1# RECORD bcf745178dcc691b18c9d83f1fe5e6d55eff9a852# TITLE: Three essays on real estate finance3# YEAR: 2011.0 VENUE: nan DOI: 10.31390/gradschool_dissertations.16534# AUTHORS: Shuang Zhu5# PAGES: 69 CANDIDATE TABLE PAGES (1-based): [20, 23, 24, 39, 40, 42, 45, 46, 47, 58, 61, 63, 64]6# ABSTRACT: time structure in the housing market such that only earlier housing transactions are taken for predicting future house values. Our findings show that accounting for spatial and temporal dependence in traditional hedonic pricing model is not only theoretically warranted, but also contributing to better prediction performance. As a789===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) =====1011Louisiana State University 12Louisiana State University 13LSU Scholarly Repository 14LSU Scholarly Repository 15LSU Doctoral Dissertations 16Graduate School 172011 18Three essays on real estate finance 19Three essays on real estate finance 20Shuang Zhu 21Louisiana State University and Agricultural and Mechanical College 22Follow this and additional works at: https://repository.lsu.edu/gradschool_dissertations 23 Part of the Finance and Financial Management Commons 24Recommended Citation 25Recommended Citation 26Zhu, Shuang, "Three essays on real estate finance" (2011). LSU Doctoral Dissertations. 1653. 27https://repository.lsu.edu/gradschool_dissertations/1653 28This Dissertation is brought to you for free and open access by the Graduate School at LSU Scholarly Repository. It 29has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU 30Scholarly Repository. For more information, please contactgradetd@lsu.edu. 313233===== PAGE 20 (score 50, numeric-paren 36, table-words 2, var-words 2) =====3435TABLE 1.2. Differencing Regressions for Appraisal Bias36(1)37(2)38(3)39Lender-Borrower40Lender-Referee41Borrower-Referee42Experienceδ430.0103∗∗440.0118∗∗∗45−0.0072∗∗∗46(0.0040)47(0.0016)48(0.0009)49Specializationδ50−0.021851−0.0295∗∗520.011853(0.0169)54(0.0136)55(0.0105)56LAδ570.0217∗∗580.0263∗∗∗59−0.0169∗∗60(0.0085)61(0.0090)62(0.0077)63RSδ640.1197∗∗∗650.0622∗∗∗660.0238∗∗∗67(0.0221)68(0.0126)69(0.0066)70CEδ71−0.0443∗∗∗72−0.0322∗∗730.002574(0.0158)75(0.0138)76(0.0100)77Land78−0.003179−0.004380−0.001281(0.0082)82(0.0060)83(0.0038)84Pop85−0.0620∗∗86−0.0270870.012888(0.0249)89(0.0181)90(0.0115)91Black920.0048930.0014940.004395(0.0108)96(0.0078)97(0.0050)98Income99−0.0279100−0.01811010.0169102(0.0278)103(0.0201)104(0.0128)105HousePrice1060.0616∗∗1070.0427∗∗108−0.0052109(0.0257)110(0.0186)111(0.0119)112Owner1130.0452∗1140.0211∗115−0.0196116(0.0263)117(0.0118)118(0.0175)119Constant120−0.3024121−0.2654122−0.0448123(0.2387)124(0.1735)125(0.1109)126N127153212815321291532130R21310.09081320.17981330.0653134RMSE1350.19271360.14001370.0893138F13913.799614030.28561419.6545142Standard errors in parentheses143∗p < 0.10, ∗∗p < 0.05, ∗∗∗p < 0.0114413145146147===== PAGE 21 (score 7, numeric-paren 5, table-words 1, var-words 0) =====148149is difficult by inspection of the differences between the borrower and referee ap-150praisals as well as between the lender and referee appraisals to assess the accuracy151of the borrower and lender appraisers since the referee has knowledge of both152appraisals before forming their opinion. Although this most likely increases the153referee accuracy, it complicates the analysis of the variance.3 To address this issue,154in the following section we examine the random appraisal error from contrasting155borrower and lender appraisals. Since borrower and lender appraisals most likely156have similar random errors (after filtering out biases), this aids in estimating the157underlying accuracy of appraisers.1581.2.5159Appraiser Accuracy160According to equation (1.3), given the borrower and lender appraisals are done161independently of each other (which implies statistical independence), this yields162(1.6).163σ2164ε(B)−ε(L)165=166σ2167ε(B) + σ2168ε(L)169(1.6)170Given the further assumption that the variances of the random errors for lender171and borrower appraisers are the same yields (1.7).172σε(B)173=174σε(L) = (0.5σ2175ε(B)−ε(L))1/2176(1.7)177The RMSE for the borrower lender contrast regression (appraisal differences fil-178tered for systematic effects) is an estimate of σε(B)−ε(L). Therefore, from Table 1.2179regression one, we could calculate the standard deviation of the appraisal error as1803The referee valuation is thus “anchored” and this can increase error rates in some cases (Diaz and Hansz,1812001). However, given the magnitude of biases in this setting, a referee may serve a very useful role.18214183184185===== PAGE 23 (score 26, numeric-paren 9, table-words 7, var-words 3) =====186187in Table 1.2. According to equation (1.8), the appraisal