Houses as ATMs? Mortgage Refinancing and Macroeconomic Uncertainty

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1 Houses as ATMs? Mortgage Refnancng and Macroeconomc Uncertanty Prelmnary and ncomplete Hu Chen MIT Sloan and NBER Mchael Mchaux USC Marshall July 6, 2011 Nkola Roussanov Wharton and NBER Abstract Mortgage refnancng waves tend to concde wth economc downturns. We nvestgate the role of mortgage refnancng as a mechansm for smoothng consumpton by lqudty constraned households, focusng on the nteracton of the aggregate economc condtons, nterest rates, and dosyncratc labor ncome rsk. Usng both aggregate and state-level data we show that refnancng actvty ncreases when economc condtons deterorate, even controllng for the cyclcal behavor of nterest rates, wth a larger fracton of loans nvolvng cash-out (equty extracton) around recessons. Calbratng a quanttatve model of household decson makng that features optmal mortgage choce we show that counter-cyclcal labor ncome rsk s mportant for generatng the cyclcal behavor of refnancng. At the same tme, persstent dosyncratc shocks that are harder to smooth mtgate ths effect, whle precautonary savng drves down optmal mortgage balances. Consequently, the observed patterns of mortgage refnancng contan mportant nformaton about the dynamcs of household-level dosyncratc labor ncome. Please do not cte wthout permsson. We gratefully acknowledge comments and suggestons by Andy Abel, Erk Hurst, Urban Jermann, Greg Kaplan, Nck Souleles, Amr Yaron, and semnar partcpants at the Phladelpha Fed, USC and Wharton. 1

2 1 Introducton Long-term mortgages wth a fxed rate and an opton to prepay the outstandng balance pror to maturty, typcally by obtanng a new loan (refnancng), have long been the manstay of the U.S. housng market. Ths paper nvestgates the role of mortgage refnancng as a mechansm through whch households can relax lqudty constrants n response to aggregate and dosyncratc shocks by borrowng aganst ther home equty. Fluctuatons n nterest rates that determne the strength of the fnancal ncentve to refnance alone are not suffcent to capture all of the movement n the aggregate prepayment/refnancng actvty n the data (e.g., Boudoukh, Rchardson, Stanton, and Whtelaw (1997)). We focus on the nteracton between the nterest rate varaton and macroeconomc condtons n affectng household decsons. The decson to refnance a mortgage ether to take advantage of the lower nterest rates or to take out home equty for consumpton-smoothng purposes trades off the benefts of refnancng aganst the costs of orgnatng a new loan, both fnancal and non-pecunary. The nteracton of the two motves for refnancng that underscores ts potental mportance for the effectveness of monetary polcy. 1 Emprcally, nterest rates are pro-cyclcal, fallng n economc downturns, when both aggregate ncome falls and ts cross-sectonal dsperson rses. Consequently, the opton to prepay an exstng fxed-rate mortgage (FRM) s more lkely to be n the money at a tme when households are constraned and experencng a need to tap ther home equty (f t exsts), n effect provdng a form of nsurance. Indeed, we show that n the data, mortgage 1 Mortgage refnancng featured promnently n Alan Greenspan s defense of low nterest rates as a way of stmulatng household consumpton durng the jobless recovery from the 2001 recesson: Overall, the economy has made mpressve gans n output and real ncomes; however, progress n creatng jobs has been lmted.... The very low level of nterest rates... encouraged household spendng through a varety of channels.... The lowest home mortgage rates n decades were a major contrbutor... engenderng a large extracton of cash from home equty. A sgnfcant part of that cash supported personal consumpton expendtures and home mprovement. In addton, many households took out cash n the process of refnancng, often usng the proceeds to substtute for hgher-cost consumer debt. That refnancng also permtted some households to lower the monthly carryng costs for ther homes and thus freed up funds for other expendtures. (Testmony of Charman Alan Greenspan; Federal Reserve Board s semannual Monetary Polcy Report to the Congress Before the Commttee on Fnancal Servces, U.S. House of Representatves, February 11, 2004). 2

3 refnancng actvty appears to respond to macroeconomc condtons, even after controllng for the cyclcalty of mortgage rates, usng both aggregate and state-level data. Refnancng actvty spkes wth measures of macroeconomc uncertanty such as the mpled stock market volatlty and unemployment clams, and s lower n states that experence hgher rates of economc growth. Refnancng s postvely related to growth n house prces, whch drves the tghtness of the collateral constrant, whle more refnancng households extract home equty ( cash-out ) as the economy enters nto recessons, even before nterest rates fall. In order to provde an analytcal framework for understandng these facts we buld a dynamc model of household mortgage fnancng that replcates these stylzed facts. The model also helps quantfy the degree to whch refnancng costs as well as the lack of home equty constran the ablty of households to smooth consumpton n the face of macroeconomc uncertanty. In our model, households are facng unnsurable dosyncratc and aggregate labor ncome rsk, and ther only means of borrowng s va a home mortgage. The mortgage repayment and refnancng behavor s drven by both the purely fnancal motve of mnmzng the borrowng costs (as n Campbell and Cocco (2003)) and by the consumpton-smoothng motve of usng home equty to allevate the lqudty constrant (as n Hurst and Stafford (2004)). An mportant feature of our model s the counter-cyclcal volatlty of dosyncratc labor ncome growth, documented by Storesletten, Telmer, and Yaron (2004). Ths property of the labor ncome process combned wth the pro-cyclcal nterest rates mples that a macroeconomc downturn should concde wth a spke n refnancng actvty both due a declne n mortgage rates and because more households become lqudty constraned, provded that the cost of refnancng s low enough and households stll have enough home equty. In a quanttatve calbraton of the model that targets the man features of ncome, consumpton, and mortgage data we show that the dynamcs of labor ncome are key for generatng counter-cyclcal refnancng and cash-out behavor. On the one hand, countercyclcal dosyncratc labor ncome rsk s mportant for cyclcal behavor of refnancng. On 3

