceptiveadvertisingwithoutimposingfurtherrestrictions. In particular,thefindingsareconsistentwithamodelofdeceptiveadvertisinginwhichborrowerswho 22

should refinance are more easily deceived than those who should wait and deceptive advertising thereforeincreasesborrowerwell-being. BeforeweproceedtoSection5,webrieflypresentseveral robustnesscheckforourresponsivenessestimates. Table3: Responsiveness: BaselineEstimates. Thedependentvariableisadummythatisequalto oneiftheborrowerrefinancedwithinthreequarters. Countyandquarterfixedeffectsareincluded. Standarderrorsareclusteredatthecountylevel. (OptimalTrigger-MarketRate)x(DirectMailAdv.) 0.0159∗∗∗ (0.00415) DirectMailAdvertising(DMA) 0.0100∗ 0.0250∗∗∗ (0.00607) (0.00823) OptimalTriggerRate-MarketRate(in%) 0.0373∗∗∗ 0.0344∗∗∗ (0.00357) (0.00353) MortgageInquiries(Past3Months) 0.0890∗∗∗ 0.0893∗∗∗ (0.0154) (0.0155) FICOScore 0.000264∗∗∗ 0.000269∗∗∗ (0.0000708) (0.0000707) LTVRatio -0.0443∗∗ -0.0438∗∗ (0.0198) (0.0198) Income(in$1,000) 0.000332∗∗∗ 0.000334∗∗∗ (0.0000961) (0.0000961) Age -0.000522 -0.000532 (0.000329) (0.000329) Constant -0.103 -0.111∗ (0.0643) (0.0639) Observations 11597 11597 Standarderrorsinparentheses ∗ p<0.1,∗∗ p<0.05,∗∗∗ p<0.01 IV Estimates We use mailings from nonbank lenders as an IV to address a potential reverse causality issue. The two-stage least squares estimates are shown in Table 4 and the first stage estimatesinTable11intheAppendix. Theresultsaresimilartothebaselineestimates. 23

Table 4: Responsiveness: IV Estimates. Two stage least squares estimates using direct mail advertising by specialized mortgage firms as an instrument for direct mail advertising. The first stage regressions are shown in Table 11 in the Appendix. County and quarter fixed effects are included. Standarderrorsareclusteredatthecountylevel. (OptimalTrigger-MarketRate)x(DirectMailAdv.) 0.0140∗∗∗ (0.00456) DirectMailAdvertising(DMA) 0.0119 0.0235∗∗ (0.00834) (0.0105) OptimalTriggerRate-MarketRate(in%) 0.0373∗∗∗ 0.0348∗∗∗ (0.00359) (0.00361) MortgageInquiries(Past3Months) 0.0890∗∗∗ 0.0892∗∗∗ (0.0154) (0.0154) FICOScore 0.000264∗∗∗ 0.000269∗∗∗ (0.0000709) (0.0000709) LTVRatio -0.0445∗∗ -0.0439∗∗ (0.0198) (0.0197) Income(in$1,000) 0.000331∗∗∗ 0.000334∗∗∗ (0.0000959) (0.0000958) Age -0.000522 -0.000531 (0.000328) (0.000329) Observations 11396 11396 Standarderrorsinparentheses ∗ p<0.1,∗∗ p<0.05,∗∗∗ p<0.01 DummyforOptimalRefiPolicy Column(1)inTable5replacesd (x,r)withanthedummy ADL variable1{d (x,r)≥0}. ThisspecificationtakestheADLoptimalrefipolicy“moreseriously”. ADL Theestimatesincolumn(1)implythatadvertisinghasnoeffectonborrowerswhoshouldwait butincreasestherefiprobabilityofborrowerswhoshouldrefinancebyapproximately3.8percentagepointsorabout24%oftheunconditionalrefiprobabilityofborrowerswith1{d (x,r)≥0}. ADL These estimates support our interpretation of the baseline estimates and rules out the possibility that the positive coefficient on d (x,r) simply reflects differences in the refi probability ADL within the groups d (x,r) ≥ 0 and d (x,r) < 0, rather than different refi probabilities for ADL ADL these two groups. An advantage of these estimates compared to the baseline estimates is that they do not imply a negative effect of advertising, even for borrowers with very negative d (x,r). In ADL columns (2) and (3) we include the dummy 1{d (x,r)≥0} and d (x,r). In these specifica- ADL ADL 24

tionsd (x,r)appearstoexplainrefinancingbehaviorbetterthand (x,r)≥0. ADL ADL Table 5: Dummy for Optimal Refi Policy. Using the variable Should Refinance, which is equal to one if the borrower should refinance, i.e. 1{d (x,r)≥0}. County and quarter dummies are ADL included. Standarderrorsareclusteredatthecountylevel. (1) (2) (3) ShouldRefinancex(DirectMailAdv.) 0.0381∗∗ 0.0448∗∗∗ 0.0241 (0.0165) (0.0163) (0.0192) (OptimalTrigger-MarketRate)x(DirectMailAdv.) 0.0105∗∗ (0.00429) DirectMailAdvertising(DMA) 0.00420 0.000418 0.0147 (0.00584) (0.00556) (0.00916) ShouldRefinance 0.0656∗∗∗ -0.000752 0.00357 (0.0154) (0.0165) (0.0165) OptimalTriggerRate-MarketRate(in%) 0.0356∗∗∗ 0.0339∗∗∗ (0.00359) (0.00354) MortgageInquiries(Past3Months) 0.0913∗∗∗ 0.0896∗∗∗ 0.0895∗∗∗ (0.0157) (0.0155) (0.0155) FICOScore 0.000224∗∗∗ 0.000271∗∗∗ 0.000274∗∗∗ (0.0000709) (0.0000706) (0.0000706) LTVRatio 0.0656∗∗∗ -0.0411∗∗ -0.0410∗∗ (0.0156) (0.0200) (0.0200) Income(in$1,000) 0.000378∗∗∗ 0.000336∗∗∗ 0.000337∗∗∗ (0.0000942) (0.0000953) (0.0000953) Age -0.000301 -0.000513 -0.000523 (0.000325) (0.000328) (0.000328) Constant -0.200∗∗∗ -0.112∗ -0.117∗ (0.0611) (0.0633) (0.0631) Observations 11597 11597 11597 Standarderrorsinparentheses ∗ p<0.1,∗∗ p<0.05,∗∗∗ p<0.01 FurtherRobustnessChecks AppendixCpresentsfurtherrobustnesschecks. WeconsideralternativeparametersfortheADLtriggerrate(Table17),includeinteractiontermsbetweenborrower characteristics such as age and income with advertising and d (x,r) (Table 18), allow for het- ADL erogeneous moving propensity across borrowers (Table 19), heterogeneous mortgage rates across borrowers(Table21),andvarythetimewindowafteradvertisingexposure(Table22). Thefinding 25

