Vol. 44 (2001) 249–267
The effects of community characteristics on
community social behavior
Nancy Brooks
∗Department of Economics, University of Vermont, 231 Old Mill, PO Box 54160, Burlington, VT 05405-4160, USA
Received 9 November 1998; received in revised form 15 September 1999; accepted 29 September 1999
Abstract
The purpose of this paper is to examine the impact of a community’s economic characteristics on its ability to generate adherence to socially efficient norms. These norms prescribe a behavior for an individual when his/her preferred behavior imposes a negative externality on others. This paper explores social norms as a mechanism of how neighborhood characteristics can affect in-dividual behavior. Understanding the mechanism through which community characteristics affect individual behavior is important in that it enables the development of a testable structural empirical model which is purged of the omitted variable bias arising from the potential endogeneity of the neighborhood choice. © 2001 Elsevier Science B.V. All rights reserved.
JEL classification: D71
Keywords: Analysis of collective decision making; Social choice; Clubs; Committees
1. Introduction
The causes of behavior patterns found in poor, socially isolated urban areas are a widely discussed and studied topic. In most US cities large segments of the poor are physically and socially isolated. William Julius Wilson opens his 1987 book, The Truly Disadvantaged by noting that “in the mid-1960s urban analysts began to speak of a new dimension to the urban crisis in the form of a large sub-population of low-income families and individuals whose behavior contrasted sharply with the behavior of the general population”.1
Research on the urban poor has so far been mainly the domain of sociologists and social historians (e.g. Katz, 1993; Wilson, 1987; Jencks and Peterson, 1991). Economists’ research
∗Tel.: 802-656-0946.
E-mail address: nbrooks@zoo.uvm.edu (N. Brooks).
1See Wilson (1987, p. 3).
on behavior patterns has thus far mainly emphasized the relationship between changes in policy variables, such as income transfers and in-kind benefits, on changes in individual behavior. Some empirical work has been done that investigates the relationship between neighborhood macro variables and behavior patterns, such as testing the effect of living in a poor neighborhood on dropping out of school or teenage childbearing. Case and Katz (1991) find that the behaviors of neighborhood peers appear to substantially affect youth behaviors in a manner suggestive of contagion models. Similarly Crane (1991) finds evidence in favor of an epidemic theory from empirical work investigating teenage child bearing and dropping out. On the other hand Evans et al. (1992) find that when you account for the endogeneity of the peer group, the peer group effect disappears. Plotnick and Hoffman (1993), in work using sister pairs in the panel study of income dynamics to control for unobservable family characteristics, also conclude that researchers should be skeptical of findings of significant neighborhood effects in models that do not account for the endogeneity of the neighborhood. Jencks and Meyer (1990) summarized the empirical literature on neighborhood effects up to 1990 and came to the conclusion that there is no general pattern of neighborhood effects. Manski (1993) has pointed out that many of these empirical tests are flawed in that they are not able to identify whether the neighborhood is really influencing the individual or merely reflecting the average characteristics of the community. He, in fact, coined the phrase the “reflection problem” to describe this empirical problem of identifying endogenous social effects from observations of the distribution of behavior in a population. This is an important problem for many reasons, in particular, in terms of policy, the existence of neighborhood effects can imply potential efficiency gains from redistributive policies that address the source of the externality. Manski states in his paper that the only way to improve the prospects for the identification of endogenous social effects are to develop new data sources or develop tighter theory. We pursue the latter avenue. To solve this “reflection problem” it is important first to understand the underlying mechanism(s) of how neighborhood characteristics affect individual behavior.2
The mechanism that is explored in this paper is one that involves the relationship between community characteristics, particularly the neighborhood’s income distribution (or more specifically the distribution of returns associated with participating in the “mainstream” economy) and the ability of a community to generate adherence to socially efficient norms. The norms that will be considered in this paper prescribe a behavior for an individual when his/her behavior could impose a negative externality on the rest of the community. The simplest example is a norm that would prescribe cooperation in a prisoner’s dilemma sit-uation. When the individual return from a particular opportunistic choice of behavior, like theft, is less than the cost that it imposes on others, then it might be socially efficient for a norm to be prescribed which ameliorates the costly behavior. A norm will be desirable in cases when an individual’s action imposes a externality on a group of others, and it is not possible to set up markets to exchange the “right of control” (Coleman, 1990) easily. Coase (1960) shows that norms would not be necessary to have efficiency in the absence of transaction costs if markets in the “right of control” exist. In general, though, for many actions it would be difficult if not impossible to set up these markets, consequently com-munities have an incentive to develop norms, norms that are prescribed to prevent behavior
that is socially costly for the community.3 This paper develops a theoretical model of how community characteristics affect adherence to these socially efficient norms. The model is then empirically tested.
