The cyclical dynamics of illiquid housing, debt, and foreclosures

Hedlund, Aaron Article The cyclical dynamics of illiquid housing, debt, and foreclosures Quantitative Economics Provided in Cooperation with: The Econometric Society Suggested Citation: Hedlund, Aaron (2016) : The cyclical dynamics of illiquid housing, debt, and foreclosures, Quantitative Economics, ISSN 1759-7331, The Econometric Society, New Haven, CT, Vol. 7, Iss. 1, pp. 289-328, https://doi.org/10.3982/QE483 This Version is available at: https://hdl.handle.net/10419/150410 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ Quantitative Economics 7 (2016), 289–328 1759-7331/20160289 The cyclical dynamics of illiquid housing, debt, and foreclosures Aaron Hedlund Department of Economics, University of Missouri This paper quantitatively accounts for the cyclical dynamics of key macroeconomic housing and mortgage market variables using a tractable, search-theoretic model of housing with equilibrium mortgage default. To explain these dynamics, the model highlights the importance of liquidity spirals that arise from the interaction of search frictions and endogenous credit constraints. During housing busts, longer selling times spill over into higher foreclosure risk, thereby magnifying the response of credit constraints to the depressed housing market. This contraction in credit then deepens the downturn. During booms, the reverse occurs. Based on these insights, I consider a foreclosure reform that makes all mortgages full recourse, and I show that implementing such a reform would reduce foreclosures and dampen housing dynamics. Keywords. Housing, liquidity, search theory, credit constraints, household debt, foreclosure. JEL classification. D31, D83, E21, E22, G11, G12, G21, R21, R31. 1. Introduction Much has been written about the recent unprecedented boom and bust in the U.S. housing market, which saw real house prices climb by 60% between 1998 and 2005 before subsequently falling by 30% from 2006 to 2010. House sales followed a similar run up and collapse, and many people have argued that the surge in foreclosure activity helped precipitate the Great Recession. Although frequently overlooked, months supply1—a measure that reflects average time on the market—exhibited equally dramatic behavior, jumping from 4months to over 11 months at the trough of the bust. This paper draws motivation from the experience of the past decade but takes a step back to look at the behavior of housing market dynamics over the period 1975–2010. Despite the fact that the housing and mortgage markets have undergone significant changes in the past two decades, some striking patterns emerge that link previous Aaron Hedlund: [email protected] I thank Dirk Krueger, Guido Menzio, Harold Cole, Kurt Mitman, Grey Gordon, David Weiss, Cezar Santos, and seminar participants at the Federal Reserve Bank of Richmond, the Federal Reserve Bank of St. Louis, Lancaster University, Royal Holloway University, the Congressional Budget Office, Baylor University, the Federal Reserve Bank of Dallas, Texas A&M, the Federal Reserve Bank of Kansas City, SUNY Albany, and the University of Missouri for many useful comments. I also thank Karl Schmedders and two anonymous referees for comments that helped improve the paper. Any errors are my own. Comments are welcome. 1Months supply equals the ratio of unsold inventories to the sales rate. Copyright ©2016 Aaron Hedlund. Licensed under the Creative Commons Attribution-NonCommercial License 3.0. Available at http://www.qeconomics.org. DOI: 10.3982/QE483 290 Aaron Hedlund Quantitative Economics 7 (2016) housing cycles to the one the United States just went through. First, real house prices, sales, and residential investment are procyclical and substantially more volatile than output. In fact, the high volatility of house prices remains a particularly difficult fact for the housing literature to explain. Months supply and foreclosures also demonstrate high volatility compared to output, but they move in a countercyclical manner. Prior to the Great Recession, months supply skyrocketed into the double digits during the early 1980s housing bust and nearly reached that level in the early 1990s. Last, aggregate mortgage debt tends to move in concert with housing aggregates: as prices and sales rise, so too does debt. This paper has three primary objectives. First, I seek to explain the previous stylized facts using a quantitative macroeconomic model of the U.S. economy that pays careful attention to some of the unique features of the housing and mortgage markets. Along the way, the model makes substantial progress in explaining other aspects of housing dynamics that continue to confound. Second, I investigate the degree to which two unique features of the housing and mortgage markets affect housing dynamics. Specifically, I look at the interaction of decentralized trade in the housing market—which makes housing an illiquid asset—and endogenous credit constraints that arise from the ability of homeowners to default on their mortgage obligations. Last, I consider the effects of a foreclosure reform that reduces debtor protections in an effort to discourage default. In service of the first objective, I develop a two-sector macroeconomic model that features uninsurable, idiosyncratic earnings risk, aggregate shocks to productivity, directed search in the housing market, and long-term defaultable mortgage debt. Directed search makes trade in the housing market a decentralized activity that affords a degree of price setting power to buyers and sellers. Specifically, buyers can choose which size and price of house they want to search for, while sellers can choose the price at which to attempt to sell their houses. As a result, equilibrium does not determine a unique market clearing price but rather an endogenous distribution of market tightnesses (and thus trading probabilities) corresponding to the range of submarkets for each house size and price combination. Given the presence of aggregate shocks and the nondegenerate, time-varying distribution of agents over individual wealth, debt, and income states, solving such a model could easily prove completely intractable. However, I extend the novel approach developed in Hedlund (2015) that establishes block recursivity in the housing market, which allows me to use the time path of one sufficient statistic—the shadow housing price—to calculate the dynamics of the entire distribution of house prices and trading probabilities. The introduction of one-period-lived real estate agents who passively intermediate trades between buyers and sellers allows me to obtain this result by following similar reasoning to that in Menzio and Shi (2010). This modeling innovation makes it possible to integrate housing markets with search frictions into an otherwise rich heterogeneous agent setting. Beyond this important theoretical contribution, the model proves quite successful quantitatively in matching the above stylized facts on the dynamics of house prices, sales, residential investment, months supply, foreclosures, and household portfolios. Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 291 Notably, the model generates co-movements and volatilities of house prices, existing sales, and months supply almost identical to those in the United States from 1975 to 2010. I should stress that the model calibration targets only first moments of the U.S. economy, so the success of the model in matching these dynamics arises solely from its various amplification and propagation mechanisms. Some of these mechanisms should appear familiar. In the model, shocks to productivity generate fluctuations in household income and equilibrium interest rates. During good economic times, households respond by increasing their consumption and their demand for housing. The increased demand for housing, combined with partially inelastic construction of houses, generates a boom in house prices and sales. The reverse chain of events occurs during downturns. In line with recent research by, among others, Head, Lloyd-Ellis, and Sun (2014) and Díaz and Jerez (2013), the introduction of search frictions propagates the effects of economic shocks across time. Similarly, as in Stein (1995), credit constraints in the mortgage market magnify the effect of income shocks. This paper makes several important strides forward by showing the importance of jointly considering search frictions and endogenous credit constraints. First, the interaction between the two generates liquidity spirals á la Brunnermeier and Pedersen (2009), where movements in the degree of housing market liquidity—as measured by the probability of trade—and in the degree of mortgage market liquidity—as measured by default spreads priced into new mortgages—reinforce each other. As first identified by Hedlund (2015), search frictions create substantial selling risk for homeowners. During housing downturns, homeowners must lower their price to avoid long selling delays. However, homeowners with large mortgages find themselves debt-constrained and forced to set a high price. As a result, heavily indebted homeowners may fail to quickly sell their house in the event of financial necessity, causing many of them to end up in foreclosure. The wave of mortgage defaults causes a flood of foreclosure properties to depress the housing market. To make matters worse, banks anticipate the heightened foreclosure risk during times of low house prices and liquidity and respond by pricing higher default premia into new mortgages. This chain of events cascades into a vicious cycle of decreasing prices, lower selling probabilities, higher foreclosures, and tighter credit. The reverse happens in booms. I quantify the impact of these liquidity spirals and conclude that they contribute an additional 20% volatility to house prices and 27% volatility to residential investment. The interaction of search frictions and endogenous credit also helps explain the prolonged, asymmetric nature of housing cycles. By delaying trades, search frictions spread out the impact of economic shocks on housing. Therefore, housing booms tend to evolve gradually and exhibit price momentum, as discussed in Case and Shiller (1989) and recently in Head, Lloyd-Ellis, and Sun (2014). However, the evolution of housing busts depends largely on their severity. During mild downturns, downward price stickiness emerges from a reluctance of homeowners to lower their price because they expect housing to rebound and because they took out long-term mortgages during more favorable conditions. However, after a post-boom large productivity drop, a spike in 292 Aaron Hedlund Quantitative Economics 7 (2016) foreclosures and distressed sales contributes to a precipitous drop in house prices, followed by a prolonged decline drawn out by debt overhang. These scenarios reflect the shallow U.S. housing bust in the early 1990s and the recent sharp downturn, respectively. Last, I consider the effects of a foreclosure reform that makes all mortgages legally as well as effectively full recourse. In particular, I allow banks to costlessly initiate deficiency judgments and seize up to 90% of the assets of foreclosed borrowers whose houses do not cover the full balance of their mortgage. I show that such a reform dramatically alters housing and foreclosure dynamics, with house price and residential investment volatilities dropping by 12% and 17%, respectively, and existing sales volatility increasing by over 38%. Furthermore, fluctuations in months supply drop by over 85% and foreclosures essentially disappear. Less cyclical movement in credit constraints and fewer high leverage borrowers prevent liquidity spirals from emerging, which explains much of the change in dynamics. However, even without liquidity spirals, the economy with recourse mortgages still generates protracted booms and busts. 1.1 Related literature This paper makes substantial theoretical and quantitative contributions to the modeling and understanding of housing market movements. In doing so, I build upon multiple areas of related research. One strand of the literature, including seminal papers by Stein (1995) and Ortalo-Magné and Rady (2006), establishes how credit constraints magnify income shocks and amplify house price movements. Even so, the literature has struggled to develop housing models that produce sufficient house price volatility. Davis and Heathcote (2005) make one of the earliest attempts and successfully generate sufficient volatility in residential investment, but not in house prices. Several recent papers model housing in an incomplete markets setting, such as Iacoviello and Pavan (2013),Kiyotaki, Michaelides, and Nikolov (2011),Ríos-Rull and Sánchez-Marcos (2008),Chu (2013),andFavilukis, Ludvigson, and Van Nieuwerburgh (2013). The latter two, along with Kahn (2009), make progress in generating volatile house prices and highlight the importance of inelastic construction, time-varying risk premia, and inelastic substitution between housing and consumption, respectively. However, none of the previous papers addresses all of the stylized facts described in the Introduction, including notably the strong countercyclicality of months supply and foreclosures. Another strand of the literature deviates from the Walrasian framework by developing search models of housing, as in early papers by Wheaton (1990) and Krainer (2001). Most related to my work here are recent contributions by Novy-Marx (2009),Burnside, Eichenbaum, and Rebelo (2014),Caplin and Leahy (2011),Díaz and Jerez (2013),and Head, Lloyd-Ellis, and Sun (2014).Novy-Marx (2009) and Díaz and Jerez (2013) both show how search frictions magnify shocks to fundamentals, with Díaz and Jerez (2013) emphasizing the importance of directed search, rather than random search, in housing markets. Burnside, Eichenbaum, and Rebelo (2014) introduce learning and social dynamics to generate housing booms that are only sometimes followed by busts. Head, Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 293 Lloyd-Ellis, and Sun (2014) generate house price momentum in a city-level model of housing with free entry of buyers. I add to this literature by integrating a frictional, decentralized housing market into a fully closed production economy with imperfect credit markets and substantial household