TIME PREFERENCES AND MORTGAGE CHOICE STEPHEN A. ATLAS, ERIC J. JOHNSON, JOHN W. PAYNE

Transcription

1 WA 1 TIME PREFERENCES AND MORTGAGE CHOICE STEPHEN A. ATLAS, ERIC J. JOHNSON, JOHN W. PAYNE WEB APPENDIX A: SIMULATION OF TIME PREFERENCES, CHOOSING BACK-LOADED MORTGAGES AND DEFAULT While our simple analytic model is meant to demonstrate the possible interactions of nonstandard time preferences and mortgage choice and maintenance, it is possible, through numeric simulation to look at more realistic applications. To further examine our hypotheses for the relationship between time preference, mortgage choice, and maintenance, we developed a series of simulations based on our model and possible extensions. These simulations examine: 1) Whether our predictions are consistent with values for typical mortgage values and durations, and for time preferences commonly elicited in the field 2) Whether the differences in preferences are economically meaningful 3) Whether the results are robust to interactions between present bias and long-term discounting, and 4) Whether they are robust to for risk preferences. Our simulations suggest that the predicted relationships between time preferences, mortgage choice and maintenance are broadly present and robust to these considerations. Mortgage Choice This simulation extends the 3-period analytic model to a decision between a standard and back-loaded 2-28 mortgage, assuming 30 pay periods remain, beginning in the present year. We compare the difference in present value of the standard 30-year mortgage and back-loaded 2-28

2 WA 2 mortgage, for homeowners with various levels of present bias and long-term discounting. In a second model we also examine risk preferences. We assumed the 30-year mortgage decision was a choice between a front-loaded mortgage and a back-loaded mortgage. The utility from choosing a front-loaded mortgage is the present value of 30 years of fixed payments (f), discounted by time preferences. In contrast, the back-loaded 2-28 mortgage has a low initial payment (b 1 ) in the first two periods and a higher payment (b 2 ) in the remaining years. These are given by equations W1 and W2. W1. u f = f βδf βδ 2 f βδ 29 f W2. u b = b 1 βδb 1 βδ 2 b 2 βδ 29 b 2 With this model, a homeowner selects the front-loaded mortgage, given his or her time preferences, when the difference between the present value of the front-loaded and back-loaded mortgages is positive. This happens when u f u b 0. Equation W3 is the result of combining equations W1 and W2. 29 W3. u f u b = (1 + βδ)(b 1 f) + β[ n=2 (δ n )] (b 2 f) We calibrated house prices and amount borrowed to match typical values found in the SBI data set, a representative sample of US households, which was collected in 2010 and validated internally and through the of Consumer Finances and Flow of Funds report by the US Federal Reserve s Board. Thus, the average home was purchased in 1999 for $161,049, has a $130,594 mortgage balance and, in 2010, had 19 years left to pay. At the prevailing 1999 interest rates (7.5%) and points (1%), taxes (1.2%), homeowners insurance ($800 yearly) and mortgage insurance ($133), a standard 30-year fixed monthly mortgage payment is $1,500, annualized to $18,000. A 2-28 payment with a 4.5% initial interest rate and 10.5% final interest rate costs $1,179 monthly for the first two years, and $1,803 for the remaining 28.

3 WA 3 The results of the simulation are shown in Table W1. Consistently with Hypothesis 1, more patient homeowners choose front-loaded mortgages, while homeowners who are present biased or have long-term discount rates choose back-loaded mortgages. These results are both economically meaningful (for example, a change from a β and δ from.8 to.9 increases the present value of a front-loaded mortgage by $15,162 more than a back-loaded mortgage) and consistent across all combinations of present bias and discounting. --- Insert Table W1 around here --- Next, to account for risk preferences, we adapted the value function for front-loaded and back-loaded mortgages equations (W1 and W2) to account for prospect theory parameters. In particular, we focus on two features of the value function under prospect theory as diminishing sensitivity and loss aversion each distort risk preferences. Diminishing sensitivity provides curvature in the value function which favors a certain, smaller gain over an uncertain larger gain (Kahneman and Tversky 1979). Similarly, loss aversion affects risk preferences because it would affect evaluations of mixed gambles involving a potential gain and a potential loss, and for example, can cause rejection of gambles (Novemsky and Kahneman 2005). We incorporate each in our model, by applying a diminishing sensitivity parameter, σ =.64, and a loss aversion parameter, λ = 2.26, both calibrated to levels found in our experimental results. The difference in present value of a front-loaded and a back-loaded mortgage becomes characterized by equation W4: W4. u f b = (1 + βδ)(λb σ 1 λf σ ) 29 + β[ t=2 (δ t )] (λb σ 2 λf σ ) The simulation results, shown in Table W2, again support that patient homeowners select front-loaded mortgages while present biased and long-term impatient homeowners choose backloaded mortgages. In contrast, very patient homeowners would require several thousand dollars

4 WA 4 today to switch to back-loaded mortgages. We converted the utility differences to making an equivalent cash payment today, given by P = ( u f u b λ 1 ) σ. These results are again economically meaningful. For example, a change from a β and δ from.8 to.9 increases the present value of a front-loaded mortgage by $7,811 more than a back-loaded mortgage) and consistent across all combinations of present bias and discounting. --- Insert Table W2 around here --- We conclude from these simulations that the predictions relating time preferences and choosing back-loaded mortgages are present in an extension of our analytical model to a more realistic setting. The simulation suggests that we should expect impatient homeowners to prefer to choose back-loaded mortgages given typical mortgage amounts over a 30-year time spans. The differences in preferences are economically meaningful in size, and persist after accounting for risk preferences. Mortgage Maintenance Next, we use simulation to address the relationship between time preferences and mortgage default. We examine this relationship in several ways, all involving realistic mortgage and home values, economic conditions over long time horizons. First, we will examine the individual effects of present bias and long-term discounting on mortgage default and assess whether differences across time preferences match Hypothesis 2 and are economically meaningful. We then consider present bias and long-term discounting jointly to examine interactions between these two types of time preferences on mortgage maintenance choice. Finally, we will account for risk preferences and discuss the implications for the relationship between time preferences and mortgage default. The simulation examines a homeowner s mortgage maintenance choice between