4 the other hand, rsker dosyncratc ncome mpled greater precautonary savng,.e. greater lqud asset holdngs and lower mortgage balances on average. Further, hghly persstent labor ncome processes advocated n the recent lterature mply that dosyncratc shocks are very dffcult to smooth, and therefore dampen the effect of economc cycles on refnancng behavor. Thus observed refnancng behavor contans useful nformaton for understandng the dynamcs of ndvdual labor ncome. A better understandng of the lnks between mortgage refnancng and macroeconomc condtons s mportant for several reasons. Frst, whle prevous models have predomnantly focused on refnancng as exercse of an nterest rate opton, our results show that the lqudty-drven motve can sgnfcantly amplfy the demand for refnancng under certan macroeconomc condtons. Ths s mportant for prcng prepayment rsk n mortgagerelated assets (e.g., Duarte, Longstaff, and Yu (2007) show that agency-backed mortgage backed securtes are subject to macroeconomc rsk captured by stock returns), as well as for understandng the relaton between refnancng actvty n the mortgage markets and volatlty n other fxed ncome markets (see, e.g., Duarte (2008)). Second, our model can quantfy the welfare mplcatons of refnancng costs n a rather rch economc settng, whch can help evaluate polcy proposals of stmulatng the economy through relaxng refnancng constrants. 1.1 Lterature There s a large lterature on mortgage refnancng decson, wth dfferent strands focusng on dfferent facets of the optmal soluton to the problem faced by the household. The fxed-ncome asset prcng lterature focuses on the optmal exercse of the call opton embedded n the mortgage (e.g. Dunn and McConnell (1981), Dunn and Spatt (2005)). The wde dvergence of prepayment behavor across households has been modeled by attrbutng t to mplct heterogenety n the costs of refnancng (e.g. Stanton (1995), Deng, Qugley, and Van Order (2000), Downng, Stanton, and Wallace (2005)), both explct and mplct, n 4

5 partcular those arsng from behavoral bases (e.g. Agarwal, Drscoll, and Labson (2002)). Campbell and Cocco (2003) and Kojen, Van Hemert, and Van Neuwerburgh (2009) analyze the choce between adjustable and fxed-rate mortgages. The lterature on housng collateral emphaszes the mplct rsk-sharng role of mortgage fnance and ts mpact on rsk prema (e.g. Lustg and Van Neuwerburgh (2005), Favluks, Ludvgson, and Van Neuwerburgh (2011)). Some evdence supportng the mportance of housng collateral has been documented usng varaton n consumpton responses to ncome at the regonal level (Capln, Freeman, and Tracy (1997), Lustg and Van Neuwerburgh (2010)). Hurst and Stafford (2004) explctly consder the role of mortgage refnancng as a mechansm of accessng home equty for the purpose of smoothng consumpton over tme and provde household-level evdence. 2 Emprcal evdence 2.1 Aggregate data In ths secton, we dscuss emprcal evdence on how refnancng actvty at the aggregate level relates to nterest rates and macroeconomc condtons. The key varable capturng mortgage refnancng by households that we use s the ndex of mortgage applcatons compled by the Mortgage Bankers Assocaton (MBA Ref Index), whch s avalable from 1990 to In addton, we also examne the quarterly cash-out data from Fredde Mac for the perod from 1985 to Fgure 1 Panel A plots the Ref ndex (weekly) along wth the 30-year mortgage rates. Not surprsngly, refnancng ncreased n both the early 90s and especally around 2003, both of whch are tmes when mortgage rates came down sgnfcantly. Ths s consstent wth households refnancng to take advantage of newly avalable low mortgage rates. Panel B plots the Ref ndex wth the VIX ndex, a measure of the mpled volatlty of the S&P 500 stock market ndex. The spkes n Ref n 1998, 2001, 2008, and 2009 all appear to concde 5

6 A. Refnancng and Mortgage Rates Mort Ref Jan92 Jan94 Jan96 Jan98 Jan00 Jan02 Jan04 Jan06 Jan08 Jan10 B. Refnancng and VIX VIX Ref Jan92 Jan94 Jan96 Jan98 Jan00 Jan02 Jan04 Jan06 Jan08 Jan10 C. Refnancng and Industral Producton IP Ref Jan92 Jan94 Jan96 Jan98 Jan00 Jan02 Jan04 Jan06 Jan08 Jan10 Fgure 1: Refnancng, Interest Rates, and Macroeconomc Uncertanty 6

7 wth spkes n the VIX. Panel C plots the Ref ndex wth the year-on-year growth rate n ndustral producton. The Ref ndex rose sgnfcantly durng the 2001 recesson, and agan n early 2008, the onset of the Great Recesson. Panels B and C are suggestve evdence that households borrow aganst home equty (whle they are not yet under water ) when experencng bad ncome shocks or n antcpaton of worsenng economc condtons n the future. We regress the (monthly average) Ref Index on a host of fnancal and macroeconomc varables: REF I t = b 0 + b r R 3M t + b r30 R 30Y t + b r30l R 30Y t 12 + b V IX V IX t + b IP IP t + ɛ t, (1) where R 3M t s the 3-month Treasury Bll rate, R 30Y t the 30-year fxed mortgage rate, R 30Y t 12 the 30-year fxed mortgage rate lagged by one year, and IP t the year-on-year change n the Industral Producton ndex (IP). Table 1 reports the results. The most mportant drver of mortgage refnancng s the 30-year mortgage rate, whch comes n wth a negatve and robustly sgnfcant coeffcent n all of the regressons. Ths s natural, as one of the prmary reasons to refnance a mortgage s to take advantage of lower nterest rates and thus lower nterest payments. The other rght-hand sde varables are meant to capture the senstvty of refnancng to the economc condtons: the short rate, whch s typcally pro-cyclcal also comes n wth a negatve coeffcent, as does the Industral Producton growth, whch s the most drect measure of economc actvty. However, the short rate appears to drve out IP as an explanatory varable. Ths could ndcate that ether the nterest rate contans more relevant nformaton about the state of the economy, or that t s n fact drvng refnancng snce t captures the attractveness short-duraton borrowng optons, such as adjustable rate mortgages (ARMs). Fnally, VIX s sgnfcantly postvely related to Ref. It also drves out IP, possbly for the reason that fnancal data are forward-lookng and better capture the nformaton set of the 7

