Exploring the Foreclosure Contagion Effect Using Agent-Based Modeling

Transcription

1 J Real Estate Finan Econ (2013) 46: DOI /s Exploring the Foreclosure Contagion Effect Using Agent-Based Modeling Marshall Gangel & Michael J. Seiler & Andrew Collins Published online: 15 May 2011 # Springer Science+Business Media, LLC 2011 Abstract Over the last several years, the United States has experienced a significant recession. During this downturn, the number of real estate foreclosures has risen drastically. Recent studies have demonstrated a reduction in property values due to neighboring foreclosures known as the foreclosure contagion effect. This study uses an agent-based modeling approach to explore market-wide emergent behavior that results from the interconnected property-agent behavior. Specifically, we find that the magnitude of the foreclosure contagion effect is a less powerful cause of eventual market collapse than the time a foreclosed property is allowed to linger on the market. This is important because disposition time is much easier to address from a policymaker perspective than is the strength of the foreclosure contagion effect. Keywords Foreclosure contagion effect. Disposition time. Agent-based modeling Introduction The real estate market is currently experiencing the worst crisis since the Great Depression. Unemployment has caused people to involuntarily default on their M. Gangel: A. Collins Virginia Modeling, Analysis, and Simulation Center (VMASC), Old Dominion University, 2154 Constant Hall, Norfolk, VA , USA M. Gangel mgang002@odu.edu A. Collins ajcollin@odu.edu M. J. Seiler (*) Finance, Old Dominion University, 2154 Constant Hall, Norfolk, VA , USA mseiler@odu.edu

2 340 M. Gangel et al. mortgages, while falling home prices have encouraged others to voluntarily stop paying their mortgages. 1 Whether by choice or necessity, as foreclosures increase, they have an increasingly negative impact on the price of the healthy homes around them. One default does little to negatively impact the price of surrounding homes. However, as more and more mortgages in the neighborhood go into default, the negative impact is felt at an increasing rate. Much the same way as a disease spreads throughout a population, so too do falling home prices. Past studies have used traditional methodologies to measure the impact of foreclosure contagion on surrounding home prices in terms of both time and distance. The results of such efforts have produced extremely different measures of contagion severity. We take a different approach. Instead of measuring the contagion effect, we use the wide range of results from past studies as a starting point, and then determine the impact this range will have on the housing market under varying market conditions experienced over time. To accomplish this goal, it is necessary to use an agent-based modeling (ABM) approach. Specifically, we begin by creating a simulated real estate market that reasonably resembles the real world. We are then able to perform a wide range of sensitivity analyses that encompass all values found within the range of extant literature findings. In this sense, we are not focused on debating the merits of past studies or which studies are correct. Instead, we measure the impact of foreclosure contagion on a real estate market that covers all scenarios whether or not those scenarios have been observed in the past. 2 We find that the time a foreclosed property is left to flounder on the market is more detrimental to a market s stability than even the most severe contagion effect found in the literature. Therefore, when policymakers are debating where to focus solution efforts, one obvious place to begin is in streamlining the process of dissolving foreclosed properties. This could not only save taxpayer dollars, but it might also prevent the displacement of countless homeowners. Background The real estate market has a significant role in the nation s financial system which was made evident in the recent recession of 2007 through the present. Former lending practices allowed high risk individuals to obtain subprime mortgages. These subprime mortgages inundated the market which eventually produced a surge of foreclosures as subprime homeowners defaulted. The increase in foreclosures caused instability within the financial system which caused financial investment losses, high unemployment, and even more foreclosures. This positive feedback loop created one of the worse recessions 1 The voluntary decision to walk away from a mortgage obligation even when a homeowner can afford to continue making payments because the property is underwater is known as strategic default. More formally, it is known as exercising one s put option. 2 Our goal is not to measure the foreclosure process associated with a particular state or region within a state. There is no question that because different states have very different real estate laws (power-of-sale versus judicial foreclosure, recourse versus non-recourse, etc.) that they are differentially effective at moving foreclosed properties through the system. The expediency of this clearing is also a function of how far down home prices have fallen because people will almost certainly not default on a mortgage when their home has equity.