thatborrowerswhoshouldrefinancearemoreresponsivetoadvertisingisrobusttothesechanges. 5 Advertising Benefit and Targeting Counterfactuals In this section, we calculate the effect of advertising on borrower welfare E[δ(a,r,x)]. Recall that δ isdefinedasfollows: (cid:2) (cid:3) δ(a,r,x) = [σ(a,r,x)−σ(0,r,x)] NPV (r,x;σ)−NPV (r,x;σ) (4) wait refi = ∆σ(a,r,x)∆NPV(r,x;σ). First,weexplainhowwecalculatetheexpectedNPVofmortgagepaymentsforeachborrower to obtain ∆NPV(r,x;σ). We then obtain ∆σ(a,r,x) from our responsiveness estimates in the previoussectionandcombiningthesetwopartsallowsustocalculateE[δ(a,r,x)]. Next,wequantify how borrower composition, targeting and differential responsiveness affect E[δ(a,r,x)]. Finally, we simulate the effect of a counterfactual targeting policy, to study how much borrower welfare couldbeenhancedwithbettertargeting. 5.1 Calculating Expected NPV WecalculateNPV (i ,x ;σ)for j∈{refi,wait}asfollows: j t t NPV (r,x;σ) = p (r,x) (5) j t t j t t (cid:34) (cid:40) (cid:41)(cid:12) (cid:35) T (cid:12) + βE ∑ pr move u move (x t(cid:48) )+(1−pr move ) ∑ σ j (r t(cid:48) ,x t(cid:48) ,0)p j (r t(cid:48) ,x t(cid:48) ) (cid:12) (cid:12) r t ,x t t(cid:48)=t+1 j∈{refi,wait} (cid:12) wheretheexpectationistakenoverrealizationsoffuturemortgageratesr andloancharacteristics t(cid:48) x . Futureloancharacteristicsx aredeterminedinpartbyaborrower’sfuturedecisiontorefinance t(cid:48) t(cid:48) as prescribed by her policy function σ. This means that we are allowing for the possibility that a borrower refinances in period t(cid:48) >t even if she does not refinance in period t. Notice that we use σ ratherthantheoptimalrefipolicyσ∗ to calculate the net present value, because it would be unrealistic to assume that the borrower follows the optimal strategy in the future. For simplicity, weholdadditionalcharacteristics,suchastheborrower’sage,FICOscoreandhousepricefixedin thefuture. Weassumethattheannualdiscountrateis5percent,whichimpliesthatβ = (cid:0) 1 (cid:1) 1 1 2. 1.05 The first term p (r ,x ) denotes the payment a borrower has to make depending on her action j t t j. If j = wait, then p (r ,x ) is equal to the monthly payment with the existing mortgage. If wait t t j = refi, then p (r ,x ) is the sum of the new monthly payment as a result of refinancing and refi t t thecostofrefinancing,whichwesetequalto$2,000plus1%oftheremainingprincipalfollowing Agarwal, Driscoll, and Laibson (2013). Next, pr and u (x ) refer to the probability and move move t(cid:48) 26

payoff from moving, respectively. Following Agarwal, Driscoll, and Laibson (2013), we assume that borrowers move with a probability of 10% each year and that if a borrower moves she must pay the remaining principal balance in one lump-sum payment. Thus, u (x ) is equal to the move t(cid:48) remainingprincipalbalanceinperiodt(cid:48). Thefactthatthestreamofafuturemortgagepaymentsdependsonσ allowsforthepossibility that the borrower refinances in a period later than t. We assume that the number of refi ads a in the future is zero, so the probability of refinancing in future periods is σ (r ,x ,0). We make this j t(cid:48) t(cid:48) assumption because it is difficult to estimate the stochastic process that governs the evolution of advertising a with our data. Moreover, to avoid predicted probabilities outside of [0,1], we use a logitestimatesofσ,whichareshowninTable13inAppendixBinsteadoftheestimatesfromthe linearprobabilitymodelpresentedintheprevioussection.35 Calculating NPV (r ,x ;σ) exactly is difficult because of the large number of possible future j t t states involved in the calculation. Thus, we approximate NPV (r ,x ;σ) by averaging simulated j t t mortgagepaymentsforsimulationsoffuturepathsof{(r ,x )}T given(r ,x ). t(cid:48) t(cid:48) t(cid:48)=t+1 t t To model the evolution of the mortgage rate we follow Campbell and Cocco (2015) and estimatethefollowingAR(1)process: log(1+r )=α +α log(1+r )+ε , t 0 1 t−1 t wherer istheratefor30yearfixedratemortgages,t isamonthbetween1971and2015andε isa t t normallydistributederrorterm. Weestimateα =0.000117andα =0.998sothisprocessreverts (cid:99)0 (cid:99)1 back to its mean α(cid:99)0 = 0.0530, which corresponds to a mortgage rate of 5.44%. The standard 1−α(cid:99)1 deviationofε isestimatedtobe0.00255. t Note that the loan characteristics in x other than the remaining balance will change only if a t borrower refinances. Without refinancing, the remaining balance evolves in a deterministic way, following the standard mortgage amortization schedule for a fixed rate mortgage. If a borrower refinances, the evolution of future remaining balances changes slightly because of a change in the interestrateoftheloan. Lastly,wesimulatepathsfor{(r ,x )}T andthenobtain∆NPV(r,x;σ)byaveragingover t(cid:48) t(cid:48) t(cid:48)=t+1 thesimulatedpaths. 35We also omit county and quarter fixed effects from the specification used for the future refi policy, because we haveonlyfewobservationsformostcountiesandsomequartersandcanthereforenotconsistentlyestimatethefixed effects. Noticehowever,thatweuseourbaselineestimatestocalculate∆σ(a,r,x)inequation(4),becausethefixed effectscanceloutinthisdifferenceandpredictedrefiprobabilitiesoutsideof[0,1]arenotproblematic. 27

5.2 The Effect of Advertising on Borrower Welfare In this subsection we calculate E[δ(a,r,x)] by combining ∆σ(a,r,x) and ∆NPV(r,x;σ), and then study the roles of borrower composition, targeting and differential responsiveness. First, to quan- ´ tifytheimportanceconsumercompositionwecalculate ∆NPV(r,x;σ)dG(r,x). Second,toquantifytheimportanceoftargetingwerecalculatethebenefitofadvertisingunderacounterfactualtar- ´ geting policy F(cid:48) such that the average advertising intensity adF(a|x)dG(x) remains unchanged but no longer varies with x. Third, to quantify the importance of differential responsiveness we recalculate the benefit of advertising under a counterfactual σ(cid:48) such that the average effect of ad- ´ vertising ∆σ(a,x)dG(x)remainsunchanged,buttheeffectofadvertisingunderσ(cid:48) doesnotvary withx. 5.2.1 BorrowerComposition Table 6: Borrower Composition. Results are obtained through simulation and rounded to the nearestdollarvalue. OverallBorrowers E[∆NPV(r,x;σ)] -$499 ShouldWait E[∆NPV(r,x;σ)|r∗ (x)<r] -$1282 ADL ShouldRefinance E[∆NPV(r,x;σ)|r∗ (x)≥r] $5064 ADL AdRecipientsinData E[∆NPV(r,x;σ)|a>0] -$58 AdNon-recipientsinData E[∆NPV(r,x;σ)|a=0] -$585 ´ The first row of Table 6 shows that E[∆NPV(r,x;σ)] = ∆NPV(r,x;σ)dG(x) = −$499, so the average borrower would be approximately $500 worse off if she decides to refinance. Thus refinancing is “harmful” to the average borrower, and advertising of refi loans could therefore be harmful. Whether advertising is beneficial or harmful depends on whether targeting and differentialresponsivenessdominatetheeffectofborrowercomposition. RefiloansarelikelytobesimilartomostadvertisedproductsforwhichE[∆u(x)]ispresumably also negative, so the average consumer would make a mistake if she buys the product. Unlike for refi loans, we cannot measure E[∆u(x)] for most product. However, E[∆u(x)] is likely to be very negative for products such as prescription drugs. Moreover, E[∆u(x)]is likely somewhat negative for most products except for those that are purchased by the majority of consumers. Hence, to the extent that advertising affects only ∆σ and not ∆u(x), advertising for these products can only be beneficialiftheeffectsofdifferentialresponsivenessdominatetheeffectofconsumercomposition. Table6alsoshowsthebenefitfromrefinancingforthosewhoshouldwaitandthosewhoshould wait in rows two and three. While the average borrower who should wait would lose $1282 by refinancing, the average borrower shouldshould refinance would gain $5064. Keys, Pope, and Pope 28