Individuals have many interactions in their day-to-day lives in which there are opportuni-ties to get short term immediate gains. Ullmann-Margalit (1977) analyzes Hobbes’ original situation of mankind as a version of a prisoner’s dilemma. Hobbes states that “For he that should be modest, and tractable, and perform all his promises, in such time and place, where no man else should do so, should make himself a prey to others and procure his own certain ruin”.4 Societies can potentially gain by having social institutions or norms which can limit the opportunistic behavior and thus enable more cooperative behavior.
When individuals have repeated interactions with the same people, the folk theorem states that behavior that is not opportunistic can be supported as a subgame perfect equilibrium if the two players are sufficiently patient and the encounters are infinite (Fudenberg and Maskin, 1986). Strategies such as tit-for-tat have been shown in simulations to be very effec-tive in increasing cooperation in repeated two person prisoner’s dilemma games (Axelrod, 1986). When, though, as in many community interactions, meeting the same person occurs infrequently or not at all, it is more difficult to limit opportunistic behavior. This is because there are very limited opportunities or incentives for the “victim” to sanction or retaliate in any way that might make the opportunistic individual reconsider his/her actions.
Social norms which prescribe that if someone is opportunistic they lose not only the returns from interacting in the future with the person they harmed but with a whole set of people, can potentially limit opportunistic behavior.5 Third party sanctions may allow behavior to be supported as an equilibrium that could not be supported with only personal enforcement. The question then to ask is: When can third party sanctioning be supported in equilibrium? In a situation where two communities have a similar norm why might it be true that one community is able to enforce the norm and another community is not? The explanation developed in this paper is that the relative costs and benefits of enforcing norms differ among communities. It is costly for individuals to engage in third party sanctioning since sanctioning is a public good with private costs.6 The overall costs and benefits of sanctioning vary in different communities because of differences in the individual’s and the community’s returns to cooperative behavior.
In this model, individuals are randomly matched with different partners to play an infinite sequence of prisoner’s dilemma games. These games are meant to represent a sequence of social interactions with various acquaintances. Consider the following simple story to get a
3Coleman (1990) refers to norms of this type as essential norms, and Ullmann-Margalit (1977) calls them
prisoner’s dilemma norms. These are different from norms of convention or coordination which are typically modeled as the equilibria of coordination games as opposed to prisoner’s dilemma games (see, e.g., Young, 1993, 1998; Jones, 1984). Examples of conventional norms include driving on the left-hand side of the road verses the right or using IBM computers instead of Apples.
4See Hobbes (1948, p. 103).
5Examples of community sanctions could include being stigmatized by the community or suffering a reputation
loss.