8 Table 1: Explanng the MBA Refnancng Index - monthly R 30Y t R 3M t R 30Y t 12 VIX IP Adj. R ( 1.30) ( 1.03) ( 0.86) ( 1.22) ( 0.24) ( 0.90) ( 1.05) ( 0.27) ( 1.09) ( 0.20) ( 0.33) ( 2.22) ( 0.86) ( 1.64) ( 0.15) Note: Monthly data, January February Numbers n parentheses are Newey- West standard errors wth 24 lags. households, and t survves when short rates and lagged mortgage rates are ncluded. Next, we run smlar regressons as (1) usng weekly data, where the measures of aggregate economc condtons are V IX and the Intal Clams Unemployment seres avalable from the Federal Reserve Bank of Phladelpha (U IC). The results are smlar to those obtaned at the monthly frequency. Whle the 30-year mortgage rate s stll the strongest determnant of refnancng, the short-term nterest rate and the Intal Clams unemployment ndex have a negatve and a postve sgn, respectvely, both sgnfcant when the other regressor s not present, but nether sgnfcant n a jont regresson. Both of the varables weaken n the presence of the lagged mortgage rate, consstent wth the fact that the level of nterest rates changes n the response to changng economc condtons, affectng the attractveness of refnancng. Agan, the stock market volatlty ndex VIX s always strongly sgnfcant, drvng out all of the other varables except for the key mortgage rate. 8

9 Table 2: Explanng the MBA Refnancng Index - weekly R 30Y t R 3M t R 30Y t 52 VIX UIC Adj. R ( 1.41) ( 1.00) ( 0.92) ( 1.18) ( 0.17) ( 0.94) ( 1.15) ( 0.19) ( 1.08) ( 0.18) ( 0.20) ( 2.13) ( 0.87) ( 1.60) ( 0.14) Note: Weekly data, from January March Numbers n parentheses are Newey- West standard errors wth 52 lags. 2.2 State level evdence To nvestgate the response of mortgage refnancng to economc actvty further, we use statelevel data on the orgnaton of home mortgage loans at the state level. Ths potentally allows us to separate the effect of low nterest rates from that of deteroratng economc condtons, nsofar as there s heterogenety n busness condtons across states so that local economc actvty varables are less synchronzed wth the nterest rates than are aggregate quanttes, and that households cannot dversfy away state-level shocks. We frst use quarterly data on the mortgage loans (both refnance and purchase) for each of the 50 states and DC, normalzed by the state populaton based on aggregated Home Mortgage Dsclosure Act (HMDA) reportng. We regress the quarterly changes n the number of loans taken n order to refnance exstng mortgages (adjusted by the state populaton) on measures of economc condtons. We use two such measures: growth rates of nonfarm payroll employment and of the State Concdent Economc Actvty Index (CEAI), whch combnes nformaton contaned n nonfarm payrolls, unemployment, hours worked 9

10 and wages, and trends wth the Gross State Product (GSP). 2 We use year-on-year (log) growth rates at the quarterly levels of these measures as the man explanatory varables. House prces determne both the motve to refnance due to a wealth effect and the ablty of households to borrow aganst the value of ther homes (perhaps for reasons unrelated to consumpton smoothng). Snce economc condtons are correlated wth the level of house prces, refnancng actvty could be hgh under good economc condtons due to hgh house prces. Thus, to better capture the effect of consumpton smoothng on refnancng, t s mportant to control for house prce apprecaton n our regresson. We use the FHFA house prce ndces for the 50 states and DC as our measure of house prces. As before, we also control for several aggregate varables: the 30 year mortgage rate, the short-term nterest rate, and the VIX volatlty ndex. We run pooled tme seres/cross-sectonal regressons of the form: REF I State t = b Cycle Cycle State t + b CycleLag Cycle State t 4 + b HP I HP I State t + b CH Cycle State t HP I State t + b w W AC State t + b r R t + b r30 R M30 t + b r30l R M30 t 12 + b vx V IX t + b t + b State + ɛ t, (2) where Cycle State s the varable that measures state-level aggregate economc condtons, HP I t measures house prce apprecaton usng the 1-year growth n the FHFA state-level house prce ndex, W AC State t s the weghted average coupon on conformng mortgage loans outstandng n the state n the frst month of the quarter, b t s the vector of quarter fxed effects, and b State a vector of state fxed effects. State fxed effects are mportant snce there s substantal heterogenety across states n the fxed costs assocated wth refnancng a mortgage (such as ttle nsurance, taxes, etc.), whch result n dfferent average levels of refnancng as well as ts senstvty to aggregate varables. Gven ths specfcaton, we are dentfyng the effect of wthn-state varaton n economc condtons on refnancng. We nclude the lagged Cycle varable to capture delayed response of households to economc 2 Unlke the payroll growth measure, ths varable s not avalable for DC. 10

11 condtons, and nclude an nteracton term between Cycle and the house prce growth, orthogonalzed wth respect to both varables, to test whether hgher level of house prces help relax the borrowng constrant especally n bad tmes. Table 3 presents the results of the state-level regressons for dfferent specfcatons (two dfferent economc actvty measures). The coeffcents on the state-level busness cycle varables n the frst column are all negatve and statstcally sgnfcant n all but one specfcaton (CEAI wthout tme fxed effects), consstent wth the vew that households are more lkely to refnance ther mortgages n a downturn. The one-year lagged Cycle varables are even more strongly negatve nd always statstcally sgnfcant, suggestng that local economc condtons are persstent. The lagged varables may have a stronger effect than the contemporaneous ones because more prolonged regonal recessons are lkely to exert greater pressure on the fnancal resources of households, drvng them to rely more on housng collateral to smooth the temporary but persstent fluctuatons. The state-level cycle varable remans sgnfcantly negatvely related to refnancng when the quarter fxed effects are ncluded, ndcatng that ther presence does not smply proxy for varaton n the aggregate term structure varables. As expected, house prce apprecaton s postvely related to refnancng. The effects of the busness cycle varables become stronger (more negatve) after house prce apprecaton s taken nto account, whch helps tease out the rse n refnancng n good tmes due to house value apprecaton. Moreover, the nteracton terms of house prces and the cycle varables are negatve and typcally statstcally sgnfcant, suggestng that hgher levels of house prces are partcularly mportant for refnancng durng economc downturns. Both the 30-year mortgage rates and the short-term nterest rate have a sgnfcant negatve effect on refnancng, as expected. Smlarly, the WAC has a sgnfcant postve coeffcent, consstent wth the fact that t captures the rates currently pad by borrowers, so that hgher WAC translated nto a greater ncentve to refnance f current rates are low. In the specfcaton wth tme fxed effects (where aggregate nterest rates are not ncluded) 11