(2016) find that the median borrower who should refinance could gain $11,500, which is significantlyhigherthanourestimate. Thisdifferenceispartlyexplainedbythefactthattheyassumethat borrowers who fail to refinance never refinance until the end of the mortgage, whereas we assume that their future refinancing behavior is governed by σ. Recall that “Should Wait” and “Should Refinance” are derived from the optimal refinancing policy by ADL. Therefore, ∆NPV(r,x;σ) is positive for some borrowers who “should wait”. This is because ∆NPV(r,x;σ) does not assume thatborrowersrefinanceoptimallyinthefuture. Instead,weassumethattheyfollowtheestimated refinancing policy. As the borrowers will not be able to exploit low interest rates in the future optimally, some borrower who should wait according to the ADL model, would be better off by refinancing today. For the same reason, all borrowers who should refinance according to ADL do indeedhavepositive∆NPV(r,x;σ). Lastly,Table6showsthebenefitfromrefinancingforthosewhoreceivedadvertisingandthose whodidnotinrowsfourandfive. Borrowerswhoreceivedadvertisingwouldloseonaverage$58 while borrowers who did not receive advertising would lose $585. This suggests that advertising issomewhattargeted. However,thegapbetweenadvertisingrecipientsandnonrecipients($585− $58)ismuchsmallerthanthegapbetweenthosewhoshouldrefinanceandthosewhoshouldwait ($5064+$1282),sotargetingcouldbemuchmorebeneficialforborrowers. Inthenextsubsection wequantifytheeffectoftargetingonborrowerwelfareinmoredetail. 5.2.2 Targeting Table 7: TargetingandBorrowerWelfare. Results are obtained through simulation and rounded to thenearestdollarvalue. E(cid:48) istheexpectationusingthecounterfactualadvertisingpolicyF(cid:48). ObservedAdvertisingPolicyF EvenlyDistributedAdvertisingF(cid:48) AllBorrowers E[δ(r,x,a)] $13 E(cid:48)[δ(r,x,a)] $11 AdNon-recipientsintheData E[δ(r,x,a)|a=0] $0 E(cid:48)[δ(r,x,a)|a=0] $11 AdRecipientsintheData E[δ(r,x,a)|a>0] $81 E(cid:48)[δ(r,x,a)|a>0] $12 ShouldWait E[δ(r,x,a)|r∗ (x)<r] $5 E(cid:48)[δ(r,x,a)|r∗ (x)<r] $6 ADL ADL ShouldRefinance E[δ(r,x,a)|r∗ (x)≥r] $70 E(cid:48)[δ(r,x,a)|r∗ (x)≥r] $45 ADL ADL In Table 7 we compare the benefit of advertising under the observed advertising policy F(a|x,r) withacounterfactualadvertisingpolicyF(cid:48)(a|x,r)suchthatF(cid:48)isuntargeted,i.e. doesnotvarywith ´ x and r and such that the average advertising intensity adF(a|x,r)dG(x,r) remains unchanged. Hence,underF(cid:48)theadvertisingexposureofeveryborrowerissimplyequaltotheaverageexposure ´ a= adF(a|x,r)dG(x,r)=0.23. The main results in Table 7 are obtained by using our baseline responsivenessestimatesinTable3toobtain∆σ(a,r,x)=0.0159d (x,r)×a+0.0250. InTable ADL 29

14 in the Appendix we present results that use the the dummy variables estimates from Column (1)inTable5toobtain∆σ(a,r,x)=0.0381×1{d (x,r)≥0}×a+0.0042. ADL The first column of Table 7 shows the benefits of advertising under the observed advertising policy F and the second column under F(cid:48). To avoid confusion we briefly clarify our notation. We denote the welfare of the average borrower under F(cid:48) by E(cid:48)[δ(r,x,a)]. The welfare of the average borrower who received advertising under F, but now is exposed to F(cid:48) is denoted by E(cid:48)[δ(r,x,a)|a>0]. We find that the observed advertising policy F decreases the expected NPV for the average borrower by $13. Hence, advertising helps borrowers on average even though the benefit of refinancing for the average borrower is -$499, because the effects of targeting and differential responsiveness dominate the effect of borrower composition. As the benefit of refinancing for the average borrower who should refinance is more than $5,000 the benefit of advertising could theoretically be much larger. This difference is due to two reasons. First, some borrowers are harmed by advertising, because ∆NPV(r,x;σ)<0. Second, even for the remaining borrowers the benefit of advertising is much smaller than ∆NPV(r,x;σ) because they receive only a small amount of advertising and respond only to a small fraction of ads they receive. The benefit of advertising is arguablylarge,however,incomparisontothemarginalcostsofsendingrefiadvertising. UnderthecounterfactualpolicyF(cid:48)thebenefitwoulddecreaseto$11. Hencetargetingincreases borrower welfare by $2 because advertising is somewhat targeted at borrowers who benefit from refinancing.36 The benefit of $13 under the observed advertising policy consists of a benefit of $81 for advertising recipients and a benefit of $0 for non-recipients as shown in rows (2) and (3). Underevenlydistributedadvertisingthebenefitofborrowerswhodonotreceiveadvertisinginthe data would increase to $11, whereas the benefit of borrowers who receive advertising in the data woulddecreaseto$12. Rows(4)and(5)splittheborrowersintothosewhoshouldwaitandthosewhoshouldrefinance. Undertheobservedadvertisingpolicyborrowerswhoshouldrefinancegain$70,whereasborrowers who should wait gain $5. The benefit for borrowers who should wait is small but still positive, which is perhaps surprising. To understand this recall that ∆NPV(r,x;σ) is positive for borrowers who should wait with relatively high d (x,r), because unlike the ADL rule ∆NPV(r,x;σ) ADL does not assume that borrowers refinance optimally in the future, and that these borrowers are fairly responsive to advertising.37 Under evenly distributed advertising the benefit of borrowers who should refinance would decrease substantially to $45, whereas the benefit of borrowers who 36Table12inAppendixBisatargetingregressionwhichshowsthatthenumberofadvertisementsaincreasesby 0.04ifd (x,r)increasesbyonepercentagepoint. ADL 37In Table 14 in the Appendix, we use the dummy variable estimates from Column (1) in Table 5. In this specification there is no differential responsiveness within the group of borrowers who should wait and E[δ(r,x,a)|r∗ (x)<r]isnegative,butalsosmallinmagnitude. ADL 30