5 WA 5 continuing to pay a mortgage and defaulting on the loan. Naturally, there are different time frames involved for a choice between initial 30-year mortgages and the choice between maintaining a mortgage and defaulting on that mortgage, because the mortgage maintenance choice necessarily occurs after some payments have already been made. We extend the 3-period analytic model to the average situation faced by homeowners in the SBI data set: 11 years after purchasing a home, the homeowner owes $130,594 in mortgage debt. If this homeowner maintains the mortgage, they will pay a monthly mortgage payment (m = $18,000, i.e. $1,500 per month) for 19 years, and after that they will enjoy the full residual home value (M = $161,049). The utility of mortgage maintenance is captured by equation W5: W5. u stay = m βδm βδ 2 m βδ 18 m + βδ 19 M Alternatively, the homeowner could walk away, pay a one-time short-term cost of moving (s), pay rent indefinitely (r), and will not enjoy the residual home value in the distant future. The utility of choosing to default is shown in equation W6: W6. u default = s r βδr βδ 2 r βδ 18 r Since homeowners will continue to pay the mortgage provided that u stay u walk, there exists a threshold short-term cost (s*) that makes a homeowner indifferent between choosing to maintain the mortgage and choosing to default. If s s, the homeowners maintains the mortgage, since moving costs are sufficiently high, and if s s, the homeowner defaults on the mortgage, since moving costs are sufficiently low. In other words, s* is a threshold which increases with willingness to default. Equation W7 combines equations W5 and W6 to characterize s, willingness to default. W7. s = m + β 18 t=1 (δ t )] (m r) βδm We simulate mortgage preferences using annual quasi-hyperbolic discount rates used in

6 WA 6 prior simulations and empirical results. Laibson (1997) uses models with present bias (β) set to.6 and annual long-term discounting (δ) set to.99. Angeletos et al. (2001) simulates using values (β =.7; δ =.957). For our simulation, we examine ranges of present bias ranging from.50 to.95 and long-term discounting ranging from.9 to 1. One difference across quasi-hyperbolic models is the time period comprising the present. While Tanaka et al. (2010) define the present as today, Laibson defines the present as this year, and Phelps and Pollak (1968), this lifetime, all share the conclusion that time preferences are not well-captured by a single parameter. Following Laibson, for the simulation we adopt annualized time periods to make our simulation consistent and comparable with past simulations. Notably, our simulation and empirical parameter estimates differ because our empirical estimation follows Tanaka et al. (2010) in denoting time on a daily basis. These approaches provide ordinal estimates of time preferences, because we do not observe respondents beliefs about actually receiving payment. We find that in both the elicitation of daily preferences in our empirical results and the annualized parameters of this model, present bias and long-term discounting have distinguishable relationships with mortgage maintenance choices. Mortgage Maintenance and Independent Time Preferences Since we predict opposite relationships between present bias, long-term discounting and mortgage maintenance choice, we first individually relate each type of time preference with choosing to default on a mortgage. We calibrated rent to cost half of the mortgage payment (r=.5*m), since a high rent results in always choosing to maintain the mortgage and a low rent results in always defaulting on the mortgage. We first fixed present bias to individually consider the relationship between long-term discounting and choosing to default, and then fixed long-term discounting to individually relate present bias and choosing to default.

7 WA 7 Following Angeletos et al. (2001) we first fixed β to be.7 and explored mortgage maintenance given long-term discount rates between.9 and 1. Figure W1 shows willingness to default on a mortgage, at each level of long-term discounting, given that β =.70. In this case, willingness to default is captured by the maximum short-term payment a homeowner would be willing to pay and still choose to default rather than maintain mortgage payment. For each longterm discounting value, a short-term cost in excess of this threshold (s ) would induce the homeowner to maintain the mortgage, so a higher threshold indicates a greater willingness to default on the loan. Long-term impatient homeowners (with annual discount factors of.9) would be willing to pay more than four times as much in the short term as part of a mortgage default, compared with their long-term patient counterparts (δ = 1). As with the simple 3-period model, defaulting increases with long-term discounting (i.e. when δ is low). --- Insert Figure W1 around here --- Figure W2 shows the reverse relationship holds for present bias. We fixed the long-term discount rate (δ =.957, following Angeletos et al. (2001)) and explored present bias between.5 and 1. The maximum short-term payment a homeowner would be willing to pay in a default is smaller for present biased homeowners (i.e. when β is low). A.5 increase in β corresponds with a 69% increase in willingness to endure short-term costs in a mortgage default. In other words, as with the 3-period model, more present biased homeowners are more likely to continue to maintain their mortgage payment. --- Insert Figure W2 around here --- Mortgage Maintenance and Time Preference Interactions We next considered interactions between present bias and long-term discounting in mortgage maintenance choices. For each (β, δ) pair of time preferences, we calculate the