variance could be explained188by appraiser characteristics and neighborhood characteristics.189ˆσ2190i,ε(o)191=192x(o)193i γ + ziδ(o) + ϵ(o)194i , o = L, B195(1.8)196However, we could not observe the variance of lender or borrower appraisals. But197we could use the residuals ei from regression one in Table 1.2 as the proxy for198σε(B)−ε(L). Substituting equation (1.8) into equation (1.6) yields (1.9) which reduces199to the estimation equation (1.10). As shown in equation (1.9), Xa is the average of200borrower and lender appraiser characteristics. Thus, Experiencea, Specializationa,201LAa and RSa for the residual regression are defined as the average of lender and202borrower appraisers’ experience, specialization, LA and RS. The estimation results203appear in Table 1.3.204ln(e2205i /2)206=2070.5(x(L)208i209+ x(B)210i211)γ + 0.5zi(δ(L) + δ(B)) + 0.5(ϵ(L)212i213+ ϵ(B)214i215)216(1.9)217y218=219Xaγ + Zδa + ϵ220(1.10)221Table 1.3 shows that experience and licensing strongly reduce the variance of222the residuals, and real estate agents are less accurate. None of the census variables223is statistically significant.224To make this more concrete we examine specific cases in Table 1.4 to see how225the implied standard deviation and mean absolute error of appraisal error vary by226appraiser licensing and experience. We examine licensed and unlicensed appraisers227with three levels of experience (5, 50, and 250 appraisals performed for distressed228properties in the past two years) in Table 1.4. Census data and the specialization229variable are evaluated at their mean values.23016231232233===== PAGE 24 (score 25, numeric-paren 11, table-words 4, var-words 2) =====234235TABLE 1.3. Residual Regression for Appraisal Accuracy yi = ln(e2236i /2)237Residual Regression238Experiencea239−0.4744∗∗∗240(0.0793)241Specializationa2420.4132243(0.4965)244LAa245−1.1010∗∗∗246(0.3031)247RSa2482.5480∗∗∗249(0.5884)250Land2510.0164252(0.1083)253Pop254−0.2114255(0.3275)256Black2570.0400258(0.1422)259Income2600.0945261(0.3647)262HousePrice263−0.1823264(0.3386)265Owner266−0.1133267(0.2144)268Constant269−0.5448270(3.1512)271N2721532273R22740.0970275RMSE2762.5414277F27816.3363279Standard errors in parentheses280∗p < 0.10, ∗∗p < 0.05, ∗∗∗p < 0.01281TABLE 1.4. Implied Standard Deviation and Mean Absolute Error of Random Appraisal282Error For Varying Appraiser Licensing and Experience283Cases284Licensed Appraiser285Experience286Std. Dev.287MAE2881289No29052910.22032920.17572932294No295502960.12762970.10182983299No3002503010.08713020.06953034304Yes30553060.12703070.10133085309Yes310503110.07363120.05883136314Yes3152503160.05023170.040131817319320321===== PAGE 25 (score 6, numeric-paren 0, table-words 1, var-words 4) =====322323Table 1.4 makes the role of experience and licensing clear. Although the average324appraisal has an implied MAE of 10.88 percent, experienced licensed appraisers325can perform much better than that. In the best scenario of a very experienced326licensed appraiser as in case 6, the appraisal accuracy is 4.01 percent, slightly327higher than the relocation appraisers examined by Dotzour (1988) who have a328MAE of 2.77 percent. Going to a licensed appraiser who has done 50 appraisals329of distressed properties in the last two years raises the MAE to 5.88 percent. In330contrast, unlicensed appraisers with almost no experience can have an implied331MAE of 17.57 percent as shown in case 1.332The inaccuracy of inexperience appraisers has implications for programs rely-333ing on appraisals. Any major program that requires a large number of distressed334properties to be revalued in a short time will need to rely on inexperienced ap-335praisers to handle the workload as the number of appraisers that perform a large336number of appraisals in this specialized area is limited. However, inexperienced337appraisers will likely not perform well and this will pose a problem for programs338that assume accurate valuations are possible. Various loan modification programs339such as the Home Affordable Modification Program, the practice of “lien strip-340ping” where the principal on a second mortgage is reduced so that the principal on341both the first and second mortgages do not exceed the estimated market value (set342by appraisals), and refinancing guidelines (such as those in the Home Affordable343Modification Program) all tacitly assume that an appraiser can make an accurate344determination of market value for a distressed property.345Similarly, attempts to reduce bias in appraisal sometimes may result in lower346accuracy. The Home Valuation Code of Conduct promotes the use of Appraisal347Management Companies (AMC) which may hire inexperienced appraisers that are348not