3 Exploring the Foreclosure Contagion Effect Using Agent-Based Modeling 341 in the history of the United States. It is clear that the real estate market is a critical element to the health of the nation s financial system. The goal of this study is to contribute to the real estate and foreclosure body of knowledge by using agent-based modeling in the hopes of suggesting at least a partial solution. ABM is a modeling and simulation technique that allows for the representation of many individual entities and their actions within a system. Once entity level behaviors and rules are established and executed, macro or system level behaviors emerge from the aggregate actions of the agents (North and Macal 2007). ABM analysis can be considered a bottom-up approach since the lower level behaviors are understood and implemented to observe the total system behavior. Other analysis techniques, such as systems dynamics, should be considered top-down approaches because they implement equations which represent the total system behavior (Gilbert 2008). 3 ABM has been used extensively to show emergent behavior in the social sciences. For instance, Schelling (1969) developed an ABM to explore segregation in urban centers; he demonstrates that even minor racial prejudices create massive segregation. Previous research efforts to explore the foreclosure contagion effect within the real estate market use a hedonic regression methodology. Hedonic models decompose complex, incomparable entities into smaller, comparable constituents for analysis. Once decomposed, the constituents are evaluated to determine their contribution to the state of the original entity. In the case of foreclosure contagion, relationships between foreclosures and neighboring property sale prices are explored by decomposing sales prices with two of the constituents being the number and distances of foreclosures within the proximity of the selling property. This approach has been used to identify and quantify relationships between foreclosures and property values from datasets that contain real estate sale prices and foreclosure events (Immergluck and Smith 2006; Harding et al. 2009; Lin et al. 2009; and Rogers and Winter 2009). This study incorporates the aforementioned foreclosure contagion effects into an ABM model which establishes real estate properties as agents. An ABM approach was selected to explore relationships between foreclosure variables and market behavior that cannot be studied from real world data because these variables do not vary in the real market. For instance, when a property is foreclosed it is typically owned by the bank, commonly called Real Estate Owned (REO), and unoccupied for a lengthy amount of time. During this time period, the neighboring properties experience the negative contagion effect of the foreclosure which is quantified by decreasing property values. The ABM approach allows us to adjust the amount of time that foreclosures sit on the market before they are sold what we refer to as disposition time; This allows the effects on the market from the adjustment to be observed. This can only be seen in the actual market if foreclosure policy and procedures are redefined. Implementing changes to the actual system would be costly in terms of both time and effort. Furthermore, changes to the system without the ex-ante knowledge that the changes are warranted may not be politically or economically advantageous. Understanding the potential consequences of the changes before they are implemented is essential. ABM is a critical tool that may illustrate the potential consequences of changing the real estate market s foreclosure policy. Operationally, it enables the 3 Systems dynamics techniques are applicable when the system behavior is already fully understood.

4 342 M. Gangel et al. exploration of relationships and emergent behaviors within the system that cannot be gathered from direct observations of the real estate market s historicaldata. Foreclosure Literature Foreclosure Discount Involuntary foreclosures within the real estate market occur when the borrower is no longer able to fulfill the mortgage contract and eventually defaults. 4 A legal process then begins which allows the creditor, typically a bank, to gain possession of the property and then sell it to a third party. The money received from the sale is applied to the remaining balance on the original loan. The foreclosure process is extremely detrimental for all entities involved. Lin et al. (2009) find that foreclosure costs are estimated to be between $7,200 and $58,759, while Rogers and Winter (2009) measure this window to be between $27,000 and $30,000. Moreover, Harding et al. (2009) state that foreclosed properties usually experience gross neglect, abandonment, and vandalism which further lower the value of the property. Finally, neighborhood crime rates may increase as gangs and/or drug dealers squat in the vacated properties (Rogers and Winter 2009). These recent studies have demonstrated that the negative effects of foreclosure are not felt solely by the involved parties, but are also experienced by real estate properties that are located within proximity to foreclosure events. This externalization of the negative consequences of foreclosure events is known as the contagion effect. The effect is contagious because foreclosures are shown to decrease neighboring property values which may lead to additional foreclosures. Surrounding property prices are also negatively influenced by the mere fact that more homes are available for sale nearby. Basic economics would predict that a greater level of home inventory (supply) would drive down prices when demand is held constant. The extant literature suggests that the contagion effect of foreclosed properties is a local one. The effect diminishes as a function of both time and distance. A foreclosure event will have a minimal impact on properties that are located significant distances from it and a maximum impact on properties that are neighbors. Likewise, a foreclosure event that occurred in the distant past will have a minimal effect on its neighbors, while a recent foreclosure will have the largest impact. The extent to which this effect occurs varies greatly between studies. Harding et al. (2009) suggest the contagion effect is significant within approximately 0.9 miles and 5 years of a foreclosure event. Immergluck and Smith (2006) state their most conservative estimate to be a 0.9% discount for every foreclosure within one eighth of a mile radius of a given property. On the upper end of estimation, Lin et al. (2009) find that the foreclosure effect is as high as 8.7%. On the lower extreme, Rogers and Winter (2009) conclude the contagion effect to be 1% or less. Although the literature offers different values for quantifying the contagion effect, all agree the effect is 4 Freddie Mac lists the most common reasons for default, in order, as unemployment, illness/death, excessive obligations, and marital difficulties.