8 WA 8 difference in present value of mortgage maintenance and default, as given in equation W8: W8. u stay u default = s + r m + β 18 t=1 (δ t )] (r m) + βδ 19 M Table W3 shows willingness to maintain the mortgage as a function of present bias and long-term discounting, with time preference interactions. For this analysis, short-term cost of moving is set to $20,000, and all other values retain prior calibration to realistic assumptions. Higher values of δ correspond with greater utility for mortgage maintenance over defaulting, long-term impatience is linked with greater willingness to default. Higher values of β correspond with greater utility for defaulting over mortgage maintenance, which links presentbias with greater willingness to maintain the mortgage. The utility differences are economically significant. For example, a homeowner with (β,δ)= (.75,1) would maintain the loan and would require $10,287 be persuaded to default on the loan, while a homeowner with (β,δ)=(.8,.98) would default on the loan and require $8,787 to be persuaded to maintain the loan. These simulation results are consistent with the Hypothesis 2 and the prediction of the analytical model. --- Insert Table W3 around here --- Mortgage Maintenance, Time Preferences, and Risk Preferences Finally, we explored a model of defaulting that accounted for risk preferences in the utility function. Incorporating risk preferences into a model of defaulting is a complicated prospect that depends highly on how homeowners mentally account for the multitude of payments associated with a mortgage. For example, is diminishing sensitivity applied to rent and mortgage individually or to the difference between them? How should a model incorporate risks arising from unexpected shocks to the housing or rental markets? Does loss aversion apply to mortgage, or rent, or the difference between rent and mortgage? This last consideration is particularly pronounced if homeowners are expecting to make these payments, which would

9 WA 9 mitigate the impact of loss aversion for those payments but not the alternative payments (Novemsky and Kahneman 2005). Similarly, does loss aversion apply to the residual home value (if it is lost due to a default) or not, because it is a gain if homeowners continue to pay the mortgage? These issues offer a complex array of possible utility functions somewhat outside the scope of this paper focusing on the relationship between time preferences and mortgage choice, and should be addressed by future research. We consider one representative model that applies diminishing sensitivity (σ) to all values and loss aversion (λ) to all potential costs (but not residual home value), as summarized by equation W9: W9. u stay u default = λs σ + λr σ λm σ + β 18 t=1 (δ t )] (λr σ λm σ ) + βδ 19 M In this model, we test whether mortgage default decreases with present bias and increases with long-term impatience, as predicted by the analytical model. We set diminishing sensitivity (σ) to.64 and loss aversion (λ) to 2.26, and calibrate rent to 80% of mortgage, short-term moving costs set to $10,000. We converted the utility differences to making an equivalent cash payment today, given by P = ( u stay u default λ 1 ) σ. We are particularly interested to know whether the focal relationships are robust to diminishing sensitivity and loss aversion. While both factors affect risk preferences, diminishing sensitivity particularly diminishes emphasis on single large events like residual home value. The results of this simulation, summarized in Table W4, are generally consistent with the predictions of the analytical model and Hypothesis 2. Even after accounting for diminishing sensitivity and loss aversion, more present biased homeowners (low β) generally prefer to maintain the mortgage while homeowners who discount the long-term more (low δ) tend to walk away. These results, while smaller in magnitude than the model without risk preferences, are

10 WA 10 again economically meaningful. For example, a homeowner with a present bias of.65 and longterm discount rate of 1 will pay $1,083 to avoid default. In contrast, a homeowner with a present bias of.85 and a long-term discount rate of.95 would pay an extra $1,080 to be able to default. We also used this model as an opportunity to quantify how robust our model is to reversals following risk preferences. We find some pockets where the opposite of the predicted relationships are found, though it only affects the default decision when β is in the range [.7,.75] and δ is in the range [.90,.91]. We consider this reversal to be rather immaterial to our general predictions as it does not hold for a large range of β and δ, is not substantially large (it is equivalent to making an additional $15 payment in the present) nor expected to be statistically detectable in estimation. In this model, our results are generally robust to risk. --- Insert Table W4 around here --- In closing, we have tested our hypotheses through a series of mortgage choice and maintenance models which use realistic mortgage and market values as well as extended time horizons. We found broad support for Hypothesis 1, that both present bias and long-term discounting encourage homeowners to choose back-loaded mortgages, and Hypothesis 2, that present bias encourages mortgage maintenance while long-term discounting encourages default. We found our predictions recur in these realistic simulations, persist when considering interactions between time preferences, have effects that are economically meaningful and, to the extent we could include risk preferences, are generally robust to risk. References Angeletos, George-Marios, David Laibson, Andrea Repetto, Jeremy Tobacman, and Stephen Weinberg (2001), "The Hyperbolic Consumption Model: Calibration, Simulation, and

11 WA 11 Empirical Evaluation," Journal of Economic Perspectives, 15 (Summer), Laibson, David (1997), "Golden Eggs and Hyperbolic Discounting," Quarterly Journal of Economics, 112 (May), Kahneman, Daniel and Amos Tversky (1979), "Prospect Theory: An Analysis of Decision under Risk," Econometrica, 47 (2), Novemsky, Nathan and Daniel Kahneman (2005), The Boundaries of Loss Aversion, Journal of Marketing Research, 42 (May), Phelps, E. S. and R. A. Pollak (1968), On Second-Best National Saving and Game-Equilibrium Growth, Review of Economic Studies, 35 (April), Tanaka, Tomomi, Colin F. Camerer, and Quang Nguyen (2010), "Risk and Time Preferences: Experimental and Household Data from Vietnam," American Economic Review, 100 (March),

12 WA 12 TABLE W1. MORTGAGE CHOICE AND TIME PREFERENCES Note: Difference in present value between front-loaded and back-loaded mortgages, by present bias and long-term discounting. Positive values indicate preference for front-loaded mortgages and negative values indicate preference for back-loaded mortgages.

13 WA 13 TABLE W2. MORTGAGE CHOICE AND TIME PREFERENCES, WITH RISK PREFERENCES Note: Present dollar-value difference between choosing front-loaded and back-loaded mortgages, by present bias and long-term discounting. Positive values indicate willingness to pay for a front-loaded mortgage and negative values indicate willingness to pay for a backloaded mortgage.

14 WA 14 TABLE W3. UTILITY DIFFERENCE BETWEEN MAINTENANCE AND DEFAULTING, AND TIME PREFERENCES Note: For each pair of time preferences, this table shows the present value difference between maintaining and defaulting on a mortgage. Positive values indicate a preference for maintaining and negative values indicate a preference for defaulting on the mortgage. The magnitude indicates how much money, paid immediately, which would be necessary to change the homeowner s decision. More present-biased and more long-term patient homeowners are more likely to continue to pay the mortgage.

