Regulating Mortgage Leverage: Fire Sales, Foreclosure Spirals, and Pecuniary Externalities

Abstract

This paper introduces a dynamic general equilibrium model to study how the distribution of leverage and foreclosure affect house prices. In the model, exogenous income shocks drive endogenous foreclosure and equilibrium house prices. The model shows how foreclosure sales, through their effect on housing supply, amplify and propagate house price drops. A calibration shows consumption and housing need to be sufficiently complementary to fit the data. Since leverage plays a key role in foreclosure, a regulator can reduce systemic risk by placing a cap on leverage. Counterfactual experiments show that in a world with less leverage, the same economic shock leads to less foreclosure and less severe, shorter busts in house prices.

Keywords:

• Housing
• foreclosure
• leverage
• mortgage
• default
• macro-prudential policy

Acknowledgments

I would like to thank my committee, Urban Jermann, Enrique Mendoza, and Susan Wachter, for helpful comments and support. I would also like to thank Andrew Abel, Saki Bigio, Mark Clements, João Cocco, Hal Cole, Dean Corbae, Nadia Daneshvar, Morris Davis, Anthony DeFusco, Gilles Duranton, Ronel Elul, Andra Ghent, Itay Goldstein, João Gomes, Joe Gyourko, Ben Hyman, Matteo Iacoviello, Dirk Krueger, Jianjun Miao, Christian Opp, Carol Osler, Monika Piazzesi, Nikolai Roussanov, Dan Sacks, and Todd Sinai, as well as audiences at Wharton, UPenn, National University of Singapore, Baruch College, Johns Hopkins University, and HULM, for helpful comments. All errors are my own.

Notes

1 For example, if a consumer buys a house for $V=\$100$ with a first mortgage $L_1=\$80$ and a second mortgage $L_2=\$15,$ then CLTV $\equiv (L_1+L_2)/V=95/100=95\%.$ In this paper, leverage and LTV are used interchangeably.

2 This policy limits total leverage from purchase mortgages, refinancings, and home equity loans.

3 Not all economists support MPPs. For a critique, see Cochrane (2013).

4 The propagation helps explain why US house prices kept falling after the economy stopped contracting.

5 One explanation is that Las Vegas has a larger share of homes owned by out-of-town investors who are more prone to default on their mortgages (Gao & Li, 2012). In addition, second homes are a luxury good, and demand for luxury goods is more sensitive to economic shocks.

6 See Anenberg and Kung (2014), Arefeva (2020), Campbell et al. (2011), Chatterjee and Eyigungor (2011), Corbae and Quintin (2015), Davis and Van Nieuwerburgh (2014), Elenev (2017), Ghent and Kudlyak (2011), Gilbukh and Goldsmith-Pinkham (2019), Greenwald (2018), Hatchondo et al. (2015), Iacoviello (2005), Krivenko (2018), Laufer (2014), Lin (2020), Mian et al. (2015), Piazzesi and Schneider (2016), Zevelev (2021).

7 See Anenberg and Kung (2014), Biswas et al. (2019), Campbell et al. (2011), Gerardi et al. (2015), Mian et al. (2015).

8 This paper captures the effect of less leverage only through the supply impact of foreclosure (the second distributional channel).

9 It is worth noting that regulating leverage for households in several ways parallels a large literature that studies regulating leverage for banks. See Admati and Hellwig (2014), Admati et al. (2018), Calomiris (2013), Clerc et al. (2015), Jiménez et al. (2017).

10 This paper assumes the housing stock is fixed: no depreciation and no new construction. This assumption is reasonable because the calibration will target the housing bust years during which there was very little new construction, and this period was too short for depreciation to make a big difference.

11 This paper takes the initial leverage distribution to be exogenous. Endogenous default decisions and equilibrium prices are computed given this distribution. This paper does not aim to explain why lenders offered credit contracts with such high leverage or why borrowers got these loans. There does not yet exist a quantitative model that endogenously matches the cross-sectional LTV distribution. For a theoretical treatment of endogenous leverage see Geanakoplos (2010) and Zevelev (2018).