6Some recent papers on social norms (see Lindbeck et al., 1999; Bernheim, 1994) have assumed, less realistically,
flavor for the model. In community life we have interactions with many types of people, in this story for tractability we will just consider two types. Two randomly matched individuals are making a commercial transaction in a shop. One individual is a customer and the other is the shopkeeper. Each individual has a different return to cooperating (honest trading in this example). You would expect that the more successful shopkeepers would have a higher profit margin and the smarter customers, who are able to extract the greatest gains from trade, are also the ones who receive the highest income from cooperative trade. Consequently, the gains to trade are assumed to be positively correlated with income. The match works in the following way. Each period half of the population are customers. A customer realizes he needs to buy something which determines the shopkeeper with whom he is matched. When the customer and the shopkeeper meet they must each decide how to do business with the other. They can be trustworthy and honest in the transaction; they can deviate or they can refuse to transact business at all (this form of sanctioning will be referred to as ostracism in the model). For the shopkeeper to be deviant may mean selling a lower quality product than advertised. For the customer to be deviant may mean shoplifting. For the shopkeeper to ostracize may mean refusing to sell to someone; and for the customer to ostracize may mean boycotting.7 The shopkeepers and customers consider the costs and benefits to deviating when there is a possibility that they can be sanctioned in the future. In this model then, the lower a person’s income the greater his/her net gain from deviating from a norm that would potentially sanction his/her from mainstream activities. In another example, a jobless individual would have less to lose from shoplifting than someone who had a job they could lose if they were found to be a shoplifter or vandal. To be ostracized from neighborhood social events because you associate with, instead of sanctioning, the community crooks may be more costly if you are a college graduate hoping to use neighborhood connections to network for a well-paying job than if you are a high school drop-out. In this model, it is shown how a community with a lower income distribution can have more individuals who will choose to deviate. Additionally, as more people are deviating from the prescribed behavior, it becomes more costly for others to sanction, since each sanction is costly. Fewer individuals will then choose to sanction. It is shown that the incentives to follow the norm by both not being opportunistic and by being a third party sanctioner depend not only on the economic characteristics of the individuals themselves, but on the economic characteristics of the other community members.8
This model illustrates one view of why it might be difficult to support particular norms in poor communities. This view is that there are neighborhood effects. The decision to follow a norm depends on the costs and benefits of sanctioning, which are a function of not only the individual’s economic characteristics but the characteristics of the community. In poor communities some individuals, particularly the poorest, may not find it in their interest to sanction under any circumstance because the cost is too high but there may be others in the community who would have sanctioned if pressured. There is an externality in that if an
7See Milgrom et al. (1990) for a similar story from an historical example in which a system of medieval judges
was able to successfully encourage merchants to behave honestly, impose sanctions on violators, become informed about others behavior, and to pay imposed penalties.
8Since third party sanctioning is generally costly, individuals would like to free ride and let others do the
individual who sanctions leaves the community not only are they not there to sanction but they will cause others to stop sanctioning since the percentage of sanctioners, and thus the potential costliness of not sanctioning, has decreased.
Another view of why some communities might find it difficult to support a particular norm is that there is sorting (Tiebout, 1956). Individuals who behave in a particular way may also have other similar characteristics or tastes that make them tend to agglomerate together. The two views have different policy implications9 and one purpose of the theoretical model is to see if it is possible to distinguish between the two views when examining the data.
Sociologists have typically been interested in how individual behavior is determined by group norms and other informal methods of social control. Economists have typically shown little interest in norms probably because “homo economicus” would ignore norms unless they were consistent with utility maximizing. Coleman (1990) points out, though, that social norms can result from the purposive actions of rational individuals (Frank, 1992). Economists, in fact, may have much to offer in terms of developing a structure to better understand social norms, which have been focal points for qualitative sociological research for years. Game theory in particular has much to offer in terms of developing this structure, e.g., the norms we are examining in this paper arise to deal with social interactions that have a prisoner’s dilemma structure. Okuno-Fujiwara and Postlewaite (1995) and Kandori (1992) are important papers in the game theoretic modeling of prisoner’s dilemma norms. In particular, Okuno-Fujiwara and Postlewaite (1995) lay much of the foundation for this paper.
Okuno-Fujiwara and Postlewaite (1995) develop a model of how social norms and social standards of behavior influence individuals’ decisions. This paper builds on their work to develop a theoretical and empirical understanding of how community characteristics affect the equilibrium level of deviance and sanctioning in a community.
The three main theoretical results of the paper are that increasing the average return to “mainstream” behavior in the community non-linearly decreases the percentage of “deviants” in the community; decreasing the variance of returns to “mainstream” behavior in the com-munity also non-linearly reduces deviance. Finally, if the upper bound on the distribution of these returns for the community is below some threshold value then there is stable equi-librium where all individuals will want to be “deviant”. Additionally and perhaps most importantly, by developing an explicit model of how community characteristics affect in-dividual behavior it is possible to do an empirical estimation that tests the model purged of the selection problems that arise from the endogeneity of the neighborhood choice, thus helping us to move beyond the “reflection problem”.