shouldwaitwouldincreaseslightlyto$6. 5.2.3 DifferentialResponsiveness Table 8: Differential Responsiveness and Borrower Welfare. Results are obtained through simulation and rounded to the nearest dollar value in the left column and to $0.1 in the right column. E[δ(r,x,a;σ)]istheexpectedborrowerwelfareiftheestimatedσ withdifferentialresponsiveness isreplacedwiththeaverageresponsivenessσ. WithDifferentialResponsiveness NoDifferentialResponsiveness AllBorrowers E[δ(r,x,a)] $13 E[δ(r,x,a;σ)] $0.1 AdNon-recipientsinData E[δ(r,x,a)|a=0] $0 E[δ(r,x,a;σ)|a=0] $0 AdRecipientsinData E[δ(r,x,a)|a>0] $81 E[δ(r,x,a;σ)|a>0] $0.7 ShouldWait E[δ(r,x,a)|r∗ (x)<r] $5 E[δ(r,x,a;σ)|r∗ (x)<r] $-0.5 ADL ADL ShouldRefinance E[δ(r,x,a)|r∗ (x)≥r] $70 E[δ(r,x,a;σ)|r∗ (x)≥r] $4.4 ADL ADL In Table 8 we try to understand to what extent the gains from advertising are due to differential responsiveness. The left column shows the benefit of advertising with differential responsiveness as estimated in section 4. The right column shows the benefit of advertising if all borrowers were equally responsive to advertising. We replace β d (x,r)×a+β a with the average responsive- 1 ADL 2 ness β d (x,r)×a+β a=0.0023a in σ, where d (x,r)=−1.49 is the average distance to 1 ADL 2 ADL the optimal trigger rate. In Table 8 we use the baseline responsiveness estimates and in Table 15 intheAppendixwepresentresultsthatusethethedummyvariablesestimatesfromColumn(1)in Table5. WedenotetheexpectedborrowerwelfarewithaverageresponsivenessbyE[δ(r,x,a;σ)]. As the average responsiveness is fairly small, advertising has only a small effect in this scenario. Consequently,theaveragebenefitdecreasesfrom$13to$0.1. Rows(2)-(5)onthelefthandsideofTable8areidenticaltoTable7. Rows(3)ontherighthand sideshowsthatthebenefitofborrowerswhoreceiveadvertisingwoulddecreasedramaticallyfrom $81 to $0.7 without differential responsiveness. Rows (4) and (5) on the right hand side show that “shutting down” differential responsiveness has a small negative effect on borrowers who should waitandalargenegativeeffectonborrowerswhoshouldrefinance. In summary, we find that the observed advertising policy results in a positive benefit for the averageborrower,becausethosewithgreatergainsfromrefinancingaretargetedbyadvertisersand more responsive to advertising. It is clear from Table 6, however, that more targeted advertising could increase borrower surplus considerably. Because borrowers who should refinance are more responsive, advertisers are likely to benefit from better targeting as well. In the next section we investigatetheeffectsofbettertargetinginmoredetail. 31

5.3 Counterfactual With Better Targeting Table 9: Better Targeting and Borrower Welfare. Results are obtained through simulation and rounded to the nearest dollar value. E(cid:48)(cid:48) is the expectation using the counterfactual advertising policyF(cid:48)(cid:48). ObservedAdvertisingPolicy RedirectedAds AllBorrowers E[δ(r,x,a)] $13 E(cid:48)(cid:48)[δ(r,x,a)] $45 ShouldWait E[δ(r,x,a)|r∗ (x)<r] $5 E(cid:48)(cid:48)[δ(r,x,a)|r∗ (x)<r] $0 ADL ADL ShouldRefinance E[δ(r,x,a)|r∗ (x)≥r] $70 E(cid:48)(cid:48)[δ(r,x,a)|r∗ (x)<r] $368 ADL ADL In Table 9 we assume that all of advertising is redirected to those who should refinance based on the ADL model, while keeping the total amount of advertising unchanged. We denote this advertisingpolicybyF(cid:48)(cid:48). UnderF(cid:48)(cid:48) allborrowerswhoshouldrefinancereceivea/Pr(d (x,r)≥1)= ADL 0.23/0.12=1.9 refi mails and borrowers who should wait receive none. We denote the expected borrowerwelfareunderF(cid:48)(cid:48) byE(cid:48)(cid:48)[δ(r,x,a)]. InTable9weusethebaselineestimatesandinTable 16intheAppendixweusethedummyvariableestimatesfromColumn(1)inTable5. We find that the average benefit would increase from $13 to $45. The benefit for those who should refinance would increases from $70 to $368, whereas those who should wait no longer receiveadvertisingandthereforeobtainabenefitof$0. Lenders would likely benefit from better targeting as well. Under the observed advertising policy, one piece of advertising increases the refinancing probability by 0.7 percentage points for those who received advertising. This is significantly higher than a 0.2 percentage point increase in refinancing probability under the counterfactual policy that evenly distributes advertising to all borrowers. Under the counterfactual policy that redirects all advertising to those who should refinancehowever,onepieceofadvertisingincreasestherefinancingprobabilityby3.5percentage points. Noticehowever,thatifthespilloversofadvertisingarelarge,theadvertisinglendersmight notactuallybenefitfromimprovedtargeting. 5.4 Discussion and Policy Implications These findings raise the question why lenders don’t improve targeting to reach more borrowers who should refinance as they are also more responsive. First, better targeting is expensive. By law, lenders are not allowed to have direct access to a borrower’s credit file and can only purchase information about borrowers satisfying certain criteria from a credit bureau.38 It is likely that the costofacquiringsuchinformationmightbetoohigh,comparedwithbenefitsfrombettertargeting. 38Publiclyavailablerecordsonhousetransactionscanbeusedtoestimatetheremainingprincipalbalanceandthe interestrateofamortgage. 32

Second, if there is a positive spillover from advertising, then a lender might find it too costly to invest in better targeting of advertising. The positive spillover is likely present in this setting becauseamortgageisessentiallyahomogeneousproduct. Hence,ifrefiadvertisingfromalender informs a borrower about the opportunity to save money by refinancing, the newly informed borrower might still refinance with a different lender. This positive spillover decreases the return to advertising from a lender’s perspective. As a result, a lender might find it too costly to acquire betterinformationaboutborrowersgiventhepositivespillover. Our findings suggest that policy makers should facilitate targeting of refi advertising to borrowers with greater gains from refinancing rather than restricting advertising for refi loans. For example,apolicythatmakesiteasierforlenderstohaveaccesstoacreditfilefromacreditbureau might lead to better targeting. Another possibility is for government-sponsored enterprises such as Freddie Mac and Fannie Mae to make more accessible information about borrowers, on their files,withpotentiallylargegainsfromrefinancing. Moreover,althoughthereisagrowingconcern about privacy and collection of information about consumer, our findings suggest that limiting an advertiser’sabilitytotargetconsumerscanbecostly. 6 Conclusion This paper estimates the effect of advertising on refinancing mistakes and quantifies the resulting effect on borrower welfare. We find that refi advertising reduces the expected net present value of the average borrower by $13, even though the average borrower would lose approximately $500 by refinancing. In other words, the effects of differential responsiveness and targeting dominate the negative effect of borrower composition. An improved targeting policy that redirects all advertising would increase the gain in consumer welfare to $47 and lead to a fivefold increase in the responsivenessoftheaverageadrecipient. Our results highlight that firms do not only have an incentive to exploit the behavioral biases of consumers, but also to prevent consumer mistakes if they fail to buy products they need. The findings have implications for the regulation of advertising. First, advertising bans can be harmful for consumers, even if most consumers would be harmed by buying the product. Second, our results suggest that targeting of refi advertising should be facilitated as it would help borrowers and likely also advertisers. The benefits of such a policy, however, would have to be weighed againsttheprivacyconcernsofborrowers. There are several avenues for future research. First, in this paper we did not consider the equilibriumeffectsofadvertising. Ifadvertisingaffectsprice,forexample,suchequilibriumeffects couldaltertheeffectofadvertisingonconsumerwelfare. Second,whileourestimatesincorporate the spillover effects of advertising, our data does not allow us to disentangle the spillover effects 33

