Interdependence Effects of Housing Abandonment and Renovation

Abstract This study uses a methodology for analyzing the interdependence effects of abandonment and renovation for profit-maximizing landlords. After using a Prisoners' Dilemma game of abandonment to establish the existence of the interdependence phenomenon between internal rates of return, a Stackelberg framework is employed to model the interdependence effects of abandonment and renovation. The Stackelberg model appropriately defines the timing payoffs of the landlords' operational decisions. This model shows that as long as one landlord does not abandon, the optimal decision for the other landlord is to renovate their property.

Sociologist and more specifically human ecologists usually assume that if the population size or composition of a neighborhood changes then change will follow in the other components of the system as well. This perspective may be traced to the conception, developed by the Chicago School urbanists, of neighborhoods as "natural areas," (Schwirian, 1983).1

Urbanists and ecologists assert how a new social system can invade a neighborhood, which may cause a succession from the old system to a new system. With succession and the creation of new systems, changes in social characteristics, familism2 and economic status may result in neighborhood decline. If succession takes place, the newcomers may have no personal bond to the established structures. Therefore, conventional upkeep and maintenance may not be a focal concern of these immigrants. For instance, residential properties in these new social system neighborhoods may experience blight, which may result in property abandonment.

Housing abandonment may be optimal or suboptimal. Optimal abandonment may occur when a property has an alternative higher and better use than its current use, and/or it is financially feasible to walk away from the property rather than to sell it. This phenomenon is seen more often in seasoned properties. In general, as the property ages, its quality declines.3 Furthermore, the initial quality of a property may be low due to the developer using cheap building materials. Arnott, Davidson and Pines (1983) present a theoretical model, which shows a relationship between building age and optimal abandonment for a profit-maximizing landlord. They suggest that if demolition and maintenance cost were sufficiently high, then it would be optimal for a developer to construct a property, lease it for a period of time and abandon it. Landlords, who will only hold their properties for a limited time prior to abandoning, may be likely to trade better building materials for lower construction cost. Inferior quality may hasten landlords to abandon. If it is not financially feasible for landlords to walk away, then their decision to abandon may be suboptimal.4

This article discusses suboptimal housing abandonment, which may result in allocative and spatial inefficiencies. The sources of these two economically unpleasant outcomes may include subsidies to suburbanization, improper implementation of property tax levies and externalities arising from poor neighborhood infrastructure and surrounding abandoned buildings. The allocative inefficiency of housing capital may result in a reduction in the size of the lowincome housing stock, and the acceleration of decentralization (suburbanization) that can produce wasteful commuting, environmental degradation and other problems. Besides the aforementioned allocative inefficiency problems, suburbanization may lead to spatial inefficiency. Cars not paying their social cost and fiscal zoning might be examples of this inefficiency, which may also result in unequal distributions of housing locational choices across income classes. For instance, fiscal zoning may exclude low-income families from more affluent neighborhoods.

According to the 2000 U.S. Census Bureau survey, there were 115,904,641 housing units within the United States and the District of Columbia. Landlords frequently make operational decisions that affect these units. Acquiring, renovating and disposing of property are the three primary decisions faced by landlords. The decisions made by these landlords also affect individuals, communities and government entities, because property values and conditions are spatially interdependent. For instance, a renovated building might add value to a neighborhood. Furthermore, a landlord's divestment decision can influence the surrounding properties in that an abandonment decision may adversely affect adjacent property values. Suboptimal abandonment is demonstrated in a Prisoners' Dilemma game framework and with a Stackelberg model, which illustrate the interdependent effects of abandonment, and abandonment and renovation, respectively. Both models support the interdependence phenomenon of how one landlord's abandonment and/or renovation decisions may affect the other landlord's profit.

The rest of the article is organized as follows. First, the relationship between suburbanization, suboptimal abandonment and renovation is examined. Next, a Prisoners' Dilemma game framework of abandonment is discussed. This is followed by a Stackelberg model that is used to show optimal abandonment and renovation strategies. Finally, concluding comments are presented.

Suburbanization, Suboptimal Abandonment and Renovation

This section examines the relationship between suburbanization, suboptimal abandonment, and renovation. In that, why do suburban migrants leave behind and discontinue supporting established communities? Government services and attitudes may be the answer to this question. Suburbanization subsidies may hinder central city redevelopment. Cities indirectly support suburbanization to the extent of annexation by extending and increasing the capacity of sewer systems, highways, roads and/or other infrastructure out to the periphery, which is constructed for anticipated population growth. This enables developers on the fringe of cities to be able to develop within city limits and/or incur lower development cost, in which they pass this savings on to new suburban homebuyers.