heterogeneity, which allows me to simultaneously address all of the major stylized facts on housing, debt, and foreclosure dynamics. My paper also fits into the literature on mortgage default. Mitman (2014), Hintermaier and Koeniger (2011), and Jeske, Krueger, and Mitman (2013) study foreclosures in an environment with one-period mortgages, which forces homeowners to refinance each period. Chatterjee and Eyigungor (2015),Corbae and Quintin (2015),andGarriga and Schlagenhauf (2009) analyze foreclosures in steady state and transition with longterm mortgage contracts. I extend this work by studying foreclosure dynamics with longterm mortgages and aggregate uncertainty. Last, my paper complements Menzio and Shi (2010) and Hedlund (2015) by utilizing block recursivity to develop a directed search model of housing with two-sided heterogeneity and computationally tractable aggregate dynamics. A supplementary appendix with additional figures, calibration and computation details, and replication files can be found on the journal website, http://qeconomics.org/supp/483/supplement.pdf and http://qeconomics.org/supp/483/code_and_data.zip. 2. The model 2.1 Households Households inelastically supply one unit of time to the labor market and are paid wage w per unit of stochastic labor efficiency e·s,wheres∈Sfollows a finite Markov chain with transitions πs(s|s) and eis drawn from the cumulative distribution function F(e) with compact support E⊂R+. Households initially draw sfrom the invariant distribution Πs(s). Households derive utility from composite consumption cand housing services ch. Homeowners with house size h∈H={hh2h3}receive a dividend ch=hof housing services each period, while renters purchase housing services ch∈[0h]from a competitive spot market at price rh(relative to the numeraire consumption good). All homeowners are owner–occupiers and can only own one house at a time. Households save by purchasing one-period bonds with price qb∈(01)from financial intermediaries. Homeowners also have the option to borrow against their house with mortgage debt. I detail the structure of mortgage contracts in the financial intermediaries section. 2.2 Consumption good sector Consumption good firms operate a constant returns to scale production function using capital Kcand labor Ncto produce composite consumption Yc=zcFc(KcNc) 294 Aaron Hedlund Quantitative Economics 7 (2016) Total factor productivity zcfollows a finite state Markov chain with transition probabilities πz(z c|zc). Firms rent capital from financial intermediaries at rental rate rand pay wage wper unit of labor efficiency. Output can be consumed, added to the capital stock, or used to build new housing. Let Zdenote the aggregate state of the economy, which I describe in detail later. The profit maximization conditions of the composite good firm are r(Z)=zc ∂Fc(KcZNc(Z) ∂Kc (1) w(Z)=zc ∂FcKc(Z)Nc(Z) ∂Nc (2) 2.2.1 Housing services for renters Landlords convert the consumption good into housing services at the rate Ahusing a linear, reversible technology and sell these housing services competitively at price rh. The profit maximization condition of landlords is rh=1 Ah (3) 2.3 Construction sector Construction firms operate a constant returns to scale production function using land/ permits L, structures Sh, and labor Nhto produce new housing Yh=Fh(L ShNh) Firms purchase new land/permits from the government at price pl,paywagewper unit of labor efficiency, and purchase structures Shfrom the consumption good sector. The government supplies a fixed amount ¯ L>0of new land/permits each period, and all revenues go to unproductive government spending. Construction firms sell new houses in discrete sizes h∈Hdirectly to real estate firms at price phand do not experience any building delays. Individual houses depreciate stochastically with probability δh.2In the aggregate, the housing stock evolves according to H=(1−δh)H +Y h The profit maximization conditions of construction firms are pl(Z)=ph(Z)∂FhL(Z)Sh(Z)Nh(Z) ∂L (4) 1=ph(Z)∂FhL(Z)Sh(Z)Nh(Z) ∂Sh (5) 2Complete depreciation averts the need to deal with situations where mortgaged homeowners suddenly find themselves under water because a portion of their house depreciates. As I discuss later, I assume complete mortgage forgiveness in the low probability event that a house depreciates. Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 295 w(Z)=ph(Z)∂FhL(Z)Sh(Z)Nh(Z) ∂Nh (6) 2.4 Real estate sector The real estate sector is populated by a continuum of real estate firms that facilitate housing trades between buyers and sellers. In the absence of a centralized market, buyers and sellers match bilaterally with real estate agents in an environment with search frictions. First, sellers attempt to match with real estate agents to sell their house. Next, buyers attempt to match with real estate agents to purchase a house recently sold by a seller. Real estate firms simply act as conduits to transfer houses from sellers to buyers, but greatly improve the tractability of the model, as I discuss later. 2.4.1 Decentralized house selling Sellers direct their search to real estate agents by choosing a selling price xs≥0for their house h∈H. Formally, sellers choose xsto enter submarket (xsh)∈R+×H. Sellers commit to the selling price, conditional on successfully matching with a real estate agent, and pay utility cost ξif they fail to match.3 Real estate firms hire a continuum Ωs(xsh)of real estate agents to enter each submarketatcostκsh. The ratio of real estate agents to sellers in submarket (xsh),ormarket tightness, is θs(xsh)≥0, and is determined in equilibrium.4A seller in submarket (xsh)successfully matches with a real estate agent with probability ps(θs(xsh)), while a real estate agent in submarket (xsh)successfully matches with a seller with probability αs(θs(xsh))=ps(θs(xsh)) θs(xsh) . The function ps:R+→[01]is continuous and strictly increasing with ps(0)=0,andαsis strictly decreasing. Real estate agents may match with multiple sellers if αs>1, but sellers always match with at most one real estate agent. By the law of large numbers, real estate firms know exactly how many matches agents will have with sellers, and to ensure that real estate firms are passive market participants, I do not allow them to hold housing inventories. Agents and sellers take θs(xsh) parametrically. 2.4.2 Decentralized house buying Buyers direct their search to real estate agents by choosing a submarket (xbh) with purchase price xb≥0and house size h∈H.Buyers match with a real estate agent with probability pb(θb(xbh))and agents match with a buyer with probability αb(θb(xbh))=pb(θb(xbh)) θb(xbh) ,whereθb(xbh)is the market tightness. The functions pband αbhave the same properties as psand αs, respectively. Successful buyers immediately move into their house, while unsuccessful buyers remain as renters until the next period. Real estate firms hire a continuum Ωb(xbh)of real estate agents to enter each submarket at cost κbhper agent. Real estate agents and buyers take θb(xbh)parametrically. 3The utility cost discourages homeowners who are nearly indifferent about selling from posting a selling price that causes their house to take extremely long to sell. 4In unvisited submarkets, θs(xsh)is an out-of-equilibrium belief that helps determine equilibrium behavior. 