5 Exploring the Foreclosure Contagion Effect Using Agent-Based Modeling 343 local and that it is a function of both time and distance. Ultimately, we incorporate the upper and lower values found in these existing studies as range limits in the current analysis. Disposition Time The process by which a foreclosure gets resolved is a function of the state in which the property is located (Pence 2003; 2006). Judicial foreclosure states require the courts to get involved which substantially slows down the process. Alternatively, power-of-sale states allow the bank to sell the property without the court s supervision. Burge et al. (2011) empirically demonstrate that the average time on the market for judicial foreclosures is 5.8 months, whereas power-of-sale foreclosures get resolved in just 3.4 months. To further compound the problem, states with a Statutory Right of Redemption indirectly delay the resolution of a foreclosure by effectively limiting the demand pool that is willing to step forward to buy a foreclosed property. The reason is that this law allows a foreclosed upon property owner to regain ownership of the foreclosed property for a fixed period (up to 1 year), even after it has been sold to someone else. The previously cited literature acknowledges that having unresolved foreclosed properties in a neighborhood causes a magnification of the foreclosure contagion problem. Empirically, the question is, To what extent does the added time on the market cause an increase in the likelihood of a market collapse? We seek to address this question by allowing both the magnitude of the foreclosure impact to vary as well as the foreclosure time on the market. We select a minimum value of 1 month and a maximum value of 14 to provide a sufficient range to see varying results. Model Design Our real estate ABM is designed around the agents and their behavior. Since we observe the impact of individual foreclosures and the value of the surrounding properties, it is intuitive to establish real estate properties as the agents. 5 While many intricate sub-functions are constructed within the model, only the three main functions will be described in this paper. The property agents have three main functions that mimic real life events: appraise value, evaluate foreclosure, and evaluate sale. The appraisal function is directly based on the comparable sales method. It observes recent sales within a set distance from itself to determine its current value. The foreclosure function uses the property s current financial posture and attributes to determine if the property experiences a foreclosure. The sales function uses the property s current financial posture to determine if the property 5 It is possible to make individuals/people the agents instead of the homes themselves. However, this approach would add a level of complexity so great that it would likely do more to muddy the waters, than to add clarity. Over this long period of time, people can be born, die, marry (thus creating the need for fewer households), move out of and into town, and so forth. While we acknowledge this different approach as a possible alternative specification, we strongly warn against the wisdom of this approach in future studies.

6 344 M. Gangel et al. should be listed on the market for sale. The following section will decompose these three functions to provide insight into the dynamics of the model. Appraisal Value Formulae For each agent and at each time-step, which represents one month of real-world time, a function executes to generate the current value of the property. This information is needed for several reasons: for input into the foreclosure and sales formulae, and to calculate the average property value for the entire real estate market within the model. Although properties in the real world are not formally appraised every month, it could be argued that an owner does an informal appraisal of their property at periodic intervals. Property appraisals in the real world system occur locally to the property being evaluated. For residential real estate, appraisers generally rely on the comparable sales method. Specifically, they find multiple properties with similar features within the vicinity of the subject property that were recently sold (Ling and Archer 2009). The transaction prices of these similar properties are then used to determine the value of the appraised property. The properties within the model are assumed to share homogenous features which indicate that they are physically identical except for their location. This assumption simplifies the appraisal function by allowing it to find comparable sales within a recent time frame and distance. There have been several attempts within the real estate literature to mathematically express the appraisal function (Geltner et al. 2003). However, in the interests of simplicity, our model uses a weighted average to determine the price. The model observes the local properties and collects the sales information from the properties that transacted within the maximum distance and time constraints. 6 A weighting function is derived to calculate the appraisal value as follows. Let Δd t equal the difference between the i th property and some maximum distance constant, d max. Let Δt t equal the difference between the i th property and some maximum time constraint called t max. Since only properties that are within the maximum time and distance are considered, both Δd t and Δt t are strictly positive. Let d t equal the distance from the i th property and the appraisal property. Let t t equal time in months since the i th property was sold. Let p t equal the sales price of the i th property. The following function weights the sales properties that meet the maximum time and distance constraints and then averages their time and distance elements. Δd i ¼ d max d i ; Δt i ¼ t max t i Appraised Value ¼ Xn i¼1 p i 1 2 Δd P i Δt i n i¼1 Δd þ P n i i¼1 Δt i If no property sales are found within the time and distance constraints, the model will assign the average price of the entire market from the previous month. If there were any recent foreclosures within the local neighborhood, then a property s appraisal value is adversely affected by them. Mathematically, if there are m 6 We specify a 10 house radius sweep for sales within the last six months.