familiar with the area. In effect, an appraiser going into an unfamiliar area34918350351352===== PAGE 39 (score 106, numeric-paren 84, table-words 1, var-words 3) =====353354TABLE 2.3. Hazard Model of Default with Different Model Specification355(1)356(2)357(3)358(4)359(5)360State FE361No Delay362With Delay363Year FE364Mean365Smooth366ForeclosureDelay3670.0749∗∗3680.0618∗∗3690.0940∗∗3700.1013∗∗371(0.0146)372(0.0180)373(0.0218)374(0.0239)375ExoticARM3760.6443∗∗3770.6613∗∗3780.6581∗∗3790.6346∗∗3800.6340∗∗381(0.0282)382(0.0256)383(0.0248)384(0.0242)385(0.0248)386HybridARM3870.6554∗∗3880.6449∗∗3890.6525∗∗3900.6216∗∗3910.6209∗∗392(0.0187)393(0.0165)394(0.0150)395(0.0202)396(0.0204)397ExoticFRM3980.2747∗∗3990.2821∗∗4000.2740∗∗4010.2787∗∗4020.2781∗∗403(0.0431)404(0.0462)405(0.0458)406(0.0460)407(0.0465)408RegARM4090.4526∗∗4100.4302∗∗4110.4140∗∗4120.4044∗∗4130.4062∗∗414(0.0653)415(0.0634)416(0.0625)417(0.0631)418(0.0634)419LTV14200.0231∗∗4210.0240∗∗4220.0239∗∗4230.0255∗∗4240.0256∗∗425(0.0020)426(0.0020)427(0.0019)428(0.0015)429(0.0014)430PiggyBack4310.5375∗∗4320.5424∗∗4330.5469∗∗4340.5389∗∗4350.5379∗∗436(0.0376)437(0.0333)438(0.0312)439(0.0317)440(0.0313)441Interest4420.0724∗∗4430.0682∗∗4440.0659∗∗4450.0704∗∗4460.0701∗∗447(0.0084)448(0.0070)449(0.0076)450(0.0070)451(0.0070)452FICO453−0.8210∗∗454−0.8078∗∗455−0.8101∗∗456−0.8059∗∗457−0.8066∗∗458(0.0426)459(0.0426)460(0.0424)461(0.0380)462(0.0377)463FullDoc464−0.3477∗∗465−0.3516∗∗466−0.3474∗∗467−0.3518∗∗468−0.3522∗∗469(0.0346)470(0.0364)471(0.0365)472(0.0345)473(0.0345)474Investor4750.07774760.07144770.07164780.08234790.0828480(0.0445)481(0.0452)482(0.0463)483(0.0440)484(0.0440)485Purchase486−0.0125487−0.0198488−0.0092489−0.0179490−0.0184491(0.0150)492(0.0159)493(0.0144)494(0.0162)495(0.0161)496LoanAmount4970.00304980.0045∗∗4990.0046∗∗5000.00305010.0029502(0.0026)503(0.0016)504(0.0015)505(0.0019)506(0.0019)507LoanAge508−0.5046∗∗509−0.5411∗∗510−0.5917∗∗511−0.5659∗∗512−0.5620∗∗513(0.0144)514(0.0203)515(0.0319)516(0.0276)517(0.0295)518PrepayPenalty5190.11245200.14425210.1466∗∗5220.1852∗∗5230.1843∗∗524(0.0620)525(0.0564)526(0.0569)527(0.0579)528(0.0579)529RateDiff530−0.3650∗∗531−0.3120∗∗532−0.2533∗∗533−0.3502∗∗534−0.3620∗∗535(0.0425)536(0.0392)537(0.0239)538(0.0376)539(0.0314)540PastAppr541−1.0549∗∗542−1.3477∗∗543−0.9493∗∗544−1.5329∗∗545−1.2967∗∗546(0.1647)547(0.1262)548(0.1475)549(0.1470)550(0.1414)551Lag Unemployment552−0.2018∗∗553−0.2272∗∗554−0.2463∗∗555−0.2736∗∗556−0.2702∗∗557Continued on next page55832559560561===== PAGE 40 (score 60, numeric-paren 50, table-words 0, var-words 1) =====562563(1)564(2)565(3)566(4)567(5)568No Delay569With Delay570Year571Mean572Smooth573(0.0274)574(0.0300)575(0.0315)576(0.0483)577(0.0477)578Income579−0.03005800.03965810.01865820.04085830.0424584(0.1725)585(0.1563)586(0.1494)587(0.1290)588(0.1301)589Rent5900.10555910.08525920.1026593−0.0481594−0.0456595(0.2155)596(0.1511)597(0.1510)598(0.1409)599(0.1397)600Population601−0.00616020.04016030.03116040.03686050.0364606(0.0461)607(0.0455)608(0.0454)609(0.0375)610(0.0373)611White6120.02886130.00486140.0094615−0.0469∗∗616−0.0473∗∗617(0.0405)618(0.0350)619(0.0377)620(0.0175)621(0.0175)622Age656230.0067624−0.0172625−0.00526260.02646270.0272628(0.0267)629(0.0332)630(0.0313)631(0.0300)632(0.0298)633Education634−1.2855∗∗635−1.2222∗∗636−1.2992∗∗637−1.2034∗∗638−1.2043∗∗639(0.2802)640(0.3048)641(0.3091)642(0.2983)643(0.2991)644SchoolageChildren6450.48406460.86276470.88466480.51976490.5157650(0.4255)651(0.5915)652(0.5479)653(0.4202)654(0.4175)655CommuteTime6560.37796570.24376580.21136590.12606600.1305661(0.1672)662(0.1798)663(0.1762)664(0.0688)665(0.0709)666SameHouse6670.1434668−0.3609669−0.3252670−0.5641∗∗671−0.5690∗∗672(0.3265)673(0.2235)674(0.2055)675(0.1715)676(0.1741)677Default(in%)6783.13679Number of Obs6804118336681LikelihoodRatio682127756683129484684116217685125904686125834687-2 lnL68829917286892989999690275320269124870996922487170693∗∗p < 0.0169433695696697===== PAGE 41 (score 5, numeric-paren 0, table-words 1, var-words 2) =====698699Across various specifications, foreclosure delay consistently shows a statistically700significant effect in increasing the borrower’s propensity to default.15 The results701are consistent with the prediction of Ambrose et al. (1997) theoretical paper. The702next important question is, whether the expected benefit from default has a ma-703terial economic effect on default propensity? To make the economic significance704of foreclosure delays clearer, Table 2.4 reports the marginal effects and equiva-705lent changes associated with a given month increase in foreclosure delay corre-706sponding to the two different measures of delay as in regression four and five.707The marginal effects represent the