12 Including $\Pi (·)$ ensures the nonleverage households will consume their endowments of the nondurable in equilibrium. Menno and Oliviero (2020) use a similar trick. We assume the interest payments are sold off in the secondary market, which is realistic.

13 Greenwald and Guren (2019) find that rental markets and markets for owner-occupied housing are nearly fully segmented; hence we should not expect rents charged for rental properties to be a good proxy for the service flow for owner-occupied houses.

14 We deliberately assume the loans are nonamortizing because we will run a 5-year calibration (2008–2012). Over that period there was very little time for mortgages to amortize. In addition, many of the high-CLTV mortgages were delayed amortization and even negative amortization products.

15 Consistent with the evidence in Greenwald and Guren (2019).

16 For details, see Online Appendix A.2.

17 This is in the spirit of the Merton (1974) distance to default model. In this context, higher LTV ratio implies a smaller distance to default.

18 The default threshold is the level of income at which the default value is equal to the repayment value.

19 This is not crucial. In the US, households are excluded from credit markets for several years after foreclosure. Chatterjee et al. (2007) find a tractable way of modeling this by assuming a bankrupt household can be allowed to borrow again in credit markets with some exogenous probability. If we allowed defaulted households to return in this matter, then the Markov chain for the augmented state space would be irreducible.

20 We include only the nonleverage households’ consumption and housing because they are the only agents buying new homes. We also include the leverage households’ default decision because it affects equilibrium prices by increasing the supply of homes on the market.

21 This is derived in Online Appendix A.3.

22 The proof is in Online Appendix A.3.

23 The proof is in Online Appendix A.3.

24 This ignores the fact that leverage itself would raise the price level by increasing demand for housing. The point is that the expectation of foreclosure depresses house prices ceteris paribus.

25 One possible explanation is that Las Vegas has a larger share of homes owned by out-of-town investors who are more prone to default on their mortgages (Gao & Li, 2012).

26 This is a lower bound because instead of getting smaller loans (and buying smaller homes), some households will choose not to be homeowners (or delay homeownership).

27 Since ${\widehat{h}}_{-1}^i<h_{-1}^i$ for $\overline{\lambda }<1,$ the LTV reduces homeownership for the newly constrained households.

28 See Agarwal et al. (2020), An et al. (2021), Bandyopadhyay (2020), Bandyopadhyay and Yildirim (2020), Bhutta et al. (2017), Bradley et al. (2015), Campbell and Cocco (2014), Chinloy et al. (2017), Collins et al. (2015), Cunningham et al. (2021), Deng et al. (2000), Elul et al. (2010), Foote et al. (2008), Fuster and Willen (2017), Ganong and Noel (2020), Gerardi et al. (2018), Guiso et al. (2013), Gupta and Hansman (2019), Hardin and Marvin (1996), Hu (2019), Keys et al. (2012,) Laufer and Tzur-Ilan (2019), Low (2022), McCollum et al. (2017), Schelkle, 2018, Seiler (2015), Seiler and Walden (2016), Tzur-Ilan (2020), Wang et al. (2002).

29 Sometimes called the payment-to-income (PTI) ratio.

30 In contrast, a (hypothetical) perfectly ruthless borrower’s threshold would be $\overline{\mathit{\text{LTV}}}=100\%,$ and he would default once the house price falls below the mortgage balance $p_t<b_t=\$500,000.$

31 ψ is the intertemporal elasticity of substitution, $1/\psi$ is the risk aversion, σ is the intratemporal elasticity of substitution.

32 www.alexchinco.com/consumption-risk-in-modern-macro-finance-models/

33 This paper assumes the markets for rental housing and owner-occupied housing are segmented.

34 The cross-sectional distribution of leverage is taken from the data.

35 See Albanesi et al. (2017), Bhutta (2015), Foote et al. (2021), Gao and Li (2012), Haughwout et al. (2011), and Piskorski and Seru (2019).

36 It is not clear how many regained homeownership before the trough, which is when the calibration ends.

37 To my knowledge, this has not been done in the literature.

Additional information

Funding

This work was supported by Research Foundation of The City University of New York.