7 Exploring the Foreclosure Contagion Effect Using Agent-Based Modeling 345 foreclosed properties within the constrained radius, then the appraisal value is decreased by following value: Foreclosure Contagion Effect ¼ m Xm j¼1 1 2 Δd j þ Δt j To clarify, mu measures the contagion effect severity for a single home on the subject property. However, there is also a negative feedback loop which causes the effect of the foreclosed home to linger or negatively contribute to the value of the subject property even after the foreclosure has been resold in the marketplace. It s like dropping a stone into a calm body of water. Long after the stone is gone, the ripple still moves across the water s surface. This legacy or hangover effect causes a formula that is linear to create an emergent behavior which is not linear as will be seen in the Results section. Foreclosure Formulae Once an agent appraisal value has been calculated, it can then be determined whether or not that agent forecloses. Whether a property goes into foreclosure is determined by a probability likelihood function. For this study, several different reasons are given for foreclosure: financial standing, loan type, and occupant status. Each of these reasons has its own associated effect on the overall probability of foreclosure, which is discussed below. Equity Foreclosure Current appraisal value and remaining loan balance are used to calculate the equity ratio. Equity Ratio ¼ Appraised Value Outstanding Loan Balance Having positive equity carries no additional probability of foreclosure. An equity ratio less than one indicates the borrower is underwater and therefore has incurred a paper loss on the property. This loss is not realized until the property is sold to another party. However, the status of the equity influences the decision to sell. This logic is explained in the following section. As the equity ratio moves below 1, the probability of an owner defaulting, which leads to foreclosure, linearly increases. Let C Equity equal a constant that scales the effect of the equity ratio. Thus, an equity foreclosure is given by the following formula: For Equity < 1, 1 Equity Ratio Equity Foreclosure Effect ¼ ð Þ» C Equity 12 For Equity 1, Equity Foreclosure Effect ¼ 0

8 346 M. Gangel et al. Interest Rate Foreclosure Loan type is composed of two mortgage categories: fixed rate mortgages (FRM) and adjustable rate mortgages (ARM). All loans incorporate an interest rate, based on historic values, which is used to calculate a unique amortization table for each property. Monthly payments are determined by the amortization table. Borrowers are typically financially constrained by the amount of the monthly payment. FRMs have fixed interest rates so the monthly payment does not fluctuate over the entire life of the loan. Therefore, it can be assumed that the borrower can afford the monthly payments throughout the life of the loan, barring major catastrophic events which are addressed later. 7 ARMs have a fixed rate period at the beginning of the loan during which the interest rate does not change. Once the fixed period has ended, the interest rate changes annually, as determined by external market forces (Ling and Archer 2009). An associated monthly payment increase is assumed to increase the probability of default. Likewise, a decrease in monthly payment is assumed to lessen the probability of default. For simplicity, we assume there is a linear relationship between changes in monthly payments and foreclosure rates. Let C equal a constant that scales the effect of the probability of interest rate foreclosure. Let IC equal the percentage change between the original and the current monthly payment. Thus the probability of an interest rate related foreclosure is given by the following formula: IC ¼ Current Monthly Payment Fixed Period Monthly Payment IC 1 Interest Rate Foreclosure Effect ¼ ð Þ» C 12 Investor Foreclosure It has been shown that owner-occupants behave differently than an owner who is renting out a property as an investment. Specifically, an owner-occupant has to live somewhere. As such, they are much less likely to default on a mortgage even when their home is underwater (Guiso et al. 2009). The resistance to default is also persistent in the face of an ability to rent at a rate cheaper than owning. By comparison, a real estate investor is more likely to retain an investment property when their renter s payment exceeds the monthly mortgage payment and is more likely to exercise their put option when the renter s payment is below the monthly mortgage. Since the renter market is not the focus of this research, the following assumption is made to simulate the dynamics of the renter market. If the average property value growth has exceeded the expected growth for a 36-month rolling period, then it assumed average rent is sufficiently below monthly mortgage payments for new loan originations, which increases the probability of investment property 7 Alternatively stated, in the absence of income shocks such as job loss, divorce, death, etc., the tilt effect would support our contention that an affordable monthly payment today should feel more affordable as time passes.