296 Aaron Hedlund Quantitative Economics 7 (2016) 2.4.3 Market tightnesses Real estate firms purchase new housing Yhand hire agents Ωs and Ωbto intermediate trades between buyers and sellers, solving max Yh≥0Ωs(xsh)≥0 Ωb(xbh)≥0 −κsh+αsθs(xsh;Z)(−xs)Ωs(dxsdh)−ph(Z)Yh +−κbh+αbθb(xbh;Z)xbΩb(dxbdh) (7) subject to Yh+hαsθs(xsh;Z)Ωs(dxsdh)≥hαbθb(xbh;Z)Ωb(dxbdh) where the constraint (with multiplier μ(Z)) reflects the fact that all houses the real estate firm sells to buyers it must first acquire from sellers. Profit maximization implies μ(Z)=ph(Z)and that market tightnesses satisfy κbh≥αbθb(xbh;Z)xb−ph(Z)hand (8) θb(xbh;Z)≥0with comp. slackness κsh≥αsθs(xsh;Z)ph(Z)h −xsand (9) θs(xsh;Z)≥0with comp. slackness 2.5 Financial sector Intermediaries trade bonds b∈B>0and mortgages m∈M>0with households, accumulate capital to rent to firms, and manage their stock of repossessed foreclosure housing. Capital evolves according to K=(1−δc)K +I Intermediaries have access to international bond financing at interest rate i,although I focus on the closed economy case (zero net supply). 2.5.1 Mortgages Borrowers who take out a mortgage of size mreceive q0 mmat origination, where q0 m∈(01)is the mortgage price. Perfect competition partitions the mortgage market by loan size and borrower characteristics, and causes intermediaries to earn zero expected profits loan-by-loan.5Therefore, mortgage prices q0 mdepend on the initial balance m, the borrower’s house size h, the aggregate state of the economy Z,andthe borrower’s initial savings band persistent labor efficiency component s. 5The government distributes all ex post profits/losses to households through a proportional wealth tax/subsidy τ. This arrangement bypasses the need to explicitly assign ownership of intermediaries. Instead, intermediaries are risk-neutral entities that discount the future at the international bond rate i. Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 303 3.1 Model specification 3.1.1 Households Preferences Households have constant elasticity of substitution utility with constant relative risk aversion: u(cch)=ωc(ν−1)/ν +(1−ω)c(ν−1)/ν hν/(ν−1)1−σ 1−σ I follow Kahn (2009) and Flavin and Nakagawa (2008) and set the intratemporal elasticity of substitution to ν=013.12 I determine the discount factor βand risk aversion σ jointly. Labor efficiency Log labor efficiency, ln(e ·s) =ln(s) +ln(e), follows lns=ρsln(s) +ε ε∼N0σ2 ε ln(e) ∼N0σ2 e Icalibrateρs,σε,andσefollowing Storesletten, Telmer, and Yaron (2004),withsome modifications that I explain in the Appendix. Computationally, I truncate ln(e) and discretize ln(s) with a three-state Markov chain using the Rouwenhorst method. 3.1.2 Production sectors I specify Cobb–Douglas production functions in both sectors: Yc=zcAcKαKN1−αK cY h=LαLSαS hN1−αS h1−αL I normalize mean quarterly earnings to 025 using Ac,andIsetαK=026, following Díaz and Luengo-Prado (2010).Theshockzcfollows lnz c=ρzln(zc)+ε z εz∼N0σ2 εz with standard values ρz=095 and σ2 εz=0007.Idiscretizezcwithathree-stateMarkov chain using the Rouwenhorst method. In the construction sector, I follow Favilukis, Ludvigson, and Van Nieuwerburgh (2013) and set the structures share to αS=03. I set the land share to αL=033 based on data from the Lincoln Institute of Land Policy.13 Following Harding, Rosenthal, and Sirmans (2007),Isetδh=000625, which corresponds to a 25% annual housing depreciation rate. I normalize ¯ L=1and determine the housing services technology Ahjointly. 12See also Li, Liu, Yang, and Yao (2015). These papers find empirical evidence of a unit income elasticity for housing expenditures but a price elasticity substantially below 1. 13Available at http://www.lincolninst.edu/subcenters/land-values/price-and-quantity.asp. 304 Aaron Hedlund Quantitative Economics 7 (2016) 3.1.3 Real estate sector I specify constant elasticity of substitution matching functions. Therefore, buying (j=b) and selling (j=s) trading probabilities are pj(θj)=minAjθj 1+θγj j1/γj1and αj(θj)=pj(θj) θj  The Appendix gives the analytical characterization of trading probabilities for given ph. I jointly calibrate Aj,κj,γj, and utility cost ξ. 3.1.4 Financial sector I set the mortgage origination cost to 2% (ζ=002), consistent with reports from the Federal Housing Finance Board of typical closing costs of 1%– 3%.14 I set the servicing cost φ=415 ×10−5to achieve a 265% spread between steady state mortgage interest rates 1+rm=(1+φ)(1+i) 1−δhand bond yields 1+i. The annual capital depreciation rate is 10%, implying quarterly δc=0025. 3.1.5 Foreclosures and legal environment Isetγf=095 to give an expected credit flag duration of 5years.15 I jointly calibrate the REO sale loss χand search efficiency λ. 3.2 Joint calibration Following Hedlund (2015), I divide the targets of the joint calibration into three categories: macroeconomic aggregates, household financial data, and housing market data. The calibration is summarized in Table 1. 3.2.1 Macroeconomic aggregates Itargeta15% housing services-to-GDP ratio and, following Díaz and Luengo-Prado (2010), a nonresidential capital-to-GDP ratio of 164.16 3.2.2 Household financial data I use the 1998 Survey of Consumer Finances to target selected asset and debt statistics. I target mean homeowner housing wealth relative to normalized earnings of 362 and mean mortgage debt, conditional on having a mortgage, of 203, using phto valuate housing wealth. 3.2.3 Housing market data Itargeta64% home ownership rate, an annual foreclosure rate of 14%, an average foreclosure price discount of 22% as reported by Pennington- Cross (2006), an average foreclosure house selling time of 52 weeks, and mean buyer and seller search durations of 10 weeks and 17 weeks, respectively.17 To calculate search durations, I assume that housing trades in period toccur uniformly between tand t+1, as in Caplin and Leahy (2011). Trading after nperiods corresponds to a search time of (n +05)×12 weeks. 14Mortgage rates and fees can be found at http://www.fhfa.gov/Default.aspx?Page=252. 15Fannie Mae and Freddie Mac do not generally underwrite mortgages to borrowers with foreclosure records until after 5years. 16Housing services in the model equal rhchfor renters and rhhfor homeowners. 17Sources: The Census Bureau, the National Delinquency Survey, and the National Association of Realtors. The foreclosure selling duration implicitly includes any legal delays. Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 305 Table 1. Model calibration. Parameter Value Target Description Target Model Parameters determined independently Preferences ν013 Intratemporal elasticity of substitution Stochastic labor endowment ρs0952 Autocorrelation of persistent shock σe049 Standard deviation of transitory shock σε017 Standard deviation of persistent shock Production technologies ρz095 Autocorrelation of technology shock σ2 εz0007 Variance of technology shock αK026 Nonresidential capital share 26% 26% αL033 Land share in construction 33% 33% αS030 Residential structures share 30% 30% δc0025 Annual nonresidential capital depreciation 10% 10% δh000625 Annual housing depreciation 25% 25% Financial sector φ415e−5Mortgage interest rate spread 265% 265% ζ002 Mortgage origination fee 2% 2% Legal environment γf095 Average years duration of foreclosure flag 55 Parameters determined jointly Preferences β096397 Nonresidential capital to GDP 164 162 ω148e−7Homeowner housing wealth to earnings 362 362 σ470 Borrower mortgage debt to earnings 203 205 Production technologies Ac021609 Mean quarterly labor earnings 025 025 Ah54757 Housing services to GDP 15% 15% Housing markets h292 Home ownership rate 64% 647% γb255 Buyer search duration in weeks 10 996 Ab10065 Minimum buying premium 05% 05% κb0005 Maximum buying premium 25% 25% ξ0013 Seller search duration in weeks 17 1696 As22917 Average realtor fees 6% 6% κs01375 Maximum selling discount (incl. realtor fees) 20% 20% γs069 Annual foreclosure rate 14% 137% Foreclosure sales χ01199 Foreclosure selling price discount 22% 2195% λ04051 REO time on the market in weeks 52 5205 For buyers, I target a minimum buying premium xb(ph)/phhof 05% and a maximum buying premium xb(ph)/phhof 25%, consistent with Gruber and Martin (2003). For sellers, I target a minimum selling discount where sellers are guaranteed to immediately sell, (phh−xs(ph))/phh,of6% to match direct realtor expenses in the data. I target a maximum selling discount (phh−xs(ph))/phhof 20%, consistent with findings 306 Aaron Hedlund Quantitative Economics 7 (2016) in Garriga and Schlagenhauf (2009) and evidence from pre-foreclosure sales price discounts.18 4. Results I begin this section by describing the baseline model results. Next, I assess the dynamic effects of search frictions and their interaction with the mortgage market. Last, I analyze the impact on housing dynamics of a foreclosure law reform that makes all mortgages full recourse. I summarize the main takeaways as follows: 1. House prices and sales are strongly procyclical and volatile; time on the market and foreclosures are strongly countercyclical and volatile. 2. The interaction of search frictions and endogenous mortgage credit generates liquidity spirals that magnify house price swings due to the spillover of house selling risk to foreclosure risk. 3. The combination of search frictions, endogenous credit, and equilibrium default generates house price movements that exhibit short-run momentum as well as asymmetric boom–bust dynamics. 4. Enacting stringent foreclosure recourse laws dampens house price dynamics and substantially reduces foreclosures. 4.1 Baseline results To evaluate the performance of the baseline economy, I compare the dynamics of Hodrick–Prescott (HP)-filtered time series generated by the model to the equivalent HP- filtered series in the U.S. data from 1975 to 2010.19 4.1.1 Housing and foreclosure dynamics Table 2reports the co-movement of existing homeowner sales with house prices, the foreclosure rate, and months supply, which proxies for average selling time on the market.20 In the data, sales exhibit significant positive co-movement with house prices and negative co-movement with months supply and the foreclosure rate. The baseline model successfully matches these co-movements, both qualitatively and quantitatively. Furthermore, both the model and the data feature procyclical prices and existing sales alongside countercyclical months supply and foreclosures, as shown in Table 3. To understand these dynamics, recall that productivity shocks are the source of fluctuations in the model. A positive shock to aggregate productivity increases incomes, 18RealtyTrac reports pre-foreclosure discounts ranging from 128% to 3494%. Unlike REOs, which sell at a discount largely because of degradation caused by extended vacancy, pre-foreclosure houses are likely to sell at a discount because of financial urgency to sell. 19I omit 2011–2014 because of the recent spate of legal and industry practice changes in the housing and mortgage markets. Due to the protracted nature of housing booms and busts, I use a smoothing parameter of 108to avoid excessively removing variation. 20I ignore new sales because construction firms sell new housing in nondiscrete units of “putty–clay” to real estate firms. However, I do analyze the value of new housing, that is, residential investment. Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 307 Table 2. Housing co-movements. Data Model Corr(salesprices)050 059 Corr(salesmonths supply)−068 −074 Corr(salesforeclosure rate)−065 −048 Note: Model sales consists of all sales by existing owners. Sales data are the existing sales series reported by the National Association of Realtors. Table 3. Housing dynamics. σx/σoutput ρxoutput xData Model Data Model House prices 207 190 050 095 Existing sales 393 435 073 013 Months supply 611 646 −044 −088 Foreclosure rate 496 1632 −064 −088 Note: Relative standard deviations and correlations with gross domestic product (GDP) of HP-filtered time series. See Table 11 in the Appendix for definitions and sources. Figure 1. Selling price, selling probability, and time on the market (TOM) as a function of cash at hand for homeowners wishing to upgrade. which leads to higher demand for housing and a textbook response of higher prices and sales. However, standard competitive models of housing cannot account for the decrease in months supply. Under perfect competition, homeowners can only respond to changing market conditions by deciding whether or not to sell their house at the market price. However, in a decentralized housing market with search frictions, homeowners have some price-setting power. Figure 1plots homeowners’ choice of selling price as a function of cash at hand. As the first panel of the figure shows, homeowners with low cash at hand do not wish to 308 Aaron Hedlund Quantitative Economics 7 (2016) move and therefore do not put their house on the market. However, as cash at hand increases, homeowners gradually lower their selling price to sell more quickly. When the shadow housing price phincreases, more real estate agents enter the market to match with sellers, driving up market tightnesses θs(xsh)and seller trading probabilities ps(θs(xsh)) at every listing price xs. In response to the improvement in trade probabilities, homeowners sell more quickly and at a higher price because they increase xsby less than the change in ph. Therefore, unlike in competitive models of housing, selling behavior with search frictions adjusts along both the price and selling time margins. The countercyclicality of foreclosures can be attributed to three effects. First, homeowners can better afford mortgage payments when they have higher incomes during economic expansions. Second, the increase in selling probabilities from higher ph makes it easier for distressed homeowners to sell their houses. Last, both higher incomes and higher trading probabilities loosen credit constraints, which makes refinancing easier. I delve into these effects in my discussion of the effects of search frictions. Also consistent with the data, the model generates significant volatility in prices, sales, months supply, and foreclosures. The model’s almost exact matching of price, sales, and months supply volatilities represents a particular