Mortgage Design, Repayment Schedules, and Household Borrowing

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Mortgage Design, Repayment Schedules, and Household Borrowing Claes B¨ackman, Patrick Moran, Peter van Santen 2024-077 Please cite this paper as: B¨ackman, Claes, Patrick Moran, and Peter van Santen (2024). “Mortgage Design, Repayment Schedules, and Household Borrowing,” Finance and Economics Discussion Series 2024-077. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2024.077. 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.

∗ Mortgage Design, Repayment Schedules, and Household Borrowing Claes B¨ackman† Patrick Moran‡ Peter van Santen§ June 4, 2024 Abstract How does the design of debt repayment schedules affect household borrowing? To answer thisquestion,weexploitaSwedishpolicyreformthateliminatedinterest-onlymortgagesfor loan-to-valueratiosabove50%. Wedocumentsubstantialbunchingatthethreshold,leading to5%lowerborrowing. Wealthyborrowersdrivetheresults,challengingcreditconstraintsas theprimaryexplanation. Wedevelopamodeltoevaluatethemechanismsdrivinghousehold behavior and find that much of the effect comes from households experiencing ongoing flow disutility to amortization payments. Our results indicate that mortgage contracts with low initial payments substantially increase household borrowing and lifetime interest costs. JEL Classification: G51, G21, E21, E6 Keywords: Mortgage design; Amortization payments; Macroprudential policy; Bunching ∗We thank Rob Alessie, Johan Almenberg, Olga Balakina, Vimal Balasubramaniam, Eirik Brandsaas, Taha Choukhmane,TobinHanspal,StephanieJohnson(discussant),RagnarJuelsrud,KarinKinnerud,KavehMajlesi, Clemens Sialm (discussant), Jakob Sogaard, Lars E.O. Svensson, Nikodem Szumilo and seminar participants at the ECB, Sveriges Riksbank, University of Groningen, Lund University, Nordic Junior Macro Seminar, EFA, Central Bank of Ireland Workshop on Borrower Finances, the NFN Young Scholars Finance Webinar series, IAAE, EEA-ESEM, the Federal Reserve Board, the Federal Reserve Bank of Philadelphia, Goethe University, the IMF, and ASSA 2024 for helpful comments. We gratefully acknowledge research support from the Leibniz Institute for Financial Research SAFE. Claes Ba¨ckman would like to thank Jan Wallanders och Tom Hedelius stiftelse for generous financial support. The empirical analysis in this paper was done when van Santen worked at the Financial Stability Department of Sveriges Riksbank. The views expressed in this paper are solely those of the authors and do not represent the views of the Federal Reserve Board, the Federal Reserve System, or the Sveriges Riksbank. †Leibniz Institute for Financial Research SAFE (claes.backman@gmail.com) ‡Federal Reserve Board, CEBI, and IFS (patrick.e.donnellymoran@frb.gov) §Faculty of Economics and Business, University of Groningen (p.c.van.santen@gmail.com)

1 Introduction One of the most important features of the mortgage contract is the repayment schedule. Most mortgages force the borrower to gradually repay the mortgage and build wealth in the form of home equity. Mandatory mortgage repayment represents a large share of aggregate household savings, similar in magnitude to pension contributions (Bernstein & Koudijs, 2023). While historicallyhouseholdshadlittlechoiceovertherepaymentschedule,financialinnovationduring recent decades created a wide variety of alternative mortgage products that allow households to delay mortgage repayment (Cocco, 2013). Perhaps the most famous example is the interestonly mortgage, which surged in popularity in the mid-2000s, jumping to roughly 25 percent of mortgage originations in the United States during the run-up of mortgage debt prior to the financialcrisis(Amrominetal.,2018). Financialregulatorsaroundtheworldcontinuetograpple with the question of how to regulate this important feature of the mortgage contract.1 Despite the important role of the repayment schedule, we have little evidence on how this featureofthemortgagecontractaffectshouseholdborrowing. Thereareatleasttwocontrasting views. Ononehand, interest-onlyloansrelaxcreditconstraints, helpingconstrainedhouseholds borrow when they expect income or house prices to grow (Piskorski & Tchistyi, 2010; Cocco, 2013). On the other hand, many commentators have suggested that consumers may suffer from behavioral biases that lead them to increase borrowing due to interest-only mortgages. According to one such theory, both constrained and unconstrained consumers may prioritize a low monthly payment, which is highly salient, rather than minimize the net present value of future interest payments (Argyle et al., 2020). While we already have clear evidence on the role of credit constraints in mortgage lending, we know little about the latter mechanism. To better understand how the repayment schedule affects household borrowing, we require quasi-experimental variation in repayment schedules that affects households who are far from their credit constraints. To achieve this goal, we exploit a policy reform in Sweden that eliminated interest-only mortgages for borrowers with loan-to-value (LTV) ratios above 50 percent. In response to the reform, we find that many homebuyers make larger down payments, and existing borrowers extract less equity, leading to bunching just below the 50 percent LTV threshold. The reduction in borrowing is driven by relatively wealthy households with substan- 1Countrieshavetakendrasticallydifferentapproaches. WhiletheUSstronglydiscouragesinterest-onlymortgages, many European countries continue to allow them. In contrast, the UK has recently begun to encourage banks to offer mortgages with longer maturities to counteract rising interest rates. 1

tial additional borrowing capacity, thus ruling out credit constraints as the primary driver of our results. Motivated by the empirical evidence, we develop a theoretical framework to clarify the mechanisms that may lead wealthy, unconstrained households to reduce borrowing to avoid amortization. We find that much of the response is driven not by financial considerations but rather by psychic costs. More specifically, we find that households suffer ongoing flow disutility toamortizationpayments, whichleadsthemtochooseamortgagewithalowmonthlypayment, even if it comes with higher lifetime costs. Identification is driven by the fact that most of the bunching is generated without a missing mass, which alternative versions of the model without flow disutility fail to generate. Our results provide evidence that households suffer from “Net Present Value (NPV) neglect” in the spirit of Shu (2013) and Argyle et al. (2020). As a result, new mortgage products with delayed repayment schedules may substantially increase household debt and the lifetime costs of interest expenditure. In our empirical analysis, we exploit an amortization requirement introduced in Sweden in 2016 with the intent of reducing mortgage debt. Before 2016, interest-only mortgages constituted the majority of mortgage contracts in Sweden. The amortization requirement introduced minimum mandatory mortgage payments based on the borrower’s loan-to-value (LTV) ratio. More specifically, for all mortgages issued after June 2016, borrowers with LTV ratios above 50 percent are required to repay at least 1 percent of the original loan each year, while borrowers with LTV ratios above 70 percent are required to repay at least 2 percent. Mortgages with LTV ratios below 50 percent are not required to be amortized. Borrowers can reduce amortization payments once they get below the LTV thresholds. We estimate the response to the requirement using a difference-in-bunching estimator, using pre-requirement years to form the counterfactualLTVdistributionatorigination. WedocumentsignificantbunchingatbothLTV thresholds. NewborrowersreducetheirLTVratiosby5percentinresponsetoaonepercentage point higher average amortization rate. While it would be easy to rationalize bunching by binding credit constraints, most households at the policy threshold have substantial additional borrowing capacity, thus challenging credit constraints as the primary driver of our empirical results. First, borrowers can take out substantially larger mortgages, up to a maximum LTV ratio of 85 percent. Second, while a payment-to-income (PTI) requirement may interact with the amortization requirement, most bunching households still have substantial additional borrowing capacity. More specifically, 2

while roughly 14 percent of borrowers that bunch at the 50 percent LTV threshold are constrained by the PTI requirement, the remaining households could borrow at least an additional $67,000 (44 percent of our sample average) before facing binding payment constraints. Credit constraints are thus unable to explain our empirical results. We assess the validity of our empirical approach and the robustness of our results along several dimensions. First, we confirm the validity of our empirical strategy using placebo tests, whichshowthatpreviousyearsindeedprovideavalidcounterfactualLTVdistribution. Second, estimating the counterfactual distribution using a polynomial approach (Kleven, 2016) yields larger estimates of the impact of the amortization requirement on household borrowing. Third, wefindsimilarresultsforhouseholdsthatpurchaseapropertycomparedtothosewhorefinance, alleviating concerns about housing choice.2 Finally, we investigate various supply-side factors (e.g., mortgage approval, collateral assessments, and refinancing costs) but find that none can explainourresults. Forinstance, theinterestrateisflatovertheLTVthreshold, thusindicating that bunching is not driven by mortgage pricing. Motivated by the empirical evidence, we develop a theoretical framework to clarify the mechanisms that may lead wealthy households to bunch below the policy threshold to avoid amortization payments. We begin with a traditional life-cycle model of consumption, housing, and mortgage decisions in the spirit of Campbell & Cocco (2003) and Cocco (2005). In the model, credit-constrained households borrow to purchase housing while faced with uninsurable idiosyncratic income risk. Households borrow using long-term mortgage contracts with mandatory minimum payments. We allow for two policy regimes: interest-only (IO) mortgages and mandatory amortization payments for households above the 50 percent LTV threshold. The two policy regimes broadly represent the institutional framework in Sweden before and after the 2016 reform. Whilethetraditionalmodeldescribedabovecouldeasilygeneratereducedborrowingforpoor households facing binding credit constraints, it cannot generate bunching by wealthy borrowers atthe50percentLTVthreshold. Weprovideintuitionforthelackofbunchingatthisthreshold by inspecting how expected discounted utility varies according to the LTV ratio. We find that the amortization requirement reduces expected utility for all households due to reduced 2For refinancers, the bank sets the home value exogenously based on their assessment of the collateral value. TheseresultssupportourinterpretationthattheobserveddeclineinLTVratioscomesfromlowerloandemand (the numerator in the LTV ratio) and not from changes in housing choices (the denominator). 3

flexibility to smooth consumption a la Cocco, 2013. That said, the amortization requirement does not create a discontinuous change at the policy threshold, and therefore does not result in bunching. The lack of bunching by wealthy households is robust to a wide variety of alternative assumptions related to preference parameters, asset returns, and refinancing costs. Indeed, even when we give households access to a high-return liquid asset, we still do not find wealthy households bunching at the 50 percent LTV threshold. If the standard model does not generate bunching for wealthy, unconstrained households, what potential extensions can help the model replicate our empirical results? Kleven (2016) explains that four mechanisms may generate bunching: notches or kinks in the budget constraint or notches or kinks in household preferences. As mentioned previously, we find a very limited role for mechanisms operating through the budget constraint. We therefore turn our attention towards household preferences, extending the model with two broad classes of behavioral mechanisms that may generate either a notch or kink in preferences. We adopt a reduced-form approach to behavioral modeling, remaining agnostic about the specific behavioral biases that may create the wedge in household preferences, following Mullainathan et al. (2012). The first mechanism is that households may experience a one-off disutility cost that applies whenborrowersturnoffamortizationpayments. Thismechanismgeneratesanotchinhousehold preferences,astakingoutamortgagejustabovethe50percentLTVthresholdisdiscontinuously worse than taking out a mortgage just below the threshold. This one-off disutility may occur if households experience a cost to mortgage renegotiation when calling the bank to turn off amortization payments once eligible. We model this as a utility cost, as monetary refinancing costs are low in Sweden. That said, various behavioral factors could generate a similar one-off cost, and our approach nests these possibilities. For instance, if households are uncertain about their ability to turn off amortization, this would create a one-off cost. Similarly, if the policy threshold serves as a target that agents strive to achieve, then reference dependence could also generate a notch in household preferences (Kleven, 2016). The second mechanism is that households may suffer ongoing flow disutility from amortization payments. This mechanism generates a kink in preferences, as the effect is stronger for households further from the 50 percent LTV threshold; as such, households must make amortization payments for more periods. There are various related mechanisms that may generate ongoing flow disutility from amortization payments. For instance, households may perform 4

“monthly payment targeting,” where they focus on targeting a specific monthly mortgage payment rather than minimizing the lifetime cost of the loan, in the spirit of Argyle et al. (2020). Similarly, householdsmayviewamortizationpaymentsasacostratherthanaformofsaving, in the spirit of Camanho & Fernandes (2018).3 In either case, such preferences imply that households do not fully consider the net present value (NPV) of future interest costs when choosing between mortgage contracts with alternative repayment schedules. As a result, households may choose contracts with lower initial payments and higher lifetime costs, even when they could afford to do otherwise. We refer to this concept as “NPV neglect” following Shu (2013). To disentangle the relative contribution of these two very different mechanisms, we exploit that the one-off disutility cost generates a notch in household preferences while ongoing flow disutility generates a kink. This distinction is useful for identification, as notches generate bunching due to a dominated region with missing mass directly above the threshold, while in contrast, kinks alter the incentives for all households above the threshold, thus generating bunching without a missing mass. In the data, we find that less than 15 percent of bunching is explained by missing mass directly above the threshold. The lack of missing mass is difficult to rationalize with optimizing frictions since borrowers can choose the LTV value directly and since the consequences of choosing a higher LTV are highly salient. We conclude that while both mechanisms play a role, most of the response is driven by households suffering ongoing flow disutility to amortization, consistent with the theory of “NPV neglect.” Our results have important implications for understanding the link between financial innovation and household borrowing. In a world with NPV neglect, new mortgage products with interest-only payments (or longer maturities) have large aggregate effects on household debt. Moreover, such products substantially increase lifetime interest expenses. To demonstrate, we use our model to study one of the key aspects of financial innovation in US mortgage markets during the late 1990s and early 2000s: the transition from traditional 30-year mortgages to alternative mortgage products with less stringent repayment schedules. We begin with an economy where households only have access to 30-year amortizing mortgages, then suddenly allow households to borrow using IO mortgages. Introducing IO mortgages increases mortgage debt by about 33 percent in our calibrated model. The structural model allows us to decompose the different channels driving the increase in borrowing. We find that roughly two-thirds of the 3InSwedishsurveyevidence,38percentofrespondentsstatethatamortizationpaymentsareacost,44percent state that amortization payments are a form of savings, and 18 percent do not know (SBAB, 2018). 5

increase comes from “NPV neglect,” while the remaining one-third comes from relaxed credit constraints (in the spirit of Cocco, 2013). The policy change has a similar effect on interest expenditures, which also increase by 33 percent over the life-cycle. In short, we find that “NPV neglect” amplifies the effects of financial innovation on household borrowing. The degree of amplification is heightened by the fact that we find a kink rather than a notch in household preferences. Had households’ observed behavior been driven by a notch, there would have been only a local effect on household borrowing and, thus, a smaller amplification relative to the traditional model. Taking stock, our findings have important implications for understanding household preferences for debt repayment. And while we focus on the mortgage market, many of our results extend to other forms of consumer borrowing, where there is a similar debate about how households respond to new financial products with longer maturities or lower initial payments. Understanding these preferences is crucial for both consumer protection agencies concerned about the welfare effects of new financial products, as well as macroprudential regulators concerned about aggregate debt levels. Related Literature. Weseethreemaincontributionsofthispaper. First,weprovidenovel evidencethatrepaymentschedulesaffectborrowingdecisions,evenforunconstrainedborrowers, which helps improve our understanding of household preferences for debt repayment. We view ourresultsascomplementarytoArgyleet al.(2020),whofindthatconsumersperform“monthly payment targeting” when choosing between auto loans, even in subsamples of unconstrained borrowers. In a similar spirit, Shu (2013) provides survey evidence of “NPV neglect,” the tendency of borrowers to target initial payment size instead of minimizing the net present value of future interest costs. Further survey evidence by Camanho & Fernandes (2018) shows that many individuals decide whether to purchase housing based on the difference between monthly rental payments and monthly mortgage payments, even when the latter includes amortization payments. Relative to the existing literature, we are the first to evaluate the presence of “NPV neglect” in observed mortgage decisions, as well as the first to evaluate this theory using quasiexperimental evidence. Second,wecontributetothegrowingliteratureonmortgagedesign,whichhasrecentlyshown increasing interest in mortgage repayment schedules.4 Bernstein & Koudijs (2023) show that 4See also seminal contributions from Cocco (2013) and Piskorski & Tchistyi (2010). Recent papers on the topic also include Vihri¨ala¨ (2023) and Ferrari & Loseto (2023). 6

amortization payments contribute substantially to household wealth accumulation. Campbell et al. (2020) study a model where an option to lower amortization payments in a recession helps to stabilize consumption. Guren et al. (2021) study an equilibrium model where countercyclical payment reductions reduce default and stimulate housing demand. Attanasio et al. (2021) evaluate the role of amortization payments as a savings commitment device. Ganong & Noel (2020) find that extending mortgage maturity has a large impact on default rates. Amromin et al. (2018) show that interest-only mortgages were used by prime borrowers in the US housing boom. Garmaise (2013) shows that increased flexibility in mortgage contracts led to higher borrowing. We also note that amortization payments represent a de-facto constraint on savings and borrowing for payment-constrained borrowers. Amortization payments have recently been included in several theoretical models that incorporate realistic features of the mortgage contract (Greenwald, 2017; Kaplan et al., 2020; Boar et al., 2022), but the interaction with credit constraints has received less attention. Within this literature, we are the first to consider the possibility that households may suffer from behavioral biases when choosing between mortgage contracts with alternative repayment schedules. Third, ourresultsarerelevantforunderstandingtheroleoffinancialinnovationincontributing to the accumulation of mortgage debt prior to the 2008 financial crisis. Lower amortization payments in the first years after origination were a common feature of interest-only mortgages, option ARMs, and balloon mortgages in the run-up to the Great Recession in the United States (Amromin et al., 2018; Barlevy & Fisher, 2020; Justiniano et al., 2021). Similar occurred in other countries: Australia, Denmark, Finland, Greece, Korea, and Portugal all introduced interest-only mortgages between 1995 and 2005 (Scanlon et al., 2008). Our results suggest that theincreasedavailabilityandsubsequentdisappearanceofnon-traditionalmortgageswithlower amortization payments can explain large movements in household debt in the United States. Looking forward, policymakers should be aware that debt repayment schedules could have large consequences for credit growth. Our results, therefore, also contribute to the growing literature on the effect of macroprudential policies (e.g. Cerutti et al., 2017; Laufer & Tzur-Ilan, 2019; Peydr´o et al., 2020; DeFusco et al., 2020). Methodologically, the present paper builds upon a growing literature that uses bunching to understand preferences. The use of bunching to identify preferences has received attention in review articles by Kleven (2016) and DellaVigna (2018). Prominent examples in household 7