percentage change in the hazard ratio associ-708ated with an increase of the delay. Since hazard ratio is not very intuitive,16 a709more intuitive way to gauge the economic importance of a variable is by com-710paring the marginal effects between variables in the same regression. That is by711calculating the equivalent changes in other variables corresponding to the same712marginal effects of the variable of interest. We pick updated LTV ratio and Fico713score as the benchmark variables since those are important risk factors and are714also continuous variables. Based on state mean foreclosure measures as in regres-715sion four, a three-month increase in foreclosure time increases the hazard of default716by 32.58 percent (exp (0.094 · 3) −1 = 32.58%). In terms of equivalent changes,717that matches the same marginal effect of increasing the LTV ratio by 11.06 percent718(exp (0.0255 · 11.06) −1 = 32.58%), or a decrease in the Fico score by 34.99 points719(exp (−0.8059 · −34.99/100)−1 = 32.58%). Note that these estimates are based on720the overall sample including those borrowers with positive equity on their house.72115As a robustness check, the results are similar when using lagged state median foreclosure delays as the proxy722for borrower expected delays.72316For example, for the Cox hazard model, the marginal effect tends to be larger for all variables for samples724with lower default rates and be lower for samples with higher default rates.72534726727728===== PAGE 42 (score 10, numeric-paren 0, table-words 2, var-words 4) =====729730For borrowers with negative equity, we expect that the economic impact would be731even stronger.732TABLE 2.4. Marginal Effects of Foreclosure Delays and Equivalent Changes in Other733Variables734Increase in Foreclosure Delay (in month)735Variable7361737273837396740Panel A741State Mean742Marginal Effect (%)7439.8674420.6874532.5874675.77747LTV1 (%)7483.697497.3775011.0675122.12752FICO753−10.94754−21.89755−32.83756−65.66757Panel B758Smooth759Marginal Effect (%)76010.6676122.4676235.5176383.64764LTV1 (%)7653.967667.9176711.8776823.74769FICO770−12.56771−25.12772−37.68773−75.35774Other explanatory variables have the expected signs. The results show that de-775fault reflects borrower expectations, incentives, and preferences. Specifically, bor-776rowers with less equity as measured by a higher updated LTV ratio, second lien777status, and thus with less equity, have a higher propensity to default. Borrowers778that have selected more exotic and complicated loans have a higher propensity779to default. Borrowers with a lower credit score and less documentation are more780likely to default. Borrowers with a greater payment burden such as those with781higher contract rates or higher borrowed amounts tend to have a higher chance of782default. Borrower with a longer payment history are less likely to default. Areas783with better educated population reduce the probability of default. Macroeconomic784conditions also affect the performance of loans.7852.4.2786Robustness Checks787This section conducts robustness checks of the impact of foreclosure time on bor-788rower’s default behavior. Because regression four has the highest model fit as shown789in Table 2.3, we pick regression four as our baseline regression. All following re-79035791792793===== PAGE 43 (score 6, numeric-paren 0, table-words 2, var-words 2) =====794795gressions in this section and next section include the same explanatory variables796as the baseline regression, including the state fixed effect and using the lag year797state mean foreclosure delay.798Our first concern is whether the effect is driven by a specific state. For example,799California constitutes a substantial proportion of our sample. In order to check800this, we take one state out of the sample at a time and run the regression using801the mortgages from the rest of the states, Table 2.5 reports the results for the five802largest states in our sample.17 Panel A reports the estimate and model fit statistics803and panel B reports the marginal effect and the equivalent changes corresponding804to a three-month increase in delay. The results show that the impact of delay is805not driven by a specific state. The marginal effect of a three-month increase in806delay, is equivalent to an increase of LTV ratio by 10.14 percent to 18.20 percent807or a 31.81 to 58.43 points decrease in Fico score. Interestingly, when California or808Florida is taken out of the sample, the impact of delay is increased, although the809increase might not necessarily be significant.810Our second concern is the accuracy of the data since mortgage data has many811limitations. Typically, borrower characteristics are measured