12 WAC has a negatve coeffcent, potentally due to the fact that t may capture persstent state-specfc varaton n mortgage spreads that we cannot control for separately wthout detaled state-level data on mortgage rates. Table 3: State-level refnancng actvty Cycle t Cycle t 4 HP I t Cycle t HP I t WAC Rt M30 R t Rt 4 M30 R Robust [ 0.04] [ 0.06] [ 0.01] [ 0.01] [ 0.03] [ 0.30] [ 0.05] [ 0.32] NW [ 0.05] [ 0.06] [ 0.01] [ 0.00] [ 0.05] [ 0.26] [ 0.05] [ 0.25] Robust [ 0.05] [ 0.04] [ 0.02] [ 0.01] [ 0.77] NW [ 0.05] [ 0.04] [ 0.02] [ 0.00] [ 0.69] Robust [ 0.02] [ 0.03] [ 0.01] [ 0.01] [ 0.03] [ 0.33] [ 0.05] [ 0.33] NW [ 0.03] [ 0.04] [ 0.01] [ 0.00] [ 0.05] [ 0.26] [ 0.05] [ 0.26] Robust [ 0.04] [ 0.03] [ 0.02] [ 0.00] [ 0.77] NW [ 0.04] [ 0.03] [ 0.02] [ 0.00] [ 0.72] Quarterly data, 1993.III IV. Cycle refers to the year-on-year growth n ether the nonfarm payroll employment ndex scaled by the state populaton (Payroll, specfcatons 1-2) or the State Concdent Economc Actvty ndex n columns (CEAI, specfcatons 3-4 ). HPI s the annual growth rate of the state-level house prce ndex, WAC s weghted average coupon rate for conformng fxed-rate mortgages (equal-weghted average across FNMA and FHLMC loans) n a gven state. Specfcatons 2 and 4 have quarter fxed effects. Standard errors are n brackets (Robust are clustered by state, and NW are Newey-West wth 20 lags). If households use refnancng n order to take advantage of housng collateral to smooth consumpton n downturns, we should expect the sze of new refnance loans to ncrease relatve to household ncome durng perods of low economc growth. Table 4 present the results of a regresson for the changes n the state-level average loan-to-ncome ratos (LTI): LT I State t = b Cycle Cycle State t + b w W AC State t + b HP I HP I State t + b r R t + b r30 R M30 t + b CH Cycle State t HP I State t + b r30l R M30 t 12 + b vx V IX t + b t + b State + ɛ t, (3) 12

13 where LT I s the year-on-year change n the logarthm of the average loan-to-ncome rato by state. We use frst dfferences rather than levels of LTI due to the fact that the LTI levels appear to trend upwards over our sample, perhaps due to the effects of fnancal nnovaton and regulaton on the avalablty of mortgage loans to low ncome households, n partcular va subprme mortgages. The results reported n the table ndcate that the average loan-to-ncome ratos on refnance loans do tend to ncrease when macroeconomc condtons (especally as captured by payroll employment) deterorate. Not surprsngly, LTI s postvely related to house prces, but there s vrtually no nteracton between the two effects. LTI s negatvely related to current nterest rates, suggestng that larger mortgages become more affordable to households n low nterest rate envronments, and the postve relaton to WAC and lagged mortgage rates suggest that households ncrease ther mortgage balances upon refnancng especally f the current coupon rates they pay on exstng loans are hgh. Overall, ths evdence, albet only suggestve, s consstent wth the vew that households use refnancng to access home equty durng economc downturns. 2.3 Cash-out evdence Measures of aggregate and state refnancng actvtes do not dstngush between cash-out refnances (takng out a loan wth a larger balance than the prevous one) from those that result n the same or lower loan balances. We now examne how cash-outs react to macroeconomc condtons, whch provde a more drect measure of household borrowng. Fgure 2 Panel A plots the tme seres of the percentage of refnances for whch the loan amount () s rased by 5% or more, () remans the same, or () s reduced by 5% or more. The data s from Fredde Mac for the perod of Q1 of 1985 to Q1 of On average, 61% of refnances over ths perod are cash-outs, whch hghlghts the mportance of cash-outs n mortgage refnancng. The share of cash-outs s vsbly hgher towards the end of each expanson, and t becomes lower after a recesson. In contrast, the fracton of refnances that do not result n a hgher loan balance does not appear to have a clear busness 13

14 Table 4: Average loan-to-ncome ratos Cycle t HP I t Cycle t HP I t WAC Rt M30 R t Rt 4 M30 R Robust [ 0.23] [ 0.05] [ 0.03] [ 0.33] [ 2.04] [ 0.22] [ 1.20] NW [ 0.21] [ 0.05] [ 0.02] [ 0.37] [ 1.84] [ 0.21] [ 1.30] Robust [ 0.17] [ 0.09] [ 0.02] [ 8.23] NW [ 0.17] [ 0.09] [ 0.02] [ 7.40] Robust [ 0.12] [ 0.06] [ 0.01] [ 0.37] [ 2.25] [ 0.18] [ 1.29] NW [ 0.12] [ 0.06] [ 0.01] [ 0.40] [ 2.02] [ 0.19] [ 1.38] Robust [ 0.20] [ 0.12] [ 0.01] [ 8.08] NW [ 0.18] [ 0.11] [ 0.01] [ 7.34] Note: Quarterly data, 1993.III IV (tme subscrpt t s n monthly unts). Yearon-year log growth n average loan to ncome rato (for refnance loans only) at the state level, n percentage ponts (based on HMDA data). Cycle refers to the year-on-year growth n ether the non-farm payroll employment ndex scaled by the state populaton (Payroll, specfcatons 1-2) or the State Concdent Economc Actvty ndex n columns (CEAI, specfcatons 3-4 ). HPI s the annual growth rate of the state-level house prce ndex, WAC s weghted average coupon rate for conformng fxed-rate mortgages (equal-weghted average across FNMA and FHLMC loans) n a gven state. Specfcatons 2 and 4 have quarter fxed effects. Standard errors are n brackets (Robust are clustered by state, and NW are Newey-West wth 20 lags). cycle pattern. The waves n the md-90s and early 2000s nstead correspond to perods of declnes n mortgage rates, whch s ntutve snce the goal of such refnances should be to reduce nterest payments. Fnally, the fracton of pay-down refnances, those that result n a reducton n loan balance, typcally rses followng a recesson, as households repay the loans they take out enterng the recesson. These pay-downs should also be assocated wth lower rates, for otherwse households could prepay rather than refnance ther mortgages. Lke other types of refnancng, cash-outs can also be due to low nterest rates. Thus, t s nformatve to examne under what condtons refnancng tends to lower loan rates Panel B of Fgure 2 plots the rato of the medan new mortgage rates on refnance loans to the old mortgage coupon rates k. Households tend to refnance despte hgher rates towards the 14