finance include Andersen et al. (2022) who study reference dependence in housing markets, Choukhmane (2021) who studies opt-out costs in retirement decisions, Collier et al. (2021) who study collateral aversion in lending markets, and Best et al. (2020) who estimate the intertemporal elasticity of substitution using mortgage decisions. Other prominent examples include Lacetera et al. (2012) and Strulov-Shlain (2023) who study left-digit bias in pricing. To the best of our knowledge, we are the first to use bunching to study “NPV neglect.” Several studies examine the effect of the Swedish amortization requirement. Andersson & Aranki (2017) use a difference-in-difference strategy to show that the amortization requirement reduced household borrowing. Andersson & Aranki (2019) analyze the additional amortization requirement introduced in 2018 that mandated that mortgages with a debt-to-income ratio above 4.5 had to be amortized by an additional percentage point. The authors show that householdsareborrowing, onaverage, 8.5percentlessthantheyotherwisewouldhavedoneand that they are also buying less expensive homes. Wilhelmsson (2022) finds that the amortization requirement led to a 7 percent reduction in house prices. The paper is organized as follows. Section 2 describes the Swedish mortgage market and the amortization requirement. Section 3 presents the data and discusses the empirical strategy. Section 4 provides the main empirical results. Section 5 develops a theoretical framework to understand households’ response to the amortization requirement. Section 6 summarizes and discusses potential extensions. 2 The Amortization Requirement The Swedish housing and credit markets experienced rapid growth in the early 2010s. House prices increased by 31 percent between 2011 and 2015, and credit growth increased from 5 percent in 2012 to over 8 percent in 2015. Concerned with financial and macroeconomic stability, the Swedish Financial Supervisory Authority (Finansinspektionen, or FSA) announced that they would propose new regulation in November 2014 – the amortization requirement – intending to reduce debt levels over time. The purpose was to limit macroeconomic risks posed by high household debt levels. The FSA considered households with higher LTV ratios a higher risk; consequently, regulation targeted this group. The requirement came on top of the current recommendation by the Swedish Bankers Association (SBA), which recommended that borrowers amortize if their LTV values exceeded 70 percent. The amortization requirement was finally 8

Amortization rate (%) 2.0 1.5 Requirement 1.0 2016-2018 Recommendation 2014-2015 0.5 Recommendation 2011-2013 0.0 0 10 20 30 40 50 60 70 80 LTV (%) Figure 1. Required Amortization Rates for new mortgages Notes: ThefigureplotsrequiredorrecommendedamortizationratesbyLTVratiosfordifferentperiods. Thedashedblue lineanddottedgreenlineplotthenon-bindingrecommendationsfromtheSwedishBankers’Association. proposed in December 2015, and the law was enacted in June 2016. The FSA introduced an additional amortization requirement in March 2018, which mandates that any mortgage where thedebt-to-incomeratioisabove4.5istobeamortizedbyanadditionalpercentagepoint. The Swedish amortization requirement mandates that all new mortgages issued after June 1st, 2016, with LTV ratios above 50 percent must be amortized. New mortgages with LTV ratios below 50 percent are exempt. Borrowers switching banks with no change in contract terms are also exempt. The requirement, along with the previous recommendations from the SBA, is summarized in Figure 1. Before 2016, the SBA recommended that borrowers amortize loans with an LTV ratio above 75 percent (2011-2013, blue dotted line) and 70 percent (2014- 2015, blue dashed line), respectively. Compared to the requirement introduced in 2016, the recommended rates were lower and implied an increase in the marginal amortization rate. The implemented amortization requirement instead mandates that new borrowers must amortize at least 1 percent per year on any mortgage where the initial LTV ratio exceeds 50 percent and at least 2 percent per year on any mortgage where the LTV ratio exceeds 70 percent. Since continuous re-evaluation of property values could have pro-cyclical effects, the law states that the valuation can only be made every five years. Moreover, any re-evaluation must be based on changes to the property value due to renovation or rebuilding, not due to aggregate house price changes. At any point, a borrower can be granted an exemption from amortization due 9

to extenuating circumstances, such as unemployment, illness, or a death in the family.5 Once a borrower has amortized down to a threshold, the borrower is legally allowed to reduce the amortization rate. We contacted all banks in our sample to ask for clarification on how reducing amortization payments would work for their customers. All banks state that the borrowers must contact the bank to request a reduction in amortization payments. No bank except one offers a contract where the amortization rate is reduced automatically. While the mortgage contract specifies the amortization rate or repayment plan, no new contract is required. Instead, a phone call or a request on the bank’s online portal is sufficient to reduce the amortization rate once the customer reaches the threshold. There is no fee for reducing the amortization rate, except for one bank that charges 1500 SEK (approximately USD 150). Finally, thereisnonewcreditcheck, andbanksrarelydenyarequestforareducedamortization rate once the borrower hits the threshold. Several banks state that a customer is never denied a lower amortization rate. For banks stating that denials happen, the denial was related to being delinquent or having missed mortgage payments. Therequirementhadalargeimpactonamortizationratesfornewborrowers. Fromthedata, whichwediscussindetailinSection3,Figure2plotstheshareofinterest-onlymortgagesamong new mortgages against LTV values for different years.6 In the pre-requirement years between 2013 and 2015, around 60 percent of mortgages around the lower threshold were interest-only. In the post-requirement years between 2016 and 2018, the interest-only share is still around 60 percent to the left of the threshold. To the right of the threshold, the interest-only share is zero, as the policy requires. We also see a spike in interest-only mortgages precisely at the threshold, consistent with borrowers deliberately moving to the threshold to qualify for interest-only mortgages. 2.1 Swedish mortgages TheSwedishmortgagemarketsystemworksasfollows(see,e.g.Riksbank,2014). Banksprovide mortgage credit to borrowers directly, subject to a credit assessment. Mortgage debt is full recourse, with unlimited liability of the borrowers and lifetime wage garnishing to compensate lendersincaseofdefault. Thisfeatureisimportantasitlimitsthebenefitsprovidedbyinterest- 5Inaddition,theamortizationrequirementwastemporarilypausedduringthecovidpandemictogivehouseholds greater flexibility during the crisis (Andersson & Aranki, 2021). 6Figure A2 plots the average rate of amortization rate against LTV values 10

2013 2014 2015 80 60 40 20 0 40 45 50 55 60 40 45 50 55 60 40 45 50 55 60 2016 2017 2018 80 60 40 20 0 40 45 50 55 60 40 45 50 55 60 40 45 50 55 60 )%( ylno-tseretni erahS LTV Ratio Figure 2. Share interest-only mortgages at the 50 percent LTV threshold Notes: Thefigureplotstheshareofinterest-onlymortgagesbyLTVbinandyear. Thetopthreepanelswithdashedblue linesplottheinterest-onlyshareforthethreeyearsbeforetheamortizationrequirement,andthebottomthreepanelswith solidorangelinesplottheinterest-onlyshareforthethreeyearsaftertherequirement. only mortgages when borrowers wish to speculate on rising house prices (Barlevy & Fisher, 2020). All Swedish mortgages are subject to a maximum loan-to-value ratio of 85 percent as of 2010, and 30 percent of interest payments are deductible against capital gains and labor income. The banks set mortgage rates. Several Swedish banks use (or have used) a system where the portion of the mortgage with an LTV ratio above 75 percent has a higher interest rate (a so-called “top loan”).7 Importantly,Swedishmortgagesarenot annuitycontracts. Instead,totalmortgagepayments consist of the sum of interest payments and amortization payments. Total interest payments are the interest rate on the mortgage times the outstanding mortgage debt. Total amortization payments are the amortization rate times the mortgage debt at origination (i.e., the loan is repaid linearly over time). The increase in mortgage payments at the threshold is then fully due to higher amortization payments. An implication of this empirical setup is that the mortgage interest payments are falling over time.8 7Top loans refer to the slice of the mortgage loan not eligible for funding with covered bonds. Covered bond regulation in Sweden puts a maximum LTV ratio of 75 percent for residential real estate. 8Effectively, the difference in interest payments on Swedish-style mortgages and US-style annuity contracts 11

Swedish banks are required to assess the borrower’s financial status. Banks assess financial status through a discretionary income limit, which requires the household to have enough disposable income to afford basic consumption and housing (including amortization payments). This limit, functionally equivalent to a payment-to-income constraint (Grodecka, 2020), is calculated using a high, “stressed” interest rate to ensure that borrowers’ finances are resilient to higherinterestrates.9 Whenapplyingforamortgage,Swedishborrowersfirstseeka“borrowing pledge” from their preferred bank. On the pledge, the bank states the maximum amount they are willing to lend to the borrower, given, for example, household income and household size. Importantly, banks givethispledgebefore theborrower makesahousingpurchase, whichmakes manipulation of the LTV ratio from the bank unlikely. 3 Data and Empirical Strategy 3.1 Data We use data from the Mortgage Survey (Bol˚aneunders¨okningen) from 2011 until 2018. The FSA collects this data directly from the eight largest Swedish banks as part of its micro- and macroprudential mandate. The dataset contains information on all new mortgages issued by these banks during certain days between August and October. The FSA varies the exact dates andannouncesthemafterwardtosurprisebanksandpreventthemfromapplyingdifferentcredit standards during these survey dates.10 The survey includes household-level data on (gross and disposable)incomes, totaldebtdividedintosecuredandunsecuredloans, andcertainhousehold characteristics, as well as loan-level data on loan size, interest rates, monthly amortization payments, and collateral value. The data also includes the bank’s calculation of discretionary income, evaluated at a stressed interest rate. Collateral values are usually based on banks’ internal valuation models using previous transaction prices and local hedonic price indices. The transactionpriceistypicallyusedfornewhomebuyers. Weusethetotalmortgagedebtdivided by collateral value to calculate LTV ratios. We cannot link our mortgage data to other register data as households are reported anonymously. Table B1 provides summary statistics for the full sample and groups based on financial constraints. are small over the initial years of the mortgage duration. 9While mortgage rates were typically below 2 percent during the end of our sample, stressed rates were on the order of 6-7 percent, thus ensuring households can manage much higher interest rates. 10Thenumberofdaysandexactdatesvaryperyear. Typically,banksreportallissuedmortgageloansforfive days in late August and another five days in early October. To the extent the chosen days are representative of the rest of the year, the sample is representative of the flow of new mortgage loans. 12

3.2 Empirical strategy We now describe our approach to estimating the counterfactual distribution and the amount of bunching induced by the amortization requirement. Our empirical strategy hinges on estimating the counterfactual LTV distribution that would have occurred without the amortization requirement. We exploit the availability of repeated cross-sections to estimate the counterfactual distribution. In other words, we compute a difference-in-bunching estimate, where the distribution observed before the requirement serves as the counterfactual distribution in the post-requirement years. Our identifying assumption is that for each bin, the fraction of loans in the post-reform period would have been equal to the fraction of loans in the pre-reform period in the absence of the policy: no other change or policy caused the distribution of LTV ratios to shift between the pre-and post-reform periods. We note that this is a different assumption than intheempiricalbunchingliterature,whereitismorecommontoassumethatthecounterfactual distribution is smooth in the absence of the policy change (see, e.g. Kleven & Waseem, 2013). Our approach can account for any spikes in the distribution at the thresholds related to, e.g., round number bunching or supply-side factors that would generate bunching. Our identifying assumption is that such spikes are constant across time. We conduct several robustness checks andruleoutseveralpotentialmechanismstoensurethisassumptionisplausibleinAppendixC. Forcompleteness,weprovideresultsusingthestandardpolynomialapproachandshowthatour results are conservative. Since the spike at 50 is larger than the spikes at other potential round numbers in pre-requirement years, it is more conservative to use the difference-in-bunching approach. Appendix C.4 details the flexible polynomial approach. We group borrowers into LTV bins with a width of half a percentage point. The goal is to estimate the counterfactual fraction of borrowers in each LTV bin j post-requirement period if the amortization requirement is not introduced, denoted nˆ .11 We measure the amount of j bunchingB(cid:98) asthedifferencebetweentheobservedandcounterfactualbinfractionsintheregion at and to the left of the threshold located at R: R (cid:88) B(cid:98) = (n j −nˆ j ) (1) j=L 11WecalculatethefractionofborrowersineachLTVbininsteadofusingthecountofborrowerssincewehave differentsamplesizesforeachyear. Sincethesamplesizereflectsthenumberofdaysdataiscollected,thecount is uninformative. As we are using the previous years to form the counterfactual distribution, using the count instead may result in level differences solely due to differences in sample size. We have verified that using the fraction instead of the count does not affect our empirical estimates. 13

Theamountofbunchingequalsthefractionofadditionalborrowerswhoplacethemselvesatthe threshold beyond what the counterfactual distribution based on previous years would predict. Similarly, but to the right of the threshold, the amount of missing mass is equal to: U (cid:88) M(cid:99)= (n j −nˆ j ) (2) j>R Missing mass equals the difference between the observed and counterfactual distribution in the regiontotherightofthethreshold. Notethatborrowersmakingupthemissingmasscouldshift towardsthethreshold(intensivemargin)orexitthemarketaltogether(extensivemargin). Ifall borrowers in the region defining the missing mass bunch at the threshold, the intensive margin effect equals the amount of bunching. If some borrowers drop out of the market because of the requirement,thisisequivalenttostatingthatnotallborrowersshifttowardthethreshold. We use the bunching estimate B(cid:98) to calculate the behavioral response to the requirement, ∆LTV, following DeFusco & Paciorek (2017). The equation states that the response to the requirement by the marginal borrower, ∆LTV, is equal to the amount of bunching B(cid:98) divided by the counterfactual density around the notch g(cid:92)(LTV): linear (cid:92) B(cid:98) ∆LTV = (3) g(cid:92)(LTV) linear Wecalculatebootstrappedstandarderrorsforallparametersbydrawing500randomsamples with replacement from the full sample of borrowers. We then re-calculate the LTV distribution and re-estimate the parameters at each iteration. We use the estimated change in LTV from the reform to estimate the amortization elasticity of mortgage demand. The semi-elasticity of borrowing with respect to the amortization rate is: ∆LTV/LTV eα = (4) α∗(LTV +∆LTV)−α 0 where we relate the percent change in the LTV ratio (calculated as the behavioral response, ∆LTV, dividedbytheLTVatthethreshold, LTV), tothechangeinthemarginalamortization rate α∗−α for the marginal buncher. Appendix C.1 provides further details. 0 Our estimates capture the intensive margin response to the amortization requirement – the response of borrowers who still borrow after the requirement was implemented. This margin 14

sufficiently demonstrates our primary goal: to identify the effect of higher amortization payments on LTV ratios. Identifying the extensive margin response convincingly would require strong assumptions about the distribution to the right of the threshold and extrapolation from the threshold up until the maximum borrowing limit of 85 percent (see DeFusco et al., 2020). As the Swedish amortization requirement affected 90 percent of the new mortgage flow, we lack a counterfactual and instead focus on the intensive margin response. 4 Empirical results This section presents the main results of the analysis. Our main results focus on the lower threshold, located at LTV ratios of 50. Although all our results are consistent across both the lower and upper thresholds, the lower threshold provides cleaner identification for a number of reasons. First, some new borrowers may already choose an LTV ratio of 70 percent in the pre-requirement years because of a previous recommendation that households amortize on the portion of the mortgage in excess of a 70 percent LTV ratio. The previous recommendation represents a potential downward bias in our estimates, as borrowers may bunch even in the pre-requirement period. Second, several banks offer mortgages with a higher marginal interest rate on the part of the mortgage with an LTV above 75 percent (a so-called “top loan”). This incentive was phased out over time as banks abolished the top-loan system but did provide an incentive to bunch at a nearby threshold in the years before the requirement. The marginal interest rate changes above LTV ratios of 75 percent, and a borrower may want to reduce their borrowing to avoid this higher interest rate. This threshold is clearly noticeable in the counterfactual distribution in Figure C2. We provide all results for the upper threshold in Appendix C.3, and the interested reader can compare the bunching estimates for the lower and upper threshold in Table B2. Figure 3 illustrates the identification strategy and main empirical results. The figure plots the percent of new mortgages in specific LTV bins in pre- and post-requirement years. At this threshold, the minimum amortization rate on new mortgages jumps from zero to one percentage point for mortgages with an LTV ratio above 50 percent. In the post-requirement years, a considerable mass at the threshold indicates that many new borrowers choose lower LTV ratios to avoid mandatory amortization payments. Notably, the amount of bunching is consistent across the post-requirement years, implying that the effect that we uncover is not 15