15 WA 15 TABLE W4. UTILITY DIFFERENCE BETWEEN MAINTAINING AND DEFAULTING, AND TIME PREFERENCES WITH RISK AVERSION Note: Present value difference between maintaining a mortgage and defaulting. Positive values indicate a preference for maintaining on the mortgage and negative values indicate a preference for defaulting on the mortgage. The magnitude indicates how much a homeowner would pay without changing their maintenance choice. In general, present-biased homeowners have a higher utility from paying the mortgage while long-term discounters derive more utility from walking away.

16 WA 16 FIGURE W1. WILLINGNESS TO DEFAULT, BY δ $45, $40, $35, $30, $25, $20, $15, $10, $5, $- Willingness to Default and δ Note: Maximum short-term cost a homeowner would be willing to pay and default on the loan rather than maintain the mortgage, by long-term patience (δ).

17 WA 17 FIGURE W2. WILLINGNESS TO DEFAULT, BY β Willingness to Default and β $60, $55, $50, $45, $40, $35, $30, $25, $20, Note: Maximum short-term cost a homeowner would be willing to pay and still default on the loan, by lack of present bias (β).

18 WA 18 WEB APPENDIX B: ADDITIONAL PILOT STUDY DETAILS Our first empirical analysis tests the relationship between time preferences and mortgage choice in a nationally representative survey sample. We added a measure of overall impatience to a large commercial survey of a nationally-representative sample of US households to examine if impatient homeowners were more likely to select back-loaded mortgages. In particular, we looked at two indicators of back-loading mortgage payments, namely, having an adjustable-rate mortgage and having mortgages that allow interest-only payments that do not reduce the total outstanding mortgage debt. Both of these forms of mortgage back-loading are fairly common: according to the nationally representative sample we analyze, 13% of mortgaged US homeowners have adjustable-rate mortgages and 18% have or had interest-only loans. Consistent with Hypothesis 1, we found more mortgage back-loading among impatient homeowners. Method Strategic Business Insights (SBI) MacroMonitor is nationally-representative 1 survey of US households financial decisions and included in 2010 at our request, a time preference elicitation similar to measures widely used in economics (where it is called a price list) and psychology (where it is termed a titrator). Given limitations on administrative time, this item does not decompose time preferences into present bias and long-term discount rates but it does allow the estimation of each respondent s yearly discount fraction based on his or her 1 SBI s MacroMonitor survey is, in turn, validated through the of Consumer Finances and the Flow of Funds report by the US Federal Reserve's Board as well as internal wave-to-wave validation

19 WA 19 hypothetical choices between $100 today and an increasing series sums ($110, $125, $150, $175, $200, $225) in twelve months. Since in our model present bias and long-term discount rates have the similar effects on mortgage choice, we can test this hypothesis using this single compound parameter. We estimated each respondent s yearly discount fraction based on the rate corresponding with the midpoint between the smallest delayed payment accepted and largest delayed payment rejected. The SBI data set also asked about homeowners mortgage characteristics, including whether the loan had an adjustable or fixed interest rate, whether it had an interest-only period, the initial amount borrowed, the current amount owed on the mortgage and the length of the mortgages and many other financial characteristics. We first validated whether loans with adjustable-rate mortgages were more back-loaded than fixed-rate mortgages. We then ran a series of survey-weighted logistic regressions to assess the relationship between the impatience estimate and the two indications of back-loading, that is, having adjustable-rate mortgages and interest-only mortgages. As a robustness check we added a series of controls to the analysis of the SBI data. First, we controlled for loss aversion, also measured using a similar titrator as that used for time preferences (Fehr and Goette 2007). Second, we controlled for demographic factors including income, marital status, gender, age and education, as well as the year in which the home was purchased. Third, we controlled for measures of liquidity including checking account balance, savings account balance and credit card balance, each as a fraction of income, along with net worth. Finally, we simultaneously controlled for all of these factors. Results Are impatient households more likely to have back-loaded mortgages, as suggested by

20 WA 20 Hypothesis 1? We ran logistic regressions on the probability of choosing a back-loaded mortgage and found that impatience was associated with choosing a back-loaded mortgage. Table W5 shows results from a series of logistic regressions relating impatience with adjustable-rate mortgages using the survey sampling weights. Across regressions, for each 10% decrease in the discount fraction (i.e. increase in impatience), the likelihood of having an adjustable rate mortgage increases by roughly 15%. This result is largely consistent across models with controls including measures of income and education, measures of credit card debt, checking account balances and savings balances and net-worth. These controls have no significant effect. Loss aversion, age, and gender also have no significant effect. Including fixed effects for purchase year does not change the effect of impatience, suggesting that the effect of impatience is unrelated to changes in the characteristics of mortgage buyers across time. The only significant variable is the marital status: Married couples are more likely to choose a fixed rate mortgage. Table W6 reports similar analyses for interest-only mortgages. Discount rates have similar effects: For each 10% decrease in the discount rate (i.e. increase in impatience), the likelihood of having an interest only loan increases by roughly 15% across specifications. This effect survives the inclusion of identical controls. However, several controls now predict the choice of such a mortgage, including being younger, male, and having more credit-card debt. --- Insert Tables W5 and W6 around here --- Table W7 verifies that adjustable and interest only mortgages represent back-loaded contracts by examining other characteristics and repayment status of these two mortgage types, relative to fixed rate mortgages. As expected, adjustable rate mortgages involve borrowing more initially, owing more currently, and having a smaller fraction of the initial amount borrowed paid off. The two mortgage types had the same duration and had the same average origination date.