15 100 A. Components of refnances Percentage of Refs cash-out no change pay-down New Rate/Old Rate B. Rato of new to old loan rates Fgure 2: Panel A plots the percentage of refnances resultng n 5% hgher loan amount (cash-out), no change n loan amount, or lower loan amount (pay-down). Panel B plots the medan rato of new to old loan rates upon refnance. end of economc expansons, but at lower rates comng out of recessons. The correlaton between ths rate rato and the cash-out share n Panel A s 78%. Together, they suggest that macroeconomc factors other than nterest rates play an mportant role n determnng the aggregate amount of cash-out refnancng. Why do households refnance ther mortgages at hgher rates? One possblty s that they are borrowng aganst hgher expected future ncome. Gven that labor ncome s not tradable and other non-collateralzed personal loans (e.g., credt card loans) are expensve, the house becomes a source of credt for lqudty constraned households. A second, and related, reason s that households borrow when they are experencng or antcpatng a temporary 15

16 drop n ncome (consumpton smoothng). Frctons such as loan-to-ncome rato restrcton, and more severe adverse selecton due to hgher ncome volatlty n the cross secton can make t more dffcult (costly) to borrow n bad tmes, whch wll generate precautonary demand for borrowng before ncome has fallen. Thrd, households mght expect long term mortgage rates to rse n the future, so they may be attemptng to tme the market by takng out larger mortgages n antcpaton and lockng n the low rate. Fourth, households mght expect house value to fall, whch affects ther future borrowng capacty through the loan-to-value rato restrcton. 3 Fnally, f households expect hgher returns from other types of nvestment (e.g., from the stock market), they mght borrow aganst the house n spte of hgh rates. We explore some of these alternatve explanatons n Table 5. The rato of new to old loan rates predcts future GDP growth wth a sgnfcantly negatve coeffcent and an R 2 of 22%, whch s consstent wth the precautonary demand for cash-out due to lqudty constrant. Ths effect survves after controllng for short rate, term spread, and the medan apprecaton of refnanced property. Hgh rate rato predcts lower future long term mortgage rates, suggestng that cash-out at the onset of recesson s not for the purpose of lockng n the rate. It also predcts lower short rates and lower house prce growth. It s possble that households refnance nto adjustable rate mortgages (ARMs) when they expect short rates to fall, although the share of ARMs n total new loans s typcally low when the rate rato s hgh. Fnally, hgh rate ratos predcts lower excess returns for stocks one year ahead, makng t a poor strategy to cash out and nvest n the stock markets when the rate rato s hgh. We cannot rule out that households rratonally beleve that future market returns wll be hgh. Overall, however, the tme-seres behavor of cash-out and the rate rato are consstent wth households takng out loans to smooth consumpton as they enterng nto a recesson and ther fnancal poston deterorates. 3 Hgher expected house prce mght also lead to more cash-out f the households are wllng to move down to cheaper (and lower qualty) houses, or f they own nvestment propertes. 16

17 Table 5: Predctng Macro Varables wth Refnancng Varables (1) (2) (3) (4) (5) (6) (7) GDP t+4 Rt+4 M30 R t+4 HP I t+4 ERt+4 m k new /k old (0.032) (0.036) (0.041) (1.559) (2.811) (0.047) (0.336) R t (0.001) (0.002) (0.116) Rt 10Y R t (0.003) (0.003) H (0.029) Rt M (0.078) HP I t (0.119) Adj. R Note: Quarterly data, Q Q The left-hand-sde varables are one-year ahead annual real GDP growth rate (GDP), one-year ahead 30-year mortgage rate (R M30 ), oneyear ahead 3-month treasury bll rate (R), one-year ahead annual growth rate n house prce (HP I), and one-year ahead market excess return (ER m ). Numbers n parentheses are Hansen-Hodrck standard errors wth 4 lags. k new /k old s the medan rato of new to old loan rates. H s the medan apprecaton of the refnanced property. 3 Quanttatve Model Ths secton presents a dynamc model of household decsons. Ths model wll focus on understandng households decsons on how much to consume, save and fnance a house over tme, as a functon of dosyncratc shocks to ncome and aggregate shocks to short-term nterest rates, real growth, house value, and nflaton. 3.1 Envronment The economy s populated by ex-ante dentcal households. Each household s denoted by the ndex. Each household s endowed wth a house wth tme-varyng market prce H t, and one unt of labor suppled nelastcally that receves an after-tax wage (1 τ)y t. The 17