Percent of households 2013 2014 2015 16 12 8 4 0 40 45 50 55 60 40 45 50 55 60 40 45 50 55 60 2016 2017 2018 16 12 8 4 0 40 45 50 55 60 40 45 50 55 60 40 45 50 55 60 LTV (%) Figure 3. LTV distributions around the requirement threshold Note: The figure plots the percent of borrowers per loan-to-value bin for each year. Pre-requirement years are marked withblueinthetoprow,andpost-requirementyearsfeaturingaminimum1percentamortizationrateforLTVabove50 aremarkedwithorangeinthebottomrow. short-lived. Since Swedish mortgages feature linear repayment schedules and are not annuity contracts, the increase in total mortgage payments at the threshold is entirely due to higher amortization payments, notinterestexpenses. Notethataffectedborrowersincludehomebuyersandexisting homeowners who refinance their mortgage and that the requirement does not affect existing mortgages. We later focus on each sample separately. 4.1 Bunching at the 50 percent LTV threshold The main result for the lower threshold is presented in Figure 4. The figure plots the observed distribution of loans by LTV ratio and the counterfactual distribution estimated from the bunching procedure around the threshold at an LTV ratio of 50. The solid orange line plots the empirical distribution, i.e., the distribution in 2016-2018, and the solid blue line plots the counterfactual distribution. The estimation procedure uses LTV ratios up to 65 percent to avoid the upper threshold affecting the results. The vertical axis shows the percent of loans in eachbin, whereeachbinis0.5percentagepointswide. WechooseL = 48.5andU = 51.5asour 16

Percent of households 10 B = 7.47 (0.31) Empirical M = 0.83 (0.16) D LTV = 2.57 (0.16) 8 6 4 Counterfactual 2 0 40 42 44 46 48 50 52 54 56 58 60 LTV (%) Figure 4. Bunching at LTV=50 Notes: ThefigureplotstheempiricalandcounterfactualdensityofmortgageloansbyLTVratio. Theestimationusesall loans with LTV ratios between 20 and 65 percent but only shows the distribution between 40 and 60. The solid orange lineplotstheempiricaldensity,i.e.,thepercentofmortgageswithineach0.5percentLTVbin. Thedashedbluelineplots thecounterfactualdensityestimatedusingtheproceduredescribedinSection3. Thefigurereportstheestimatedpercent ofloansthatbunchatthethreshold(B),themissingmass(M),andthebehavioralresponsebyborrowers(∆LTV). The calculationofthesenumbersisdescribedinSection3. Standarderrorsarecalculatedbybootstrappingandareshownin parentheses. main specification (see equations (1) and (2)). Our estimates of ∆LTV, B, and M are robust to changing these limits of the excluded area in either direction (see Table B3). Using a placebo test,AppendixC.2furthershowsthatthecounterfactualdensityobtainedfrompre-requirement datapresentsagoodestimateofthefractionofborrowersineachbin, akeyidentifyingassumption in our approach. We also show that the results are more conservative compared to the standard approach of fitting a flexible polynomial to the distribution and excluding an area around the threshold in Appendix C.4. The figure contains several key results. First, the counterfactual distribution fits the empirical distribution well up to an LTV ratio of 47.5 percent and again from an LTV ratio of 52 percent. The difference between the two distributions comes in the area where we expect that the amortization requirement has an impact, namely around the threshold. Second,thereisaconsiderableamountofbunchingatthethreshold. Thebinatthethreshold contains approximately 9 percent of borrowers, compared to around 3 percent in the same bin in the counterfactual density. We find 7.47 percent (B(cid:98) = 7.47, standard error 0.31) more borrowerswithLTVratiosbetween48.5and50percentinthepost-requirementyearscompared 17

to the pre-requirement years. Interestingly, there is considerable bunching even at relatively low LTV ratios. These borrowers have access to considerable amounts of home equity, making it difficult to argue that they face collateral constraints related to their LTV ratio. However, they can still face credit constraints related to payments due to the discretionary income limit applied in Sweden. We will evaluate this shortly. In response to the requirement, the marginal (cid:92) buncher reduces its LTV ratio by 2.57 percentage points (∆LTV = 2.57, standard error 0.16). Relative to the threshold, this yields an approximately 5 percent decrease in LTV ratios. We use this elasticity to calculate an amortization elasticity using equation (4). With the estimated ∆LTV of 2.57, the marginal reduction in borrowing in the numerator equals 2.57/50 = 0.0514. The marginal amortization rate in the denominator equals 0.204, and the elasticity equals 0.0514/0.204 = 0.25. A one percentage point increase in the amortization rate decreases LTV ratios by 0.25 percent. Third, missing mass is small. We find 0.83 percent (M(cid:99) = 0.83, standard error 0.16) fewer households borrowing slightly more than 50 percent of the value of their home in the postrequirement years compared to the pre-requirement years. This finding will be important to identify between alternative explanations of why households bunch (see Section 5.5.) 4.2 Bunching for constrained and unconstrained borrowers In this section, we examine whether binding payment constraints can explain our results, ultimately concluding that bunching occurs for both constrained and unconstrained borrowers. Recall that banks in Sweden evaluate a borrower’s ability to repay based on a discretionary income limit, where the borrower has to have sufficient income to meet expenses. At the time of borrowing, the banks intend to ensure that after-tax household income is sufficient to cover subsistence consumption and borrowing payments, which include interest and amortization payments. Borrowers facing binding constraints may be unable to borrow more because of the discontinuous jump in mortgage payments above the LTV threshold (B¨ackman & Khorunzhina, 2022). Note that the credit checkis only in effect at the time of borrowing and that there are no newcreditchecksiftheborrowerwishestoreduceamortizationpaymentsatalaterstage. How prevalent are binding payment-to-income (PTI) constraints for borrowers at the lower threshold? To answer this question, we calculate the counterfactual discretionary income as the discretionary income given your chosen LTV minus the extra payments if you would have 18

borrowed one percentage point more in LTV compared to the closest-by threshold. We find a small fraction of constrained borrowers at the threshold: 13.6 percent would not comply with the payment-to-income constraint set by Swedish banks if they were to amortize more. The remaining 86.4 percent of borrowers who bunch are not constrained by the PTI constraint. On average, therefore, payment constraints are not driving our results. WethengrouphouseholdsbasedoncounterfactualdiscretionaryincomeintoaNear-constraint, anIntermediate, andaFar-from-constraintsample,withacounterfactualmonthlydiscretionary income of less than 5,000 SEK, 5,000-15,000 SEK, and greater than 15,000 SEK, respectively.12 The Near-constraint group is close to their debt capacity, as they have nearly maxed out their PTI. Note that this group includes borrowers with positive discretionary income who are close to but not at the constraint. The Far-from-constraint group is far from their debt capacity and could borrow a substantial amount more. For example, a discretionary income of 15,000 SEK impliesthehouseholdcouldincreaseitsdebtuntiltheadditionalmonthlyexpensesequal15,000 SEK.Ata(stressed)interestrateof7percentandamortizationrateof2percent, theadditional loan size equals 12×15,000/(0.07+0.02) = 2 million kronor, which is more than the average debt level in our sample. For the Far-from-constraint group, increasing leverage and starting to amortize entails a reduction in discretionary income of 8 percent, on average. Naturally, this decrease is much larger for more constrained households: The average reduction for the Near-constraint group is 62 percent, and for the Intermediate group, the average reduction is 16 percent. Areconstrainedborrowersdrivingthebunchingresultabove? Table1showsthattheanswer isno. Thetableprovidesbunchingestimatesforthethreeseparategroupsbasedondiscretionary income. Figure A3 provides the corresponding figures. The results show that ∆LTV and the elasticity are generally comparable across constrained and unconstrained borrowers. We conclude that payment-to-income constraints cannot explain our results. Animportantquestioniswhethertheunconstrainedgroupisdifferentinothercharacteristics that imply they face other financial constraints. Table B1 provides summary statistics for borrowers in the three groups, showing that the constrained, intermediate, and unconstrained groups appear similar on most observable dimensions. The Unconstrained group has higher income, lower debt-to-income, and lower debt-service-to-income, likely indicating that they are 12Recallthatdiscretionaryincomeisincomeaftertaxes,housingexpensessuchasmaintenance,carpayments, basic consumption needs, and a stressed interest rate of 7 percent. 19

Table 1. Bunching estimates by distance from payment constraints PTI Constraint Near constraint Intermediate Far from constraint Bunching (Bˆ) 5.01 10.17 9.41 (0.49) (0.63) (0.70) Missing mass (Mˆ) -0.49 -0.90 -1.34 (0.27) (0.32) (0.32) ∆ LTV 1.98 3.45 2.92 (0.27) (0.34) (0.30) Elasticity 0.15 0.45 0.32 (0.04) (0.09) (0.06) Number of households 13,350 10,471 10,182 Notes: Thetablecomparesthemainbunchingestimatesacrossgroupsbasedonpayment-to-incomeconstraints. We calculatethecounterfactualdiscretionaryincomeasthediscretionaryincomegivenyourchosenLTVminustheextra paymentsifyouwouldhaveborrowedonepercentagepointmoreinLTV.Thenear-constraint,Intermediate,andFarfrom-constraint samples have a counterfactual discretionary income of less than 5,000 SEK, 5,000-15,000 SEK, and greaterthan15,000SEK,respectively. Bunching isthepercentofhouseholdsbunching,calculatedusingequation(1). ∆LTVthepercentagepointchangeinLTVratioforthemarginalbuncher,calculatedusingequation(3). Elasticity is the amortization elasticity of mortgage demand, calculated using equation 4. Bootstrapped standard errors in parenthesesarecalculatedbydrawingrandomsampleswithreplacementfromthefullsampleofborrowers. Wethen re-calculatetheLTVdistributionandre-estimateallparametersateachiteration. less financially constrained. Interestingly, these characteristics correlate with higher financial literacy (Almenberg & S¨ave-S¨oderbergh, 2011). 4.3 Endogenous housing demand response The leverage ratio is a function of mortgage debt and property value. Homebuyers can adjust to the requirement by taking out a smaller loan (L) or adjusting the type of home they purchase (V). To isolate borrowing from value effects, we focus on borrowers who refinance to a new mortgage. For these borrowers, the bank sets the value exogenously based on the bank’s assessment of the collateral value. Because of institutional design and the incentives faced by banks (see Section 2), we argue that banks do not have an opportunity to manipulate property valuation. The reduction in LTV then has to come from a change in the loan size, L, derived from borrower preferences. For homebuyers, banks almost exclusively use the purchase price to form the collateral assessment. Onlyinrarecasesdobanksdeviatefromusingthepurchasepriceforhomebuyers.13 In the case of refinancing, the bank uses either an external or internal valuation, based in most cases on statistical models of the property value. The external valuation includes using taxassessedvaluesforhousesdonebythetaxauthorityandassessmentsbyindependentappraisers. 13Apartmentsinthemaincities,themostcommontypeofdwelling,arealwaysassessedusingpurchaseprices. For homes in rural areas, mortgage banks might use external appraisers when transaction prices are high. 20

Table 2. Bunching estimates by type of valuation Valuation Internal External Purchase price Bunching (Bˆ) 7.10 7.38 9.30 (0.34) (0.88) (1.46) Missing mass (Mˆ) -0.81 -0.81 -1.25 (0.19) (0.48) (0.76) ∆ LTV 2.44 2.89 2.18 (0.17) (0.47) (0.56) Elasticity 0.23 0.32 0.18 (0.03) (0.10) (0.09) Number of households 28,588 4,948 2,211 Notes: Thetablecomparesthebunchingestimatesacrossvaluationmodesforcollateralassessments. Forrefinancers, banks use either an internal (statistical) valuation model or an external method, either a tax-assessed value or an independentappraisal. Forhomebuyers,thepurchasepriceisused. Bunching isthepercentofhouseholdsbunching, calculatedusingequation(1). Missingmassisthepercentofhouseholdsmissingattherightofthethreshold,calculated using equation (2). ∆ LTV is the percentage point change in LTV ratio for the marginal buncher, calculated using equation(3). Elasticity istheamortizationelasticityofmortgagedemand,calculatedusingequation4. Bootstrapped standard errors in parentheses are calculated by drawing random samples with replacement from the full sample of borrowers. Wethenre-calculatetheLTVdistributionandre-estimateallparametersateachiteration. WediscussthevalidityofthecollateralassessmentsfurtherinSection4.4. Wefindlittleevidence of discontinuities in house values, either in levels or relative to income, around the thresholds in Figure A5. We therefore estimate bunching by type of valuation. Table C2 shows that the estimated bunching is similar across valuation methods. The estimated ∆LTV is 2.44, 2.89, and2.18forinternalvaluation, externalvaluation, andpurchaseprice, respectively. Whilethere are some differences in the bunching estimate across the valuation methods and the elasticity, the results are generally aligned of a similar magnitude as the baseline results. The share of refinancers in the data is large, and we find identical bunching estimates for this group even at theupperthresholdinAppendix. Thisimpliesthatvalueeffectsarenotdrivingourmainresult, and the decline in loan-to-value ratios stems from lower loan demand, not house prices. 4.4 Validating the results In this section, we discuss supply-side factors, other than the payment-to-income constraint, that would cause borrowers to bunch. For example, banks may have an incentive to recommend their clients to place themselves below the threshold or may have an incentive to manipulate the collateral assessments to obtain lower amortization rates on behalf of their customers (Mayordomo et al., 2020). Below, we discuss these supply-side factors in the context of the approval process for mortgages, collateral assessments, risk weights, and capital requirements. We confirm that our empirical results are valid, primarily because of institutional features in 21

Interest rate (%) 1.8 1.7 Pre-requirement 1.6 1.5 Post-requirement 1.4 1.3 1.2 40 45 50 55 60 LTV (%) Figure 5. Interest rates around the lower LTV threshold Notes: The figure plots the average mortgage rate by LTV bin. The blue lines use data from the pre-requirement years (2012-2015), and the orange lines use data from the post-requirement years (2016-2018). The solid lines represent the average mortgage rate by bin, and the dashed lines are the average mortgage rates above (LTV between 40 and 50) or below(LTVbetween50and60)thethreshold. Thethresholdismarkedwithadashedblackline. Sweden. Mortgage rates around the thresholds. Figure 5 shows that the mortgage interest rate does not vary around the threshold. While banks may charge different interest rates for borrowers around the threshold in response to higher credit risk for borrowers who do not amortize (Garmaise, 2013; Elul et al., 2010), we do not find any evidence of this in our setting. Panel a) of Figure 5 plots the interest rate by LTV ratios around the lower threshold. As interest rates vary over time, reflecting Swedish monetary policy, we normalize them to have the same average as in 2017. Importantly, there are no systematic differences in interest rates: average rates are nearly identical below or above the thresholds. Similar results hold for the upper threshold, available in Panel b) of Figure 5. There is little evidence that mortgage banks charged higher mortgage rates to households placing themselves at the threshold, which Best et al. (2020) show is a key factor explaining LTV choices in the UK. As we discuss below, lower amortization payments in a full-recourse setting like Sweden do not imply higher credit risk and therefore limit the incentive for banks to charge higher interest rates for borrowers that do not amortize.14 14Figure 5 also implicitly shows that the fixation period was similar across the threshold, as borrowers are 22