21 WA 21 Similarly, interest-only mortgages also involve borrowing more initially, borrowing more initially, owing more currently, and having a smaller fraction of the initial amount borrowed paid off. Interest-only and principal-paying mortgages had the same duration and the same average origination date. Thus, while both interest-only and adjustable-rate mortgages are back-loaded, they are of similar duration (and vintage) as fixed rate mortgages. --- Insert Table W7 around here --- Discussion Together, these results show strong support for Hypothesis 1, demonstrating that impatient homeowners are more likely to have back-loaded mortgages. In particular, impatient homeowners are more likely to have adjustable-rate mortgages and to have or have had interestonly loans. Both of these results are robust to the inclusion of several controls. In addition, we note that the current status of the back-loaded mortgages is consistent with Corollary 1: Because they owe more on their housing than those with fixed rate mortgages, they would be more vulnerable to a decrease in housing prices and more likely to have negative equity in such an event. While the use of a large-scale representative sample is a strength of this data, these surveys allow limited time for responses, requiring an abbreviated measure of time preferences. In the main study we are able to use a more sophisticated estimation of time preference assessing both long-term discounting and present bias. That study attempts to replicate the pilot study s findings relating time preferences to mortgage choices, extend the results to both present bias and personal discount factors and examines mortgage management. To do this we turn from an existing survey to a custom survey augmented with administrative data.

22 WA 22 References Fehr, Ernst and Lorenz Goette (2007) "Do Workers Work More If Wages Are High? Evidence from a Randomized Field Experiment." American Economic Review, 97 (March)

23 WA 23 1-Year Impatience (1-βδ) TABLE W5. IMPATIENCE AND ADJUSTABLE-RATE MORTGAGE CHOICE (1) (2) (3) (4) (5) 1.76** 1.54* 1.48* 1.76* 1.24 (.67) (.65) (.71) (.68) (.68) Loss Aversion.027 (.03) Income ($100,000s).00 (.16) Married.50* (.26) Gender (1=male) -.18 (.23) Age -.00 (.01) Has bachelor s degree Has graduate degree Credit card debt to income Checking account balance to income -.33 (.29).13 (.29) -.26 (.64) -.52 (.72).03 (.03).06 (.17).56* (.26) -.08 (.24) -.01 (.01) -.32 (.28).13 (.29) -.12 (.40) -.14 (.38) Savings account balance to income.09 (.31).43 (.33) Net Worth ($m) Intercept -1.92*** (.11) -1.94*** (.11) Purchase Year Fixed Effects.00 (.08) -1.92*** (.11) -.01 (.12) Purchase Year Fixed Effects N Pseudo R Note: -weighted logistic regression, continuous measures centered. *** p<.001; ** p<.01; * p<.05; p<.10.

24 WA 24 TABLE W6. IMPATIENCE AND INTEREST-ONLY MORTGAGES 1-Year Impatience (1-βδ) (1) (2) (3) (4) (5) 1.45** (.53) 1.39* (.56) 1.48* (.59) 1.54** (.54) 1.58** (.60) Loss Aversion -.02 (.03) Income ($100,000s) -.03 (.16) -.01 (.03) -.15 (.17) Married -.18 (.23) Gender (1=male).42 (.22) Age -.02* (.01) Has bachelor s degree -.35 (.26) -.22 (.23).41 (.22) -.02* (.01) -.34 (.26) Has graduate degree.34 (.29).35 (.28) Credit card debt to income Checking account balance to income Savings account balance to income -2.33** (.88) -.54 (.69) -.37 (.40) -2.46* (1.01) -.35 (.63) -.22 (.38) Net Worth ($m) -.01 (.07) Intercept -1.49*** (.10) -1.51*** (.11) Purchase Year Fixed Effects -1.54*** (.10).08 (.07) Purchase Year Fixed Effects N Pseudo R Note: -weighted logistic regression, continuous measure centered. *** p<.001; ** p<.01; * p<.05; p<.10.

25 WA 25 TABLE W7. ADJUSTABLE RATES, INTEREST-ONLY PAYMENTS AND BACK-LOADING Adjustable Fixed d.f. F p Amount Borrowed 233, ,913 2, <.0001*** Amount Owed 206, ,123 1, <.0001*** Proportion Repaid , * Duration , Origination Year , Interest Only Principal-Paying d.f. F p Amount Borrowed 252, ,409 1, <.0001*** Amount Owed 229, ,002 1, <.0001*** Proportion Repaid , Duration , Origination Year , p<.10 Note: F-tests. Data does not contain initial home prices. *** p<.001; ** p<.01; * p<.05;

26 WA 26 WEB APPENDIX C: ADDITIONAL DETAILS FOR THE EMPIRICAL STUDY Participants began by reading a passage orienting them to concepts and terminology commonly available through mainstream media sources about a particular mortgage maintenance choice, namely, whether to walk away from an underwater mortgages. To identify the relationship between time preferences and mortgage maintenance choices for underwater homes, we posed a choice between two clear, if simplified, options: (1) moving into a rental unit in their area and allowing the bank to foreclose on the house, or (2) staying in their current house and continuing mortgage payments. We elicited willingness to default as the walk-away value, the dollar amount to which the home would need to fall for a given respondent to walk away from the mortgage. These values were elicited through an adaptive titrator, which asked a series of binary questions about whether the respondent would stay or walk away if their home s market value changed to a specific value determined by prior responses. The titrator was calibrated to each subject s current home market value (as reported at the outset of the survey), and the range of possible walk-away values was considered to be between 0 and 120 percent of their current home value (see Guiso, Sapienza and Zingales 2010 for a similar measure). In each round, subjects responded with whether they would move out and stop paying their mortgage at that home value. After each round, if they indicated a willingness to stay (default) at a particular home value, the ceiling (floor) walk-away value was reduced (increased) by 42% of the range of values. This process repeated until it achieved sufficient specificity, which occurred when the range of potential values was reduced to below 5% of their current home market value. 2 2 The range constricted by 42% each round to ensure efficient convergence to an

