# RECORD bcf745178dcc691b18c9d83f1fe5e6d55eff9a85 # TITLE: Three essays on real estate finance # YEAR: 2011.0 VENUE: nan DOI: 10.31390/gradschool_dissertations.1653 # AUTHORS: Shuang Zhu # PAGES: 69 CANDIDATE TABLE PAGES (1-based): [20, 23, 24, 39, 40, 42, 45, 46, 47, 58, 61, 63, 64] # 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 a ===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) ===== Louisiana State University Louisiana State University LSU Scholarly Repository LSU Scholarly Repository LSU Doctoral Dissertations Graduate School 2011 Three essays on real estate finance Three essays on real estate finance Shuang Zhu Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://repository.lsu.edu/gradschool_dissertations Part of the Finance and Financial Management Commons Recommended Citation Recommended Citation Zhu, Shuang, "Three essays on real estate finance" (2011). LSU Doctoral Dissertations. 1653. https://repository.lsu.edu/gradschool_dissertations/1653 This Dissertation is brought to you for free and open access by the Graduate School at LSU Scholarly Repository. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Scholarly Repository. For more information, please contactgradetd@lsu.edu. ===== PAGE 20 (score 50, numeric-paren 36, table-words 2, var-words 2) ===== TABLE 1.2. Differencing Regressions for Appraisal Bias (1) (2) (3) Lender-Borrower Lender-Referee Borrower-Referee Experienceδ 0.0103∗∗ 0.0118∗∗∗ −0.0072∗∗∗ (0.0040) (0.0016) (0.0009) Specializationδ −0.0218 −0.0295∗∗ 0.0118 (0.0169) (0.0136) (0.0105) LAδ 0.0217∗∗ 0.0263∗∗∗ −0.0169∗∗ (0.0085) (0.0090) (0.0077) RSδ 0.1197∗∗∗ 0.0622∗∗∗ 0.0238∗∗∗ (0.0221) (0.0126) (0.0066) CEδ −0.0443∗∗∗ −0.0322∗∗ 0.0025 (0.0158) (0.0138) (0.0100) Land −0.0031 −0.0043 −0.0012 (0.0082) (0.0060) (0.0038) Pop −0.0620∗∗ −0.0270 0.0128 (0.0249) (0.0181) (0.0115) Black 0.0048 0.0014 0.0043 (0.0108) (0.0078) (0.0050) Income −0.0279 −0.0181 0.0169 (0.0278) (0.0201) (0.0128) HousePrice 0.0616∗∗ 0.0427∗∗ −0.0052 (0.0257) (0.0186) (0.0119) Owner 0.0452∗ 0.0211∗ −0.0196 (0.0263) (0.0118) (0.0175) Constant −0.3024 −0.2654 −0.0448 (0.2387) (0.1735) (0.1109) N 1532 1532 1532 R2 0.0908 0.1798 0.0653 RMSE 0.1927 0.1400 0.0893 F 13.7996 30.2856 9.6545 Standard errors in parentheses ∗p < 0.10, ∗∗p < 0.05, ∗∗∗p < 0.01 13 ===== PAGE 21 (score 7, numeric-paren 5, table-words 1, var-words 0) ===== is difficult by inspection of the differences between the borrower and referee ap- praisals as well as between the lender and referee appraisals to assess the accuracy of the borrower and lender appraisers since the referee has knowledge of both appraisals before forming their opinion. Although this most likely increases the referee accuracy, it complicates the analysis of the variance.3 To address this issue, in the following section we examine the random appraisal error from contrasting borrower and lender appraisals. Since borrower and lender appraisals most likely have similar random errors (after filtering out biases), this aids in estimating the underlying accuracy of appraisers. 1.2.5 Appraiser Accuracy According to equation (1.3), given the borrower and lender appraisals are done independently of each other (which implies statistical independence), this yields (1.6). σ2 ε(B)−ε(L) = σ2 ε(B) + σ2 ε(L) (1.6) Given the further assumption that the variances of the random errors for lender and borrower appraisers are the same yields (1.7). σε(B) = σε(L) = (0.5σ2 ε(B)−ε(L))1/2 (1.7) The RMSE for the borrower lender contrast regression (appraisal differences fil- tered for systematic effects) is an estimate of σε(B)−ε(L). Therefore, from Table 1.2 regression one, we could calculate the standard deviation of the appraisal error as 3The referee valuation is thus “anchored” and this can increase error rates in some cases (Diaz and Hansz, 2001). However, given the magnitude of biases in this setting, a referee may serve a very useful role. 14 ===== PAGE 23 (score 26, numeric-paren 9, table-words 7, var-words 3) ===== in Table 1.2. According to