Even if interest rates are constant, the bank may get higher interest income when borrowers enter an interest-only loan compared to a loan just above the 50 percent LTV threshold, which keeps amortizing at a 1 percent rate. This is because, over the lifetime of the loan (typically 6-7 years), the average debt balance is larger for the interest-only loan.15 The extra interest income from this nudge is likely small and depends on how long the loan stays on the bank’s balance sheet and the interest margin. In any case, such a strategy is second-best for the bank: simply informing the borrower when they cross the LTV threshold yields higher revenues. Riskweightsandcapitalrequirements. Apotentialconcernisthatcapitalrequirements mayincentivizebankstonudgeborrowerstowardsalowerLTVmortgageiftherearethresholds in the capital requirements at set LTV ratios. Even though revenues increase with borrower LTV ratios, expected profits need not when expected losses (due to credit risk) or funding costs increase for banks. Regarding credit risk, it is clear that a loan with a higher LTV ratio should be riskier than a corresponding loan with a lower LTV ratio. However, we expect the marginal increase in credit risk to be negligible when moving from a loan with an LTV ratio of 50 percent to a loan with an LTV ratio of 51 percent, given the low LTV levels and fullrecourse mortgages. Even in default, the properties’ market value is more than sufficient to compensate the lender, and borrowers are liable for any residual debt. Correspondence with theSwedishBankersAssociationandtheindividualbanksdidnotrevealanyevidencetosuggest that risk weight increases discontinuously at the thresholds. Even if level differences exist, our difference-in-bunching strategy will account for any discontinuity that is fixed over time. Most Swedish banks use the IRB approach to credit risk, using (unobserved) internal models for PDs, LGDs and ultimately risk weights. Importantly, Swedish regulation mandates a minimum risk weight of 25 percent on all loans secured by residential real estate since 2014. Even if the (unobserved) internal models of mortgage banks assumed that the risk weight exhibited a discrete jump at exactly the LTV threshold, it is very unlikely that the risk weight would exceed the floor. Mortgage approval. Mortgage approval in Sweden depends highly on i) discretionary income(whatwecall“PTI”),ii)adownpaymentrequirementof15percent,andiii)creditscores basedon,forexample,arrearsorpaymentremarksregisteredatacreditbureau,UC(thereisno charged a premium for longer fixation periods. A shorter fixation period would lead to lower interest rates, but this is not apparent in the figure. We verified that fixation periods are indeed stable around the thresholds. 15AsimilarargumentholdsfortheupperLTVthreshold,assumingloansabovethisthresholdkeepamortizing at a rate of 2 percent even after crossing the 70 percent threshold. 23

systemofcontinuouscreditscoringinSweden). InSweden,borrowersapplyforapledgefromthe bankbeforemakingthepurchasedecision. Thispledgestatesthemaximumamountthebankis willing to lend, which depends on the household’s income and composition as well as the value of the collateral. The household purchases a home based on this maximum loan promise and available net worth. The household’s borrowing decision comes after the assessment, provided the requested amount does not exceed the promised amount. In other words, the bank assesses the value of the collateral and approves the loan before the borrower makes their purchase decisions. In the case of a home equity loan, valuations are done by appraisers or statistical models employed by the bank. If the household purchases a new home, appraisal values come fromtransactionprices, whichthebankcannotmanipulate. Theamortizationrequirementdoes not seem likely to impact the mortgage approval process, except when the PTI constraint is violated (which we have investigated above). Collateral assessments. A potential concern is that banks are manipulating the value of the collateral to lower the LTV ratio. As described in the previous paragraph, however, collateral assessments are done before the borrowing decision and are done by statistical models without much discretion on behalf of the loan officer. Therefore, it is very unlikely that banks are systematically manipulating the values just around the threshold to create the kind of bunching we observe. Figure A5 plots the distribution of house value by LTV ratio. There is little evidence in the figure that the house values from the assessments are manipulated around either threshold. Moreover, since Swedish banks are reliant on covered bonds and other wholesale funding to a large extent, manipulation could have large repercussions for the banks’ reputation and funding costs. Nearly 50 percent of total funding comes from wholesale funding, half of which is covered bonds (Sandstr¨om et al., 2013). 5 Understanding the determinants of bunching We develop a theoretical framework that allows us to clarify the different mechanisms that may cause households to borrow less to avoid amortization payments. We begin with a traditional life-cycle model of consumption, housing, and mortgage decisions in the spirit of Campbell & Cocco (2003).While such a model can easily explain why poor households want to avoid amortization payments, we demonstrate that this model cannot replicate the observed behavior of relatively wealthy households who reduce their initial principal balance to get just below the 24

threshold and lower their monthly principal payments. How should we understand wealthy households’ desire to make larger downpayments to avoid amortization? Kleven (2016) explains that there are four mechanisms that can generate bunching: kinksornotchesinthebudgetconstraintorkinksornotchesinhouseholdpreferences. As mentioned previously, we found no evidence of kinks or notches in the budget constraint, with the one exception of the PTI constraint that accounted for only 14 percent of bunching households (Section 4.4). As a result, we rule out the budget constraint as the primary driver of observed behavior and instead turn our attention toward potential mechanisms operating through household preferences. Weconsidertwobroadclassesofpreferencesthatmaygeneratebunching: aone-offdisutility cost to amortizing mortgages and an ongoing flow disutility to amortization payments. As there are various motivations for each class of preferences, we adopt a reduced-form approach to behavioral modeling in the spirit of Mullainathan et al. (2012). Briefly, the one-off disutility captures that Swedish borrowers must contact the bank to turn off amortization and that this refinancing may be costly to the borrower. The ongoing flow disutility captures the idea that households consider amortization payments a cost akin to interest payments. We later discuss additional motivations for each psychic cost. We demonstrate that the one-off disutility cost generates a notch in household preferences whiletheongoingdisutilitycostgeneratesakink. Whilebothmechanismsgeneratebunchingat the policy threshold, they do so in different ways, which forms the basis for identification. More specifically, the notch in preferences generates bunching through a dominated region directly above the policy threshold, while the kink generates bunching without a missing mass. Based on this distinction, we disentangle the relative importance of the two potential mechanisms, assess the sensitivity of our results to possible threats to identification, such as optimization frictions, and then evaluate the implications of our findings for the aggregate economy. 5.1 Theoretical framework We develop a life-cycle model of consumption, housing, and mortgage decisions in the spirit of Campbell & Cocco (2003) and Cocco (2005). In the model, credit-constrained households face idiosyncraticanduninsurableincomeriskoverthelifecycle. Householdsareheterogeneouswith respect to initial assets and income, as well as realized income shocks. Households get utility 25

from both consumption and housing, can save in either liquid deposits or illiquid housing, and can borrow using long-term mortgages. As shown by previous authors, such a model performs well at matching the hump-shaped profile of nondurable spending, the gradual accumulation of housing wealth over the life-cycle, and the fact that the vast majority of wealth is held in housing rather than liquid assets (see, e.g. Attanasio et al., 2011, 2023). We build upon the above framework in two main dimensions. First, we extend the model to include a realistic mortgage repayment schedule with two different policy regimes. In the initialregime, householdsareonlyrequiredtopayinterestontheirmortgagebalances, although they can choose to pay more than that if they desire. In the second regime, households must amortize if their LTV ratio exceeds a given threshold but can revert to interest-only payments when their LTV ratio falls below that threshold. These two policy regimes broadly represent the institutional framework present in Sweden before and after the 2016 reform. Second, we extend household preferences to include either a one-off disutility to amortizing mortgages or an ongoing flow disutility from amortization payments. That said, we begin with the baseline model without either disutility costs. Baseline Model – Households choose consumption (c ), liquid assets (a ), housing (h ), t t t and mortgages (m ) each period to maximize their expected discounted lifetime utility: t T (cid:88) max E βtu(c ,h ,δ ) (5) 0 t t t {ct,at,ht,mt} t=0 subject to the household budget constraint, the law-of-motion for mortgages, and an exogenous income process. We require that liquid assets must always be positive (a ≥ 0) and mortgage borrowing (m > 0) is only allowed when a household owns a home. Households derive utility from both consumption and housing and a behavioral wedge (δ ), which we set to zero in the t initial analysis but later extend to capture potential psychic costs to amortization. Demographics – Households live for T years, receiving exogenous labor income during their working life, then social security income after retirement at age W. Household income gradually rises during working life. Heterogeneity – In the model, households are ex-ante heterogeneous with respect to initial assets, initial income, and realized income shocks. This leads to ex-post heterogeneity in liquid assets, housing, and mortgage balances. This heterogeneity leads to a wide distribution 26

of loan-to-value ratios, which is our main object of interest. Assets – Households have access to two different saving vehicles: a fully liquid asset a and t a partially illiquid housing asset h . The liquid asset yields a certain return r. We impose the t assumptionthata ≥ atocapturethepresenceofcreditconstraints. Forsimplicity, weabstract t away from return risk, although this assumption is not critical to our results. The presence of both a liquid asset and relatively illiquid housing allows us to capture hand-to-mouth behavior in the spirit of Kaplan & Violante (2014). Housing – Housing exists on a discrete grid with k different sizes: hk ∈ {h1,h2,...,hk}. The price of each house p (hk) = hk ∗p¯ depends on both house size hk and the price index p¯. t t t House prices grow at a constant rate over time, p¯ = (1+rH)p¯ . t t−1 Allhouseholdsarebornasrentersbutcanpurchasehousing. Buyingorsellingahomeincurs a transaction cost f that is a fraction of the house price p . Households are allowed to own 1 t or rent any unit. If households choose to rent, they must pay rent in proportion to the house price, with rent = ηp . t t Mortgages – Homeownerscanborrowusinglong-termmortgagesm withinterestraterM. t We allow for both borrowing to finance housing purchases and cash-out refinancing. Mortgage balances are constrained by a maximum loan-to-value (LTV) constraint: m ≤ (1−ψ)p (h ) (6) t t t whereψ determinesthemandatoryminimumdownpayment. Forhouseholdsthatdonotchoose to extract equity, their next-period mortgage balance is constrained by: m ≤ m (1+rM)−ρ (m ,p ) (7) t+1 t t t t where ρ (m ,p ) represents the mandatory minimum mortgage payment. t t t Households that choose to extract equity are required to pay a proportional (f ) and fixed 2 (f ) cash-out refinancing cost. Households extract equity when they select m > m (1 + 3 t+1 t rM)−ρ (m ,p ). The LTV constraint binds at both the time of purchase and in any periods of t t t cash-out refinancing. Mortgage Repayment – Themandatoryminimummortgagepayment(ρ )representsour t 27

main policy instrument. We model two different policy regimes. First is an interest-only policy where the borrower only needs to make interest payments, similar to Sweden pre-2016: ρ (m ,p ) = m ∗rM (8) t t t t Second is a mandatory amortization policy, where the minimum payment depends on the LTV ratio of the borrower, similar to the amortization requirement in Sweden after 2016:    0 if mt/pt ≤ 0.5 ρ (m ,p ) = m ∗rM +m ∗ (9) t t t t t   0.01 if mt/pt > 0.5 Note that the mortgage repayment schedule only defines the minimum payment each period, as the household is always allowed to repay more than the minimum requirement. In our main policy experiments, we switch between the interest-only policy and the amortization requirement.16 Income – Householdsfaceexogenousandidiosyncraticincomerisk. Wemodeltheearnings process using a household-specific fixed effect α , a deterministic life-cycle profile that follows i a third-order polynomial in age, and an idiosyncratic component z that follows an AR(1) i,t Markov process: lny = α +g +z , where z = ρz +ε , ε ∼ N(0,σ2) i,t i t i,t i,t i,t−1 i,t i,t ε After retirement, the household earns a fraction ω of its last working period’s income. Functional form – We assume that households obtain utility from both consumption and housing based on the following utility function: (cid:0) c1−θϕ(h )θ(cid:1)1−γ u(c ,h ,δ ) = t t −δ (10) t t t t 1−γ where γ is the coefficient of relative risk aversion, and θ is the preference for housing relative to consumption. The above utility function closely follows Cocco (2005) with two modifications. First, we allow for the possibility of owning or renting, where ϕ(h ) captures the relative utility t 16Forsimplicity,weonlymodelthe50percentthresholdoftheamortizationrequirement,althoughourresults would generalize to multiple thresholds. 28

of either tenure decision:    h t if owner ϕ(h ) = (11) t   ζh t if renter where ζ is the disutility of renting. Second, we allow for a psychic cost to amortization, denoted by δ . In the baseline model, we set δ = 0. We find that this model is unable to generate t t bunching at the amortization threshold. This motivates us to extend the model by allowing δ t to depend on amortization rates in Section 5.4. 5.2 Parameter values We set the model parameters based on the existing literature and institutional details from the Swedish mortgage market. We calibrate asset returns and interest rates based on Swedish data and set the loan-to-value and amortization requirements based on Swedish law. We set the main household preference parameters following Cocco (2005) and set the income process parameters following Kovacs & Moran (2021). The details are contained in Appendix D. We set r = 0.018 based on the real risk-adjusted return of the Swedish 3-month T-Bill. We set rH = 0.029 based on the real risk-adjusted return to housing, which we calculate using the house price index from Statistics Sweden augmented with housing service flows, maintenance costs, and home insurance. We explicitly account for imputed rents in housing returns using the balance-sheet approach (Piazzesi et al., 2007; Kaplan & Violante, 2014). We set the real mortgage rate to rM = 0.043 based on the average real rate for a floating-rate mortgage in Sweden between 1985 and 2015. Following Swedish mortgage regulation, we set the maximum loan-to-value ratio of 1−psi to 85 percent. 5.3 Thebaselinemodeldoesnotgeneratebunchingbywealthyhouseholds How does mandatory principal repayment affect household borrowing in the traditional model? We implement a policy where households are required to make amortization payments if the LTV ratio exceeds 50 percent, similar to Sweden. While such a policy could easily generate bunching for low-wealth households at the credit constraint, we find that the traditional model does not generate bunching for the relatively wealthy households purchasing a home with a 50 percent down payment. Figure 6 shows the results from our baseline model. The left panel shows the distribution 29

Percent Expected value 20 -5 15 -5.5 10 Baseline with amortization Interest-only -6 5 0 -6.5 40 45 50 55 60 40 45 50 55 60 LTV (%) LTV (%) (a) LTV distribution (b) Value function Figure 6. LTV distribution and value function in baseline model Notes: The figure plots results from the model in Section 5. Panel a) plots the LTV distribution at origination in the baselinemodelwithamortizationrequirement,wheretheminimumamortizationrateincreasesfrom0percentto1percent per year when the LTV ratio exceeds 50 percent. Panel b) plots the expected value function from the model, separately forthebaselinemodelwith(bluesolidline)andwithout(orangedashedline)theamortizationrequirement. of LTV ratios around the policy threshold at the time of mortgage origination in a world with mandatoryamortization. ThemodelgeneratessubstantialvariationinLTVratiosduetoexogenous variation in household resources (coming from age, initial resources, and realized income shocks). However, we find no bunching at the 50 percent LTV threshold despite mandatory amortization for all loans above the threshold. The value function in the right panel provides intuition for the lack of bunching around the policy threshold. The figure plots the expected discounted utility (the value function) as a function of the LTV ratio, with all other state variables held constant. The solid blue line shows the expected value in the baseline model with the Swedish mandatory amortization policy. The dashed orange line shows the expected value in the alternative model with interestonly mortgages, similar to Sweden prior to 2016. Mandatory amortization reduces expected discountedutilityforallhouseholds,ashouseholdswouldprefertoliveintheworldwithinterestonly mortgages due to the benefits of improved consumption smoothing (Cocco, 2013). That said, mandatory amortization reduces expected discounted utility in a smooth manner, without generating a notch or kink around the policy threshold. As a result, mandatory amortization does not generate bunching at the threshold. Intuitively, while the amortization requirement forces households to save, this does not induce households to choose larger downpayments to avoid amortizing. This is especially easy to see if households in the interest-only regime were already saving more than what is mandated in the amortization requirement regime. In addition, households can undo the effects of amortization, either by borrowing more at 30

origination (Svensson, 2016) and making payments from the borrowed amount or through cashout refinancing (Hull, 2017). The lack of bunching holds despite the existence of realistic credit constraints in the model. While such credit constraints are binding for households purchasing a home with the maximum 85 percent LTV ratio, households near the 50 percent LTV policy threshold are relatively far from the credit constraint and have substantial additional borrowing capacity. The lack of bunching in the baseline model is invariant to key model parameters. More specifically, we do not find bunching in the baseline model even when a) households are highly impatient, b) income grows more steeply over the life-cycle, thus exacerbating the role of credit constraints, c) households are not allowed to perform home equity withdrawal or refinancing, d) householdshaveaccesstoahighreturnliquidasset,ore)householdsonlyhaveaccesstoaliquid asset that gives negative real returns. While the above model parameters affect the curvature of the expected value function and may increase households’ desire to be in a world with interestonly mortgages, none of the above parameters introduce a kink or notch into the expected value function and thus are unable to generate bunching at the 50 percent threshold.17 5.4 Extending household preferences to generate bunching Weaugmenthouseholdpreferencestocapturethepossibilitythathouseholdsmaydislikemandatory amortization due to behavioral biases or other psychological reasons. We consider two broad classes of psychic costs: a one-off disutility to amortization and an ongoing flow disutility to amortization payments. We adopt a reduced-form approach to behavioral modeling, using psychic costs that may capture various behavioral biases in the spirit of Mullainathan et al. (2012). We now motivate and describe these costs in more detail. One-off disutility cost to amortization – The first psychic cost we consider is a one-off disutility cost that applies to all mortgage contracts with amortization. While there are various ways we could model this cost, we choose to do so by assuming that households suffer a psychic cost to turning off amortization payments once they cross below the mandatory amortization 17For instance, when we include a high return liquid asset, we find that most wealthy households increase borrowing to the maximum LTV ratio of 85 percent, allowing them to benefit from higher returns, even if they are required to gradually payback the principal balance when their LTV is above 50 percent. Households would be leaving money on the table if they only borrowed to 50 percent. 31