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A ADL Trigger Rate Theoptimaltriggerrateisgivenby 1 r∗ = [φ+W(−exp(−φ))], ADL ψ ,whereW istheprincipalbranchoftheLambertW−functionand (cid:112) 2(ρ+λ) ψ = σ κ/M φ = 1+ψ(ρ+λ) (1−τ) i 0 λ = µ+ +π exp(i Γ)−1 0 (cid:20) (cid:20)(cid:18) (cid:19)(cid:18) (cid:19) (cid:21)(cid:21) τ 1−exp(−N(θ +ρ+π)) ρ+π κ = F+ fM 1− +θ θ +ρ+π N θ +ρ+π Here, λ is the expected real rate of exogenous mortgage repayment and κ is the tax-adjusted refinancingcost. Table10summarizesthevariablesandparametersthatentertheADLthreshold. The tablealsoshowstheparametervaluessuggestedbyADL,whichweuseinourbaselineestimates. Inrobustnesschecksweexplorethesensitivityofourfindingstochangesinthediscountrateρ and the standard deviation of the mortgage rate σ. The discount rate affects the trade-off between paying the upfront refinancing cost and future interest savings. For example consider a borrower with a remaining principal of M = $300,000, a remaining term of Γ = 25 years and a mortgage rate of i = 0.06. Under the standard value for ρ = 0.05 we obtain an optimal trigger rate of 0 0.0467forthisborrower. Thethresholdincreasesto0.0474forρ =0.025anddecreasesto0.0461 for ρ =0.075. The standard deviation of the mortgage rate that the borrowers expect affects the optionvalueofwaiting. Forexample,underthestandardvalueσ =0.0109theoptimaltriggerrate is0.0467,whichincreasesto0.0501forσ =0.0218anddecreasesto0.0419forσ =0.0054. 39

.)3102(nosbiaLdna,llocsirD,lawragAnialumrofetarreggirtlamitpoehtrofsretemaraP :01elbaT eulaV retemaraP/elbairaV 50.0 etaRtnuocsiDlaeR ρ 9010.0 etaRegagtroMfonoitaiveDdradnatS σ ataD lapicnirPegagtroMgniniameR M 82.0 etaRxaTlanigraM τ 1.0 gnivoMfoytilibaborPlaunnA µ ataD egagtroMdlOfoetaR i 0 ataD efiLegagtroMgniniameR Γ 30.0 etaRnoitaflnIegarevAdetcepxE π 000,2 gnicnanfieRfotsoC F 10.0 001/stnioPegagtroMforebmuN f 1.0+µ )gnicnanfiertneuqesbusroevom(tnevEytilibatcudeDlluFfoetaRlavirrAdetcepxE θ 03= N egagtroMweNfomreT N 40

B Additional Tables Table 11: First Stage for the Two Stage Least Squares Estimates in Table 4. The first column shows the first stage for Table 4(1). The second column shows the first stage for the interaction term (Optimal Trigger - Market Rate) x Direct Mail Advertising for Table 4(2). The third column shows the first stage for Direct Mail Advertising for Table 4(2). County and quarter fixed effects areincluded. DMA (OptimalTrigger-MarketRate)xDMA DMA (1) (2) (3) (OptimalTrigger-MarketRate)xDMA:Nonbanks 1.051∗∗∗ 0.00373 (0.0200) (0.00778) DMA:Nonbanks 1.060∗∗∗ 0.00688 1.063∗∗∗ (0.0183) (0.0175) (0.0175) OptimalTriggerRate-MarketRate(in%) 0.0128∗∗∗ 0.0652∗∗∗ 0.0124∗∗∗ (0.00354) (0.00869) (0.00352) MortgageInquiries(Past3Months) -0.00394 0.0145 -0.00384 (0.0140) (0.0165) (0.0140) FICOScore 0.000241∗∗ -0.000192 0.000242∗∗ (0.0000982) (0.000156) (0.0000985) LTVRatio 0.0373 -0.0511 0.0374 (0.0258) (0.0514) (0.0258) Income(in$1,000) 0.000132 -0.000337∗ 0.000132 (0.000157) (0.000176) (0.000157) Age -0.000424 0.00127∗ -0.000423 (0.000396) (0.000687) (0.000396) Observations 11396 11396 11396 Standarderrorsinparentheses ∗p<0.1,∗∗p<0.05,∗∗∗p<0.01 41

Table 12: Targeting Estimates. The dependent variable is the number direct mail advertisements for refinancing the borrower received in a month. County and quarter dummies are included. Standarderrorsareclusteredatthecountylevel. OptimalTriggerRate-MarketRate(in%) 0.0410∗∗∗ (0.00772) MortgageInquiries(Past3Months) -0.000848 (0.0218) FICOScore -0.000327 (0.000205) LTVRatio 0.113∗∗ (0.0528) Income(in$1,000) 0.000518∗∗ (0.000234) Age 0.000283 (0.000626) Constant 0.430∗∗ (0.194) Observations 12301 Standarderrorsinparentheses ∗ p<0.1,∗∗ p<0.05,∗∗∗ p<0.01 42

Table13: LogitEstimates UsedtoSimulateNPV (r,x)andNPV (r,x). Asthese estimates refi wait are used to predict future refinancing probabilities we do not include county and quarter fixed effects. (OptimalTrigger-MarketRate)x(DirectMailAdv.) 0.118∗∗∗ (0.0432) DirectMailAdvertising(DMA) 0.154∗∗∗ (0.0477) OptimalTriggerRate-MarketRate(in%) 0.413∗∗∗ (0.0293) MortgageInquiries(Past3Months) 0.718∗∗∗ (0.0749) FICOScore 0.00495∗∗∗ (0.000813) LTVRatio -0.0204 (0.184) Income(in$1,000) 0.00394∗∗∗ (0.000696) Age -0.00469∗ (0.00283) Constant -5.802∗∗∗ (0.662) Observations 11599 Standarderrorsinparentheses ∗ p<0.1,∗∗ p<0.05,∗∗∗ p<0.01 Table 14: Targeting and Borrower Welfare. These results use the dummy variable estimates from Column(1)inTable5. E(cid:48) istheexpectationusingthecounterfactualadvertisingpolicyF(cid:48). ObservedAdvertisingPolicyF EvenlyDistributedAdvertisingF(cid:48) AllBorrowers E[δ(r,x,a)] $9 E(cid:48)[δ(r,x,a)] $5 AdNon-recipientsinData E[δ(r,x,a)|a=0] $0 E(cid:48)[δ(r,x,a)|a=0] $4 AdRecipientsinData E[δ(r,x,a)|a>0] $57 E(cid:48)[δ(r,x,a)|a>0] $8 ShouldWait E[δ(r,x,a)|r∗ (x)<r] $-1 E(cid:48)[δ(r,x,a)|r∗ (x)<r] $-1 ADL ADL ShouldRefinance E[δ(r,x,a)|r∗ (x)≥r] $82 E(cid:48)[δ(r,x,a)|r∗ (x)≥r] $50 ADL ADL 43