carefully only at orig-812ination. After origination, most servicers do not rescore the borrower’s credit or813reappraise the property value using either traditional appraisals or automated val-814uation models. In addition, most data files do not contain accurate amounts for815junior liens after origination. Consequently, the most accurate data exists at orig-816ination. In order to control for the accuracy of data, we report the results by817tracking the first one, two, three or four years of loan performances after loan orig-818ination. Table 2.6 reports the estimate and the comparative statics. The magnitude81917Other states have similar results. For simplicity, we included only the largest states results.82036821822823===== PAGE 45 (score 12, numeric-paren 4, table-words 2, var-words 2) =====824825TABLE 2.6. Robustness Checks by Number of Years of Loan Performance Tracked826(1)827(2)828(3)829(4)830Panel A831One Year832Two Years Three Years Four Years833ForeclosureDelay8340.1094∗8350.1354∗∗8360.1011∗∗8370.0949∗∗838(0.0542)839(0.0469)840(0.0195)841(0.0218)842Default(in%)8430.948441.928452.728463.09847Number of Obs848666546849219711285032792248513865093852LikelihoodRatio85373948544728485593570856118313857-2 lnL85810863785982097086017454918612343463862Panel B863Marginal Effects (3M) and Equivalent Changes864Marginal Effect (%)86538.8586650.1186735.4386832.94869LTV1 (%)87010.5587113.9187211.1187310.99874FICO875−55.21876−51.37877−37.30878−35.27879∗∗p < 0.01∗p < 0.05880default, transaction costs, and reputation costs (Kau and Kim, 1994; Kau et al.,8811994; Foote et al., 2008). Higher initial combined LTV ratio loans are less resistant882to house price depreciation and more likely to have an “in the money” default883option. When the default option is “in the money,” foreclosure delay tends to have884a material effect on changing the borrower’s propensity to default.885Table 2.7 reports the results by different initial combined LTV ratio subsamples.886For loans with combined LTV ratio greater than 80 percent, the borrower’s default887decision is statistically very sensitive to expected delay. As the combined LTV ratio888decreases, to below 80 percent, the statistical significance declines, and the effect889disappears when combined LTV ratio is less than 70 percent. As for economic890significance, the magnitudes of effect are much higher for loans with combined891LTV ratio greater than 95 percent than loans with combined LTV less than 80892percent. Our empirical findings are very consistent with the theoretical prediction.893The results indicate that in a deteriorated housing market, when borrowers are89438895896897===== PAGE 46 (score 16, numeric-paren 6, table-words 3, var-words 1) =====898899likely to have negative equity, the increase in expected delay tends to have a larger900and more significant impact in increasing default.901TABLE 2.7. Subsamples by Initial CLTV Ratios902(1)903(2)904(3)905(4)906(5)907(6)908Panel A909CLTV<7091070-8091180-9091290-9591395-100914100<CLTV915ForeclosureDelay9160.03609170.0649∗9180.0627∗∗9190.0483∗∗9200.1235∗∗9210.1491∗∗922(0.0327) (0.0305)923(0.0235)924(0.0180)925(0.0271)926(0.0268)927Default(in%)9281.189292.349303.519314.489324.659336.16934Number of Obs9351136076936798112937626715938441045939192625940514574941LikelihoodRatio94218216943169589442834794512579946539194712936948-2 lnL949218957950302258951610022952304996953120200954501589955Panel B956Marginal Effects (3M) and Equivalent Changes957Marginal Effect (%)95821.4995920.7096015.5996144.8596256.41963FICO964−19.42965−23.16966−19.50967−51.32968−73.39969∗∗p < 0.01∗p < 0.05970Next we investigate if the effect of expected delay is sensitive to different loan971types or borrower’s credit score. We focus on loans with initial combined LTV972greater than 95 percent. Table 2.8 report the results of subsamples of different973loan types. Table 2.9 reports the results of the subsamples according to different974borrower’s credit score. Across different types of loans and different borrower’s975credit scores, expected delays consistently increase the default propensity. For very976high credit score borrowers, the effect is only significant at the 5 percent level. This977may due to the cost of damaging credit score and reputation cost, which may offset978the benefits from “free rent.”979In conclusion, the effect of foreclosure delay is stronger when borrowers are980likely to have negative equity such as in the current housing market. The increase981in foreclosure time might change borrower’s expected benefit from default, and982thus at the margin make default the optimal decision.98339984985986===== PAGE 47 (score 18, numeric-paren 10, table-words 2, var-words 