Percent Expected value -5 40 30 -5.5 Baseline 20 One-off disutility Baseline -6 10 One-off disutility 0 -6.5 40 45 50 55 60 40 45 50 55 60 LTV (%) LTV (%) (a) LTV distribution (b) Value function Figure 7. LTV distribution and value function with one-off disutility to amortization payments Notes: The figure plots results from the model in Section 5. Panel a) plots the LTV distribution at origination in the modelwithaone-offdisutilitytoamortizationpayments(orange)relativetothebaselinemodel(blue). Panelb)plotsthe expectedvaluefunctionsfrombothspecificationsofthemodel. threshold.18 More specifically, we model the one-off cost as: δ = −∆ ×1 (12) t n amortt=0, amortt−1>0 whereforsimplicitywedefineamort = ρ (m ,p )−m ∗rM astherequiredprincipalpayment. In t t t t t our model, households suffer a one-off disutility (∆ ) when they start with an LTV ratio above n 50 percent, gradually pay down their mortgage, and eventually cross below the policy threshold and turn off amortization. This disutility cost captures the fact that Swedish borrowers must contact the bank to turn off amortization. Refinancing costs can represent both monetary and psychic costs to the individual to refinance. In our setting, we model these as psychic costs through the utility function since 97 percent of mortgages in our sample are issued by Swedish banks that allow eligible households to turn off amortization payments without a fee.19 We show the result of including a one-off disutility cost in Figure 7. The histogram shows that a one-off disutility cost affects households close to the threshold and leads to a dominated region directly above the threshold. As a result, the bunching at the threshold is generated by missing mass directly above the threshold. The bunching and missing mass result from a notch in preferences at the threshold, illustrated in panel b), where expected utility shifts down exactly at the 50 percent LTV threshold. The notch causes households who otherwise would 18That said, this psychic cost is isomorphic to a one-off cost at the time of mortgage origination. 19MonetaryandpsychiccoststorefinancinghavebeenstudiedinAgarwaletal.(2016),Keysetal.(2016)and Andersen et al. (2020). In the Swedish setting, just one bank charges a small fee (of slightly less than $200) to turn off amortization payments. This bank represented 3 percent of total mortgages in 2017. 32

have chosen an LTV ratio just above the 50 percent threshold to choose lower LTV ratios to avoid the one-off utility cost to amortization. Since households far away from the threshold can discount the cost, it will not affect their borrowing decisions. Flow disutility to amortization payments – The second psychic cost we consider is flow disutility to amortization payments. We model the psychic cost as follows: δ = −∆ ×1 (13) t k amortt>0 Householdssufferadisutilitycost(∆ )ineveryperiodwheretheyarerequiredtomakepositive k principal payments. This disutility flow may occur if households mistakenly view principal repayment as a cost rather than a form of savings or, alternatively, if households try to target a specific monthly mortgage payment when choosing how much to borrow.20 Therearevariouswaystomotivatetheabovepsychiccostbasedonproposalsfromtherecent literature. For instance, Argyle et al. (2020) argue that consumers perform “monthly payment targeting” when choosing between auto loans with different terms, paying more attention to the initial monthly payment than the lifetime cost of the loan. Camanho & Fernandes (2018) propose that households suffer from the “mortgage illusion,” where housing decisions are driven by heuristics, such as how the monthly mortgage payment compares with the rental payment, whichmayoccurifhouseholdsdonotinternalizethefactthatamortizationpaymentsrepresenta formofsaving. Indeed,onerecentsurveyinSwedenfoundthat38percentofSwedishhouseholds view amortization payments as a cost rather than a form of savings (SBAB, 2018). All of the above explanations are consistent with the concept of “NPV neglect”, in which households do not fully consider the net present value of future interest costs when choosing between contracts with alternative repayment schedules (Shu, 2013). While we are not the first to propose such a theory, it has historically been challenging to identify such behavior in observed financial decision-making, and we know of only one other paper that evaluates the importanceofsuchamechanism, althoughinaverydifferentinstitutionalsetting(Argyleet al., 2020). As those authors discussed, the key challenge for identification is distinguishing between 20We choose to model flow disutility as a behavioral wedge, as it allows us to remain agnostic about the specific behavioral biases driving such preferences. That said, there are various ways that we could micro-found such behavior. For instance, households may suffer ongoing disutility from mandatory mortgage payments each period and thus try to lower their monthly payments (similar to monthly payment targeting). Alternatively, households may not understand that amortization payments today affect the expected value of their assets and debt tomorrow (similar to the mortgage illusion.) It would be straightforward to add either to our model. 33

Percent Expected value 30 -5 -5.5 Baseline 20 Flow disutility Baseline -6 10 -6.5 Flow disutility 0 -7 40 45 50 55 60 40 45 50 55 60 LTV (%) LTV (%) (a) LTV distribution (b) Value function Figure 8. LTV distribution and value function with flow disutility to amortization Notes: The figure plots results from the model in Section 5. Panel a) plots the LTV distribution at origination in the modelwithaflowdisutilitytoamortization(green)relativetothebaselinemodel(blue). Panelb)plotstheexpectedvalue functionsfrombothspecificationsofthemodel. credit constraints and NPV neglect, as both mechanisms may incentivize households to choose debt contracts with lower initial payments. Our quasi-experiment provides an ideal setting for identification, given that bunching is primarily driven by wealthy households with substantial additional borrowing capacity, thus allowing us to identify preferences separately from credit constraints. Flowdisutilitytoamortizationpaymentsgeneratesbunchingatthethresholdbutnomissing mass. Figure8providestheresults, wherepanela)showsthathouseholdnowbunchinresponse to higher amortization payments. We see the intuition behind this result in panel b): the value function has a kink at exactly the amortization threshold. The kink implies that all households above the amortization threshold are affected, and consequently all households adjust their borrowing. The spike at the threshold occurs because households close enough to the threshold will, inthe amortizingregime, chooseto avoidbearingthe utilitycost vialargerdownpayments. But missing mass does not occur, as households with somewhat higher LTV levels also put in more cash, though not enough to avoid the flow disutility completely. These households now fill up the distribution to the right of the threshold.21 21An interesting extension would be to allow households to be heterogeneous in their dislike of mortgage payments. Indeed, as Figures 2 and A2 show, some households below the 50 percent threshold do amortize. We leavethistofutureresearch,asourmodelintendstohighlightthemechanismandnotgivequantitativeestimates. 34

5.5 Identification: Flow disutility obtains a better fit of the data How do we evaluate the relative importance of the two different mechanisms described above? Fortunately, the two mechanisms have drastically different implications for what drives bunching. More specifically, the notch in household preferences generates bunching at the threshold based on a dominated region just about the threshold with missing mass. In contrast, the kink generates bunching at the threshold by altering the incentives for all households above the threshold, thus generating bunching without a corresponding missing mass. This difference in implications allows us to determine the relative importance of the two opposing channels. Our empirical results show little evidence for a large missing mass. The summary of our main estimates in Table B2 shows that missing mass is generally less than 15 percent of the bunching estimate. This result holds across specifications and, in particular, for unconstrained borrowers. The lack of missing mass suggests that most of the effect comes from a kink in household preferences generated by flow disutility to amortization payments. 5.6 Evaluating robustness to potential threats to identification Hereweassesstherobustnessofourresultstovariousalternativemechanisms. Wefindthatthe empirical results cannot be explained by policy uncertainty, better investment opportunities, or households viewing the policy as an endorsement. Further, the lack of missing mass is not easily explained by optimization frictions in our setting. Policy uncertainty. Onepotentialconcernisthathouseholdsmaynotfullyunderstandthe policy. For instance, households might not know that they can turn off amortization payments once they pay down their mortgage and get below the 50 percent LTV threshold, or they may feel some uncertainty about whether they will be allowed to do so. In practice, turning off amortization payments once a borrower has passed below the policy threshold is relatively straightforward in Sweden, which we verified by email correspondence with the eight main banks. For example, there is no new credit check or discretionary income calculation when the borrower decides to turn off amortization payments.22 That said, we think this is not driving the majority of our results. Policy uncertainty would 22In their replies, the banks stated that there are no associated costs, that the borrower does not need a new mortgage contract or reassessment of collateral values, and that a simple phone call to the bank advisor is sufficienttoturnoffamortization. Threeoftheeightbanksstatedthatborrowersareneverdeniedtheabilityto turnoffamortization. Theremainingbanksstatedthatdenialisveryrareandonlyrelatedtoinsolvencyissues, such as not paying bills. 35

generate a notch, as it would imply that taking out a mortgage just above the 50 percent threshold is discontinuously worse than taking out a mortgage just below. As mentioned above, this notch would thus generate bunching at the threshold based on missing above the threshold, something which we find is relatively small in the data. Thus, while policy uncertainty could explain some of our results, we believe it could explain no more than 15 percent of the bunching. Better investment opportunities. Another concern is that households may have other investment opportunities that give a better return than they would get on their mortgage principalpayments.23 Whilesuchinvestmentopportunitieswouldcertainlyincreasehouseholds’ dislike of mandatory amortization, we have found through model simulations that it is not sufficient to generate bunching at the threshold. More specifically, we simulated the model with an alternative calibration with a return on liquid assets r = 0.06, far greater than the interest rate on mortgage borrowing rM. We found that the amortization policy increased the welfare costs of mandatory amortization, but did not generate either a kink or notch at the 50 percent LTV threshold, and similarly did not induce bunching at the threshold. The intuition for this result is that the presence of a high-return investment opportunity compels households to increase their borrowing. In short, they would rather borrow up to the maximum LTV limit and gradually pay down their principal balance (and occasionally cash-out refinance back to the maximum LTV), rather than reduce leverage to avoid the amortization requirement. Endorsement of a recommended down payment or amortizing. By choosing a specific threshold at which policies change, governments may inadvertently create focal points that individuals strive to achieve. In this case, if the 50 percent LTV threshold becomes a goal that agents try to meet when taking out a mortgage, such reference dependent preferences could also generate bunching at the policy threshold. That said, while there are various forms of reference dependence that may generate either notches or kinks, Kleven (2016) states that the notch-based theory is “arguably more natural in settings in which reference points represent goals that agents strive to meet.” As a result, such a theory would imply a substantially larger missing mass, contrary to what we see in the data.24 In addition, if individuals strive to achieve a 50 percent or seek to increase their amortization payments because of the requirement, we 23For instance, households may prefer to invest in the stock market rather than pay down their mortgage. 24In contrast, loss aversion would generate a kink in household preferences (Andersen et al., 2022), although we see little reason why households would feel loss aversion as a result of this policy. 36

wouldexpecttoseearesponsebelowandabove thethresholdineitherborrowingoramortization payments. Figure 4 shows that the number of borrowers with LTV ratios below 47 is essentially unchanged, and Figure 2 shows that the share of interest-only mortgages at lower LTV values is similarly unchanged when comparing pre-and post-requirement years. Optimization frictions. Finally, one remaining concern is that optimization frictions may prevent borrowers from fully reacting to incentives around the policy threshold (Best et al., 2020; Anagol et al., 2022). As a result, we might think that the lack of missing mass is not indicative of a kink, but rather a notch combined with optimization frictions. In our setting, optimization frictions are potentially related to inattention, misperception, or real adjustment costs.25 That said, there are various reasons why we think the issue of optimization frictions should be relatively minor in our setting. First, the consequences of choosing a higher LTV are highly salient for the borrower at the time of mortgage origination. All Swedish banks provide online tools that show the borrower how different LTV ratios affect total mortgage payments (seeFigureA6foranexample). Thecalculatortypicallyallowstheborrowertoenteraproperty value and a down payment and calculate the monthly cost. The amortization payment is highly salientinthesecalculators, anditiseasytoseehowdifferentLTVvaluestranslateintodifferent payments. Further, loan officers at banks generally advise their clients about the consequences of choosing different LTV ratios. We believe that the institutional setup related to mortgage choice in Sweden strongly limits the relevance of inattention or misperception. Second, optimization frictions could also arise due to real adjustment costs, such as the cost of liquidating other assets or adjusting large purchase decisions (like a home renovation) to comply with the requirement. However, for households who own just under 50 percent of the equity in their homes, the amounts required to comply with the requirement do not appear to be prohibitive. Complying with the requirement requires lowering the borrowed amount by 1 percent for borrowers just above the threshold. This percentage represents about 16,000 SEK (approximately1,600USD),or3percentofannualdisposableincome. Further, ifthehousehold really needs immediate liquidity, they could always borrow more and then gradually pay down themortgagebalance(Svensson,2016). Overall, giventhesalienceofthemortgagedecisionand other institutional details, we believe that the lack of missing mass above the policy threshold is not due to optimization frictions. 25See Søgaard (2019) and Anagol et al. (2022) for an overview of different optimization frictions. 37

5.7 The aggregate effects of financial innovation on household debt Our results have important implications for understanding the effects of financial innovation on household borrowing. Financial innovation in the 1990s and early 2000s generated a wide variety of new mortgage products with alternative repayment schedules in the US and other countries. During the same period, household debt increased substantially. Some commentators have suggested that new mortgage products, such as interest-only mortgages, contributed substantially to this increase in mortgage borrowing. Of course, it is impossible to isolate the effect of IO mortgages on overall debt by looking at aggregate time series alone. We use our model to shed new light on the link between financial innovation and aggregate borrowing. Importantly, our model allows us to isolate the effect of financial innovation on household behavior, something which would not be possible without a model. Overall, we find that interest-only mortgages substantially increase household borrowing. We find that “NPV neglect” amplifies the effect of financial innovation on aggregate household debt and lifetime debt servicing expenses. To demonstrate, we use our model to study the transition from traditional mortgages with fully amortizing repayment schedules to alternative mortgage products with interest-only (IO) repayment schedules, similar to the US experience during the late 1990s and early 2000s. We begin with a model economy where households only have access to fully amortizing mortgages with constant-level repayment plans, then suddenly allow households to borrow using IO mortgages. We model fully amortizing mortgages following Attanasio et al. (2023), who assume that households must make equal mortgage payments every year that they own the house until retirement, based on the following formula:26 (1+rM)s ρ (m ,p ) = ∗m (14) t t t (cid:80)W−t(1+rM)j t j=1 We compare the steady state distribution of mortgage balances in a model economy with fully amortizing mortgages to the steady state distribution of mortgage balances with interest-only mortgages, given by equation (8). For simplicity, we assume that only the repayment schedule changes and that no other model parameters are affected. We assume households suffer from ongoing flow disutility to amortization payments, given by equation (13). We later turn off this 26We calculate the repayment schedule based on time to retirement so that we do not need to keep track of the maturity of each mortgage, which allows us to save a state variable in the household decision problem. 38

mechanism to decompose the relative importance of NPV neglect. We find that the introduction of interest-only mortgages increases mortgage debt by 33.4 percent relative to the world with traditional amortizing mortgages, according to our calibrated model,ashouseholdsincreaseborrowingandpaymoreininterestexpenses. Indeed,debtservice payments also increase by 33.4 percent over the course of households’ lives, in line with the increase in mortgage borrowing. Using our model, we decompose the different channels driving the observed increase in borrowing. We find that over two-thirds of the increase in mortgage debt comes from “NPV neglect,” while just under one-third comes from improved flexibility. Whenwesimulatetheintroductionofinterest-onlymortgagesinthemodelwithoutNPVneglect (∆ = 0), mortgage balances increase by only 9.1 percent. Overall, our results indicate that k NPV neglect amplifies the effects of financial innovation on household borrowing.27 6 Conclusion This paper provides evidence that amortization payments directly affect household borrowing decisions. We document that new borrowers reduce their loan-to-value ratios by five percent at origination in response to a one percentage point higher amortization rate. Our results are not driven by supply-side factors, such as interest rates, credit assessments, or fees, and apply to homebuyers and refinancers. We find that the results are driven mainly by wealthy, unconstrained borrowers, indicating that credit constraints are not the primary driver of our results. Based on the empirical evidence, we develop a model to help us better understand why wealthy borrowers bunch to avoid amortization payments. While a traditional model with housingandmortgagescaneasilyaccountforbunchingbylow-wealth, credit-constrainedhouseholds, it cannot easily account for bunching by wealthy, unconstrained households. We amend the traditional model with two novel mechanisms – a one-time disutility to amortization and a flow disutility to amortization payments – two mechanisms that generate either a notch or a kink in the discounted utility of households. We disentangle the two mechanisms by showing that a one-time disutility to amortizing generates missing mass above the threshold, which is 27The degree of amplification is heightened by the fact that we find a kink rather than a notch in preferences. Hadhouseholdbehaviorbeendrivenbyanotch,therewouldhavebeenonlyalocaleffectonborrowingandthus less amplification relative to the traditional model. This is because a notch reduces borrowing for households who otherwise would have located themselves directly above the threshold, while a kink reduces borrowing for all households above the threshold, which is a substantially larger group. 39

in contrast to our empirical results. The evidence is thus more consistent with an ongoing flow disutility to amortization. This suggests that households either target monthly payments or do not fully recognize amortization as a form of savings. Either way, our findings indicate that consumers suffer from “NPV neglect” when making large long-term borrowing decisions, and thus may substantially increase borrowing and lifetime interest expenditure when offered mortgage products with delayed repayment schedules. There are several ways that one could extend our analysis. First, it would be possible to extend our analysis using the empirical moments to estimate the preference parameters of the model. Indeed, we have already calibrated the amount of flow disutility to match the amount of bunching observed at the policy threshold (see Appendix D) and could use other moments to discipline the other preference parameters in the model. Second, while we have focused on how flow disutility to amortization affects household borrowing, it may be worthwhile to study how such preferences affect the types of contracts affected by banks. For instance, if banks understand that households suffer from such behavioral biases, there may be a role for exploitative contracting.28 As a result, consumer protection agencies may want to consider the role of regulation designed to prevent banks from encouraging “NPV neglect” in mortgage markets and other forms of consumer lending. Third, we have demonstrated how households respond to the amortization requirement at origination. Investigating borrowing and saving choices in subsequent periods is interesting and relevant from a financial stability perspective, but our data is not ideally suited to answering such questions, which are therefore left for future work. 28We do not model bank incentives, but it would be possible to extend our model to include the optimization problem faced by banks, who might have an incentive to increase lending by offering longer loan maturities or interest-only repayment schedules if they understand the biases faced by households. 40

References Agarwal, Sumit, Rosen, Richard J, & Yao, Vincent. 2016. Why do borrowers make mortgage refinancing mistakes? Management Science, 62(12), 3494–3509. 32 Almenberg, Johan, & S¨ave-S¨oderbergh, Jenny. 2011. Financial literacy and retirement planning in Sweden. Journal of Pension Economics & Finance, 10(4), 585–598. 20 Amromin, Gene, Huang, Jennifer, Sialm, Clemens, & Zhong, Edward. 2018. Complex mortgages. Review of Finance, 22(6), 1975–2007. 1, 7 Anagol, Santosh, Davids, Allan, Lockwood, Benjamin B, & Ramadorai, Tarun. 2022. Diffuse Bunching with Frictions: Theory and Estimation. Centre for Economic Policy Research. 37 Andersen, Steffen, Campbell, John Y, Nielsen, Kasper Meisner, & Ramadorai, Tarun. 2020. Sources of inaction in household finance: Evidence from the Danish mortgage market. American Economic Review, 110(10), 3184–3230. 32 Andersen, Steffen, Badarinza, Cristian, Liu, Lu, Marx, Julie, & Ramadorai, Tarun. 2022. Reference dependence in the housing market. American Economic Review, 112(10), 3398–3440. 8, 36 Andersson,MichaelK,&Aranki,Ted.2017. Amortisationrequirementreducedhouseholddebt. FI Analysis. 8 Andersson, Michael K, & Aranki, Ted. 2019. Fewer vulnerable households after stricter amortization requirement. FI Analysis. 8 Andersson, Michael K, & Aranki, Ted. 2021. Temporary amortisation exemption led to new mortgagors borrowing more. FI Analysis. 10 Argyle, Bronson S, Nadauld, Taylor D, & Palmer, Christopher J. 2020. Monthly payment targeting and the demand for maturity. The Review of Financial Studies, 33(11), 5416–5462. 1, 2, 5, 6, 33 Attanasio, Orazio, Leicester, Andrew, & Wakefield, Matthew. 2011. Do house prices drive consumption growth? The coincident cycles of house prices and consumption in the UK. Journal of the European Economic Association, 9(3), 399–435. 26 41