Table15: DifferentialResponsivenessandBorrowerWelfare. Theseresultsusethedummyvariable estimates from Column (1) in Table 5. E[δ(r,x,a;σ)]is the expected borrower welfare if the estimatedσ withdifferentialresponsivenessisreplacedwiththeaverageresponsivenessσ. WithDifferentialResponsiveness NoDifferentialResponsiveness AllBorrowers E[δ(r,x,a)] $9 E[δ(r,x,a;σ)] $0.5 AdNon-recipientsinData E[δ(r,x,a)|a=0] $0 E[δ(r,x,a;σ)|a=0] $0 AdRecipientsinData E[δ(r,x,a)|a>0] $57 E[δ(r,x,a;σ)|a>0] $2.9 ShouldWait E[δ(r,x,a)|r∗ (x)<r] $-1 E[δ(r,x,a;σ)|r∗ (x)<r] $-1.9 ADL ADL ShouldRefinance E[δ(r,x,a)|r∗ (x)≥r] $82 E[δ(r,x,a;σ)|r∗ (x)≥r] $17.6 ADL ADL Table 16: Better Targeting and Borrower Welfare. Results are obtained through simulation and rounded to the nearest dollar value. E(cid:48)(cid:48) is the expectation using the counterfactual advertising policyF(cid:48)(cid:48). TheseresultsusethedummyvariableestimatesfromColumn(1)inTable5. ObservedAdvertisingPolicy RedirectedAds AllBorrowers E[δ(r,x,a)] $9 E(cid:48)(cid:48)[δ(r,x,a)] $50 ShouldWait E[δ(r,x,a)|r∗ (x)<r] $-1 E(cid:48)(cid:48)[δ(r,x,a)|r∗ (x)<r] $0 ADL ADL ShouldRefinance E[δ(r,x,a)|r∗ (x)≥r] $82 E(cid:48)(cid:48)[δ(r,x,a)|r∗ (x)<r] $404 ADL ADL 44

C Differential Responsiveness Robustness Checks Alternative Parameters for the Optimal Trigger Rate For our baseline estimates we use the parameters for the optimal trigger suggested by Agarwal, Driscoll, and Laibson (2013) that are also used in Keys, Pope, and Pope (2016) and Agarwal, Rosen, and Yao (2015). Tables 17 shows results for alternative parameter values. The discount rate ρ = 0.05 is either increased to ρ = 0.075, which leads to a lower trigger rate, or decreased to ρ = 0.025, which leads to a higher trigger rate. Similarly, the annualized interest rate of the mortgage rate σ = 0.01 is either increased to σ = 0.02, which reduces the optimal trigger rate, or decreased to σ = 0.005, which increases the optimal trigger rate. These changes have only a minorimpactontheestimates. Estimatesforthemaincoefficientofinterestβ rangefrom0.0142 1 to0.0157. Further Interaction Terms Table18includesinteractionsofborrowercharacteristicssuchasageandincomewithdirectmail advertising and the gap between the optimal trigger rate and the market mortgage rate in columns (2) and (3). Columns (4) and (5) include quadratic terms for direct mail advertising and the gap between the optimal trigger rate and the market mortgage rate. These changes have only a minor effect on the estimates of β which range from 0.0149 to 0.0177. The estimates suggest that 1 borrowers with higher income, higher FICO scores, higher LTV ratios and more previous mortgage inquiries are more responsive to d (x,r), but no evidence that these variables affect the ADL responsivenesstoadvertising. 45

eht dna ρ etar tnuocsid eht fo snoitanibmoc tnereffid rof setamitsE .etaR reggirT lamitpO rof sretemaraP evitanretlA :71 elbaT ni 520.0 = ρ ,)7( dna )4( ,)1( snmuloc ni 50.0 = ρ slauqe etar tnuocsid ehT .σ etar egagtrom eht fo noitaived dradnats dezilaunna ni 9010.0= σ slauqe etar egagtrom eht fo noitaived dradnats ehT .)9( dna )6( ,)3( snmuloc ni 570.0= ρ dna ,)8( dna )5( ,)2( snmuloc .dedulcnierastceffedexfiretrauqdnaytnuoC .)9(-)7(snmulocni8120.0= σyltsaldna)6(-)4(snmulocni4500.0= σ,)3(-)1(snmuloc .levelytnuocehttaderetsulcerasrorredradnatsehT )9( )8( )7( )6( )5( )4( )3( )2( )1( ∗∗∗7410.0 ∗∗∗3510.0 ∗∗∗0510.0 ∗∗∗7510.0 ∗∗∗2610.0 ∗∗∗0610.0 ∗∗∗6510.0 ∗∗∗1610.0 ∗∗∗9510.0 ).vdAliaMtceriD(x)etaRtekraM-reggirTlamitpO( )62400.0( )52400.0( )52400.0( )20400.0( )11400.0( )60400.0( )31400.0( )61400.0( )51400.0( ∗∗∗0430.0 ∗∗∗8130.0 ∗∗∗0330.0 ∗∗∗9910.0 ∗∗∗5710.0 ∗∗∗7810.0 ∗∗∗1620.0 ∗∗∗8320.0 ∗∗∗0520.0 )AMD(gnisitrevdAliaMtceriD )7010.0( )99900.0( )4010.0( )61700.0( )07600.0( )39600.0( )15800.0( )49700.0( )32800.0( ∗∗∗6040.0 ∗∗∗4830.0 ∗∗∗5930.0 ∗∗∗9130.0 ∗∗∗2030.0 ∗∗∗1130.0 ∗∗∗4530.0 ∗∗∗4330.0 ∗∗∗4430.0 )%ni(etaRtekraM-etaRreggirTlamitpO )51400.0( )19300.0( )30400.0( )13300.0( )22300.0( )72300.0( )06300.0( )74300.0( )35300.0( ∗∗∗0980.0 ∗∗∗1980.0 ∗∗∗0980.0 ∗∗∗4980.0 ∗∗∗4980.0 ∗∗∗4980.0 ∗∗∗2980.0 ∗∗∗3980.0 ∗∗∗3980.0 )shtnoM3tsaP(seiriuqnIegagtroM )5510.0( )4510.0( )5510.0( )5510.0( )5510.0( )5510.0( )5510.0( )5510.0( )5510.0( ∗∗∗282000.0 ∗∗∗972000.0 ∗∗∗082000.0 ∗∗∗162000.0 ∗∗∗952000.0 ∗∗∗062000.0 ∗∗∗072000.0 ∗∗∗862000.0 ∗∗∗962000.0 erocSOCIF )3070000.0( )4070000.0( )3070000.0( )8070000.0( )7070000.0( )8070000.0( )7070000.0( )7070000.0( )7070000.0( ∗∗∗3950.0- ∗∗∗7350.0- ∗∗∗7650.0- ∗∗1930.0- 2620.0- ∗8230.0- ∗∗8840.0- ∗∗4830.0- ∗∗8340.0oitaRVTL )7020.0( )3020.0( )5020.0( )7910.0( )0910.0( )3910.0( )1020.0( )5910.0( )8910.0( ∗∗∗292000.0 ∗∗∗013000.0 ∗∗∗103000.0 ∗∗∗443000.0 ∗∗∗463000.0 ∗∗∗453000.0 ∗∗∗523000.0 ∗∗∗443000.0 ∗∗∗433000.0 )000,1$ni(emocnI )4590000.0( )6590000.0( )5590000.0( )2690000.0( )3690000.0( )3690000.0( )0690000.0( )1690000.0( )1690000.0( 325000.0- 335000.0- 925000.0- 725000.0- 415000.0- 125000.0- 335000.0- 925000.0- 235000.0egA )823000.0( )923000.0( )823000.0( )923000.0( )033000.0( )033000.0( )923000.0( )923000.0( )923000.0( 3270.0- 5680.0- 1970.0- ∗221.0- ∗∗731.0- ∗∗921.0- 301.0- ∗811.0- ∗111.0tnatsnoC )1560.0( )6460.0( )8460.0( )6360.0( )1360.0( )4360.0( )1460.0( )7360.0( )9360.0( 79511 79511 79511 79511 79511 79511 79511 79511 79511 snoitavresbO sesehtnerapnisrorredradnatS 10.0<p∗∗∗,50.0<p∗∗,1.0<p∗ 46