equation (1.8), the appraisal variance could be explained by appraiser characteristics and neighborhood characteristics. ˆσ2 i,ε(o) = x(o) i γ + ziδ(o) + ϵ(o) i , o = L, B (1.8) However, we could not observe the variance of lender or borrower appraisals. But we could use the residuals ei from regression one in Table 1.2 as the proxy for σε(B)−ε(L). Substituting equation (1.8) into equation (1.6) yields (1.9) which reduces to the estimation equation (1.10). As shown in equation (1.9), Xa is the average of borrower and lender appraiser characteristics. Thus, Experiencea, Specializationa, LAa and RSa for the residual regression are defined as the average of lender and borrower appraisers’ experience, specialization, LA and RS. The estimation results appear in Table 1.3. ln(e2 i /2) = 0.5(x(L) i + x(B) i )γ + 0.5zi(δ(L) + δ(B)) + 0.5(ϵ(L) i + ϵ(B) i ) (1.9) y = Xaγ + Zδa + ϵ (1.10) Table 1.3 shows that experience and licensing strongly reduce the variance of the residuals, and real estate agents are less accurate. None of the census variables is statistically significant. To make this more concrete we examine specific cases in Table 1.4 to see how the implied standard deviation and mean absolute error of appraisal error vary by appraiser licensing and experience. We examine licensed and unlicensed appraisers with three levels of experience (5, 50, and 250 appraisals performed for distressed properties in the past two years) in Table 1.4. Census data and the specialization variable are evaluated at their mean values. 16 ===== PAGE 24 (score 25, numeric-paren 11, table-words 4, var-words 2) ===== TABLE 1.3. Residual Regression for Appraisal Accuracy yi = ln(e2 i /2) Residual Regression Experiencea −0.4744∗∗∗ (0.0793) Specializationa 0.4132 (0.4965) LAa −1.1010∗∗∗ (0.3031) RSa 2.5480∗∗∗ (0.5884) Land 0.0164 (0.1083) Pop −0.2114 (0.3275) Black 0.0400 (0.1422) Income 0.0945 (0.3647) HousePrice −0.1823 (0.3386) Owner −0.1133 (0.2144) Constant −0.5448 (3.1512) N 1532 R2 0.0970 RMSE 2.5414 F 16.3363 Standard errors in parentheses ∗p < 0.10, ∗∗p < 0.05, ∗∗∗p < 0.01 TABLE 1.4. Implied Standard Deviation and Mean Absolute Error of Random Appraisal Error For Varying Appraiser Licensing and Experience Cases Licensed Appraiser Experience Std. Dev. MAE 1 No 5 0.2203 0.1757 2 No 50 0.1276 0.1018 3 No 250 0.0871 0.0695 4 Yes 5 0.1270 0.1013 5 Yes 50 0.0736 0.0588 6 Yes 250 0.0502 0.0401 17 ===== PAGE 25 (score 6, numeric-paren 0, table-words 1, var-words 4) ===== Table 1.4 makes the role of experience and licensing clear. Although the average appraisal has an implied MAE of 10.88 percent, experienced licensed appraisers can perform much better than that. In the best scenario of a very experienced licensed appraiser as in case 6, the appraisal accuracy is 4.01 percent, slightly higher than the relocation appraisers examined by Dotzour (1988) who have a MAE of 2.77 percent. Going to a licensed appraiser who has done 50 appraisals of distressed properties in the last two years raises the MAE to 5.88 percent. In contrast, unlicensed appraisers with almost no experience can have an implied MAE of 17.57 percent as shown in case 1. The inaccuracy of inexperience appraisers has implications for programs rely- ing on appraisals. Any major program that requires a large number of distressed properties to be revalued in a short time will need to rely on inexperienced ap- praisers to handle the workload as the number of appraisers that perform a large number of appraisals in this specialized area is limited. However, inexperienced appraisers will likely not perform well and this will pose a problem for programs that assume accurate valuations are possible. Various loan modification programs such as the Home Affordable Modification Program, the practice of “lien strip- ping” where the principal on a second mortgage is reduced so that the principal on both the first and second mortgages do not exceed the estimated market value (set by appraisals), and refinancing guidelines (such as those in the Home Affordable