Attanasio, Orazio, Kovacs, Agnes, & Moran, Patrick. 2021. Temptation and Incentives to Wealth Accumulation. National Bureau of Economic Research Working Paper No. 28938. 7 Attanasio, Orazio, Kovacs, Agnes, & Moran, Patrick. 2023 (October). Temptation and Commitment: A Model of Hand-to-Mouth Behavior. Working Paper 27944. National Bureau of Economic Research. 26, 38 Attanasio, Orazio P, Bottazzi, Renata, Low, Hamish W, Nesheim, Lars, & Wakefield, Matthew. 2012. Modelling the demand for housing over the life cycle. Review of Economic Dynamics, 15(1), 1–18. 66, 67 B¨ackman, Claes, & Khorunzhina, Natalia. 2022. Interest-Only Mortgages and Consumption Growth: Evidence from a Mortgage Market Reform. 18 Barlevy, Gadi, & Fisher, Jonas DM. 2020. Why Were Interest-Only Mortgages So Popular During the U.S. Housing Boom? 7, 11 Bernstein, Asaf, & Koudijs, Peter. 2023. The Mortgage Piggy Bank: Wealth Building through Amortization. The Quarterly Journal of Economics, forthcoming. 1, 6 Best, Michael Carlos, Cloyne, James S, Ilzetzki, Ethan, & Kleven, Henrik J. 2020. Estimating the elasticity of intertemporal substitution using mortgage notches. The Review of Economic Studies, 87(2), 656–690. 8, 22, 37 Boar, Corina, Gorea, Denis, & Midrigan, Virgiliu. 2022. Liquidity constraints in the US housing market. Tech. rept. 3. 7 Camanho, Nelson, & Fernandes, Daniel. 2018. The mortgage illusion. Available at SSRN 1856325. 5, 6, 33 Campbell, John Y, & Cocco, Joao F. 2003. Household risk management and optimal mortgage choice. The Quarterly Journal of Economics, 118(4), 1449–1494. 3, 24, 25 Campbell, John Y, Clara, Nuno, & Cocco, Joao F. 2020. Structuring mortgages for macroeconomic stability. The Journal of Finance, forthcoming. 7 Cerutti, Eugenio, Claessens, Stijn, & Laeven, Luc. 2017. The use and effectiveness of macroprudential policies: New evidence. Journal of Financial Stability, 28, 203–224. 7 Chetty, Raj, Friedman, John N, Olsen, Tore, & Pistaferri, Luigi. 2011. Adjustment costs, firm 42

responses, and micro vs. macro labor supply elasticities: Evidence from Danish tax records. The Quarterly Journal of Economics, 126(2), 749–804. 63 Choukhmane, Taha. 2021. Default options and retirement saving dynamics. Working Paper. 8 Cocco, Joao F. 2005. Portfolio choice in the presence of housing. The Review of Financial Studies, 18(2), 535–567. 3, 25, 28, 29, 66, 67 Cocco, Joao F. 2013. Evidence on the benefits of alternative mortgage products. The Journal of Finance, 68(4), 1663–1690. 1, 4, 6, 30 Collier,BenjaminL,Ellis,Cameron,&Keys,BenjaminJ.2021. The cost of consumer collateral: Evidence from bunching. Tech. rept. National Bureau of Economic Research. 8 DeFusco, Anthony A, & Paciorek, Andrew. 2017. The interest rate elasticity of mortgage demand: Evidence from bunching at the conforming loan limit. American Economic Journal: Economic Policy, 9(1), 210–40. 14, 57, 65 DeFusco, Anthony A, Johnson, Stephanie, & Mondragon, John. 2020. Regulating household leverage. The Review of Economic Studies, 87(2), 914–958. 7, 15, 58 DellaVigna, Stefano. 2018. Structural behavioral economics. Pages 613–723 of: Handbook of Behavioral Economics: Applications and Foundations 1, vol. 1. Elsevier. 7 Elul,Ronel,Souleles,NicholasS,Chomsisengphet,Souphala,Glennon,Dennis,&Hunt,Robert. 2010. What” triggers” mortgage default? American Economic Review, 100(2), 490–94. 22 Federal Reserve Board. 2008. A Consumer’s Guide to Mortgage Refinancings. https://www. federalreserve.gov/pubs/refinancings/. Accessed: 2022-09-01. 66 Ferrari, Alessandro, & Loseto, Marco. 2023. Liquidity constraints and demand for maturity the case of mortgages. ECB Working Paper No. 2023/2859. 6 Ganong, Peter, & Noel, Pascal. 2020. Liquidity versus wealth in household debt obligations: Evidence from housing policy in the Great Recession. American Economic Review, 110(10), 3100–3138. 7 Garmaise, Mark J. 2013. The attractions and perils of flexible mortgage lending. Review of Financial Studies, 26(10), 2548–2582. 7, 22 43

Greenwald, Daniel L. 2017. The Mortgage Credit Channel of Macroeconomic Transmission. Working Paper, MIT Sloan. 7 Grodecka, Anna. 2020. On the Effectiveness of Loan-to-Value Regulation in a Multiconstraint Framework. Journal of Money, Credit and Banking, 52(5), 1231–1270. 12 Guren, Adam M., Krishnamurthy, Arvind, & McQuade, Timothy J. 2021. Mortgage Design in an Equilibrium Model of the Housing Market. The Journal of Finance, 76(1), 113–168. 7 Guvenen,Fatih.2009. Anempiricalinvestigationoflaborincomeprocesses. ReviewofEconomic dynamics, 12(1), 58–79. 66 Hull, Isaiah. 2017. Amortization requirements and household indebtedness: An application to Swedish-style mortgages. European Economic Review, 91, 72–88. 31 Justiniano, Alejandro, Primiceri, Giorgio E, & Tambalotti, Andrea. 2021. The mortgage rate conundrum. Journal of Political Economy, forthcoming. 7 Kaplan, Greg, & Violante, Giovanni L. 2014. A model of the consumption response to fiscal stimulus payments. Econometrica, 82(4), 1199–1239. 27, 29, 68 Kaplan, Greg, Mitman, Kurt, & Violante, Giovanni L. 2020. The Housing Boom and Bust: Model Meets Evidence. Journal of Political Economy, 128(9), 3285–3345. 7 Keys, Benjamin J, Pope, Devin G, & Pope, Jaren C. 2016. Failure to refinance. Journal of Financial Economics, 122(3), 482–499. 32 Kleven, Henrik J, & Waseem, Mazhar. 2013. Using notches to uncover optimization frictions and structural elasticities: Theory and evidence from Pakistan. The Quarterly Journal of Economics, 128(2), 669–723. 13, 57, 65 Kleven, Henrik Jacobsen. 2016. Bunching. Annual Review of Economics, 8, 435–464. 3, 4, 7, 25, 36, 63 Kovacs, Agnes, &Moran, Patrick.2021. BreakingtheCommitmentDevice: TheEffectofHome Equity Withdrawal on Consumption, Saving, and Welfare. 29, 66, 67, 68 Lacetera, Nicola, Pope, Devin G, & Sydnor, Justin R. 2012. Heuristic thinking and limited attention in the car market. American Economic Review, 102(5), 2206–2236. 8 44

Laufer, Steven, & Tzur-Ilan, Nitzan. 2019. The Effect of LTV-Based Risk Weights on House Prices: Evidence from an Israeli Macroprudential Policy. SSRN Working Paper series. 7 Leombroni, Matteo, Piazzesi, Monika, Schneider, Martin, & Rogers, Ciaran. 2020. Inflation and the price of real assets. Tech. rept. National Bureau of Economic Research. 66, 67, 68 Low, Hamish, Meghir, Costas, & Pistaferri, Luigi. 2010. Wage risk and employment risk over the life cycle. American Economic Review, 100(4), 1432–67. 66 Mayordomo, Sergio, Rachedi, Omar, & Moreno, Maria Rodriguez. 2020. Bank Regulatory Capital Arbitrage: Evidence from Housing Overappraisals. 21 Mullainathan, Sendhil, Schwartzstein, Joshua, & Congdon, William J. 2012. A reduced-form approach to behavioral public finance. Annu. Rev. Econ., 4(1), 511–540. 4, 25, 31 OECD. 2011. Housing and the economy: policies for renovation. 66, 68 Peydr´o, Jos´e-Luis, Rodriguez Tous, Francesc, Tripathy, Jagdish, & Uluc, Arzu. 2020. Macroprudential policy, mortgage cycles and distributional effects: Evidence from the UK. 7 Piazzesi, Monika, Schneider, Martin, & Tuzel, Selale. 2007. Housing, consumption and asset pricing. Journal of Financial Economics, 83(3), 531–569. 29 Piskorski, Tomasz, & Tchistyi, Alexei. 2010. Optimal mortgage design. Review of Financial Studies, 23(8), 3098–3140. 1, 6 Riksbank. 2014. From A to Z: the Swedish mortgage market and its role in the financial system. 10 Sandstr¨om, Maria, Forsman, David, von Rosen, Johanna Stenkula, & Wettergren, Johanna Fager. 2013. The Swedish covered bond market and links to financial stability. 2, 22–49. 24 SBAB. 2018. Mer ¨an var tredje svensk ser amorteringen som en kostnad. https://www.sbab. se/1/om_sbab/press/arkiv_publicering/pressmeddelande/2018-03-27_mer_an_ var_tredje_svensk_ser_amorteringen_som_en_kostnad_.html. [Online: Accessed 2019-08-19]. 5, 33 Scanlon, Kathleen, Lunde, Jens, & Whitehead, Christine. 2008. Mortgage product innovation 45

in advanced economies: more choice, more risk. European journal of housing policy, 8(2), 109–131. 7 Shu, Suzanne B. 2013. NPV Neglect in Consumer Behavior for Multi-Period Borrowing Decisions. Tech. rept. UCLA Working Paper. 2, 5, 6, 33 Søgaard, Jakob Egholt. 2019. Labor supply and optimization frictions: Evidence from the Danish student labor market. Journal of Public Economics, 173, 125–138. 37 Strulov-Shlain, Avner. 2023. More than a penny’s worth: Left-digit bias and firm pricing. Review of Economic Studies, 90(5), 2612–2645. 8 Svensson, Lars EO. 2016. Amortization requirements may increase household debt: a simple example. IMF Working Paper No. 16/83. 31, 37 Vihri¨al¨a, Erkki. 2023. Self-imposed liquidity constraints via voluntary debt repayment. Journal of Financial Economics, 150(2), 103708. 6 Wilhelmsson, Mats. 2022. What is the impact of macroprudential regulations on the Swedish housing market? Journal of Housing Economics, 57, 101840. 8 46

FOR ONLINE PUBLICATION A Internet Appendix: Figures Share low amortization (%) Pre-reform Post-reform 80.0 80.0 Up to 1 % Up to 1 % 60.0 60.0 40.0 40.0 Interest only Interest only 20.0 20.0 0.0 0.0 60 65 70 75 80 60 65 70 75 80 LTV (%) Figure A1. Share interest-only mortgages at the upper threshold Notes: Theorangelineplotstheshareofinterest-onlyloansbyLTVintheyearsbeforetheamortizationrequirement(left panel)andintheyearsaftertherequirement(rightpanel). Thebluelineplotstheshareofloanswithamortizationrates upto1%oftheloanamount. 47

Amortization rate (%) 2.5 Pre-requirement 2.0 1.5 1.0 Post-requirement 0.5 0.0 40 45 50 55 60 LTV (%) (a) Lower Threshold Amortization rate (%) 2.5 Post-requirement 2.0 1.5 1.0 Pre-requirement 0.5 0.0 60 65 70 75 80 LTV (%) (b) Upper threshold Figure A2. Amortization rate by year and LTV ratio for both thresholds Notes: The figure plots the average amortization rate by LTV bin (blue dashed line) and the average amortization rate (orange solid line) above or below the LTV threshold marked by the black dashed line. Panel a) plots these around the lowerthreshold,andpanelb)aroundtheupperthreshold. 48

12 10 8 6 4 2 0 sdlohesuoh fo tnecreP 25 B = 5.01 (0.49) M = 0.49 (0.27) D LTV = 1.98 (0.27) 20 15 10 5 0 40 42 44 46 48 50 52 54 56 58 60 LTV ratio Empirical Counterfactual (a) Constrained borrowers, lower threshold sdlohesuoh fo tnecreP B = 13.16 (0.58) M = 1.28 (0.32) D LTV = 2.84 (0.20) 60 62 64 66 68 70 72 74 76 78 80 LTV ratio Empirical Counterfactual (b) Constrained borrowers, upper threshold 12 10 8 6 4 2 0 sdlohesuoh fo tnecreP B = 10.17 (0.63) 25 M = 0.90 (0.32) D LTV = 3.45 (0.34) 20 15 10 5 0 40 42 44 46 48 50 52 54 56 58 60 LTV ratio Empirical Counterfactual (c) Intermediate, lower threshold sdlohesuoh fo tnecreP B = 13.29 (0.71) M = 0.94 (0.40) D LTV = 2.92 (0.22) 60 62 64 66 68 70 72 74 76 78 80 LTV ratio Empirical Counterfactual (d) Intermediate, upper threshold 12 10 8 6 4 2 0 sdlohesuoh fo tnecreP 25 B = 9.41 (0.70) M = 1.34 (0.32) D LTV = 2.92 (0.30) 20 15 10 5 0 40 42 44 46 48 50 52 54 56 58 60 LTV ratio Empirical Counterfactual (e) Unconstrained borrowers, lower threshold sdlohesuoh fo tnecreP B = 13.10 (0.96) M = 2.15 (0.42) D LTV = 2.57 (0.24) 60 62 64 66 68 70 72 74 76 78 80 LTV ratio Empirical Counterfactual (f) Unconstrained borrowers, upper threshold Figure A3. Bunching by Payment-to-income at LTV=50 (left) and LTV=70 (right) Notes: ThefigureplotstheempiricalandcounterfactualdensityofmortgageloansbyLTVratioforthreedifferentgroups basedontheircounterfactualdiscretionaryincome. Theestimationforthelowerthresholdontheleftiscarriedoutusing allloanswithLTVratiosbetween20and65percent,butonlyshowsthedistributionbetween40and60. Theestimation for the upper threshold on the right is carried out using all loans with LTV ratios between 55 and 80 percent, but only shows the distribution between 60 and 80. The orange lines plots the empirical density, where each dot represents the percentofmortgageswithineach0.5percentLTVbin. Thebluelinesplotsthecounterfactualdensityestimatedusingthe proceduredescribedinSection3. Thefiguresreportstheestimatedpercentofhouseholdsthatbunchatthethreshold(B), the missing mass (M), and the behavioral response by borrowers (∆LTV). The calculations are described in Section 3. Standarderrorsarecalculatedusingabootstrapprocedureandareshowninparentheses. 49

Interest rate (%) 1.8 1.7 Post-requirement 1.6 1.5 Pre-requirement 1.4 1.3 1.2 60 65 70 75 80 LTV (%) Figure A4. Interest rates around the upper LTV threshold Notes: ThefigureplotstheaveragemortgageratebyLTVbinfortheupperthreshold. Thebluelinesusedatafromthe pre-requirement years (2012-2015) and the orange lines use data from the post-requirement years (2016-2018). The solid linesrepresenttheaveragemortgageratebybin,andthedashedlinesaretheaveragemortgageratesabove(LTVbetween 60and70)orbelow(LTVbetween70and80)thethreshold. Thethresholdismarkedwithadashedblackline. 50

House value (Multiple of income) House value (Multiple of income) 8 9 7 8 6 7 5 6 4 5 20 25 30 35 40 45 50 55 60 65 70 75 80 20 25 30 35 40 45 50 55 60 65 70 75 80 LTV (%) LTV (%) a) Ratio, pre-requirement b) Ratio, post-requirement House value (Million SEK) House value (Million SEK) 3.5 4.5 3.0 4.0 2.5 3.5 3.0 2.0 2.5 1.5 20 25 30 35 40 45 50 55 60 65 70 75 80 20 25 30 35 40 45 50 55 60 65 70 75 80 LTV (%) LTV (%) c) Level, pre-requirement d) Level, post-requirement Figure A5. Housing values by LTV ratio Notes: The figure plots the distribution of house values by LTV ratio. Using data for the pre- and post-requirement periods,eachdotdisplaystheaveragehousevalueperLTVbin,afterfilteringoutregion-by-yearanddwellingtypefixed effects. The linear fitted curves are estimated separately for the LTV intervals ranging from 20-50, 50-70 and 70-80, respectively. Panelsa)andb)plotthedistributionsforhousevaluesasaratiotoannualdisposableincome. Panelsc)and d)plotthedistributionsforhousevaluesinmillionsofSwedishkrona. Thedashedverticallinesdisplaytheamortization requirement’sLTVthresholdsat50and70percent. 51