1) =====987988TABLE 2.8. Subsamples by Loan Types for Initial CLTV>95% Loans989(1)990(2)991(3)992(4)993Panel A994ExoticARM HybridARM ExoticFRM995FRM996ForeclosureDelay9970.1598∗∗9980.1311∗∗9990.2023∗∗10000.1469∗∗1001(0.0271)1002(0.0503)1003(0.0222)1004(0.0534)1005Default(in%)10066.7010077.0510084.6810092.791010Number of Obs10113154201012844951013691791014662651015LikelihoodRatio101672571017204510181549101913621020-2 lnL10213290781022746551023393141024207631025∗∗p < 0.01∗p < 0.051026TABLE 2.9. Subsamples by Fico Scores For Initial CLTV>95% Loans1027(1)1028(2)1029(3)1030(4)1031(5)1032(6)1033Panel A1034Fico≤6201035620-6601036660-7001037700-7401038740-7801039780<Fico1040ForeclosureDelay10410.1200∗∗10420.1818∗∗10430.2174∗∗10440.2278∗∗10450.1945∗∗10460.1553∗1047(0.0336)1048(0.0355)1049(0.0453)1050(0.0356)1051(0.0476)1052(0.0791)1053Default(in%)10549.6110557.8410566.2710575.0110583.8010593.011060Number of Obs106154715106291792106314346910641389471065827361066256461067LikelihoodRatio10686116510699091410701241201071968621072408451073183271074-2lnL10759661076153910772361107825431079151710803431081∗∗p < 0.01∗p < 0.05108240108310841085===== PAGE 48 (score 3, numeric-paren 0, table-words 0, var-words 3) =====108610872.51088Conclusion1089The benefit of default rises with the length of the interval between the first miss-1090ing payment and the date of foreclosure sale. Therefore, the higher option value1091associated with the expected longer foreclosure periods increase the incentive to1092default.1093This paper empirically investigates the influence of expected foreclosure delays1094on borrower’s default propensities. The paper uses the actual time-varying state-1095level foreclosure times as proxies for the borrowers’ expected benefit from default in1096the form of “free rent.” While existing literature includes a single-year state non-1097contested foreclosure times as proxies for lengthiness of the foreclosure process,1098our measure includes the actual delay and captures the variation in foreclosure1099delays over time. We document the increase of delay in recent years and find a1100statistically and economically significant impact of expected delay on borrower1101default behavior. The results are robust to various specifications including state1102fixed effects, different measures for delays, and temporal fixed effects. The results1103are not driven by major states in the sample nor by the number of years of tracked1104loan performances. For high initial combined LTV ratio mortgages, the delay has1105stronger impact on default and the effect is consistent across various loan types1106and borrowers with different credit scores. Our empirical findings are consistent1107with the predictions of Ambrose et al. (1997) theoretical paper.1108From the viewpoints of elected leaders in state and local government, not much1109good comes from foreclosures. Mortgage borrowers are potential voters and survival1110bias ensures that elected leaders pay attention to such groups. Therefore, it is1111tempting for officials such as elected judges, sheriffs, and legislators to delay the1112foreclosure process through slow performance or through more explicit tactics such1113as a moratorium.111441111511161117===== PAGE 58 (score 38, numeric-paren 30, table-words 1, var-words 0) =====11181119TABLE 3.3. Pearson Correlation Coeffients between Housing Expectations from Futures1120and other Proxies1121CBSA Past CSI Past FHFATime Series1122144601123−0.294611240.05681125−0.39451126(0.0522)1127(0.7144)1128(0.0081)11291698011300.318911310.226711320.30611133(0.0348)1134(0.1389)1135(0.0433)11361974011370.214211380.29091139−0.02561140(0.1626)1141(0.0554)1142(0.8692)1143298201144−0.21701145−0.14311146−0.10581147(0.1571)1148(0.3541)1149(0.4942)11503110011510.627911520.566411530.69071154(0.0000)1155(0.0001)1156(0.0000)11573310011580.13311159−0.143311600.56121161(0.3892)1162(0.3535)1163(0.0001)11643562011650.703611660.656011670.70801168(0.0000)1169(0.0000)1170(0.0000)11714174011720.516911730.482011740.70941175(0.0003)1176(0.0009)1177(0.0000)1178418601179−0.032311800.093511810.02031182(0.8352)1183(0.5459)1184(0.8958)11854790011860.05991187−0.04591188−0.02341189(0.6994)1190(0.7673)1191(0.8800)119251119311941195===== PAGE 59 (score 5, numeric-paren 2, table-words 0, var-words 3) =====11961197a semi-parametric technique that does not require choosing a specific probability1198distribution of the survival time, and is considered a more robust approach.1199The model specification is as in (3.1), where h(t) is the hazard function of de-1200fault and λ0(t) is called the baseline hazard function. The explanatory variables1201in X include both static variables which are obtained at origination and