These suburban residents are now no longer responsible for taxes in the metropolitan area in which they probably still heavily rely on for employment, recreational activities, social events and other daily necessities. Thus, the city loses tax dollars from these suburban commuters, which may never be replaced as the composition of metropolitan neighborhoods change. For instance, New York City's out-of-state resident's commuter tax, which was successful in recouping lost tax revenue was repealed in April 2000, and retroactive to July 1, 1999 for providing refunds to commuters.

If cities were not as accommodating to annexation, then we might see more redevelopment in the center of cities. This alternative behavior by cities might result in lowering the number of abandoned buildings. Conversely, if suburbanization subsidies continue to encourage households to flee to the suburbs, there might be an increase in the number of abandoned buildings. The unwanted result for the cities amight be a dramatic rise of suboptimal housing abandonment. Thus, viable communities might fizzle away.

A Prisoners' Dilemma Game of Abandonment

To analyze the problem of housing abandonment, consider that property values are interdependent. The rationale underlying interdependence is that decisions made by landlords may have a domino effect. For example, if landlord i's abandonment decision adversely affected landlord j's cash flows then the result is a negative externality. Consequently, landlord j may abandon if the adverse cash flows result in insolvency.5 A repercussion of this negative externality is the removal of both properties as tax paying entities within their respective municipality. A decrease in taxes implies fewer resources for infrastructure expansion and maintenance. According to O'Sullivan (1993), non-tax paying, boarded-up and idled abandoned buildings will likely result in a deteriorated community. Besides a decline in tax revenue, other social cost may be an increase in criminal activity within the immediate area, which may induce another landlord to abandon due to unwanted demand shocks. Basically, tenants who have the resources to move will not live in an undesirable location. This perpetual cycle of unfavorable housing abandonment coupled with increased tenant mobility might cause a continual snowball effect of neighborhood deterioration. Thus, a landlord's decision to abandon will affect another landlord's decision to abandon. Exhibit 1 illustrates this situation in a Prisoners' Dilemma game. Davis and Whinston (1957) display a similar application of a Prisoners' Dilemma game to explain how the interdependence of property values can cause urban blight. Following their lead, an interdependence game of housing abandonment is developed here. The game assumes that a landlord's abandonment decision will have a negative effect on another landlord's cash flows. The cash flows can be translated into rates of return. The rules of the game are outlined as follow:

* Players: The game consists of two players. The players are landlord i and landlord j.

* Actions: The landlords' actions are a best response to his opponents' actions. The actions the landlords can choose are do not abandon or abandon. The landlords' actions are based on them being profitmaximizing individuals.

* Strategies: Landlord i's strategies are independent of landlord j's strategies. The strategies are based on payoff maximization given the opponent's actions.

* Payoffs: The payoffs, symbolized as u, are dependent on the other landlord's actions. The payoffs, each internal rate of return (IRR), are in the interior of the bi-matrix. If the landlord does not abandon then the IRR is the ratio of cash flows from operations divided by the building value. However, if the landlord abandons then the IRR is .0 because the landlord walked away from the property. In the bi-matrix, the values enclosed in brackets represent IRR to landlord i and j, respectively. Payoffs are {u^sub i^, u^sub j^}:{u^sub i^ = IRR for landlord i given an action by landlord j, u^sub j^ = IRR for landlord j given an action by landlord i}.

Exhibit 1 represents the Prisoners' Dilemma game with hypothetical payoffs. The Nash equilibria are {.05, .05} and {.0, .0} where both landlords do not abandon and abandon, respectively. The Nash equilibrium is defined as the best mutual response. The first equilibrium of {.05, .05} yields the highest payoff. Therefore, it is the most efficient strategy, which consists of both landlords exercising a riskdominated strategy, do not abandon. The second Nash equilibrium is the maximin choice, which consists of both landlords exercising their dominant strategy, abandonment. It is the safe strategy because each landlord believes the other will abandon. The abandonment strategy is dominant and safe because it allows the landlords to be risk-averse by hedging their operational decision to maximize profits by minimizing potential losses.