(a) No amortization (LTV = 50%) (b) With amortization (LTV = 51%) Figure A6. Online tool for calculating mortgage payments Notes: The figure provides an example of a mortgage calculator provided by a large Swedish bank. To generate the figure,wehaveselectedanapartment(bostadsr¨att)withanexpectedpriceof2millionSEK(Fo¨rv¨antatslutpris”)andan interestrate(exempelra¨nta)of2percent,closetotheaverageof2.19fromTableB1. Thetoppanelusesadownpayment value (kontantinsats) of 1 million SEK, which corresponds to a loan-to-value (bel˚aningsgrad) of 50%. The corresponding amortizationpayment(amortering)is0%,asseenontherightofthefigure. Thetotalcostforthemortgage(boendekostnad) is then 1,166 SEK. The bottom panel uses a downpayment value of 999,000 SEK, which corresponds to a loan-to-value ) of51%. Thecorrespondingamortizationpaymentis1%or834SEK,asseenontherightofthefigure. Thetotalcostfor themortgageisthen1,996SEK. 52

FOR ONLINE PUBLICATION B Internet Appendix: Tables 53

Table B1. Summary statistics (1) (2) (3) (4) FullSample Nearconstraint Intermediate Farfromconstraint Demographics Mainborrowersage 44.63 44.01 43.91 46.47 (14.89) (15.83) (14.79) (13.25) Householdsize 2.18 1.98 2.07 2.62 (1.14) (1.15) (1.09) (1.07) Largecity 0.45 0.46 0.43 0.45 (0.50) (0.50) (0.49) (0.50) Disposableincome,KSEK 40.68 32.58 39.15 55.26 (83.31) (14.97) (139.20) (50.22) Loan sizes (MSEK) Totaldebt 1.86 1.80 1.73 2.12 (1.63) (1.53) (1.44) (1.93) Mortgagedebt 1.49 1.48 1.39 1.61 (1.24) (1.23) (1.14) (1.34) Houseprice 2.45 2.50 2.20 2.68 (2.15) (2.26) (1.82) (2.28) Interest Rates Mortgagerate 2.19 2.07 2.21 2.34 (0.83) (0.75) (0.84) (0.92) Mortgagefixationperiod(months) 13.30 12.77 13.54 13.85 (15.65) (15.37) (15.69) (15.99) Adjustableratemortgage 0.61 0.63 0.60 0.59 (0.49) (0.48) (0.49) (0.49) Amortization Amortization,KSEK 1.61 1.57 1.58 1.70 (1.92) (1.81) (1.79) (2.20) Amortizationrate 1.73 1.62 1.81 1.84 (2.60) (2.30) (2.66) (2.96) Amortizationtoincome 4.11 4.71 4.07 3.22 (4.15) (4.49) (4.00) (3.56) Mortgage Characteristics Loantovalue 65.43 64.65 67.30 64.45 (22.97) (23.41) (22.05) (23.20) Totaldebttoincome 377.95 432.41 359.95 313.28 (218.47) (227.32) (206.73) (195.36) Netinteresttoincome 5.55 6.04 5.41 4.95 (3.76) (3.78) (3.72) (3.66) Debtservicetoincome 10.87 11.96 10.70 9.35 (6.80) (7.05) (6.57) (6.33) N 120,307 50,490 37,823 31,994 Notes: Thetablereportsmeansandstandarddeviations(inparentheses). Column1providesresultsforthefullsample. Columns 2-4 divides by sample according to the borrowers’ counterfactual discretionary income (see Section 4.2. We calculatethecounterfactualdiscretionaryincomeasthediscretionaryincomegivenyourchosenLTV,minustheextra payments if you would have borrowed 1%-point more in LTV. The Near constraint, Intermediate and unconstrained sample have counterfactual discretionary incomes of less than 5,000 SEK, 5,000-15,000 SEK and greater than 15,000 SEK, respectively. KSEK is thousands of Swedish krona, and MSEK is millions of Swedish krona. Demographic variables include the main borrower age and household size. Large city is a dummy variable equal to one if the borrower lives in one of the three largest cities (Stockholm, Malm¨o or Gothenburg). Disposable income, KSEK is disposable income adjusted for inflation in thousands of Swedish krona per month. Total debt is defined as mortgage debtplusunsecuredcredit. HousepriceisthecollateralvalueinmillionsofSEK,whichinmostcasesisbasedonbank’s internal valuations of properties, or transaction prices otherwise. These internal valuations use previous transaction prices and local hedonic price indices. Mortgage fixation period is the number of months for which the mortgage has a fixed interest rate. Adjustable rate mortgage is a dummy equal to one if the fixation period 3 months or less, i.e. if themortgagehasavariableinterestrate. Amortization,KSEK isthemonthlyamortizationpaymentinthousandsof SEK.Amortizationrate iscalculatedasmortgageamortizationdividedbymortgagedebt. Amortizationtoincome is calculatedasmortgageamortizationdividedbydisposableincome. Loantovalueiscalculatedasmortgagedebtdivided by house price. Total debt to income is calculated as total debt divided by annual disposable income. Net interest to income is calculated as interest payments divided by disposable income. Debt service to income is calculated as the sumofinterestpaymentsandamortizationpayments,dividedbydisposableincome. 54

Table B2. Summary of main estimates Lower threshold Upper threshold (Notch at LTV=50) (Notch at LTV=70) Bunching (Bˆ) 7.47 12.93 (0.31) (0.38) Missing mass (Mˆ) -0.83 -1.43 (0.16) (0.20) ∆ LTV 2.57 2.73 (0.16) (0.12) Elasticity 0.25 0.15 (0.03) (0.01) Number of households 35,747 39,946 Notes: Thetablesummarizesthemainbunchingestimates. Bunchingisthepercentofhouseholdsbunching,calculated using equation (1). Missing mass is the percent of households missing, calculated using equation (2). ∆ LTV is the estimateofthebehavioralresponse,orthepercentagepointchangeinLTVratioforthemarginalbuncher,calculated usingequation(3). ElasticityistheestimatedpercentagechangeinLTVforaonepercentagepointhigheramortization rate, calculated using equation (4). Bootstrapped standard errors in parentheses are calculated by drawing random sampleswithreplacementfromthefullsampleofborrowers. Wethenre-calculatetheLTVdistributionandre-estimate allparametersateachiteration. 55

Table B3. Robustness of empirical results Notch at LTV = 50 Bin width = 0.5 Bin width = 1 Preferred Lower limit (L) 47.5 48 48.5 49 49.5 47 48 49 Bunching(Bˆ) 8.00 7.92 7.47 7.12 6.43 7.98 7.80 7.03 (0.34) (0.34) (0.31) (0.30) (0.27) (0.36) (0.34) (0.32) ∆ LTV 3.05 2.91 2.57 2.26 1.80 3.20 2.97 2.43 (0.18) (0.18) (0.16) (0.15) (0.12) (0.19) (0.18) (0.16) Elasticity 0.35 0.32 0.25 0.19 0.12 0.39 0.33 0.23 (0.04) (0.04) (0.03) (0.03) (0.02) (0.04) (0.04) (0.03) Upper limit (U) 50.5 51 51.5 52 52.5 51 52 53 Missing mass (Mˆ) -0.26 -0.64 -0.83 -0.88 -1.10 -0.58 -0.83 -1.22 (0.09) (0.14) (0.16) (0.20) (0.23) (0.14) (0.20) (0.26) Number of households 35,747 Notch at LTV = 70 Bin width = 0.5 Bin width = 1 Preferred Lower limit (L) 67.5 68 68.5 69 69.5 67 68 69 Bunching (Bˆ) 13.82 13.43 12.93 12.28 10.75 13.82 13.39 12.37 (0.41) (0.39) (0.38) (0.37) (0.34) (0.44) (0.41) (0.38) ∆ LTV 3.36 3.06 2.73 2.29 1.75 3.42 3.21 2.61 (0.14) (0.13) (0.12) (0.10) (0.08) (0.14) (0.13) (0.12) Elasticity 0.22 0.18 0.15 0.10 0.06 0.23 0.20 0.13 (0.02) (0.01) (0.01) (0.01) (0.01) (0.02) (0.02) (0.01) Upper limit (U) 70.5 71 71.5 72 72.5 71 72 73 Missing mass(Mˆ) (M) -0.48 -0.75 -1.43 -1.88 -2.50 -0.93 -1.89 -2.92 (0.11) (0.16) (0.20) (0.23) (0.26) (0.17) (0.24) (0.30) Number of households 39,946 Notes: ThetablesummarizestherobustnessofthebunchingestimateswhenvaryingthewidthofLTVbinsandthe upper and lower limits of the excluded region around the notch. Bunching is the percent of households bunching, calculated using equation (1). ∆ LTV is the estimate of the behavioral response, or the percentage point change in LTVratioforthemarginalbuncher,calculatedusingequation(3). Elasticity istheamortizationelasticityofmortgage demand,calculatedusingequation4. Missingmass isthepercentofhouseholdsmissingattherightofthethreshold, calculatedusingequation(2). Bootstrappedstandarderrorsinparenthesesarecalculatedbydrawingrandomsamples with replacement from the full sample of borrowers. We then re-calculate the LTV distribution and re-estimate all parametersateachiteration. 56

FOR ONLINE PUBLICATION C Internet Appendix: Additional bunching estimates This section provides additional bunching estimates. Section C.1 describes how we measure the amortization elasticity of mortgage demand. Section C.2 provides placebo tests to verify our identification approach. Section C.3 provides the results for the upper threshold. Section C.4 describes how we estimate bunching using a flexible polynomial approach, and provides the results. C.1 Calculating the amortization elasticity of mortgage demand The amortization requirement creates a jump in mortgage payments for borrowers because the rate above the threshold applies to the entire mortgage instead of the excess amount above the threshold. In other words, the requirement creates a discontinuous change in the average amortization payment instead of a discontinuous change in the marginal rate. Since elasticities relate marginal changes in costs to marginal changes in quantities, we cannot use the jump in payments created by the requirement to calculate the elasticity. We instead follow DeFusco & Paciorek (2017) and Kleven & Waseem (2013) and calculate an implicit marginal amortization rate on the mortgage. The idea behind the approach is to relate the reduction in LTV ratios to the change in the implicit marginal amortization rate created by the requirement. Specifically, define the implicit marginal amortization rate α∗ for LTV > LTV such that: (LTV −LTV)·α∗ = LTV ·(α +∆α)−LTV ·α (15) 0 0 The above equation states that the implicit marginal amortization rate α∗ on the mortgage above the requirement threshold (LTV − LTV) is equal to the amortization rate above the threshold (α + ∆α), minus the amortization rate at the LTV threshold (α ). Solving this 0 0 equation for α∗, we have LTV α∗ = α +∆α+∆α· (16) 0 (LTV −LTV) Theequationshowsthatα∗ isequaltotheamortizationratebelowthethresholdplusthechange in the amortization rate above the threshold, plus the change times a term that is decreasing in 57

thedistancebetweentheLTVratioandthethreshold. Placingyourselfjustabovethethreshold gives a small increase in the LTV but a large increase in amortization payments, as the jump in the rate applies to the whole mortgage. Loans just above the limit imply a very large marginal amortization rate: for example, the marginal amortization rate for a mortgage with an LTV of 51 percent on the last 1 percent of the LTV is then equal to α∗ = 0+0.01+0.01· 50 = 51 (51−50) percent. WecanrelatethesemarginalamortizationratestothepercentreductioninLTVs. Thesemielasticity of borrowing with respect to the amortization rate is equal to the following: ∆LTV/LTV eα = (17) α∗(LTV +∆LTV)−α 0 where we relate the percent change in the LTV ratio (calculated as the behavioral response, ∆LTV, divided by the LTV at the threshold, LTV), to the implicit change in the level of the marginal amortization rate for the marginal buncher from equation (16). C.2 Placebo tests We now study whether the counterfactual density obtained from pre-requirement data presents a good estimate of the fraction of borrowers in each bin, a key identifying assumption in our approach. We create a placebo test to assess whether the counterfactual distribution presents a good estimate of the fraction of borrowers without the requirement (DeFusco et al., 2020). Specifically, each pre-requirement year from 2011 to 2015 is designated a “placebo” year. We then estimate the counterfactual distribution for both requirement thresholds in these years. By estimating the counterfactual distribution as if the requirement had passed in a placebo year, we can assess whether the procedure can yield a good match between the empirical and counterfactual distribution in a year without an amortization requirement. If our assumption is valid, the two distributions should coincide. Figure C1 shows that our preferred approach passes this placebo test. Panels a) and b) plot the empirical and counterfactual distribution in 2014 for the upper and lower amortization requirement, showing a close correspondence between the distributions in both cases. Using other years than 2014 yields similar charts. Importantly, the spikes at 50, 70, and 75 percent LTV ratios are well captured by this procedure. Panels c) and d) provide histograms of the ratio between the percentage of borrowers in each bin in the empirical and counterfactual 58

Percent of households 8.0 7.0 6.0 5.0 Empirical Counterfactual 4.0 3.0 2.0 1.0 40 42 44 46 48 50 52 54 56 58 60 LTV (%) (a) Lower threshold: Placebo reform in 2014 Percent of bins 10 Summary stats Mean = 0.026 Median = -0.003 8 SD = 0.23 IQR = [-0.13, 0.16] 6 4 2 0 -0.4 -0.2 0.0 0.2 0.4 0.6 Ratio between counterfactual and empirical distribution (b) Lower threshold: Ratio, empirical to counterfactual Figure C1. Counterfactual and empirical distribution in placebo years Notes: Panels a) plots the empirical (solid orange line) and estimated counterfactual (dashed blue line) distribution of LTV ratios for 2014 for the lower threshold. Plotted LTV ratios are limited to be between 40 and 60 percent. The figures designate the placebo treatment to take place in 2014 and uses data from 2011, 2012, 2013, and 2015 to create thecounterfactual. Panelsb)providesahistogramoftheratiobetweentheempiricalandcounterfactualdistribution,for all binsin allplaceboyears. Foreachyearweuse datafrom theother pre-requirement years asthe counterfactual. LTV ratiosarerestrictedtobebetween40and60. Thesummarystatistics(mean,median,standarddeviationandinterquartile range)inthetoprightofpanelb)arebasedonthesamedata. 59

Percent of households 25 B = 12.93 (0.38) M = 1.43 (0.20) 20 D LTV = 2.73 (0.12) 15 10 5 0 60 62 64 66 68 70 72 74 76 78 80 LTV ratio Empirical Counterfactual Figure C2. Bunching at LTV=70 Notes: ThefigureplotstheempiricalandcounterfactualdensityofmortgageloansbyLTVratio. Theestimationiscarried out using all loans with LTV ratios between 55 and 80 percent, but only shows the distribution between 60 and 80. The orange line plots the empirical density, where each dot represents the percent of mortgages within each 0.5 percent LTV bin. ThebluelineplotsthecounterfactualdensityestimatedusingtheproceduredescribedinSection3. Thefigurereports the estimated percent of householdsthat bunch at thethreshold (B), the missing mass (M), and the behavioralresponse byborrowers(∆LTV). ThecalculationofthesenumbersisdescribedinSection3. Standarderrorsarecalculatedusinga bootstrapprocedureandareshowninparentheses. distribution for all the pre-requirement years. The mean and median percentage differences are close to zero, and the interquartile range covers zero. There is little evidence that our approach creates a systematic bias in either direction. C.3 Bunching at the upper threshold This section presents the results for the upper threshold. Recall that there are several potential confoundingeffectsrelevanttothisthreshold. First, somenewborrowersmayalreadychoosean LTVratioof70percentinthepre-requirementyearsbecauseofapreviousrecommendationthat households amortize on the portion of the mortgage in excess of a 70 percent LTV ratio. The previous recommendation represents a potential downward bias in our estimates, as borrowers may bunch even in the pre-requirement period. Second, several banks offer mortgages with a higher marginal interest rate on the part of the mortgage with an LTV above 75 percent (a so-called “top loan”). This incentive was phased out over time as banks abolished the toploan system but did provide an incentive to bunch at a nearby threshold in the years before the requirement. The marginal interest rate changes above LTV ratios of 75 percent, and a borrower may want to reduce their borrowing to avoid this higher interest rate. TheresultsfortheamortizationthresholdatLTVratiosof70percentarepresentedinFigure 60