18 dosyncratc ncome process s stochastc and wll be key n the optmal behavor. Households can save usng a one-perod lqud asset a t that pays the aggregate short rate n the economy, denoted by r t $. The households are also prevented from borrowng, that s a t 0 for all t. All varables are nomnal expressed n unts of account, say $ and the prce level at tme t s denoted by p t. The model wll thus feature nflaton rsk. 3.2 Mortgages For smplcty, mortgages n ths economy are assumed to be nterest-only mortgages. Households have to meet a mortgage payment every perod, defned as the (fxed) mortgage coupon rate k tmes the mortgage balance due on the house b t. Note that the households can deduct the mortgage nterest expense, whch s the full mortgage payment for an nterest-only mortgage, from ther taxable ncome y t. Households can always repay ther mortgage by reducng the outstandng loan balance on ther home, that s when b,t+1 < b t. The repayment decson s denoted by the ndcator I RP t = 1 f home loan balance s reduced and I RP t = 0 otherwse. Households also have the opton to refnance ther home by ncreasng or reducng the outstandng loan balance, that s when b,t+1 b t. The refnancng decson s denoted by the ndcator I RF t = 1 f the home loan s refnanced and I RF t = 0 otherwse. When households decde to refnance, they wll ncur a cost captured by the functon φ. For example, f a household pulls out an amount (b,t+1 b t ) from ther home equty, they wll ncur a refnancng cost equal to φ(b,t+1 ). Therefore the net proceeds from refnancng wll n fact be equal to b,t+1 b t φ(b,t+1 ), whch s the loan ncrease/decrease net of refnancng cost. These refnancng costs can be thought of the tme cost spent on the refnancng process as well as drect fnance fees assocated wth ssung a new mortgage. In ths paper, we assume that refnancng costs have a fxed and proportonal component. When a household refnances, the old outstandng mortgage b t s repad n full usng the proceeds of the new mortgage and the avalable assets. The new home loan s b,t+1 and 18

19 the new mortgage rate k,t+1 that s used to calculate future annuty payments s equal to the avalable refnancng rate R t. Therefore by refnancng a household commts to repay an nfnte stream of constant annuty payments equal to R t b,t+1, unless the house s refnanced agan n the future. The dynamcs of the mortgage rate k t wll be as follows, k,t+1 = k t (1 It RF ) + R t It RF. Fnally households can choose to merely pay ther mortgage and nether refnance nor repay ther home loan. Ths decson s denoted by the ndcator I NR t = 1 f home loan and the mortgage rate are unchanged, and I NR t = 0 otherwse. To start the economy, we assume that each household s endowed wth a mortgage balance of b 0, a mortgage rate equal to k 0, and a house of value H t. In other words, each household s endowed wth home equty equal to H 0 b 0, and has to pay a mortgage annuty payment equal to k 0 b 0. Households are allowed to borrow less than the full value of ther home, that s they face the followng constrant upon refnancng, b,t+1 ξ H t, where ξ [0, 1] s the parameter that controls the tghtness of the loan-to-value constrant. 3.3 Household Budget Constrant Each household wll choose how much to consume, save n a rskless one-perod bond that pays the short rate r, and adjust ther mortgage: both the rate and the outstandng loan amount. The budget constrant for household at tme t s gven by, a,t+1 c t (1 τ)r t $ + b t = (1 τ)(y t k t b t ) + a t + b,t+1 φ(b,t+1 )I RF t. Notce that nterests earned on the lqud asset a are taxed at the same rate τ as wage 19

20 ncome. 3.4 Exogenous States Aggregate States The real macroeconomc rsk n the economy s summarzed by the aggregate state varable Z t. Ths process gves the real growth rate of the aggregate real ncome: Z t+1 = Y t+1 /Y t. The nomnal short rate r t $ s also an aggregate state varable. Because all varables n the model are nomnal but consumers derve utlty from real consumpton, we need to specfy a process for nflaton. Recall that the prce level at tme t s denoted by p t, thus the (gross) nflaton rate s defned as π t+1 = p t+1 /p t. We make the assumpton that nomnal house prces H t have a component that grows at the same rate as the economy (.e. nomnal aggregate ncome), as well as a component that represents the aggregate rsk nherent n the housng market s transtory devatons from the trend n aggregate ncome. Therefore, the house prce process s gven by, H t = p t Y t H ht, (4) where H s the house prce level (n terms of the consumpton good), and the shocks h t are assumed to be statonary, so that real house prce level s contegrated wth real aggregate ncome. These four aggregate state varables are summarzed n the aggregate state vector S t (r t $, Z t, H t, π t ) that follows a frst-order vector autoregressve process (VAR) n logarthms. 20

21 3.4.2 Idosyncratc States The nomnal ncome process y t for each household has an aggregate component, Y t, as well as an dosyncratc component, ỹ t, and s gven by, y t = p t Y t ỹ t, (5) where the dosyncratc shocks ỹ t follow an autoregressve process wth state-dependent condtonal volatlty,.e. heteroscedastc nnovatons, gven by, log ỹ t = log µ y (Z t ) + ρ y log ỹ,t 1 + σ(z t )ɛ y t, ɛy t N (0, 1). (6) The counter-cyclcal nature of the dosyncratc labor ncome rsk s emphaszed by Storesletten, Telmer, and Yaron (2004). We calbrate µ y (Z t ) so that the cross-sectonal mean of the dosyncratc components of ncome ỹ mpled by the statonary dstrbuton equals to unty n every perod: log µ y (Z) = 1 σ 2 (Z) ρ y We assume that all households bear the same aggregate rsks snce we focus on the average households that s lkely to need to use home equty to smooth consumpton (there s some evdence n the recent lterature that wealther households are dsproportonately affected by aggregate fluctuatons - e.g. Parker and Vssng-Jorgensen (2009)). The vector of exogenous state, denoted by s t, contans the dosyncratc wage and the aggregate states: s t (y t, S t ). 3.5 Household Recursve Problem In order to smplfy notaton subscrpts t are dropped and prmes denote next perod varables. The problem for household s to choose consumpton c, the poston n a lqud asset 21

22 a, and whether to refnance I RF, repay early I RP (yeldng new mortgage balance b ), or default on the mortgage, so as to maxmze the expected lfetme utlty of real consumpton. Households choose whether to be a home-owner or a renter. As a home-owner, a household can choose to repay the mortgage and reman a home-owner, sell the house at market value or smply default on the mortgage and rent. As a renter, a household can choose to reman a renter or buy house. Fgure 3.5 shows a dagram that represents the households homeownershp decsons. Ths approach PostDefaultRenter broadly follows Campbell and Cocco (2010) n the treatment of the homeownershp and default decson. Homeowner remanhomeowner, movewthprobω purchasehouse sellhouse Renter Fgure 3: Home-owner, renter, and post-default renter dagram Home-owner Problem As a home-owner, a household chooses consumpton and stock of lqud assets, but also has access to borrowng aganst hs house. Every perod, there s a probablty ω that the household has to move for exogenous reasons (.e. geographc relocaton, buy a dfferent 22