Modification Program) all tacitly assume that an appraiser can make an accurate determination of market value for a distressed property. Similarly, attempts to reduce bias in appraisal sometimes may result in lower accuracy. The Home Valuation Code of Conduct promotes the use of Appraisal Management Companies (AMC) which may hire inexperienced appraisers that are not familiar with the area. In effect, an appraiser going into an unfamiliar area 18 ===== PAGE 39 (score 106, numeric-paren 84, table-words 1, var-words 3) ===== TABLE 2.3. Hazard Model of Default with Different Model Specification (1) (2) (3) (4) (5) State FE No Delay With Delay Year FE Mean Smooth ForeclosureDelay 0.0749∗∗ 0.0618∗∗ 0.0940∗∗ 0.1013∗∗ (0.0146) (0.0180) (0.0218) (0.0239) ExoticARM 0.6443∗∗ 0.6613∗∗ 0.6581∗∗ 0.6346∗∗ 0.6340∗∗ (0.0282) (0.0256) (0.0248) (0.0242) (0.0248) HybridARM 0.6554∗∗ 0.6449∗∗ 0.6525∗∗ 0.6216∗∗ 0.6209∗∗ (0.0187) (0.0165) (0.0150) (0.0202) (0.0204) ExoticFRM 0.2747∗∗ 0.2821∗∗ 0.2740∗∗ 0.2787∗∗ 0.2781∗∗ (0.0431) (0.0462) (0.0458) (0.0460) (0.0465) RegARM 0.4526∗∗ 0.4302∗∗ 0.4140∗∗ 0.4044∗∗ 0.4062∗∗ (0.0653) (0.0634) (0.0625) (0.0631) (0.0634) LTV1 0.0231∗∗ 0.0240∗∗ 0.0239∗∗ 0.0255∗∗ 0.0256∗∗ (0.0020) (0.0020) (0.0019) (0.0015) (0.0014) PiggyBack 0.5375∗∗ 0.5424∗∗ 0.5469∗∗ 0.5389∗∗ 0.5379∗∗ (0.0376) (0.0333) (0.0312) (0.0317) (0.0313) Interest 0.0724∗∗ 0.0682∗∗ 0.0659∗∗ 0.0704∗∗ 0.0701∗∗ (0.0084) (0.0070) (0.0076) (0.0070) (0.0070) FICO −0.8210∗∗ −0.8078∗∗ −0.8101∗∗ −0.8059∗∗ −0.8066∗∗ (0.0426) (0.0426) (0.0424) (0.0380) (0.0377) FullDoc −0.3477∗∗ −0.3516∗∗ −0.3474∗∗ −0.3518∗∗ −0.3522∗∗ (0.0346) (0.0364) (0.0365) (0.0345) (0.0345) Investor 0.0777 0.0714 0.0716 0.0823 0.0828 (0.0445) (0.0452) (0.0463) (0.0440) (0.0440) Purchase −0.0125 −0.0198 −0.0092 −0.0179 −0.0184 (0.0150) (0.0159) (0.0144) (0.0162) (0.0161) LoanAmount 0.0030 0.0045∗∗ 0.0046∗∗ 0.0030 0.0029 (0.0026) (0.0016) (0.0015) (0.0019) (0.0019) LoanAge −0.5046∗∗ −0.5411∗∗ −0.5917∗∗ −0.5659∗∗ −0.5620∗∗ (0.0144) (0.0203) (0.0319) (0.0276) (0.0295) PrepayPenalty 0.1124 0.1442 0.1466∗∗ 0.1852∗∗ 0.1843∗∗ (0.0620) (0.0564) (0.0569) (0.0579) (0.0579) RateDiff −0.3650∗∗ −0.3120∗∗ −0.2533∗∗ −0.3502∗∗ −0.3620∗∗ (0.0425) (0.0392) (0.0239) (0.0376) (0.0314) PastAppr −1.0549∗∗ −1.3477∗∗ −0.9493∗∗ −1.5329∗∗ −1.2967∗∗ (0.1647) (0.1262) (0.1475) (0.1470) (0.1414) Lag Unemployment −0.2018∗∗ −0.2272∗∗ −0.2463∗∗ −0.2736∗∗ −0.2702∗∗ Continued on next page 32 ===== PAGE 40 (score 60, numeric-paren 50, table-words 0, var-words 1) ===== (1) (2) (3) (4) (5) No Delay With Delay Year Mean Smooth (0.0274) (0.0300) (0.0315) (0.0483) (0.0477) Income −0.0300 0.0396 0.0186 0.0408 0.0424 (0.1725) (0.1563) (0.1494) (0.1290) (0.1301) Rent 0.1055 0.0852 0.1026 −0.0481 −0.0456 (0.2155) (0.1511) (0.1510) (0.1409) (0.1397) Population −0.0061 0.0401 0.0311 0.0368 0.0364 (0.0461) (0.0455) (0.0454) (0.0375) (0.0373) White 0.0288 0.0048 0.0094 −0.0469∗∗ −0.0473∗∗ (0.0405) (0.0350) (0.0377) (0.0175) (0.0175) Age65 0.0067 −0.0172 −0.0052 0.0264 0.0272 (0.0267) (0.0332) (0.0313) (0.0300) (0.0298) Education −1.2855∗∗ −1.2222∗∗ −1.2992∗∗ −1.2034∗∗ −1.2043∗∗ (0.2802) (0.3048) (0.3091) (0.2983) (0.2991) SchoolageChildren 0.4840 0.8627 0.8846 0.5197 0.5157 (0.4255) (0.5915) (0.5479) (0.4202) (0.4175) CommuteTime 0.3779 0.2437 0.2113 0.1260 0.1305 (0.1672) (0.1798) (0.1762) (0.0688) (0.0709) SameHouse 0.1434 −0.3609 −0.3252 −0.5641∗∗ −0.5690∗∗ (0.3265) (0.2235) (0.2055) (0.1715) (0.1741) Default(in%) 3.13 Number of Obs 4118336 LikelihoodRatio 127756 129484 116217 125904 125834 -2 lnL 2991728 2989999 2753202 2487099 2487170 ∗∗p < 0.01 33 ===== PAGE 41 (score 5, numeric-paren 0, table-words 1, var-words 2) ===== Across various specifications, foreclosure delay consistently shows a statistically significant effect in increasing the borrower’s propensity to default.15 The results are consistent with the prediction of Ambrose et al. (1997) theoretical paper. The next important question is, whether the expected benefit from default has a ma- terial economic effect on default