27 WA 27 Respondents then answered a series of questions about their financial position and demographic factors, including, age, gender, marital status, number of children, and education. Financial factors included employment status, income, monthly mortgage payment, years since the home was purchased, current mortgage debt, the initial cost of the home, and their selfassessment of their home equity status. Income and monthly mortgage payment were combined to produce the share of income servicing the mortgage. While some researchers have expressed concerns that individuals cannot recall mortgage details (Bucks and Pence 2008), we find that respondents assessment of their home equity and debt were largely internally consistent with their other responses in the survey and correlate strongly with zip code-level averages obtained from Zillow.com. This data contained average home sale prices at the zip code level both in the year the home was bought (for years since 2000) and around the time of the survey. Mean zip code-level home prices correlated.47 with respondents self-reported home prices. To further ensure data integrity, we dropped data from a limited number of observations that provided wildly inconsistent answers to our two housing equity questions. Additionally, we administered the three-item debt literacy scale and financial competency self-assessment of Lusardi and Tufano (2009) and a three-item cognitive reflection task (Frederick 2005) and asked additional questions characterizing their mortgage type including whether it has a fixed or adjustable interest rate and if they have a second mortgage. At the end of the survey, we used two adaptive incentive compatible tools to estimate individual-level parameters for quasi-hyperbolic time discounting (QTD) (Laibson 1997) (β, δ) individual-level walk-away price estimate while permitting response uncertainty. We verified the adaptively elicited value by directly asking respondents their walkaway price. The measures correlated.99.

28 WA 28 and cumulative prospect theory (CPT) (α, λ, σ) (Prelec 1998; Tversky and Kahnemann 1991). To estimate quasi-hyperbolic discounting parameters, subjects chose from 20 pairs of possible payments at different points in time, one of which sometimes included the present day. Present bias (β) and long-term discounting (δ) were estimated with each time period corresponding to a year, so a payment delayed one year is diminished by the discount fraction β*δ, and a one-week delay induces a discount fraction β (δ^( 1 )). We compared the fit of the QTD model to both a 52 hyperbolic and an exponential model to respondents choices, finding the QTD model was significantly superior: the quasi-hyperbolic model s log-likelihood ( ) exceeded that of an exponential ( ) and hyperbolic ( ) models. While the elicitation method structurally advantages the quasi-hyperbolic model by adaptively choosing questions to maximize informativeness toward estimating two parameters, and the models are not nested so log-likelihood has weaknesses for model comparison, we take these results as supporting the idea that the quasi-hyperbolic model captures variability in choice not recognized by the hyperbolic model. This view is further reinforced by the likelihood-ratio tests in the estimation section of the paper indicating that β and δ individually contribute to understanding mortgage choices. Similarly, to estimate CPT parameters {α, λ, σ}, we displayed 16 pairs of two outcome mixed gambles and asked respondents to indicate their choice. For a full discussion of this adaptive, method and its Bayesian estimation procedure, including validity checks of the estimation of discounting and prospect theory parameters, see Toubia et al. (2013). One in one hundred participants were randomly selected to receive the outcome of one of their choices. Control Variables: Risk, Differences in Ability/Knowledge, and Financial Status Risk attitude has a central role in standard models of mortgage and real-estate choices (Campbell and Cocco 2003, 2011; Genovese and Mayer 2001), so assessment of individual

29 WA 29 attitudes toward risk could be potentially helpful in understanding mortgage selection and management. It has also been argued that the observed high levels of discounting may be related to high levels of risk aversion (Andersen et al. 2008) so this allows us to control for the degree of risk aversion in looking at the effects of time preferences. We use a standard cumulative prospect theory framework and the probability-weighting function proposed by Prelec (1998) with a set of adaptively generated options. Value for a choice option is described by three parameters {α, σ, λ}, which capture, respectively, the distortion (nonlinear sensitivity) of the probabilities, the curvature (sensitivity) of the value function corresponding to the usual parameter for risk aversion, and loss aversion. We also build on recent work to model potential cognitive, knowledge and economic effects. We use measures of cognitive reflection (Frederick 2005) to assess cognitive ability on a 0-3 scale. Since Lusardi and Tufano (2009), Fernandes, Lynch and Netemeyer (2014) and others have documented large differences in financial and debt literacy and related them with financial decision quality, we also control for preexisting domain knowledge using Lusardi and Tufano s 2009 debt literacy scale, which we scale on a 0-1 range. Finally, as mortgage choices are influenced by economic status such as income and credit, which could be affected by time preferences, we control for these variables when relating time preferences with mortgage choice and abandonment. Market-Level Variables In addition to individual characteristics, market-level outcomes affect mortgage choices and management decisions. For example, the current house price and initial purchase price determine the current equity in the house. We use two sources of data to control for market-level shocks. The first, provided by Zillow.com, estimates of the current median home price, the price

30 WA 30 when the home was purchased, and its price at the peak of the market at the level of each homeowner s zip code. To control for the effect of the policies of current mortgage holders, we obtained from BlackBox Logic LLC the percentage of homes that are currently being foreclosed and the percentage that are involved in short sales. BlackBox tracks 90% of privately securitized US mortgages originated between 2000 and For both data sets, there were occasions (respectively, 25 and 7 percent) when zip code data were not available. In these cases, we substituted available state-level data, which correlated highly with zip code-level data. 3 References Andersen, Steffen, Glenn W. Harrison, Morten L. Lau, and E. Elisabet Rutström (2008), "Estimating Risk and Time Preferences," Econometrica, 76 (3), Bucks, Brian and Karen Pence (2008), "Do Borrowers Know Their Mortgage Terms?" Journal of Urban Economics, 64 (September), Campbell, John Y. and João F. Cocco (2003), "Household Risk Management and Optimal Mortgage Choice," Quarterly Journal of Economics, 118 (November), and (2011), "A Model of Mortgage Default," National Bureau of Economic Research Working Paper Series, No Fernandes, Daniel, John G. Lynch, and Richard G. Netemeyer (2014), Financial Literacy, Financial Education and Downstream Financial Behaviors, Management Science, Forthcoming, Available at SSRN: 3 Correlations between state- and zip code-level data were, respectively,.59 for Zillow.com data,.78 for BlackBox foreclosure data, and.51 for BlackBox short sale data. Our analysis excludes a few subjects who provided invalid zip codes.