23 house, etc.). In such an event, the household has to sell ts house, repay the exstng loan outstandng, and use the proceeds along wth ts lqud assets and possbly a new mortgage loan to buy a new house. Equvalently, households are forced to refnance ther home at the prevalng rate n the economy wth a probablty ω each perod. The household problem n the home-owner state can be formalzed as follows, U h = max a,b,irf [ ( u(c /p) + βe ω max U hh, U hr ) (, U hd + (1 ω) max U h, U hr )], U hd, (7) subject to, c + a 1 + (1 τ)r $ + b = (1 τ)(y k b ) + a + b (py φ 0 + φ 1 b )I RF, (b b ) (1 I RF ) 0, (b ξ H) I RF 0, k = k (1 I RF ) + R I RF, a, c, b 0. where we denote the value functon of the household n the home-owner state by U h (a, b, k, s ), by U hh (a, b, k, s ) n a state of refnancng the mortgage loan a current rates and remanng a home-owner, by U hr (a, b, k, s ) n a state of transton between beng a home-owner and a renter by sellng the home, and by U hd (a, b, k, s ) n a state of transton between beng a home-owner and a renter by defaultng on the mortgage. These problems wll be wrtten down explctly n what follows. Note that the cost of refnancng s the sum of a fxed component and a proportonal component. However, gven that the economy s growng over tme, the fxed cost of refnancng s assumed to be scaled wth the nomnal growth rate n the economy, that s, we 23

24 assume the followng functonal form, φ(b ) = py φ 0 + φ 1 b. The household problem n the home-owner state when forced to move can be formalzed as follows, U hh = max a,b [ ( u(c /p) + βe ω max U hh, U hr ) (, U hd + (1 ω) max U h, U hr )], U hd, (8) subject to, c + a 1 + (1 τ)r $ + b = (1 τ)(y k b ) + a + b (py φ 0 + φ 1 b ), k = R, b ξ H, a, c, b 0. Home-owners have the opton to sell ther home at any tme. When they do so, they repay the outstandng mortgage ncludng current mortgage coupon payment usng the proceeds, mnus the transacton cost φ 2, and ther stock of lqud assets. As a result, they become renters wth savngs equal to H(1 φ 2 ) (1+(1 τ)k)b +a. The transton problem for the household from the home-owner to the renter state by sellng hs home s gven by, U hr (a, b, k, s ) = max a u(c /p) + βe [U r (a, s )], (9) subject to, c + a 1 + (1 τ)r $ = (1 τ)(y k b ) + a + H(1 φ 2 ) b, a, c 0. 24

25 Home-owners have the opton to default on ther mortgage. When a household defaults on ts mortgage oblgaton b, the home s ceased, as well as a porton of ts lqud assets,.e. the household s left wth ζa (the parameter ζ could be seen as a way to capture full or partal recourse as well as other costs of default, such as ther effect on credt hstory, n reduced form). As a result, the stock of lqud assets s reduced and the household cannot borrow any more,.e. b = 0 as a renter. Furthermore, the household that defaulted on ts mortgage wll stay n the rental market for a stochastc perod of tme, and thus wll have random access to the opportunty to regan home-ownershp. In other words, households are allowed to regan home-ownershp status wth probablty θ each perod, f they fnd t optmal. The transton problem for the household from the home-owner to the renter state by defaultng on hs mortgage s gven by, U hd (a, b, k, s ) = max a u(c /p) + βe [ U d (a, s ) ], (10) subject to, c + a 1 + (1 τ)r $ = (1 τ)y + ζa, a, c 0. The value functons U h, U hh, U hr, and U hd, are condtonal on choosng that state. In addton the home-owner household has to choose whch of these states s optmal. The uncondtonal value functon for household n the home-owner state s denoted by V h (a, b, k, s ) and s defned as the best opton from remanng a home-owner, sellng or defaultng on ts mortgage and becomng a renter. When the household s not movng, wth probablty (1 ω) each perod, the value functon s defned as, V h = max ( U h, U hr ), U hd. (11) 25

26 However, when the household s movng, wth probablty ω each perod, the value functon s defned as, V h = max ( U hh, U hr ), U hd. (12) Renter Problem As a renter, a household must pay rent every perod. For tractablty, we assume that households wll allocate a constant fracton of ther consumpton toward that rent expense every perod. 4 Thus we assume that rent expense each perod s equal to ψc. In addton, we assume that households suffer a utlty loss of not beng home-owners gven by ψu(c /p), whch s decreasng n the level of rent. Ths smply states that households wll prefer, all else equal, to lve n a house they own rather than rent, and that a hgher rent wll afford a hgher qualty home, whch n turn lower the loss of utlty of rentng versus ownng. The household problem n the post sellng renter state wthout beng excluded from accessng home-ownershp s gven by, U r = max a [ ( )] (1 + ψ) u(c /p) + βe max U rh, U r, (13) subject to, (1 + ψ) c + a 1 + (1 τ)r $ = (1 τ)y + a, a, c 0. When n the post sellng renter state, the value functon for household s defned as the best opton from remanng a renter or becomng a home-owner, that s, V r = max ( ) U rh, U r. (14) 4 Ths assumpton can be mcrofunded by assumng that households choose the level of rent each perod as a statc choce and that they have a power utlty over real rent payment and that t s addtve to the utlty over real consumpton. 26

27 The transton problem for the household from the renter to the home-owner state s gven by, U rh (a, s ) = max a,b (1 + ψ) u(c /p) + β E [ U h (a, b, R, s ) ], (15) subject to, (1 + ψ) c + a 1 + (1 τ)r $ + H(1 φ 2) = (1 τ)y + a + b (py φ 0 + φ 1 b ), b ξ H, a, c, b Post Default Renter Problem The household problem n the post default renter state s gven by, U d = max a [ ( )] (1 + ψ) u(c /p) + βe (1 θ)u d + θ max U rh, U r, (16) subject to, (1 + ψ) c + a 1 + (1 τ)r $ = (1 τ)y + a, a, c 0, where we denote the value functon of the household n transton between the renter state and the home-owner state by U rh (a, s ). When n the post default renter state, the uncondtonal value functon for household s defned as the best opton from remanng a renter or becomng a home-owner f the excluson from home-ownershp perod ends,.e. wth probablty θ each perod, V d = max ( ) U rh, U r, (17) 27