C2. Similar to Figure 4, the figure plots the observed distribution using data from the postrequirement years and the counterfactual distribution estimated using pre-requirement data. The estimation procedure uses data from borrowers with LTV ratios between 55 and 80 percent to avoid the lower threshold and the maximum LTV ratio at 85 percent affecting the results. There are two spikes at LTV ratios of 70 and 75 percent in Figure C2. For the pre-requirement period, the peak at LTV ratios of 75 percent is considerably larger than the peak at LTV ratios of 70 percent. For lower LTV ratios, the empirical and counterfactual densities are almost identical, showing that the procedure is well able to approximate the distribution. The bunching statistic B(cid:98) shows that 12.93 percent of borrowers decide to bunch (standard error 0.38), an increase by a factor (cid:98)b = 1.36. Dividing the bunching statistic by the counterfactual distribution at the threshold, we find that the marginal buncher reduces its LTV ratio by 2.73 percentage points (standard error 0.12) due to the amortization requirement. The effect is marginally higher than the reduction in LTV ratios of 2.57 percent at the lower threshold. Finally, we find 1.43 percent (M(cid:99) = 1.43, standard error 0.2) fewer borrowers to the right of the threshold in the post-requirement years compared to the pre-requirement years. We again calculate the amortization semi-elasticity using equation (4). With the estimated ∆LTV of 2.73, the numerator equals 2.73/70 = 0.039. Using the implicit rates from equation (16), the denominator is equal to α∗ = 0.01+0.01+0.01· 70 = 0.276, and the semi- (72,73−70) elasticity is equal to 0.039/0.276 = 0.14. A one percentage point increase in the amortization rate decreases LTV ratios by 0.14 percent. C.3.1 Payment constraints at the upper threshold We found limited evidence that credit constraints were an important determinant of bunching for the lower threshold. We now present similar evidence for the upper threshold. We begin by noting that the share of bunchers facing binding credit constraints at this threshold is somewhat larger than at the lower threshold: 32.6 percent at the upper threshold compared to 13.6percent atthe lowerthreshold. Wedefinethree groupsof borrowerbasedon counterfactual discretionary income, and estimate bunching separately for each group. For the near constraint group, increasing leverage by one percentage point implies a reduction in discretionary income by 88 percent. The results are presented in Table C1. Overall, the results are consistent with the previous 61

Table C1. Bunching estimates by type of payment constraints PTI Constraint Near constraint Intermediate Far from constraint Bunching 13.16 13.29 13.10 (0.58) (0.71) (0.96) Missing mass -1.28 -0.94 -2.15 (0.32) (0.40) (0.42) ∆ LTV 2.84 2.92 2.57 (0.20) (0.22) (0.24) Elasticity 0.16 0.17 0.13 (0.02) (0.02) (0.02) Number of households 15,949 12,127 10,242 Notes: Thetablecomparesthemainbunchingestimatesacrossgroupsbasedonpayment-to-incomeconstraints. We calculatethecounterfactualdiscretionaryincomeasthediscretionaryincomegivenyourchosenLTV,minustheextra payments if you would have borrowed 1 percentage point more in LTV. The Near constraint, Intermediate and Far fromconstraintsamplehasacounterfactualdiscretionaryincomeoflessthan5,000SEK,5,000-15,000SEKandgreater than15,000SEK,respectively. Bunching isthepercentofhouseholdsbunching,calculatedusingequation(1). ∆LTV the percentage point change in LTV ratio for the marginal buncher, calculated using equation (3). Elasticity is the amortizationelasticityofmortgagedemand,calculatedusingequation4. Bootstrappedstandarderrorsinparentheses arecalculatedbydrawingrandomsampleswithreplacementfromthefullsampleofborrowers. Wethenre-calculate theLTVdistributionandre-estimateallparametersateachiteration. results for the lower threshold. There is little variation in bunching across the three groups, with similar levels of bunching for the Near contraint group and the Far from constraint group. The estimated ∆LTV is 2.84 for the Near contraint group and 2.57 for the Far from constraint group. C.3.2 Endogenous housing demand responses at the upper threshold We move on to estimates of the response by refinancers and homebuyers at the upper threshold. We find interesting heterogeneity across refinancers and homebuyers. Bunching and ∆LTV is considerably higher for homebuyers, with 19.13 percent of households bunching with a corresponding reduction in LTV ratios of 5.36 percentage points, or 5.36/70 = 7.6%. A natural explanation is that homebuyers are more credit constrained than refinancers, which forces them to adjust their LTV ratios by either adjusting the loan size or housing demand. Indeed, we find that homebuyers at the upper threshold are more likely credit constrained, according to the definition in section 4.2. 53 percentof these homebuyers are constrained, compared to 33 percent at the lower threshold. C.4 Bunching Estimates from Polynomials This section provides additional results where we estimate the counterfactual distribution using the standard approach in the literature of fitting a flexible polynomial to the distribution and 62

Table C2. Bunching estimates by type of valuation Valuation Internal External Purchase price Bunching (Bˆ) 12.88 6.40 19.13 (0.43) (1.05) (1.01) Missing mass (Mˆ) -1.38 -0.53 -1.68 (0.24) (0.66) (0.54) ∆ LTV 2.72 1.17 5.36 (0.13) (0.23) (0.63) Elasticity 0.15 0.03 0.54 (0.01) (0.01) (0.12) Number of households 30,500 5,111 4,335 Notes: Thetablecomparesthebunchingestimatesacrossvaluationmodesforcollateralassessments. Forrefinancers, banks use either an internal (statistical) valuation model, or an external method, either a tax-assessed value or an independentappraisal. Forhomebuyers,thepurchasepriceisused. Bunching isthepercentofhouseholdsbunching, calculatedusingequation(1). Missingmassisthepercentofhouseholdsmissingattherightofthethreshold,calculated using equation (2). ∆ LTV is the percentage point change in LTV ratio for the marginal buncher, calculated using equation(3). Elasticity istheamortizationelasticityofmortgagedemand,calculatedusingequation4. Bootstrapped standard errors in parentheses are calculated by drawing random samples with replacement from the full sample of borrowers. Wethenre-calculatetheLTVdistributionandre-estimateallparametersateachiteration. excluding an area around the threshold (see Kleven, 2016, for an overview). We begin by grouping households into bins based on their Loan-to-Value ratio and calculate the fraction of households in each bin. We then fit the following regression: p U (cid:88) (cid:88) n = β (m )i+ γ 1(m = m )+ϵ , (18) j i j k k j j i=0 k=L wheren isthefractionofhouseholdsinbinj andm isloan-to-valueratiooftheloan. Thefirst j j termisap-thdegreepolynomialinLTVratios, andthesecondtermisasetofdummyvariables for each bin in the excluded region [L,U]. The estimates of the counterfactual distribution are givenbythepredictedvaluesfromtheaboveregressionwhileomittingtheeffectofthedummies in the excluded region: p (cid:88) nˆ = βˆ(m )i (19) j i j i=0 The identifying assumption to estimate the causal effect of the amortization requirement is that the counterfactual LTV distribution is smooth. This precludes spikes in the distribution at the thresholds that are unrelated to the amortization requirement. As in the main analysis, the estimates of bunching and missing mass are calculated by comparing the counterfactual distribution to the empirical distribution in the relevant regions (seeequations1and2). WeusetheprocedureinChettyetal.(2011)tocalculatestandarderrors 63

Percent of households Percent of households 10 15 B = 8.18 (0.32) B = 13.29 (1.92) M = 1.41 (0.26) M = 3.34 (1.72) 8 D LTV = 3.30 (0.20) 12 D LTV = 2.98 (0.72) 6 9 4 6 2 3 0 0 40 42 44 46 48 50 52 54 56 58 60 60 62 64 66 68 70 72 74 76 78 80 LTV ratio LTV ratio Empirical Counterfactual Empirical Counterfactual (a) Lower threshold (b) Upper threshold Figure C3. Bunching estimates from polynomials Notes: The figure plots the empirical and counterfactual density of mortgage loans by LTV ratio, in the region around the notch at LTV = 50 (Panel a) and the notch at LTV = 70 (Panel b). The orange line is the empirical density, where eachdotrepresentsthepercentofmortgageswithineach0.5percentLTVbin. Thebluelineisthecounterfactualdensity, estimatedbyfittingaflexiblepolynomialtotheobserveddistribution,excludingtheregionaroundthenotch. Thefigure also reports the estimated percent of loans that bunch at the threshold (B), the missing mass (M), and the behavioral responsebyborrowers(∆LTV). ThecalculationofthesenumbersisdescribedinSection3. Standarderrorsarecalculated usingabootstrapprocedureandareshowninparentheses. Percent of models 80 Main estimates Lower threshold: 2.57 Upper threshold: 2.73 60 40 Pre-requirement Post-requirement 20 0 -2 0 2 4 6 Delta LTV Figure C4. Robustness of estimated behavioral responses Notes: Thefigureplotsthedistributionofestimatedbehavioralresponses(∆LTV)usingtheflexiblepolynomialapproach. The red bars use post-requirement data only (years 2016-2018) while the green bars use pre-requirement data (years 2011-2015). The vertical black dashed lines depict our main estimates of the behavioral response using the differencein-bunching approach. The specifications differ in their bin width (0.5 or 1 percent bins), the order of the polynomial (p∈[3,5,7,9,11,13])andtheinitialwidthoftheexcludedregiontotheleftofthenotch(L∈[0.5,1,1.5]forabinwidth of0.5,andL∈[1,2]usingabinwidthof1). for all estimated parameters. Specifically, we randomly draw from the residuals in equation 18 with replacement to generate new bootstrapped bin fractions. We then re-estimate the bunching parameters. Standard errors are calculated as the standard deviation of the bootstrap estimates. Figure C3 plots the empirical and counterfactual density of mortgage loans by LTV ratio, in 64

theregionaroundthenotchesintheamortizationrequirement. Thefigureisgeneratedusingthe same bin width and width of the excluded region (L and U) as for the difference-in-bunching approach, while the order of the polynomial (p) was determined to minimize the difference between bunching and missing mass. To demonstrate robustness, we follow Kleven & Waseem (2013) and DeFusco & Paciorek (2017) and estimate many specifications that vary in the order of the polynomial (p), the bin width and the width of the excluded region to the left of the notch (L), while the width of the excluded region to the right of the notch (U) is determined by an iterative procedure that aims to equate the degree of bunching with the missing mass. Figure C4 provides a histogram of the estimated behavioral response ∆LTV across all these specifications. Our main estimates are in the conservative region of the outcomes using postreform data; the figure shows that a 2 percentage points decline in LTV is roughly the lower bound. Interestingly, using pre-reform data, some specifications still result in significant, albeit lower, estimated behavioral responses, while there shouldn’t be any response. Most likely, this comes from the presence of rounding and/or the SBA’s prior recommendation to amortize loans with LTV above 70. This strengthens our choice to use pre-requirement years as the counterfactual, which controls for such factors directly and does not rely on the identifying assumption of smooth counterfactual distributions. 65

FOR ONLINE PUBLICATION D Internet Appendix: Model Calibration Table D1 shows the parameters set outside of the model of Section 5. Here we describe how we calculate the parameters in more detail. Table D1. Model parameter values Parameter Symbol Value Source Income process: Incomepersistence ρ 0.97 Kovacs&Moran(2021) Stddevincomeshocks σϵ 0.180 Kovacs&Moran(2021) Incomeconstant d0 8.2007 Kovacs&Moran(2021) IncomeAgeeffect d1 0.1378 Kovacs&Moran(2021) IncomeAge2 effect d2 -0.0019 Kovacs&Moran(2021) IncomeAge3 effect d3 0.000007 Kovacs&Moran(2021) Initial conditions: StdDevInitialIncome σ0 0.410 Kovacs&Moran(2021) Sharewithzeroinitialassets azero 0.433 Kovacs&Moran(2021) 0 Cond. meaninitialassets µa0 7.117 Kovacs&Moran(2021) Cond. stddevinitialassets σa0 1.972 Kovacs&Moran(2021) Preferences: Timepreference β 0.96 Cocco(2005) Riskaversion γ 5.0 Cocco(2005) Housingutilityshare θ 0.1 Cocco(2005) Disutilityofrenting ζ 0.03 Leombroniet al.(2020) FlowDisutilityofAmortization ∆ 0.08 Author’scalibration k One-OffDisutilityofAmortization ∆n 0.35 Author’scalibration Assets: Realreturnonliquidasset r 0.0181 Swedish3monthT-bill Realreturnonhousing rH 0.02953 StatisticsSweden Mortgageinterestrate rM 0.0087 StatisticsSweden Multiplicativecostofrefinancing f2 5.0% FederalReserveBoard(2008) Additivecostofrefinancing f3 $3000 FederalReserveBoard(2008) Liquidborrowingconstraint a 0.0 Cocco(2005) MaximumLoan-to-ValueRatio 1−ψ 0.85 Swedishlaw Financialcosttomovinghomes f1 0.05 OECD(2011) Demographics: Ageatlabormarketentry t=0 22 Attanasioet al.(2012) Ageofretirement W 65 Attanasioet al.(2012) Ageofcertaindeath T 120 Statisticallifetables Income. We set the values of the earning process following Kovacs & Moran (2021), who estimatetheearningsprocessusingthetwo-stepminimumdistanceapproachbyGuvenen(2009) and Low et al. (2010). These authors estimate the parameters of the deterministic component of income (g ) by approximating it with a third-order polynomial in age. They identify the t stochasticincomecomponentasz = lny −g . Inthesecondstep,theyestimatethepersistence it it t of income risk (ρ), the variance of income innovations (σ2), and the variance of initial income ϵ (σ2). These authors find very persistent income innovations, with a coefficient of ρ = 0.97. The 0 66

parameter estimates for the income process are generally in line with the rest of the literature. MoredetailsabouttheestimationstrategyandresultsareavailableinAppendixC.2.2inKovacs & Moran (2021). Initial conditions. We assume zero initial housing wealth. We set the initial liquid wealth distribution to match the distribution for 22-25-year old households in the PSID, following Kovacs & Moran (2021). We use that 43.3 percent of households have zero liquid assets at age 22. Conditional on observing positive assets, the mean log liquid asset holdings are estimated to be µ = 7.117, with a conditional standard deviation of σ = 1.972. a0 a0 Household preferences. We set the main preference parameters following Cocco (2005). Thatsaid, wehaveexploredalternativecalibrationsandfoundlittleimpactonourmainresults. For instance, in an earlier version of the paper, we calibrated household preferences following Attanasio et al. (2012), assuming a higher β and substantially lower γ. In this alternative calibration, we still found that the traditional model could not generate bunching for wealthy households, and found similar results regarding the importance of notches or kinks in household preferences. We set the disutility of renting following Leombroni et al. (2020). For the notch and kink in household preferences, denoted by ∆ and ∆ , we calibrate these parameters in an n k attempt to roughly match the size of the excess mass at the policy threshold (see Figure D1). Thatsaid,giventheidentificationstrategydiscussedinthepaper,itwouldbestraightforwardto extendouranalysistoestimatetheseparametersusingthemethodofsimulatedmoments. Asset returns. We calibrate the model using real risk-adjusted returns. Starting with a consumption-based pricing equation, we can write the asset return in terms of prices and dividends: p +d −p t+1 t+1 t r = (20) t+1 p t where r is the net return on the asset between periods t and t+1, p is the price of the asset t+1 t in period t, and d is the dividend in period t+1. t+1 Forliquidassets,wemeasuretherealreturnon3-monthSwedishTreasurybillsbetween1982 and 2022. To calculate the return on housing, we assume that households who invest in housing enjoy housing service flows between periods t and t + 1, but also have to pay maintenance and insurance costs related to homeownership. This allows us to write the return to housing 67

as: p +s −cm −ci −p rH = t+1 t+1 t+1 t+1 t (21) t+1 p t where s and c are housing service flow and the costs related to homeownership (maint+1 t+1 tenance cost cm and insurance costs ci ). We follow Kaplan & Violante (2014) and assume t+1 t+1 that housing service flows and costs are proportional to house prices, allowing us to rewrite Equation (21) as p +(s−cm−ci−1)p rH = t+1 t (22) t+1 p t Following Kovacs & Moran (2021), we assume that net housing service flows is 8 percent a year. This value is calculated by dividing the average housing gross value added at current dollars from the Bureau of Economic Analysis (BEA) by the residential fixed assets at current dollars. The average is calculated between 1950 and 2016. Following Kaplan & Violante (2014), we set maintenance cost to 1 percent and the insurance cost to 0.35 percent of the value of housing. We calculate risk-adjusted returns by subtracting the variance of the return from the expected return, following Kaplan & Violante (2014): rj = E(rj)−var(rj) (23) adjusted where superscript j refers to the asset type, i.e. liquid assets or housing. Housing transaction costs. We assume that moving homes requires households to pay a transaction cost F equal to 5 percent of the value of the house. F represents costs to real estateagents, lawyers, surveyors, andmovingcompanies. ThehighvalueofF isconsistentwith empirical evidence from OECD (2011). We set the rental scale equal to η = 0.035 to match the lower bound of the rent-price ratio time series in Leombroni et al. (2020). Refinancing costs. We assume that the multiplicative cost to refinancing f is 5 percent 2 and that the additive cost to refinancing f is $3000. The cost of refinancing reflects a range of 3 fees related to mortgage refinancing. Disutility costs. We calibrate the flow disutility of amortization (∆ ) to match the excess k mass at the policy threshold observed in the data (B(cid:98) = 7.47). Based on this approach, we choose to set ∆ = 0.08 which gives a model-implied excess mass of B(∆ ) = 7.53, only a touch k k 68

larger than our baseline estimate from the data. Figure D1 shows excess mass as a function of flow disutility, B(∆ ), based on simulated data k from our model. Excess mass is monotonically increasing in flow disutility. The dashed horizontal line indicates our baseline empirical estimate of excess mass B(cid:98) = 7.47, which we target. The dashed vertical line indicates our baseline calibration of flow disutility ∆ = 0.08. k Excess mass (B) 15 Bunching at different values of flow disutility 10 Empirical estimate B̂= 7.47 5 0 0 .05 .1 .15 .2 .25 Flow disutility (D ) k Figure D1. Relationship between flow disutility and excess mass Note: Thisfigureplotsthemodel-impliedexcessmassB(∆ )asafunctionoftheflowdisutilityofamortizationbasedon k simulationsofthemodelwithdifferentvaluesof∆ whileallotherstructuralparametersarekeptconstant. k 69