propensity? To make the economic significance of foreclosure delays clearer, Table 2.4 reports the marginal effects and equiva- lent changes associated with a given month increase in foreclosure delay corre- sponding to the two different measures of delay as in regression four and five. The marginal effects represent the percentage change in the hazard ratio associ- ated with an increase of the delay. Since hazard ratio is not very intuitive,16 a more intuitive way to gauge the economic importance of a variable is by com- paring the marginal effects between variables in the same regression. That is by calculating the equivalent changes in other variables corresponding to the same marginal effects of the variable of interest. We pick updated LTV ratio and Fico score as the benchmark variables since those are important risk factors and are also continuous variables. Based on state mean foreclosure measures as in regres- sion four, a three-month increase in foreclosure time increases the hazard of default by 32.58 percent (exp (0.094 · 3) −1 = 32.58%). In terms of equivalent changes, that matches the same marginal effect of increasing the LTV ratio by 11.06 percent (exp (0.0255 · 11.06) −1 = 32.58%), or a decrease in the Fico score by 34.99 points (exp (−0.8059 · −34.99/100)−1 = 32.58%). Note that these estimates are based on the overall sample including those borrowers with positive equity on their house. 15As a robustness check, the results are similar when using lagged state median foreclosure delays as the proxy for borrower expected delays. 16For example, for the Cox hazard model, the marginal effect tends to be larger for all variables for samples with lower default rates and be lower for samples with higher default rates. 34 ===== PAGE 42 (score 10, numeric-paren 0, table-words 2, var-words 4) ===== For borrowers with negative equity, we expect that the economic impact would be even stronger. TABLE 2.4. Marginal Effects of Foreclosure Delays and Equivalent Changes in Other Variables Increase in Foreclosure Delay (in month) Variable 1 2 3 6 Panel A State Mean Marginal Effect (%) 9.86 20.68 32.58 75.77 LTV1 (%) 3.69 7.37 11.06 22.12 FICO −10.94 −21.89 −32.83 −65.66 Panel B Smooth Marginal Effect (%) 10.66 22.46 35.51 83.64 LTV1 (%) 3.96 7.91 11.87 23.74 FICO −12.56 −25.12 −37.68 −75.35 Other explanatory variables have the expected signs. The results show that de- fault reflects borrower expectations, incentives, and preferences. Specifically, bor- rowers with less equity as measured by a higher updated LTV ratio, second lien status, and thus with less equity, have a higher propensity to default. Borrowers that have selected more exotic and complicated loans have a higher propensity to default. Borrowers with a lower credit score and less documentation are more likely to default. Borrowers with a greater payment burden such as those with higher contract rates or higher borrowed amounts tend to have a higher chance of default. Borrower with a longer payment history are less likely to default. Areas with better educated population reduce the probability of default. Macroeconomic conditions also affect the performance of loans. 2.4.2 Robustness Checks This section conducts robustness checks of the impact of foreclosure time on bor- rower’s default behavior. Because regression four has the highest model fit as shown in Table 2.3, we pick regression four as our baseline regression. All following re- 35 ===== PAGE 43 (score 6, numeric-paren 0, table-words 2, var-words 2) ===== gressions in this section and next section include the same explanatory variables as the baseline regression, including the state fixed effect and using the lag year state mean foreclosure delay. Our first concern is whether the effect is driven by a specific state. For example, California constitutes a substantial proportion of our sample. In order to check this, we take one state out of the sample at a time and run the regression using the mortgages from the rest of the states, Table 2.5 reports the