9 Exploring the Foreclosure Contagion Effect Using Agent-Based Modeling 347 defaults. 8 Conversely, if the average property value growth has fallen below the expected growth for a 36-month rolling period, then it is assumed that the average monthly rent is above the monthly mortgage payment which decreases the probability of foreclosure from a rent differential (only) standpoint. Let C Investor equal a constant probability that scales the effect of probability of investor foreclosure. For High Market Growth; For Low Market Growth; Catastrophic Foreclosure Investor Foreclosure Effect ¼ C Investor 12 Investor Foreclosure Effect ¼ C Investor 12 An additional probability of foreclosure value is included to represent catastrophic events such as job loss, death, divorce, etc. Specifically, let C Catastrophic equal a constant that represents the probability of a foreclosure due to a catastrophic event that results in an inability to maintain payments. Total Probability of Foreclosure Each effect just described impacts the probability of foreclosure depending on the agent, or property type. Each agent is given a classification when created (e.g., an owner-occupant with a FRM) based on historical data. 9 The following table illustrates the four property variants with the foreclosure elements that are used to determine the probability of foreclosure. Foreclosure Probability FRM ARM Elements Owner-Occupant Equity, Catastrophic Equity, Interest Rate, Catastrophic Renter/Investment Equity, Investor, Catastrophic Equity, Interest Rate, Investor, Catastrophic The probability of foreclosure for a given agent is determined by adding the appropriate component to each individual equation. For example, the following equation is the foreclosure probability for properties that are investments with an ARM loan. PðForeclosurej ARM; InvestmentÞ ¼ Equity Foreclosure Effect þ Interest Rate Foreclosure Effect þinvestor Foreclosure Effect þ C Catastrophic 8 This statement only applies to the partial effect of rental income versus mortgage payment differentials on new loans. Clearly, the positive effect of increasing property values will outweigh the economic pressure to default due to negative cash flow differentials. 9 The percentage of FRM versus ARMs, the number of owner-occupants versus investors, etc., are stochastic in that they are drawn from a Bernoulli distribution over time whenever a home is purchased and a new owner is assigned.

10 348 M. Gangel et al. Sale Formulae The sales function is executed every month directly after the foreclosure function. This function represents buyers and sellers within the market. For a property to sell, it must first be listed by a seller and then purchased by a buyer. This dynamic is complex and is not the focus of our investigation. To simplify the complexity, an assumption is made to represent the listing and purchasing actions as a single event. We determine the percentage of properties listed for sale each month as a function of overall property values. This is consistent with historical data pulled from numerous sub-markets around the country. Genesove and Mayer (2001) find that properties that have been successful investments are more likely to list than properties that are currently underwater. 10 The model sorts the properties by equity and samples a distribution to determine which properties should be solicited to be listed. This method ensures that all properties have an opportunity to sell, but the properties with the best financial posture have a higher probability of listing. After the model selects a property from the equity list, the chosen property makes the final listing determination based on its financial posture while also incorporating false reference points. False reference points are an element of the field of behavioral finance which combines mathematics and psychology. Seiler et al. (2008) find that individuals will avoid the feeling of regret by choosing not to sell when unbiased indicators signal they should. 11 Two false reference points have been identified in the decision-making process of a homeowner. The first reference point is associated with the original purchase price of the home. Genesove and Mayer (2001) show that homeowners are resistant to sell if the current value is below the original purchase price, even though they have positive equity. The second false reference point is found at the threshold of positive and negative equity or when the equity ratio equals one. Homeowners avoid selling their house when it is underwater because of both regret aversion and the monetary requirement to cover the equity shortage (Einio et al. 2008). Depending on the financial situation of the property, the property will elect to list or test one of the two false reference points. If the property agent does not list, then the model will solicit a different property until the historically consistent monthly listing percentage is obtained. The final selling price is the appraised value with an additional factor which represents local competition. Property prices decrease as supply rises and increase as supply decreases. During the sales month, the number of listings are observed and compared with the number of listings that are expected to be found within the selling property s local area. If more listings are observed compared to the expected number, then the local market is competitive. Likewise, if fewer listing are found compared to the expected number, then the local market is not competitive. Upon a sale, new starting point data is included for the property in all areas including loan type, down payment, loan amount, buyer type, etc. A linear function is used to represent this 10 Bokhari and Geltner (2011) replicate this study using commercial real estate data and support the notion that this behavior may be generalizable across asset classes. 11 Shefrin and Statman (1985), Odean (1998), and Shumway and Wu (2009) document the disposition effect in a financial context as well. That is, they find investors are more likely to sell assets that have increased in value and continue to hold assets that have gone down in value.