Table 18: Further Interactions and Quadratic Terms. Column (1) are the baseline estimates. Columns (2) and (3) include interactions of borrower characteristics such as age and income with direct mail advertising and the gap between the optimal trigger rate and the market mortgage rate. Columns (4) and (5) include quadratic terms for direct mail advertising and the gap between the optimal trigger rate and the market mortgage rate. County and quarter dummies are included. Standarderrorsareclusteredatthecountylevel. (1) (2) (3) (4) (5) (OptimalTrigger-MarketRate)x(DirectMailAdv.) 0.0159∗∗∗ 0.0155∗∗∗ 0.0180∗∗∗ 0.0158∗∗∗ 0.0181∗∗∗ (0.00415) (0.00423) (0.00545) (0.00411) (0.00544) DirectMailAdvertising(DMA) 0.0250∗∗∗ 0.0237 0.129 0.0253∗∗ 0.129 (0.00823) (0.0275) (0.106) (0.0108) (0.107) OptimalTriggerRate-MarketRate(in%) 0.0344∗∗∗ 0.0388∗∗∗ -0.194∗∗∗ 0.0354∗∗∗ -0.193∗∗∗ (0.00353) (0.0148) (0.0408) (0.00606) (0.0407) MortgageInquiries(Past3Months) 0.0893∗∗∗ 0.0883∗∗∗ 0.122∗∗∗ 0.0893∗∗∗ 0.122∗∗∗ (0.0155) (0.0156) (0.0245) (0.0155) (0.0245) FICOScore 0.000269∗∗∗ 0.000274∗∗∗ 0.000634∗∗∗ 0.000272∗∗∗ 0.000630∗∗∗ (0.0000707) (0.0000711) (0.000106) (0.0000702) (0.000111) LTVRatio -0.0438∗∗ -0.0485∗∗ 0.0147 -0.0423∗∗ 0.0156 (0.0198) (0.0201) (0.0329) (0.0203) (0.0338) Income(in$1,000) 0.000334∗∗∗ 0.000618∗∗∗ 0.000595∗∗∗ 0.000335∗∗∗ 0.000596∗∗∗ (0.0000961) (0.000143) (0.000144) (0.0000959) (0.000144) Age -0.000532 -0.00102∗ -0.000822 -0.000532 -0.000821 (0.000329) (0.000553) (0.000556) (0.000329) (0.000557) IncomexDirectMailAdvertising -0.000000114 -0.000000123 -0.000000123 (0.000000122) (0.000000122) (0.000000122) Incomex(OptimalTrigger-MarketRate) 0.000000193∗∗∗ 0.000000183∗∗∗ 0.000000185∗∗∗ (5.74e-08) (5.86e-08) (5.82e-08) AgexDirectMailAdvertising 0.000198 -0.00000325 -0.00000152 (0.000455) (0.000482) (0.000482) Agex(OptimalTrigger-MarketRate) -0.000333 -0.000227 -0.000225 (0.000220) (0.000218) (0.000219) FICOScorexDirectMailAdvertising -0.0000874 -0.0000858 (0.000129) (0.000128) FICOScorex(OptimalTrigger-MarketRate) 0.000276∗∗∗ 0.000273∗∗∗ (0.0000472) (0.0000488) LTVxDirectMailAdvertising -0.0466 -0.0468 (0.0286) (0.0287) LTVx(OptimalTrigger-MarketRate) 0.0393∗∗∗ 0.0404∗∗ (0.0137) (0.0160) MortgageInquiriesxDirectMailAdvertising -0.00361 -0.00380 (0.0296) (0.0299) MortgageInquiriesx(OptimalTrigger-MarketRate) 0.0316∗∗∗ 0.0316∗∗∗ (0.0105) (0.0105) (OptimalTriggerRate-MarketRate(in%))2 0.000328 -0.000258 (0.00129) (0.00145) DMA2 -0.0000986 -0.000284 (0.00237) (0.00220) Constant -0.111∗ -0.105 -0.420∗∗∗ -0.113∗ -0.417∗∗∗ (0.0639) (0.0717) (0.0955) (0.0632) (0.0972) Observations 11597 11597 11597 11597 11597 Standarderrorsinparentheses ∗p<0.1,∗∗p<0.05,∗∗∗p<0.01 47

Heterogeneous Moving Propensity The optimal trigger rate suggested by ADL assumes that borrowers move with a probability of 10%per year. In reality, themovingpropensity varies acrossborrowers. Importantly,ifborrowers foresee that they will move in the near future this can rationalize some of the behavior that appearstobearefimistake. Conversely,iftheborrowersknowthattheirmovingprobabilityislower than 10% this can explain some behavior that appears to be premature refinancing. If the moving propensity is not only known to the borrower, but also to the advertisers, and the advertisers target borrowers who are more likely to refinance, i.e. borrowers with low moving propensity, our findingscouldbeexplainedbyreversecausality. Toinvestigatethisissuewepredictheterogeneousmovingpropensitiesusingborrowerandloan characteristics. Weconsidernotonlymovingbutalso“windfallprepayments”becausetheyreduce theincentivetorefinanceinthesamefashionasmovingiftheyareanticipatedbytheborrower. We regress a dummy variable that captures moving and windfall prepayments on borrower and loan characteristics topredict heterogeneous movingpropensities. We normalize the estimatedmoving propensities such that the mean is 10% to isolate the effect of heterogeneity rather than a shift of themean. Table 19 shows estimates using the estimated heterogeneous moving propensities. The estimates are similar to our baseline estimates which suggests that our finding is not driven by unobservableheterogeneousmovingpropensities. 48