success, given the difficulty the literature has had in generating sufficient volatility for even a subset of these variables. Search frictions and fluctuations in endogenous credit constraints (determined by mortgage prices q0 m) play an important role in amplifying housing dynamics—channels that I explore momentarily. Though the model generates significantly higher foreclosure volatility than in the data, much of the apparent difference arises because of higher frequency fluctuations in the model, rather than larger absolute swings. During model simulations, the foreclosure rate fluctuates between 02% and 175%, which is in line with empirical foreclosure rate fluctuations before the Great Recession. Furthermore, if I expand the foreclosure rate to include all mortgages 90+days late, the empirical relative volatility nearly doubles to 892.21 4.1.2 Consumption, investment, and portfolio dynamics Turning to standard business cycle variables, Table 4shows that the model generates consumption and investment dynamics that mimic those in the data. The model and empirical volatilities of aggregate consumption and investment correspond almost exactly, and the model matches the relative volatilities of each component of investment reasonably well. In particular, the model generates 83% of the empirical volatility in residential investment. Volatile house prices largely drive these swings in residential investment—first, by causing fluctuations in the value of new housing and, second, by generating strong responses in construction, even with the constraining impact of fixed new land/permits. In fact, a moderate amount of inelasticity in construction actually contributes to higher residential investment volatility by magnifying house price movements. 21The foreclosure rate is also likely to be less volatile in the data because banks do not generally immediately foreclose on borrowers in the early stages of a housing bust, while they do in the model. Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 309 Table 4. Consumption, investment, and portfolio dynamics. σx/σoutput ρxoutput xData Model Data Model Consumption 065 055 092 093 Composite 072 062 091 094 Housing 060 033 055 075 Investment 297 299 094 096 Nonresidential 269 293 078 092 Residential 515 429 092 090 Financial assets 176 161 065 091 Mortgage debt 164 267 022 085 Note: Relative standard deviations and correlations with GDP of HP-filtered time series. See Table 10 in the Appendix for definitions and sources. Reflecting the importance of wealth and debt heterogeneity, both the model and the data demonstrate interesting cyclical behavior of household portfolios. Financial assets, housing wealth, and mortgage debt are all procyclical and more volatile than GDP. As Table 4demonstrates, the model almost exactly matches the relative volatility of assets. The model also generates procyclical, volatile mortgage debt—to excess, in fact—though the model performs well compared to the recent literature. For example, Iacoviello and Pavan (2013) generate almost four times the mortgage volatility as in the data. The fact that households increase assets and debt during economic upturns implies that households do not single-mindedly use their improved financial position to deleverage. Instead, households take on increased mortgage debt to purchase more housing and simultaneously insure themselves against the future risk of an economic downturn. By borrowing more during periods with loose credit constraints, households use the funds to purchase assets for precautionary saving, rather than being forced to borrow to smooth consumption during downturns when credit constraints are tight. Figure 6in the Appendix graphically summarizes the economic response to a small, persistent increase in zc. 4.1.3 Theroleoflandandconstruction Although this paper focuses on other novel mechanisms, Chu (2013) and Kahn (2009) point out the importance of land as a fixed factor in generating housing market volatility. In the current calibration, the share of land is 33%, in line with national data. However, Table 5shows the impact of two alternative values of the land share. First, I consider a higher land share of 08as in San Francisco. Second, I look at a land share of 015 as in Houston. Note that I do not change any other aspect of the calibration to match the economies in San Francisco or Houston. As such, Table 5should be interpreted as a comparative dynamics exercise rather than an analysis of regional housing dynamics. Strikingly, a large increase in the land share from 033 to 08only magnifies house price swings by 15%, while a decrease in the land share to 015 dampens house price dynamics by almost 30%. This same asymmetry shows up in the impact of land on sales, 310 Aaron Hedlund Quantitative Economics 7 (2016) Table 5. Dynamics with different land shares. σx/σoutput xBaseline αL=08αL=015 House prices 190 220 138 Existing sales 435 602 211 Months supply 646 696 472 Foreclosure rate 1632 2559 937 Residential investment 429 257 502 Note: Relative standard deviations and correlations with GDP of HP-filtered time series. See Table 11 in the Appendix for definitions and sources. Table 6. Dynamics without search frictions. σx/σoutput xData Baseline No Search Investment 297 299 309 Nonresidential 269 293 324 Residential 515 429 338 House prices 207 190 158 Existing sales 393 435 815 Months supply 615 646 – Foreclosure rate 496 1632 – months supply, and the foreclosure rate. The reverse pattern shows up in residential investment, however. The direct dampening effect of a higher land share on construction volatility is counteracted by the effect of endogenously higher house price volatility. This indirect price effect is small when moving from αL=033 to αL=08but shows up strongly at αL=015. Overall, the volatility of residential investment exhibits an inverse U-shape in the land share. 4.2 Search frictions and housing dynamics Search frictions greatly influence housing and foreclosure dynamics. To determine the effects of search, I compare the baseline economy to the limit economy with frictionless, competitive housing. Contrasting the dynamics of these two economies, three differences stand out. First, months supply does not fluctuate in the no-search economy because houses always sell instantly, and foreclosures almost disappear.22 Second, the co-movement between sales and prices decreases from 059 to 027. Third, the volatilities of residential investment and house prices decline substantially while existing sales volatility nearly doubles, as shown in Table 6. Below, I explain the mechanisms behind these results as well as how search frictions help resolve other housing puzzles. 22The foreclosure rate fluctuates between 0% and 014% in the no-search economy. Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 311 Figure 2. Selling discount, selling probability, and TOM as a function of mortgage debt (normalized by phlowh) for homeowners wishing to downsize or rent. 4.2.1 Liquidity spirals and amplification One of the major successes of the model is its ability to generate sufficient volatility in house prices and residential investment. Though other factors also contribute to these large swings, search frictions generate an additional 20% volatility in prices and 27% volatility in residential investment. This amplification primarily occurs because of liquidity spirals akin to those in Brunnermeier and Pedersen (2009) that arise from the interaction of search-based housing illiquidity with endogenous mortgage credit constraints. To explain the nature of liquidity spirals, I appeal to the discussion in Hedlund (2015) that establishes a link between search risk and foreclosure risk. Figure 2shows the optimal relative selling price xs/phh, selling probability, and expected time on the market as a function of mortgage debt for sellers wishing to downsize or rent. Selling price is almost invariant to mortgage debt for low values of leverage but exhibits strong nonmonotonicity as leverage approaches and exceeds an 80% loan-to-value ratio. When leverage hits moderately high levels, low asset homeowners trying to avoid financial insolvency become “distressed sellers” who sharply reduce their selling price to quickly unload their house. These sellers have sufficient home equity to absorb large losses but are unable to extract equity through refinancing because intermediaries view them as risky borrowers. With even higher leverage, homeowners have insufficient equity to sharply lower their selling price. Instead, debt overhang forces these sellers to set high prices, which causes their houses to sit longer on the market.23 Eventually, some sellers default and enter foreclosure, and an influx of REO houses for sale occurs that depresses the housing market. Banks anticipate this behavior and price higher default premia into new mortgages during times of lower prices and worse housing liquidity, thus exacerbating the debt overhang problem. These higher default premia tighten access to credit, which simultaneously makes refinancing more difficult and prevents new buyers from entering the 23Genesove and Mayer (2001) confirm this selling behavior empirically. 312 Aaron Hedlund Quantitative Economics 7 (2016) Figure 3. Example mortgage default premia. housing market to prop up prices and liquidity. In short, search magnifies booms because higher prices increase selling probabilities, which reduces foreclosures, lowers default premia, and loosens credit constraints, resulting in even higher prices. During simulations of the baseline economy, average default premia for newly originated mortgages with 80%+leverage fluctuate between 03% and 2%, while average default premia fluctuate between 05% and 35% for 90%+leverage mortgages and between 0% and 6% for 95%+leverage mortgages.24 By contrast, less default risk and fewer high leverage borrowers in the no-search economy generate only trivial default premia, as in Figure 3. 4.2.2 Momentum and asymmetry in housing dynamics Besides amplifying movements in house prices and residential investment, search frictions help resolve two important house price puzzles. First, house prices exhibit short-run momentum, as documented in Case and Shiller (1989),Capozza, Hendershott, and Mack (2004),Head, Lloyd-Ellis, and Sun (2014), and several other papers. Second, house price busts tend to be slower and shallower than booms—with some notable exceptions—which suggests a degree of downward price stickiness.25 The baseline model generates dynamics consistent with both of these phenomena, as shown in Figure 4. Specifically, the model generates prolonged booms followed at times by mild slumps, as in the second panel, or else by sharp crashes and prolonged slumps, as in the last panel. These dynamics mimic the shallow U.S. housing bust in the early 1990s and the recent sharp, prolonged housing bust, respectively. Search frictions help generate house price momentum in two ways. First, search frictions spread out the impact of economic shocks. Trading delays simultaneously reduce existing sales volatility from 815 to 435 and increase the co-movement of sales and prices from 027 to 059. Furthermore, these trading delays cause current house prices to improve current and future liquidity, which raises the resale value of housing and 24In fact, these fluctuations actually understate the cyclicality of credit constraints because homeowners are unlikely to take out mortgages with exceptionally high default premia. 25See, for example, Case and Quigley (2008) and Genesove and Mayer (2001). Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 319 from this stabilization comes to 079%. Renters come out slightly ahead due to the reform, while heavily indebted homeowners still experience welfare losses. However, the magnitude of the losses drops significantly. Last, the correlation between house prices and W (Z)is 057 for the overall population and −065 for renters. Renters prefer the implementation of the policy to occur at the trough of a housing bust because they expect prices to rise and would benefit from a greater supply of credit. Homeowners, on the other hand, suffer a smaller welfare loss if the policy gets enacted during a boom, when the insurance value of default is already smaller. As a caveat, the model omits several ingredients that could bias the welfare effects of this policy reform. First, the model abstracts from life cycle considerations. Young households that experience binding credit constraints may benefit more from the increase in credit that accompanies the reform. On the other hand, these same households may place greater value on the default option. In addition, the model does not feature any goods or labor market frictions that could generate larger spillovers from housing to the rest of the economy. Taking such channels into account may increase the stabilization benefits of the reform. 5. Conclusions Search frictions in the housing market interact with endogenous credit constraints to produce quantitatively accurate housing, mortgage debt, and foreclosure dynamics. The liquidity spirals and gradual boom–bust dynamics generated by the model accord strongly with the data, making the model a good launching point for future theoretical and policy-related research. Furthermore, the tractable formulation of directed search in the housing market with rich, two-sided heterogeneity and aggregate uncertainty allows the model to address issues that affect housing simultaneously through financial and nonfinancial channels. For example, future work could look at the role of state variation in credit conditions, housing supply factors, and government policy in explaining different regional house price dynamics. Alternatively, the model provides a useful framework in which to analyze optimal monetary and fiscal policy with frictional housing. 320 Aaron Hedlund Quantitative Economics 7 (2016) Appendix Figure 6. Economic response to a small, 10-year increase in zc. With the exception of months supply, the foreclosure rate, and the foreclosure sales share, each series is initially normalized to 1and is plotted alongside the output of the consumption good (the light curve) for reference. Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 321 Definition 1. A recursive equilibrium consists of •household value and policy functions; •production firm functions Kc(Z),Nc(Z),L(Z),Sh(Z),andNh(Z); •intermediary functions JREO(h;Z),RREO(h;Z),xREO s(h;Z),andK(Z); •prices rh,qb(Z),i(Z),rm(Z),r(Z),w(Z),pl(Z),ph(Z),andq0 m(mbhs;Z); •market tightnesses θb(xbh;ph(Z)) and θs(xsh;ph(Z)); •an aggregate law of motion Z=G(Zz c); such that the following statements hold: 1. Household Optimality: The value/policy functions solve (15)–(22). 2. Firm Optimality: Conditions (1)–(6) are satisfied. 3. Intermediary Optimality: Conditions (10)–(13) are satisfied. 4. Market Tightnesses: The variables θsand θbsatisfy (8)and(9). 5. Shadow Housing Price:WehaveDh(ph(Z);Z)=Sh(ph(Z);Z). 6. Land/Permits:WehaveL(Z)=¯ L. 7. Labor Market Clears:WehaveNc(Z)+Nh(Z)=s∈SEe·sF(de)Πs(s). 8. Capital Market Clears:WehaveKc(Z)=K(Z). 9. Bond Market Clears: There is no active trading of international bonds. 10. Resource Constraint: Total use of the consumption good equals total production, zcF(Kc(Z) Nc(Z)). 11. Aggregate Law of Motion: The law of motion Z=G(Zz c)is consistent with the Markov process induced by the exogenous processes πs,πz,andF, and all relevant policy functions. 322 Aaron Hedlund Quantitative Economics 7 (2016) Table 9. Standard business cycle statistics. xσ x/σYρxY ρxx x/Y Data Output (Y)100 100 072 100 Consumption 065 092 080 081 Composite 072 091 079 066 Housing 060 055 081 015 Investment 297 094 063 020 Nonresidential 269 078 051 014 Residential 515 092 077 005 Baseline Output (Y)100 100 087 100 Consumption 055 093 094 079 Composite 062 094 094 064 Housing 033 075 097 015 Investment 299 096 081 021 Nonresidential 293 090 077 016 Residential 429 090 093 004 No Search Output (Y)100 100 086 100 Consumption 056 093 094 080 Composite 061 094 094 065 Housing 034 082 096 015 Investment 309 096 079 020 Nonresidential 324 091 075 015 Residential 338 091 095 004 Recourse Output (Y)100 100 086 100 Consumption 057 093 094 079 Composite 064 094 094 064 Housing 029 077 096 015 Investment 293 096 080 021 Nonresidential 301 091 076 017 Residential 357 089 093 004 Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 323 Table 10. Lagged correlations—output, consumption, and investment. Cross-Correlation of Output With xσ x/σYx(−4)x(−3)x(−2)x(−1)xx(+1)x(+2)x(+3)x(+4) Data Output (Y)100 066 078 089 097 100 097 090 082 073 Consumption 065 065 075 084 090 092 090 086 081 075 Composite 072 065 075 084 089 091 089 086 081 075 Housing 060 024 028 032 037 041 045 048 049 048 Investment 297 056 069 080 089 094 090 083 073 062 Nonresidential 269 033 045 058 069 077 076 070 060 049 Residential 515 074 082 089 091 090 084 077 070 063 Baseline Output (Y)100 087 090 093 097 100 097 093 090 087 Consumption 055 079 083 086 090 093 092 092 091 090 Composite 062 080 084 087 091 094 093 092 092 091 Housing 033 061 064 067 070 074 075 075 076 076 Investment 299 085 088 091 094 096 092 087 082 077 Nonresidential 293 080 083 085 088 090 084 078 072 066 Residential 429 077 081 084 087 090 090 089 089 088 No Search Output (Y)100 086 089 093 097 100 096 093 089 086 Consumption 056 079 082 085 089 093 092 091 091 090 Composite 061 079 083 086 090 094 093 092 091 090 Housing 034 069 072 076 079 082 083 083 083 082 Investment 309 083 086 090 093 096 091 085 080 075 Nonresidential 324 079 082 085 088 091 085 078 072 066 Residential 338 078 081 084 087 091 091 091 090 089 Recourse Output (Y)100 086 090 093 097 100 097 093 090 086 Consumption 057 079 082 086 089 093 092 092 091 090 Composite 064 079 083 086 090 094 093 092 091 090 Housing 029 063 066 070 073 077 078 078 079 079 Investment 293 084 087 090 093 096 091 085 080 075 Nonresidential 301 080 082 085 088 091 084 078 072 066 Residential 357 076 079 082 086 089 089 089 088 087 Note: Quarterly data come from National Institute of Pension Administrators (NIPA) Table 1.5.5 and are deflated using the personal consumption expenditures (PCE) index. Data and model output are detrended with λ=108using the HP filter. 324 Aaron Hedlund Quantitative Economics 7 (2016) Table 11. Lagged correlations: house prices, sales, months supply, and foreclosures. Cross-Correlation of Output With xσ x/σYx(−4)x(−1)x(−2)x(−3)xx(+1)x(+2)x(+3)x(+4) Data Output (Y)100 066 078 089 096 100 097 090 082 073 House prices 207 014 025 035 043 050 056 060 063 066 Existing sales 393 073 078 081 080 073 066 060 056 052 Months supply 615 −063 −061 −057 −052 −044 −037 −031 −028 −024 Foreclosure rate 496 −065 −068 −068 −067 −064 −060 −053 −047 −040 Baseline Output (Y)100 087 090 093 097 100 097 093 090 087 House prices 190 082 085 088 092 095 094 092 091 089 Existing sales 435 010 011 012 012 013 014 015 015 016 Months supply 646 −076 −079 −082 −085 −088 −088 −088 −088 −087 Foreclosure rate 1632 −076 −079 −082 −085 −088 −084 −083 −082 −081 No Search Output (Y)100 086 089 093 097 100 096 093 089 086 House prices 158 082 085 089 092 096 095 094 092 091 Existing sales 815 026 028 030 032 033 029 025 021 017 Monthssupply–––––––––– Foreclosurerate–––––––––– Recourse Output (Y)100 086 090 093 097 100 097 093 090 086 House prices 168 081 085 088 092 095 094 092 091 089 Existing sales 599 025 026 028 029 030 031 032 033 033 Months supply 093 −075 −078 −081 −084 −087 −083 −080 −077 −075 Foreclosurerate–––––––––– Note: Existing sales and months supply data span 1982–2010 and come from the National Association of Realtors. In the model, existing sales includes all REO sales and sales by owners. Foreclosure data are from the Mortgage Bankers’ Association and cover 1979–2010. For house prices I use the Freddie Mac House Price Index. Data and model output are detrended with λ=108using the HP filter. Quantitative Economics 7 (2016) Illiquid housing, debt, and foreclosures 325 Table 12. Lagged correlations: household portfolios. Cross-Correlation of Output With xσ x/σYx(−4)x(−3)x(−2)x(−1)xx(+1)x(+2)x(+3)x(+4) Data Output (Y)100 066 078 089 097 100 097 090 082 073 Net worth 184 055 066 074 077 077 075 071 068 063 Financial assets 176 049 058 065 067 065 062 059 055 051 Housing wealth 261 016 028 038 047 054 059 063 065 065 Mortgage debt 164 −015 −006 003 013 022 031 040 047 053 Baseline Output (Y)100 087 090 093 097 100 097 093 090 087 Net worth 171 076 079 082 086 089 090 090 090 090 Financial assets 161 077 081 084 088 091 093 093 093 093 Housing wealth 218 078 081 084 088 091 091 090 090 089 Mortgage debt 267 072 075 078 082 085 086 085 083 081 No Search Output (Y)100 086 089 093 097 100 096 093 089 086 Net worth 161 073 077 080 083 087 088 088 089 089 Financial assets 177 074 077 081 084 088 090 091 092 092 Housing wealth 178 077 080 084 087 091 091 090 089 088 Mortgage debt 244 078 081 085 089 092 094 095 094 093 Recourse Output (Y)100 086 090 093 097 100 097 093 090 086 Net worth 155 074 077 081 084 088 089 089 090 090 Financial assets 178 075 079 082 086 089 091 092 093 093 Housing wealth 183 077 080 084 088 091 091 090 089 088 Mortgage debt 298 074 078 081 085 088 089 089 088 087 Note: Net worth, financial assets, housing wealth, and mortgage debt data come from Table B.100 of the Federal Reserve Flow of Funds Accounts. 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[292] Co-editor Karl Schmedders handled this manuscript. Submitted August, 2014. Final version accepted June, 2015.