28 or s smply equal to the value functon n post default renter state f the home-ownershp opton s unavalable to hm,.e. V d = U d. 3.6 Statonary Reformulaton of the Household Recursve Problem Let the household utlty be CRRA, u (c) = c1 γ, then we can rescale the problem wth 1 γ respect to the permanent aggregate ncome Y t and the prce level p t n order to make t statonary. We can rescale the varables, as well as the state vector such that the rescaled household problems are statonary. The algebrac detals are gven n the Appendx. 3.7 Household Optmal Polces The optmal polces for lqud asset holdngs, home loan, and mortgage rate are denoted by a = g,a (a, b, k, s), b = g,b (a, b, k, s), and k = g,k (a, b, k, s). In addton, the dscrete refnancng polcy s denoted by I RF = g,rf (a, b, k, s). The optmal repayment polcy denoted by I RP = g,rp (a, b, k, s) can be constructed out of the optmal loan and refnancng polces, I RP = I b b (1 I RF ). Smlarly the optmal no refnancng/repayment polcy denoted by I NR be constructed out of the optmal refnancng and repayment polces, = g,nr (a, b, k, s) can I NR = 1 I RP I RF. 4 Calbraton Results Ths secton descrbes the mplcatons of the model n Secton 3. There s no closed-form soluton for ths model, therefore we use numercal technques to approxmate t. Specfcally, 28

29 we dscretze the state space and apply standard numercal dynamc programmng and then smulate the optmal polces for a large panel of households. We explan the choce of the key parameters of the model and characterze the soluton. 4.1 Parameter Choce The model s calbrated at the yearly frequency. We estmate a VAR(1) for the aggregate state varables usng annual data: log S t+1 = µ S + Φ S log S t + Σ S ɛ S t+1. (18) The varables we use are the U.S. GDP growth rate adjusted for CPI nflaton (our proxy for the real growth varable Z n the model), the one-year Treasury bll rate as the nomnal short rate r t $, CPI growth rate (a measure of nflaton π), and demeaned log house prce-gdp rato computed usng the S&P Case-Shller house prce ndex (HPI) deflated usng the CPI. The macroeconomc varables used - the CPI, the real GDP, the real HPI, and the HPI/GDP rato are plotted n Fgure 4.1. The last varable captures the noton of hghly persstent but transtory devatons of house prces from the trend of real economc growth represented n the model by the state varable h. The descrptve statstcs for these varables (as well as the 30-year conformng mortgage rate our emprcal proxy for R) and the estmated parameters of the VAR are reported n Table 6. We then approxmate the VAR wth a dscrete-state Markov chan usng the method of Tauchen and Hussey (1991). The real growth rate of the economy Z s dscretzed usng 2 ponts to capture two macroeconomc states for growth. The bad state of the economy s denoted by Z B and s defned as the cases when the economy grows at the low rate and, conversely, the good state s denoted Z G and corresponds to the hgh growth rate. The short rate r $, the house prce process h, and the nflaton rate process π are dscretzed each as a 3-state Markov chan. Thus the aggregate state s dscretzed usng a total of 54 grd 29

30 240 CPI 70 GDP HPI 0.4 log(hpi) log(gdp) Fgure 4: Inflaton, real growth, and real house prces 30

31 Table 6: Aggregate State Varables Panel A: Descrptve Statstcs GDP r t $ CPI HPI/GDP R Mean Std Autocorrelaton correlatons: GDP r t $ CPI HPI/GDP Panel B: VAR Parameters µ Φ s Σ s 10 3 GDP r CPI HPI/GDP Panel C: Mortgage Rate Parameters κ 0 κ Z r π h (0.002) (0.050) (0.051) (0.092) (0.012) ponts. The choce of the long-run mean of the rato of house prce to ncome H = 4 s based on estmates obtaned usng mcro data (n the Survey of Consumer Fnances for 2001, a year when the house prce to GDP rato s close to ts long-run mean, the average rato of housng assets to ncome among homeowners wth postve ncome equals approxmately 3.95). For tractablty, we specfy the mortgage rate R as an exogenous functon of all the aggregate state varables. We choose the followng specfcaton, log R(S) = κ 0 + κ log S. (19) 31

32 Panel C of Table 6 reports the regresson estmates of the coeffcents of ths relaton usng the emprcal proxes for the state vector S and the mortgage rate R, wth the correspondng standard errors. Whle only the constant and the nterest-rate senstvty are statstcally sgnfcantly dfferent from zero, we use all of the estmated coeffcents n order to capture as much of potental comovement of the mortgage rate wth the macroeconomc varables as possble. The dosyncratc component of the ncome process ỹ t s dscretzed as a Markov chan wth 64 grd ponts. The condtonal volatlty depends on whether the economy s n the good or bad state, that s we choose a two-state representaton of the macroeconomc condtons, followng Storesletten, Telmer, and Yaron (2007). We use volatlty parameters that are on the hgher end of ther estmates n order to emphasze the effect of heteroscedastcty on refnancng. In our benchmark calbraton, the condtonal volatlty of the log dosyncratc ncome component n the good states (when t s low) s σ y,g = 18%, whereas n the bad state, the condtonal volatlty s hgh σ y,b = 40%. The autocorrelaton parameter ρ Y = 0.85 s n the mddle of the estmates n the lterature (see dscusson n secton 4.5 below). Table 7 summarzes the parameters we use for the numercal analyss. The preference parameters (the subjectve dscount factor β = 0.97 and the curvature of the utlty functon γ = 3) are chosen so that the mean and standard devaton of aggregate consumpton growth are close to those n the NIPA data. The mortgage rates are hgher than the subjectve rate of tme preference, so that mortgages are a costly form of borrowng and households prefer to pay down ther balances. The cost of refnancng s set so as to generate emprcally reasonable average refnancng rates. Based on anecdotal evdence of explct costs of roughly 2 5% pad when refnancng a mortgage loan of average sze n addton to non-pecunary nformaton processng costs and the opportunty cost of tme requred to process the transacton, we choose a fxed cost of 5% and a proportonal cost of 5% (whch s somewhat hgher than the costs calbrated by Campbell and Cocco (2003)). 32