Table 19: Heterogeneous Moving/Windfall Propensity. Here we use estimated heterogeneous probabilities for moving/windfall prepayments rather than a moving rate of µ = 0.1 as assumed in the baseline specification and in Agarwal, Driscoll, and Laibson (2013). Table 20 shows the estimates used to predict the heterogeneous probabilities. In column (1) the heterogeneous probabilities are normalized such that the average moving rate is µ = 0.1. In column (2) we use the estimated probabilities without normalization. County and quarter dummies are included. Standarderrorsareclusteredatthecountylevel. (1) (2) (OptimalTrigger-MarketRate)x(DirectMailAdv.) 0.0125∗∗∗ 0.0149∗∗∗ (0.00371) (0.00389) DirectMailAdvertising(DMA) 0.0221∗∗∗ 0.0214∗∗∗ (0.00787) (0.00754) OptimalTriggerRate-MarketRate(in%) 0.0396∗∗∗ 0.0357∗∗∗ (0.00386) (0.00354) MortgageInquiries(Past3Months) 0.0889∗∗∗ 0.0890∗∗∗ (0.0155) (0.0155) FICOScore 0.000301∗∗∗ 0.000286∗∗∗ (0.0000706) (0.0000708) LTVRatio -0.117∗∗∗ -0.0743∗∗∗ (0.0244) (0.0214) Income(in$1,000) 0.000356∗∗∗ 0.000366∗∗∗ (0.0000944) (0.0000954) Age -0.000684∗∗ -0.000625∗ (0.000328) (0.000329) Constant -0.0825 -0.110∗ (0.0642) (0.0638) Observations 11597 11597 Standarderrorsinparentheses ∗ p<0.1,∗∗ p<0.05,∗∗∗ p<0.01 49

Table 20: Moving/Windfall Logit. The dependent variable is an indicator that equals one if the borrowerprepaysthemortgagewithinthefollowingyeareitherbecauseshemovesorbecauseshe makes a “windfall payment”, i.e. she prepays the mortgage ahead of schedule without refinancing ormoving. RateofCurrentMortgage(in%) 0.0535 (0.0467) MarketFRMRate(in%) -0.382∗∗∗ (0.0800) LoanAge 0.0000505 (0.0000402) RemainingPrincipalBalance(in$1,000) -0.00000159∗ (0.000000815) FICOScore 0.00197∗ (0.00106) LTVRatio -3.302∗∗∗ (0.273) Income(in$1,000) 0.00000275∗∗∗ (0.000000995) Age -0.00954∗∗ (0.00374) Observations 11198 Standarderrorsinparentheses ∗ p<0.1,∗∗ p<0.05,∗∗∗ p<0.01 50

Table21: HeterogeneousInterestRate. Theseestimatesallowdifferentborrowerstohaveaccess to different interest rates at a given point in time, instead of using the average market mortgage rate as the baseline specification. We estimate the borrower specific interest rate by regressing the interest rate on the old mortgage on the average market rate, the FICO score and the loanto-value ratio — all at the time of origination. We interpret the residuals of this regression as a time-invariant borrower effect, which captures for example unobserved differences in default risk and differences in the cost of shopping for a better mortgage. We predict the borrower-specific interest rate with the updated market mortgage rate, FICO score, updated loan-to-value ratio and theborrowereffect. The dependent variable is a dummy that is equal to one if the borrower refinanced within three quarters. Countyandquarterfixedeffectsareincluded. Standarderrorsareclusteredatthecounty level. (OptimalTrigger-MarketRate)x(DirectMailAdv.) 0.0171∗∗∗ (0.00458) DirectMailAdvertising(DMA) 0.00846 0.0231∗∗∗ (0.00598) (0.00847) OptimalTriggerRate-MarketRate(in%) 0.0470∗∗∗ 0.0436∗∗∗ (0.00407) (0.00409) MortgageInquiries(Past3Months) 0.0836∗∗∗ 0.0838∗∗∗ (0.0153) (0.0153) FICOScore 0.000191∗∗∗ 0.000192∗∗∗ (0.0000733) (0.0000732) LTVRatio -0.0488∗∗ -0.0484∗∗ (0.0200) (0.0201) Income(in$1,000) 0.000307∗∗∗ 0.000312∗∗∗ (0.0000981) (0.0000980) Age -0.000470 -0.000487 (0.000339) (0.000341) Constant -0.0347 -0.0392 (0.0677) (0.0675) Observations 11334 11334 Standarderrorsinparentheses ∗ p<0.1,∗∗ p<0.05,∗∗∗ p<0.01 51

,elbairav tnedneped eht enfied ot desu wodniw emit eht yrav )4(-)1( snmuloC .gnicnanfieR rof swodniW emiT tnereffiD :22 elbaT dradnatS .dedulcni era seimmud retrauq dna ytnuoC .cte sretrauq 2 nihtiw )2( nmuloc ,retrauq 1 nihtiw sfier ylno sredisnoc )1( nmuloc .levelytnuocehttaderetsulcerasrorre )4( )3( )2( )1( sretrauQ4 sretrauQ3 sretrauQ2 retrauQ1 ∗∗∗5710.0 ∗∗∗9510.0 ∗∗∗8110.0 ∗∗∗54700.0 ).vdAliaMtceriD(x)etaRtekraM-reggirTlamitpO( )67400.0( )51400.0( )38300.0( )58200.0( ∗∗∗4520.0 ∗∗∗0520.0 ∗∗∗3120.0 ∗∗9410.0 )AMD(gnisitrevdAliaMtceriD )14900.0( )32800.0( )55700.0( )28500.0( ∗∗∗3440.0 ∗∗∗4430.0 ∗∗∗4320.0 ∗∗∗8210.0 )%ni(etaRtekraM-etaRreggirTlamitpO )81400.0( )35300.0( )38200.0( )88100.0( ∗∗∗6290.0 ∗∗∗3980.0 ∗∗∗3680.0 ∗∗∗8280.0 )shtnoM3tsaP(seiriuqnIegagtroM )9510.0( )5510.0( )5410.0( )1310.0( ∗∗∗483000.0 ∗∗∗962000.0 ∗∗∗251000.0 ∗∗∗851000.0 erocSOCIF )9480000.0( )7070000.0( )0850000.0( )4340000.0( 0910.0- ∗∗8340.0- ∗∗0430.0- ∗∗∗1920.0oitaRVTL )9420.0( )8910.0( )0710.0( )0110.0( ∗∗∗644000.0 ∗∗∗433000.0 ∗∗281000.0 ∗∗221000.0 )000,1$ni(emocnI )711000.0( )1690000.0( )9370000.0( )4940000.0( 694000.0- 235000.0- 691000.0- 241000.0egA )504000.0( )923000.0( )342000.0( )861000.0( ∗∗561.0- ∗111.0- 4550.0- ∗∗6480.0tnatsnoC )6670.0( )9360.0( )8050.0( )1530.0( 37011 79511 64811 13021 snoitavresbO sesehtnerapnisrorredradnatS 10.0<p ∗∗∗,50.0<p ∗∗,1.0<p ∗ 52