11 Exploring the Foreclosure Contagion Effect Using Agent-Based Modeling 349 phenomenon as shown below. If we let C listing equal a constant that scales the effect of the listing impact, then: Listing Impact ¼ 1 þ ðexpected Listings Observed ListingsÞ» C listing Model Implementation After designing the real estate foreclosure contagion environment, simulation runs were conducted using a software package known as Repast Simphony. Repast Simphony is an open-source ABM software developer s kit that is installed in conjunction with Eclipse. Eclipse is an open-source application that is used to build java applications. Another ABM package titled NetLogo was also considered for implementation, but Repast Simphony was selected as the primary tool for this study due to its computing speed and programming flexibility. The model s initial conditions were constructed in a Microsoft Excel spreadsheet for ease of manipulation. Prior to executing the model, Excel writes the initial conditions to a text file which is then read by the model during the initialization phase. The model consists of 2,500 real estate properties (agents) that are evenly separated in a grid formation. 12 The model reads in the initial conditions which provide the agents with the following information: name, location, loan type, loan age, purchase price, current value, resident type, foreclosure information, and listing information. Once the initial conditions have been loaded, the model executes in a discrete time step which equals a period of 1 month. Each month, the model performs six main functions for each property agent. First, the model updates loan, foreclosure, and listing information on each property, if applicable. Second, the model appraises the value of each property as a function of local sales and foreclosures. Third, the model updates the equity investment property list and computes the average property value. Fourth, the model selects properties to list as a function of the equity list and false reference points. Finally, output for the month is created. This process is repeated over and over again month after month (see Exhibit 1). We report the average results for models that are allowed to run for up to 83 years. 13 Exhibit 2 shows an example of the progression of screen captures that convey a market with an eventual catastrophic collapse. Yellow properties indicate a marginal level of being underwater. Orange properties indicate a significant state of being underwater, and red properties illustrate foreclosures. 12 Although technically the property grid must have physical boundaries such as edges and corners, the mathematics we perform implicitly assumes a toroidal or spherical space. Simply stated, the space is treated as being continuous and without boundaries. That is, a home located in the corner of our grid shares the exact same mathematical underlying drivers (and neighbors) as a property located exactly in the middle of the housing grid. 13 The results are not sensitive to the number of years we allow the simulation to run. Before we started the process, we picked a number of months that seemed long enough to capture any long-term trends, but not so long as to substantially lengthen the time it takes to generate all of the runs necessary to complete the analysis. The number 1,000 (which corresponds to roughly 83 years) was deemed sufficiently long. After generating the results, we observe that 1,000 periods is longer than we need because nothing really happens that far out in time that we did not see earlier on in the simulation run. By the same token, we were comforted that our model did not generate immediate results (like a collapse) right out of the gate. If this were the case, it would point to the possibility of poor starting parameter estimates.

12 350 M. Gangel et al. Exhibit 1 Monthly process of stepping through the calculations within the model Results Any time an ABM is created, it is a good idea to first examine a typical simulation run to see if the ABM reasonably replicates the real world. As previously discussed, agent-based models step through time in a discrete fashion. Due to the nature of the real estate market, this model was designed with a step equal to a period of 1 month. Between monthly steps, the model was configured to record the states of the variables which were identified as primary metrics. After the simulation runs finished executing, the average values of these monthly metrics were analyzed to determine the impact of various input parameters. Exhibit 3 displays the results from a single, typical run. Average property value over time is graphed with the percentage of properties underwater and the percentage of foreclosed properties. These three metrics are collocated in the same space because of their coupled nature. In our model, the fluctuations of one metric typically align with the fluctuations of the other, as expected based on real world data. This phenomenon occurs because of Exhibit 2 Sequential screen captures showing an eventual market collapse due to foreclosure contagion