It would seem the landlords would prefer to be at {.05, .05} verses {.0, .0} but the risk-dominated strategy will not take place without collusion. Collusion would occur if the landlords planned maximizing return strategies together. However, the collusion of strategies will never happen in a Prisoners' Dilemma game because one player's strategy is independent of the other player's strategy. Given landlord i does not abandon and landlord j abandons, each landlord's IRR will be {-.02, .0} where landlord i receives a -2% return and landlord j has a 0% return. The IRR is vice versa if landlord i abandons and landlord j does not abandon. Thus, both landlords prefer to abandon and receive a 0% IRR instead of risking a -2% return. However, the basis of a landlord's decision may not contain any policy-based incentives in the IRR calculation. Government intervention can be a mechanism, which will provide incentives for both landlords to play (do not abandon, do not abandon).

Interdependence Effects of Abandonment and Renovation

As illustrated in the Prisoners' Dilemma game, a landlord's bottom line profit is not only affected by their business decisions but also by the operational decisions of adjacent property landlords. Abandonment is only one of the landlord's choices. Besides abandoning, a landlord may opt to reinvest in their property. In this section, the landlord's options are extended, which are to abandon or to renovate.

Whether the abandonment option or the renovation option is chosen, one landlord's decision may indirectly affect the other landlord's profits. Incorporating the maxi-min strategy from the Prisoners' Dilemma hypothetical example with the renovation option leads to the next model. Following a Stackelberg framework, the interdependence effect of housing abandonment and renovation is mathematically illustrated. In the Stackelberg game agent i, the single landlord, moves first and agent j, the representative landlord,6 observes agent i's action prior to making a decision. In practice, a landlord's action may influence another landlord's operational decision. The solution to Stackelberg games has a backward-induction outcome. The timing of the game is as follows:

* A single landlord, s, chooses to abandon (a^sub s^ = 0), not to abandon (a^sub s^ = 1), to renovate (r^sub s^ = 1) or not to renovate (r^sub s^ = 0).

* A representative landlord, r, then chooses to abandon, (a^sub r^ = 0), not to abandon (a^sub r^. = 1), to renovate (r^sub r^ = 1) or not to renovate (r^sub r^ = 0).

* The payoff to the single and representative landlords is their profit, which incorporates the interdependence effect.

Exhibit 2 summarizes the first order conditions for the payoff equations as the interdependence effects on [pi]^sub r^, and [pi]^sub s^. These effects, which may affect the landlord's profit, will aid in determining their operational decision. In equilibrium, both landlords will have the same decision. Each cell in Exhibit 3 symmetrically depicts the single and representative landlords' profit-maximizing optimal abandonment and renovation decisions in response to each other's operational decision.

Suppose the single landlord exercises a^sub s^ = 1 and r^sub s^ = 1, then under optimality the representative landlord will exercise the same options, a^sub r^ = 1 and r^sub r^ = 1. Since the profit prior to renovation and the interdependence effects is [pi]^sub rp^ = [pi]^sub r^. = $1000, the landlord obtains outside capital to renovate the building. The renovations include painting the outside of the building, replacing broken windows, planting flowers at the building's entrance, and updating kitchen and bathroom fixtures in every unit. Although the renovations are not extensive, they do make the building more appealing within the community. Given this hypothetical example, r^sub r^b increases [pi]^sub r^. by $8000. Due to increased demand for the representative landlord's property, rents are raised. Also, the landlord benefits from the single landlord's a^sub s^ = 1 and r^sub s^ = 1 operational decision by receiving a positive externality of r^sub s^d = $2000. Therefore, prior to renovations by both landlords, [pi]^sub rp^ = [pi]^sub r^ =. $1000. After renovations [pi]^sub r^. = $11000.

As illustrated in Exhibit 3, it is optimal for a landlord to renovate as long as the other landlord does not abandon. If the representative owner did not renovate after the single owner decided to renovate, then the representative owner would have exercised a suboptimal decision. This suboptimal decision can be illustrated in Equation (1) where a negative value of r^sub s^d signals that the representative owner experienced a negative interdependent effect from the single and representative landlords exercising a^sub s^ = 1 and r^sub s^ = 1 and a, = 1 and r^sub r^. = 0, respectively. Instead of r^sub s^d increasing [pi]^sub r^ by $2000, it may have decreased [pi]^sub r^. by $2000. Therefore, when interdependence is not considered, a landlord's decision may not be optimal, which can result in an unfavorable outcome for a landlord.