results for the five largest states in our sample.17 Panel A reports the estimate and model fit statistics and panel B reports the marginal effect and the equivalent changes corresponding to a three-month increase in delay. The results show that the impact of delay is not driven by a specific state. The marginal effect of a three-month increase in delay, is equivalent to an increase of LTV ratio by 10.14 percent to 18.20 percent or a 31.81 to 58.43 points decrease in Fico score. Interestingly, when California or Florida is taken out of the sample, the impact of delay is increased, although the increase might not necessarily be significant. Our second concern is the accuracy of the data since mortgage data has many limitations. Typically, borrower characteristics are measured carefully only at orig- ination. After origination, most servicers do not rescore the borrower’s credit or reappraise the property value using either traditional appraisals or automated val- uation models. In addition, most data files do not contain accurate amounts for junior liens after origination. Consequently, the most accurate data exists at orig- ination. In order to control for the accuracy of data, we report the results by tracking the first one, two, three or four years of loan performances after loan orig- ination. Table 2.6 reports the estimate and the comparative statics. The magnitude 17Other states have similar results. For simplicity, we included only the largest states results. 36 ===== PAGE 45 (score 12, numeric-paren 4, table-words 2, var-words 2) ===== TABLE 2.6. Robustness Checks by Number of Years of Loan Performance Tracked (1) (2) (3) (4) Panel A One Year Two Years Three Years Four Years ForeclosureDelay 0.1094∗ 0.1354∗∗ 0.1011∗∗ 0.0949∗∗ (0.0542) (0.0469) (0.0195) (0.0218) Default(in%) 0.94 1.92 2.72 3.09 Number of Obs 666546 2197112 3279224 3865093 LikelihoodRatio 7394 47284 93570 118313 -2 lnL 108637 820970 1745491 2343463 Panel B Marginal Effects (3M) and Equivalent Changes Marginal Effect (%) 38.85 50.11 35.43 32.94 LTV1 (%) 10.55 13.91 11.11 10.99 FICO −55.21 −51.37 −37.30 −35.27 ∗∗p < 0.01∗p < 0.05 default, transaction costs, and reputation costs (Kau and Kim, 1994; Kau et al., 1994; Foote et al., 2008). Higher initial combined LTV ratio loans are less resistant to house price depreciation and more likely to have an “in the money” default option. When the default option is “in the money,” foreclosure delay tends to have a material effect on changing the borrower’s propensity to default. Table 2.7 reports the results by different initial combined LTV ratio subsamples. For loans with combined LTV ratio greater than 80 percent, the borrower’s default decision is statistically very sensitive to expected delay. As the combined LTV ratio decreases, to below 80 percent, the statistical significance declines, and the effect disappears when combined LTV ratio is less than 70 percent. As for economic significance, the magnitudes of effect are much higher for loans with combined LTV ratio greater than 95 percent than loans with combined LTV less than 80 percent. Our empirical findings are very consistent with the theoretical prediction. The results indicate that in a deteriorated housing market, when borrowers are 38 ===== PAGE 46 (score 16, numeric-paren 6, table-words 3, var-words 1) ===== likely to have negative equity, the increase in expected delay tends to have a larger and more significant impact in increasing default. TABLE 2.7. Subsamples by Initial CLTV Ratios (1) (2) (3) (4) (5) (6) Panel A CLTV<70 70-80 80-90 90-95 95-100 10095% Loans (1) (2) (3) (4) Panel A ExoticARM HybridARM ExoticFRM FRM ForeclosureDelay 0.1598∗∗ 0.1311∗∗ 0.2023∗∗ 0.1469∗∗ (0.0271) (0.0503) (0.0222) (0.0534) Default(in%) 6.70 7.05 4.68 2.79 Number of Obs 315420 84495 69179 66265 LikelihoodRatio 7257 2045 1549 1362 -2 lnL 329078 74655 39314 20763 ∗∗p < 0.01∗p < 0.05 TABLE 2.9. Subsamples by Fico Scores For Initial CLTV>95% Loans (1) (2) (3) (4) (5) (6) Panel A Fico≤620 620-660 660-700 700-740 740-780 780