13 Exploring the Foreclosure Contagion Effect Using Agent-Based Modeling 351 Exhibit 3 Graphical representation of relationships among: property values, percentage of properties underwater, and percentage of properties foreclosed the contagion nature of foreclosures and the probability of foreclosures as a function of equity. A property s probability of foreclosure increases as its value decreases. Therefore, as property values decrease, the percentage of properties underwater rises which increases foreclosures. Subsequently, the rise in foreclosures drives the surrounding property values even lower. Between years 49 and 52, the market experienced a substantial decline in home prices. Accordingly, the percentage of properties underwater significantly increased, and the percentage of foreclosures observed skyrocketed. The act of observing individual runs provides insight into the behavior of the model and helps to validate the internal mechanics, but the ultimate purpose of this study is to identify emergent global behaviors. To this end, we next perform a series of sensitivity analyses to evaluate the impact of key input parameters on the overall market. This was accomplished by adjusting the input variables, executing the model, and then analyzing the results. The two key variables are foreclosure discount and disposition time. These variables were selected because they are highly debated within the foreclosure contagion literature and because they are highly influential. Foreclosure discount is the percentage of price decline that is associated with each foreclosure as a function of its age and distance from the appraised property and, as previously discussed, is indicated by a μ in the foreclosure contagion effect formulae. In essence, the foreclosure discount is a negative percentage that foreclosures impose on their neighbors when the neighbor s value is determined each period. Disposition time is the number of months the foreclosed property

14 352 M. Gangel et al. remains on the market before it is sold. We perform a sensitivity analysis by combining the 14 values of disposition time (ranging from 1 to 14 months) with the 50 values of foreclosure discount (ranging from 0.01 to 0.5). 14 Both sets of numbers are ranges found in the current literature as previously cited and discussed. The result is a grid with 700 scenario combinations (14 50). Each variable combination of foreclosure discount and disposition time was executed 30 times to produce average relationships from 21,000 simulation runs. Exhibit 4 considers the relationship between disposition time and foreclosure discount using a 3-dimentional waterfall graph to show the distinction between real estate markets that crashed versus those which remained stable. The graph is composed on two key regions. The lake is the flat part at the bottom-right of the graph, and it represents combinations of discount rate and time to foreclosure that cause the market to collapse. The mountain in the graph conveys market declines (but not failures) for the remaining combinations. It is clear from this graph that the relationship between disposition time and foreclosure discount is non-linear. If it were, the side of the mountain would slope down to the lake in the shape of a plane; there would be no curvature at all. This graph conveys how a linear formula that measures only the contemporaneous impact of the surrounding home foreclosure effect creates a non-linear relationship once inter-temporal negative feedback loops are considered. 15 What is most important about this analysis is the point at which the market turns from healthy to potentially unstable. Because the equation has two unknowns, there are an infinite number of combinations of time and discount that cause the market to slip into collapse. This collapse occurs as early as 2 months or as late as 13 months if past researchers are correct in their estimates of foreclosure discount. In either extreme, the conclusion that foreclosed homes should be resold sooner rather than later is clear. Letting foreclosed homes needlessly linger in the neighborhood causes an increasing foreclosure contagion problem possibly to the point of market collapse. 16 To put a finer point on the relative strength of foreclosure discount and disposition time, we separated the results into cases where the market did and did not collapse. In cases where the market did crash, the coefficient on the foreclosure discount is $30,176, whereas the disposition time is $64,855. For non-market crashes, the 14 The foreclosure discounts we report here capture the effect from just one foreclosure on the subject property. The reality is that more than one home (usually many more) within the radius of influence can be in foreclosure at any point in time. As such, it is the aggregated effect of all these properties that is actually compared to the traditional study results cited in the Literature Review section to equate the strength of each effect. 15 Measuring the length of the ripple effect in isolation of all the other influences in the model is next to impossible. Imagine throwing multiple stones in the water. At some point, the ripples from one will be indistinguishable from the ripples caused by the next. So, while we know the effect of a particular foreclosure lingers after the home is sold to a new, healthy buyer, we have no way of knowing when the effect fully dissipates. By way of comparison, Harding et al. (2009) find the effect to last as long as 12 month afterwards. 16 Note that just because the minimum property value slips below $200,000 does not necessarily mean the market fully collapsed. It is possible that the market slipped by 25%, but managed to recover back to a healthy level.