Another instance of suboptimal decision can be interpreted by analyzing Exhibits 2 and 3. In Exhibit 2, r^sub s^ = 0 and a^sub s^ = 1 imply that the single landlord should not renovate and not abandon; however in Exhibit 3, under the interdependence scenarios A, B and C for r^sub s^ = 0 and a^sub s^ = 1, the optimal decisions are renovate, renovate and abandon, respectively. Similarly, if the single landlord abandons then it is optimal for the representative landlord to abandon as well. This rationale is part of an underlying assumption of the model, such that if the single landlord renovates then the representative landlord will not abandon, and if the representative landlord abandons then the single landlord will not renovate.

Conclusion

By understanding the interdependence phenomenon between landlords, policy makers can better promote efficiency in the housing market. Policies that focus on providing landlords with incentives not to abandon when abandonment is not socially optimal may be beneficial in preserving communities. Rational decision-making landlords faced with policy-based incentives that deter abandonment will not exercise their option to abandon when it is suboptimal.

As shown in the Prisoners' Dilemma hypothetical example, suboptimal abandonment occurs when there is no collusion of strategies between landlords. Abandonment is suboptimal because both landlords receive a lower IRR by abandoning. Contrarily, they both realize a higher IRR by not exercising their abandonment option.

Since landlords base their operational decisions on asymmetric information7 in the Prisoners' Dilemma framework, policies should focus on non-collusive strategies. The Stackelberg's sequential framework suggests an alternate choice to the Prisoners' Dilemma Nash equilibrium mini-max dominant strategy of both landlords abandoning, which is that both landlords renovate. In equilibrium, the Stackelberg model shows renovation discourages the mini-max choice, and a landlord subsequently encourages another landlord to renovate. Therefore, policies that do not necessitate collusion such as renovation could decrease the rate of abandonment. These policies can serve as a mutual agent to landlords by creating a positive interdependent Stackelberg effect.

Low-income communities can benefit the most from policy-based incentives for landlords. The results of fewer abandon buildings coupled with better-managed buildings are less criminal activity, more businesses operating within the community to service the residents' needs and low-income communities making an important contribution to the betterment of society.

Endnotes

1 Natural areas entail: (1) a geographic area physically distinguishable from other adjacent areas; (2) a population with unique social, demographic or ethnic composition; (3) a social system with rules, norms and regularly recurring patterns of social interaction that function as mechanisms of social control; and (4) aggregate emergent behaviors or ways of life that distinguish the area from others around it.

2 Familism is sometimes referred to as urbanism.

3 Paris, France is one exception to this statement.

4 See Stegman and Rasmussen (1980) for a further discussion of suboptimal abandonment.

5 Abandonment is more probable when the property value is less than the amount of liens on the property (see Scafidi, Schill, Wachter and Culhane, 1998). If not, a distressed sale may occur.

6 The representative landlord denotes the "other" landlord.

7 They do not have knowledge of each other's investment strategies.

References

Arnott, R., R. Davidson and D. Pines, Housing Quality, Maintenane and Rehabilitation, The Review of Economic Studies, 1983, 50, 467-94.

Davis, O. A. and A. B. Whinston, The Economics of Urban Renewal, MIT Press, Cambridge, MA, 1957, 50-67.

O'Sullivan, A., Essentials of Urban Economics, Homewood, IL: Irwin Inc. Press, 1993, 254-56.

Scafidi, B. P., M. H. Schill, S. M. Wachter and D. P. Culhane, An Economic Analysis of Housing Abandonment, Journal of Housing Economics, 1998, 7, 287-303.

Schwirian, K. P., Models of Neighborhood Change, Annual Review of Sociology, 1983, 9, 83-102.

Stegman, M. A. and D. W. Rasmussen, Neighborhood Stability in Changing Cities, The American Economic Review, 1980, 70, 415-19.

I thank James D. Shilling, Stephen Malpezzi, Kerry D. Vandell, Thaleia Zariphopoulou and especially Richard K. Green for invaluable discussions and critiques. I also thank John E. Williams and two anonymous referees for constructive suggestions and comments. This paper arose from my dissertation work at the University of Wisconsin-Madison, and was completed while on faculty at Lehigh University.

Tammie X. Simmons-Mosley, California State University-Hayward, CA 94542-3022 or tsimmons-mosley@csuhayward.edu.

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