time-1202varying variables which are updated quarterly. The event of interest is default,1203with prepayment as the competing risk.1204h(t, X) = λ0(t) exp(Xβ)1205(3.1)12063.3.21207Housing Expectations and Default1208In making the decision to default, borrowers weigh the benefit of keeping the house1209versus the cost of making the mortgage payments. Expected house prices play a1210central role in the valuation process. On the one side, the value of house to the1211borrower includes the expected future house price. On the other side, as Kau1212and Kim (1994) and Kau et al. (1994) noted, the cost of the mortgage payments1213to the borrower needs to take into consideration the value of the future default1214option. This future default option value is affected by the expected future house1215price. Foote et al. (2008) used a two time period model to illustrate that higher1216expectations of future house prices reduce the incentive to default even in face1217of current negative equity since borrowers are in hope of market recovery in the1218future, which may bring them to positive equity.1219Despite of the importance of housing expectations, the existing proxies are1220mainly model based and backward-looking in nature. In a normal housing market1221when housing prices are relatively predictable, these measures might work well.1222However, in the recent housing market, those model based measures performed122352122412251226===== PAGE 61 (score 91, numeric-paren 72, table-words 1, var-words 3) =====12271228TABLE 3.4. Different Proxies for Housing Expectations1229Futures1230Past CSI1231Past FHFA Time Series1232Expectation1233−0.0133∗∗12340.002012350.00761236−0.00181237(0.0040)1238(0.0037)1239(0.0036)1240(0.0012)1241CLTV12420.0229∗∗12430.0228∗∗12440.0238∗∗12450.0218∗∗1246(0.0018)1247(0.0020)1248(0.0015)1249(0.0022)1250PiggyBack12510.5780∗∗12520.5771∗∗12530.5759∗∗12540.5778∗∗1255(0.0380)1256(0.0393)1257(0.0387)1258(0.0398)1259Interest12600.0749∗∗12610.0744∗∗12620.0737∗∗12630.0753∗∗1264(0.0079)1265(0.0075)1266(0.0073)1267(0.0080)1268FICO1269−0.7787∗∗1270−0.7741∗∗1271−0.7742∗∗1272−0.7765∗∗1273(0.0406)1274(0.0421)1275(0.0426)1276(0.0428)1277FullDoc1278−0.3856∗∗1279−0.3926∗∗1280−0.3976∗∗1281−0.3865∗∗1282(0.0466)1283(0.0505)1284(0.0481)1285(0.0475)1286ExoticARM12870.5439∗∗12880.5464∗∗12890.5372∗∗12900.5499∗∗1291(0.0418)1292(0.0453)1293(0.0462)1294(0.0432)1295HybridARM12960.5855∗∗12970.5803∗∗12980.5680∗∗12990.5876∗∗1300(0.0238)1301(0.0265)1302(0.0263)1303(0.0237)1304ExoticFRM13050.2199∗∗13060.2231∗∗13070.2200∗∗13080.2248∗∗1309(0.0490)1310(0.0495)1311(0.0500)1312(0.0486)1313RegARM13140.3725∗∗13150.3635∗∗13160.3563∗∗13170.3717∗∗1318(0.0652)1319(0.0627)1320(0.0668)1321(0.0643)1322Investor13230.085113240.077813250.081813260.07411327(0.0470)1328(0.0495)1329(0.0492)1330(0.0480)1331Purchase1332−0.00661333−0.00541334−0.011413350.00091336(0.0189)1337(0.0184)1338(0.0151)1339(0.0204)1340LoanAmount13410.000413420.002413430.002313440.00201345(0.0056)1346(0.0030)1347(0.0031)1348(0.0038)1349LoanAge1350−0.4098∗∗1351−0.4272∗∗1352−0.4354∗∗1353−0.4339∗∗1354(0.0246)1355(0.0208)1356(0.0202)1357(0.0190)1358PrepayPenalty13590.021513600.037013610.045413620.02701363(0.0491)1364(0.0455)1365(0.0434)1366(0.0500)1367RateDiff1368−0.1784∗∗1369−0.1799∗∗1370−0.1594∗∗1371−0.1891∗∗1372(0.0589)1373(0.0552)1374(0.0588)1375(0.0544)1376Lag Unemployment1377−0.1809∗∗1378−0.1817∗∗1379−0.1777∗∗1380−0.1803∗∗1381(0.0349)1382(0.0385)1383(0.0381)1384(0.0392)1385Income1386−0.3858∗∗1387−0.4094∗∗1388−0.4186∗∗1389−0.4032∗∗1390(0.0651)1391(0.0676)1392(0.0689)1393(0.0664)1394-2lnL139516235391396162389213971623747139816238261399∗∗p < 0.01140054140114021403===== PAGE 62 (score 10, numeric-paren 0, table-words 2, var-words 6) =====14041405−1.32%). An expected one percent decrease in housing expectation increases the1406hazard of default by 1.34 percent (exp (−0.0133 · −1)−1 = 1.34%). Given the pes-1407simistic outlook of housing market, this indicates that the current large number1408of defaults might be partly due to strategic default which is caused by not only1409negative equity but also the low expectation of future housing prices.1410Other variables have the expected signs. Higher current loan-to-value ratio, hav-1411ing a second lien, and a higher interest rate lead to higher propensity to default.1412Higher Fico scores and full documentation decrease the propensity to default.1413Various exotic loans increase the propensity to default relative to the fully amor-1414tized fixed rate mortgages. Seasoned loans have a lower probability of default.1415Macroeconomic conditions such as the lagged unemployment also affect the loan1416performances. Neighborhoods with higher incomes have lower default