15 Exploring the Foreclosure Contagion Effect Using Agent-Based Modeling 353 Exhibit 4 Graphical representation of the relationship among: property values, disposition time, and foreclosure discount results are reasonably similar. The foreclosure discount coefficient is $64,301, while disposition time was associated with a coefficient of $104,848. After reviewing the current trade space and robustness tests between foreclosure discount and disposition time, it is apparent that disposition time has a greater impact on property values than foreclosure discount. From a policy perspective, this is important because decision-makers cannot directly change the impact of foreclosure contagion, but they can streamline the laws to expedite the time it takes to move a foreclosed property from delinquency status to being sold to a new, healthy buyer. Simply doing this should substantially reduce the spread of the contagion, and therefore reduce the likelihood of a potential market collapse. Conclusions This is the first study to apply agent-based modeling to the area of real estate foreclosures. We begin by building a simulation that reasonably tracks the intricate relationships that exist in the observable real world. Once a stable model was established, we performed a myriad of sensitivity analyses focusing on the variables that are both most important to the foreclosure contagion equations and those which are the most uncertain. We find that the greater the time a foreclosed property is allowed to remain on the market, the greater the probability the market will fail. The beginnings of a market failure can occur as early as 2 and as late as 13 months depending on the severity of the foreclosure effect. Of course, these results are also a function the severity of the decline in home prices.

16 354 M. Gangel et al. Future studies should further examine sensitivity analyses relating to the lesser important variables in our model to determine if they too might be easily changed to strengthen the support for a healthy underlying residential real estate market system. Variables that turn out to be important in magnitude and those that can more easily be changed by policymakers are ideal candidates for where to begin. In sum, no matter the politics or economic view relating to this topic, we can all agree a better understanding of real estate markets is ideal. ABM can be used to gain additional insight beyond the ability of traditional tools used in the past. References Bokhari, S., & Geltner, D. (2011) Loss Aversion and Anchoring in Commercial Real Estate Pricing: Empirical Evidence and Price Index Implications, Real Estate Economics, 39:4, forthcoming. Burge, W., Harrison, D., & Seiler, M. (2011) The Paradox of Judicial Foreclosure: Collateral Value Uncertainty and Mortgage Rates, working paper, Texas Tech. Einio, M., Kaustia, M., & Puttonen, V. (2008). Price setting and the reluctance to realize losses in apartment markets. Journal of Economic Psychology, 29, Geltner, D., MacGregor, B., & Schwann, G. (2003). Appraisal smoothing and price discovery in real estate markets. Journal of Urban Economics, 40(5/6), Genesove, D., & Mayer, C. (2001). Loss aversion and seller behavior: evidence from the housing market. Quarterly Journal of Economics, 116, Gilbert, N. (2008) Agent-Based Models, in Series: Quantitative Applications in the Social Sciences, SAGE Publications. Guiso, L., Sapienza, P., & Zingales, L. (2009) Moral and Social Constraints to Strategic Default on Mortgages, working paper, University of Chicago. Harding, J., Rosenblatt, E., & Yao, V. (2009). The contagion effect of foreclosed properties. Journal of Urban Economics, 66(3), Immergluck, D., & Smith, G. (2006). The external costs of foreclosures: the impact of single-family mortgage foreclosures on property values. Housing Policy Debate, 17(1), Lin, Z., Rosenblatt, E., & Yao, V. (2009). Spillover effects of foreclosures on neighborhood property values. Journal of Real Estate Finance and Economics, 38(4), Ling, D., & Archer, W. (2009) Real Estate Principles: A Value Approach, McGraw-Hill Irwin. North, M., & Macal, C. (2007) Managing Business Complexity: Discovering Strategic Solutions with Agent-Based Modeling and Simulation, Oxford University Press, Odean, T. (1998). Are investors reluctant to realize their losses? Journal of Finance, 53(5), Pence, K. M. (2003) Foreclosing on Opportunity: State Laws and Mortgage Credit, Board of Governors of the Federal Reserve System, Finance and Economics Discussion Series, Pence, K. M. (2006). Foreclosing on opportunity: state laws and mortgage credit. Review of Economics and Statistics, 88(1), Rogers, W., & Winter, W. (2009). The impact of foreclosures on neighboring housing sales. Journal of Real Estate Research, 31(4), Schelling, T. (1969). Models of segregation. American Economic Review, 59(2), Seiler, M., Seiler, V., Traub, S., & Harrison, D. (2008). Regret aversion and false reference points in residential real estate. Journal of Real Estate Research, 30(4), Shefrin, H., & Statman, M. (1985). The disposition to sell winners too early and ride losers too long: theory and evidence. Journal of Finance, 40(3), Shumway, T., & G. Wu, (2009) Does Disposition Drive Momentum?, working paper, University of Michigan.