31 WA 31 Frederick, Shane (2005), "Cognitive Reflection and Decision Making," Journal of Economic Perspectives, 19 (Autumn), Genesove, David and Christopher Mayer (2001), "Loss Aversion and Seller Behavior: Evidence from the Housing Market," Quarterly Journal of Economics, 116 (November), Guiso, Luigi, Paola Sapienza, Luigi Zingales (2010), "The Determinants of Attitudes towards Strategic Default on Mortgages," Journal of Finance, 68 (4), Laibson, David (1997), "Golden Eggs and Hyperbolic Discounting," Quarterly Journal of Economics, 112 (May), Lusardi, Annamaria, and Peter Tufano (2009), "Debt Literacy, Financial Experiences, and Overindebtedness," National Bureau of Economic Research Working Paper Series, No Prelec, Drazen (1998), "The Probability Weighting Function," Econometrica, 66 (May), Toubia, Olivier, Eric J. Johnson, Theodoros Evgeniou, and Philippe Delquié (2013), " Dynamic Experiments for Estimating Preferences: An Adaptive Method of Eliciting Time and Risk Parameters," Management Science, 59 (March), Tversky, Amos, and Daniel Kahneman (1991), "Loss Aversion in Riskless Choice: A Reference- Dependent Model," Quarterly Journal of Economics, 106 (November),

32 WA 32 WEB APPENDIX D: LIQUIDITY CONSTRAINTS, INTERTEMPORAL PREFERENCES AND MORTGAGE CHOICES In this section we further explore the relationship between liquidity constraints, intertemporal preferences and mortgage choices. There are two alternate explanations involving liquidity constraints that compete with our hypothesis that intertemporal preferences directly influence mortgage choices and defaulting behaviors. One possibility is that our measurements of intertemporal preferences expressed by participants are conflated with their preexisting liquidity constraints. Another possibility is that intertemporal preferences could influence choices that affect liquidity, and then facing these constraints, intertemporal preferences do not further influence mortgage choices. We test both of these competing hypotheses through a final series of simultaneous regressions that explore the relationship between intertemporal preferences, liquidity and walking away. In particular, we assessed whether liquidity confounds or mediates the relationship between intertemporal preferences and walking away by adding fraction of income servicing mortgage (inverse liquidity) as an additional endogenous factor to Models 2-5. In each case, in addition to estimating the relationship between intertemporal preferences and underwater homeownership (Equation 3) as well as with walking away (Equation 4), we also simultaneously estimated the relationship between intertemporal preferences and income servicing mortgage (inverse liquidity), Equation W10: (W10) mort_pmt_to_income i = β 0 + β l1 beta i + β l2 delta i + ε li We added to this the appropriate covariates predicting income servicing mortgage in each model. In the modified models (Models 2a-5a), underwater mortgages and walking away were

33 WA 33 as specified in Models 2-5, and income servicing mortgage was an endogeneously determined function of present bias and long-term discounting, along with (Model 2a) purchase year fixed effects, (Model 3a) debt literacy, (Model 4a) prospect theory parameters, and (Model 5a) employment security, and cognitive reasoning. In each model, we find that liquidity constraints do not account for the relationship between intertemporal preferences and walking away. After accounting for endogenously determined income servicing mortgage (inverse liquidity) the relationship between present bias, long-term discounting underwater status and walking away are unchanged, in significance and magnitude, from relationships when liquidity is assumed to be exogeneous. The fraction of income servicing mortgage is not significant in predicting walking away, though the direction of its coefficient indicates that increasing liquidity corresponds with increased willingness to default. Income servicing mortgage, in general, increases with present bias and decreases with long-term discounting (all ps <.10), except in model 3a, which accounts for debt literacy. In other words, liquidity decreases with present bias and increases with long-term discounting. Since willingness to walk away increases with liquidity, the relationship between time preferences and liquidity is directionally consistent with the relationship between time preferences and walking away. The relationship between intertemporal preferences and walking away is unchanged after accounting for the effect of liquidity.

34 WA 34 WEB APPENDIX E: DESCRIPTIVE STATISTICS FROM SURVEY OF MORTGAGED HOMEOWNERS, CORRELATION BETWEEN KEY VARIABLES AND HISTOGRAMS OF TIME PREFERENCES TABLE W8. VARIABLE DESCRIPTIONS FROM SURVEY OF MORTGAGED HOMEOWNERS Variable Description Source Level Mean St. Dev. 95% CI for mean (low) 95% CI for mean (high) (DV) Underwater Self-assessment of home equity status. Ranges from -2 to 2; 2 is most underwater. Average of two measures. Prequal. and Main survey. Individual (DV) Walk- Away Value Minimum (negative) amount home would need to change in value for mortgage abandonment. Increases with willingness to walk. Calculated based on adaptive estimation. Main ; Calculated Individual -141, , , ,786 β Percent of value retained when a payment is not received today. Decreases with present bias, ranges between zero and 1. Main ; Calculated Individual δ Percent of value retained when a payment is delayed for one year. Decreases as long-term/exponential discounting increases, ranges between zero and 1. Main ; Calculated Individual