rates.14173.3.31418Robustness Checks1419Next we conduct various robustness checks by including year and/or state dum-1420mies to capture temporal and/or state fixed effects. Other variables and model1421specifications are the same as in Table 3.4. Table 3.5 reports the regression results.1422For simplicity, we only report the estimates of housing expectations. Panel A re-1423gressions include only annual dichotomous variables. Panel B regressions include1424only the state dichotomous variables and Panel C regressions include both state1425and year dichotomous variables. Across different specifications, futures consistently1426have a better model fit and the coefficients are significant and negative. Past CSI1427and past FHFA have mixed signs and remain insignificant. When year dummies are1428included, time series forecasts become significantly negative, but turn insignificant1429as state dummies are added in the regression.143055143114321433===== PAGE 63 (score 16, numeric-paren 12, table-words 1, var-words 0) =====14341435TABLE 3.5. Robustness Checks1436Futures1437Past CSI Past FHFA Time Series1438Panel A1439Year Dummies Included1440Expectation1441−0.0195∗∗1442−0.001314430.00491444−0.0039∗∗1445(0.0050)1446(0.0051)1447(0.0052)1448(0.0014)1449-2lnL145016226161451162328614521623216145316230761454Panel B1455State Dummies Included1456Expectation1457−0.0072∗∗1458−0.00581459−0.00351460−0.00201461(0.0028)1462(0.0036)1463(0.0057)1464(0.0015)1465-2lnL146616216961467162175614681621759146916217311470Panel C1471Year and State Dummies Included1472Expectation1473−0.0121∗∗1474−0.00951475−0.01291476−0.00301477(0.0045)1478(0.0067)1479(0.0111)1480(0.0014)1481-2lnL148216199621483162011114841619982148516200951486∗∗p < 0.01148756148814891490===== PAGE 64 (score 31, numeric-paren 19, table-words 4, var-words 1) =====149114923.3.41493Information Content in Futures1494In this section, we investigate the information content of futures. In Table 3.6, ex-1495cept for expectations variables, we use the same model specifications as the regres-1496sions in Table 3.4. For the expectations variables, each regression includes futures1497and some other proxies to study whether futures contain additional information1498besides the past housing appreciations. The results show that both coefficients and1499standard error estimates of futures are very consistent and stable across various1500specifications. The coefficients are negative and significant even after controlling for1501various combinations of past price information. This indicates that futures contain1502information that are not reflected in the past housing prices, which is not surpris-1503ing since individuals use all the available information to form their expectations,1504not just past prices.1505TABLE 3.6. Combination of Forecasts in Regression150611507215083150941510515116151271513Futures1514−0.0148∗∗−0.0145∗∗−0.0132∗∗−0.0141∗∗−0.0130∗∗−0.0130∗∗−0.0130∗∗1515(0.0041)1516(0.0038)1517(0.0045)1518(0.0034)1519(0.0046)1520(0.0040)1521(0.0041)1522Past CSI15230.00491524−0.002515250.009915260.00181527(0.0029)1528(0.0063)1529(0.0077)1530(0.0116)1531Past FHFA15320.0092∗∗15330.011115340.010615350.00961536(0.0036)1537(0.0066)1538(0.0049)1539(0.0070)1540Time Series1541−0.00011542−0.00321543−0.00171544−0.00211545(0.0015)1546(0.0034)1547(0.0017)1548(0.0036)1549-2lnL155016234791551162336015521623539155316233521554162341515551623330155616233281557∗∗p < 0.0115583.41559Conclusion1560Housing price expectations play a role in borrower mortgage default decisions.1561However, because of the difficulty of obtaining a good proxy, prior mortgage re-156257156315641565===== PAGE 65 (score 2, numeric-paren 0, table-words 0, var-words 2) =====15661567search either does not include the housing expectations in the empirical work or1568uses a past price based approach.1569This paper proposes to use information of housing futures contracts as an alter-1570native proxy since the transaction prices incorporate expectations for future house1571prices. As an example, we compare the performances of four different proxies for1572expectations in explaining borrower mortgage default behavior. The results show1573that the futures based proxy outperforms other measures by having the highest1574regression model fit as well as being the only measure that shows a significant effect1575in the correct direction on mortgage default behavior. The results also show that1576futures contain additional information that is not contained in the past housing1577prices.1578Since housing expectations may affect various real estate issues such as mortgage1579credit supply, housing demand and housing supply, the use of futures may help1580these other research areas.1581581582