35 WA 35 λ Loss aversion Main ; Calculated α Probability Distortion Main ; Calculated σ Diminishing Sensitivity Main ; Calculated Age Respondent age Main Gender 1=Male Main Married 1= Married Main Income Yearly household income Main Race 1=Caucasian Main Individual Individual Individual Individual Individual Individual Individual 95,539 56,007 88, ,646 Individual Has Bachelor s Degree Has Graduate Degree Employment Security 1= Yes Main 1= Yes Main -2 to 2; 2 is most secure Main Individual Individual Individual Debt Literacy Combination of financial Main Individual

36 WA 36 & Financial Competency competency self-assessment and performance on debt literacy items (ranges 0 to near 1). CRT Number of Cognitive Reflection Task items correct (out of 3). Main Individual Morality Scale Degree to which respondent views mortgage default in moral terms, from 6 scale items. Ranges from -1 to 1. Main Individual Social Connection to Strategic Defaulters Degree of social connection to strategic defaulters. Ranges from 0 to 1, 1 is closest. Main Individual Initial Home Cost Purchase price of home Main Individual 315, , , ,728 Initial Mortgage Size Amount initially borrowed on home Main Individual 286, , , ,318 Adjustable Rate 1 = Mortgage has adjustible interest rate; 0= Mortgage has fixed interest rate Main Individual Has Second Mortgage 1 = second mortgage, 0 = no second mortgage Main Individual Years in Home Years since home purchase. Main Individual Monthly Mortgage Payment Amount paid in mortgage per month. Main Individual 1,656 1,446 1,473 1,839

37 WA 37 Share of Income Servicing Mortgage Monthly mortgage payment * 12 / Income Main ; Calculated Individual Current Mortgage Debt Amount currently owed in mortgage debt. Main Individual 228, , , ,162 Amount Paid to Date Monthly payment * Years in Home *12 Main ; Calculated Individual 54, ,112 28,207 79,900 Expectations About Housing Market Fraction increase or decrease expected in home values over next three years; between -.35 and.35. Main Individual Confidence in Housing Market Expectations Strength of confidence in housing market expectations (-2 to 2; 2 is most confident) Main Individual Avg. Change in Home Price Since Peak, for Zip Code Foreclosures, as Percent of Zip Short Sales, as Percent of Zip Percent change in average home prices, ranges from.66 to 0. Homes in foreclosure, as percent of zipcode-level total. Homes in short sale, as percent of zipcode-level total. Zillow Zip Code BlackBox Zip Code BlackBox Zip Code

38 WA 38 TABLE W9. CORRELATION BETWEEN PRIMARY MEASURES OF MORTGAGED HOMEOWNERS Under- water Walking Present Bias (1-β) Long- Term Disc. (1-δ) Loss Aversion (λ) Dim. Sens. (σ) Prob. Distortion (α) Underwater 1.00 Walking Present Bias (1-β) Long-Term Discounting (1-δ) Loss Aversion (λ) Diminishing Sensitivity (σ) Probability Distortion (α)

39 WA 39 TABLE W10. DESCRIPTIVE STATISTICS, BY HOME EQUITY AND COMPARABLE VALUES OF A NATIONAL SAMPLE. Mean St. Dev. Total Sample (n=244) Under Water (n=120) Positive Equity (n=124) SBI Respondents with Mortgage Debt** A. Demographics Age 39.8 (10.8) 37.8 (8.38) 41.7 (12.5) 50.6 (13.5) % Male.34 (.47).37 (.48).31 (.47).47 (.50) % White.82 (.39).78 (.42).85 (.35).78 (.41) % With Bachelor s Degree.67 (.47).64 (.48).70 (.46).43 (.50) % With Graduate Education.27 (.45).32 (.47).23 (.42).16 (.37) B. Real Estate Characteristics Current Home Value $277,507 (219,586) $268,806 (221,719) $285,916 (218,111) $250,216 (213,790) Current Mortgage Owed 228,904 (227,651) 283,750 (272,237) 175,441 (157,171) 130,594 (121,766) Home Purchase Price $315,246 (376,536) $335,917 (372,531) $295,242 (380,807) Initial Mortgage Size $286,906 (463,218) $326,042 (479,440) $249,032 (445,623) $161,049 (128,719) Amount Paid To Date (Home Cost Curr. Debt)* $54,053 (291,112) $21,509 (126,364) $85,777 (250,177) Percent of Home Cost Borrowed Initially 89.7% (26.7%) 95.0% (28.2%) 84.6% (24.2%) Percent of Mortgages With an Adjustable Rate 18.0% (38.5%) 20.0% (40.2%) 16.1% (36.9%) 13.1% (33.7%) Percent With a Second Mortgage 33.6% (47.3%) 41.7% (49.5%) 25.8% (43.9%) 13.9% (34.6%) Share of Income Servicing Mortgage 23.0% (14.5%) 23.8% (14.2%) 22.3% (14.8%) 21.2% (17.3%) Years Since Purchase 7.77 (5.55) 7.09 (4.75) 8.43 (6.18) (10.26)

40 WA 40 C. Time Discounting and Prospect Theory Risk Parameters β: lower values suggest more present bias.88 (.15).84 (.18) δ: lower values suggest more long-term discounting Lambda: Higher values mean more loss aversion Alpha: Prob. Weighting Sigma: Lower values mean more risk aversion/diminishing sensitivity.43 (.27) 2.26 (1.06).74 (.29).64 (.28) D. Knowledge / Cognitive Resources Cognitive Reasoning (CRT) Scale 1.14 (1.08) Debt Literacy.39 (.22).37 (.27) 2.24 (1.10).73 (.29).64 (.29) 1.13 (1.09).37 (.22).91 (.10).49 (.25) 2.28 (1.02).76 (.29).65 (.27) 1.15 (1.08).42 (.22) Notes: * Does not equal difference between means of home cost and current debt due to 9 missing values for current debt. ** Variables with no equivalent in the SBI data set are shaded gray.

41 WA 41 FIGURE W3. HISTOGRAMS OF INTERTEMPORAL PREFERENCES, BY HOME EQUITY STATUS