The remainder of this paper is organized into the following sections. The model will be presented in Section 2. The equilibrium condition given a community norm is defined and discussed in Section 3. The comparative statics results, which illustrate the effects of changes in the average income distribution and changes in the variance of the income distribution on the equilibrium level of deviant behavior in the community, are derived in
9The Tiebout model suggests that individuals efficiently sort themselves into neighborhoods. The neighborhood
Section 4. A brief discussion of the theoretical results and the policy implications is given in Section 5. The procedure for empirically testing the model is discussed in Section 6 along with a discussion of the difficulties in empirically testing for neighborhood effects. The data are described and the results of the estimation are evaluated in Section 7. A discussion of the empirical results and the conclusion is given in Section 8.
2. Model
The structure for this study is a repeated random matching prisoner’s dilemma game augmented with a sanctioning action for each player. There is a continuum of players divided into two groups. In each stage, each player is matched randomly with a player in the other group. There are an infinite number of stages in the supergame and an individual’s total payoffs are the expected sum of the payoffs in each stage discounted by a common discount factorδ(0,1).
In each stage game, individuals have a choice of three actions,Ai = {cooperate,deviate,
ostracize}. Individuals have the same linear utility functions, but each has a different return to behaving cooperatively in the social trade. These heterogenous returns to cooperation are an important feature of the game. The returns to cooperative behavior are assumed to be distributed uniformly across the community’s population. The payoff matrix for the stage game is shown in Table 1.
If both individuals behave cooperatively each receives the returnwi. If either player
decides to be opportunistic when the other player is cooperating then his return iswi+bd,
where bd is the additional gain to the opportunistic behavior. The other player incurs a cost cd. Ifcd> bdthen there is a net social loss due to the opportunistic behavior. If both players are opportunistic then each gets the same payoff that is less than if both players cooperate, and there is a definite social loss. Thus the community could possibly benefit from a prescribed social norm against opportunistic behavior if the aggregate costs of enforcing the norm in equilibrium are less than the costs to society of the opportunistic behavior which would occur without the norm.
A player who is ostracized does not get to trade and thus gets a return of zero. The punishing player also does not get to benefit from the trade since no trade occurs and he faces the cost of sanctioning. The additional returns and costs from opportunistic behavior bd, cd, and ldand the cost of punishing f (f ≤0) are assumed to be the same for each individual. Table 1
Payoff matrix for the stage gamea
Player I Player II
C D O
C w1, w2 w1−cd, w2+bd 0, f
D w1+bd, w2−cd w1−ld, w2−ld 0, f
O f, 0 f, 0 f, f
awiis the returns to trade (i=1,2) (wi ∼uniformly on the support [w,w¯], b
dthe benefit from deviating
when the other player cooperates, cdthe cost of cooperating when the other player is deviating, ldthe loss when
Moreover, the costs of sanctioning (f) are the same regardless of whether you are punishing either an opportunistic individual or a non-punisher. Similarly, the costs of being punished (0) are the same whether you are punished for either opportunism or for non-punishment of another. This payoff matrix is used because it is, perhaps, the simplest and most tractable one to investigate a community’s ability to generate adherence to prescribed social norms. The model should be used to give insights about many types of prisoner’s dilemma social situations, but to clarify the structure of the payoff matrix you might reconsider the example of the shopkeepers and customers given in Section 1.
2.1. Brief comments on the structure of the model
The repeated matching game is useful for analyzing dynamic economic relationships because repeating a prisoner’s dilemma game for many periods can provide the opportunity for individuals to cooperate and thus potentially adhere to a prescribed behavioral norm.10 There are two other features of the game that are important. The first is the potential third party sanctions. If an individual deviates he or she will not only be potentially sanctioned by the individual he or she deviated against but possibly by others too. The second is that the players are randomly matched. This is important since sanctioning is costly to the individuals in each match. A player may not be able to credibly sustain the threat to punish an opportunistic individual in every period, but if there is random matching then the player can credibly threaten to punish in one period because he knows he might not have to punish in the next period.
2.2. Status assignments
At the beginning of each period every individual has a status assignment which is derived from the history of his previous actions. After each stage game statuses are updated. Fol-lowing the notation of Okuno-Fujiwara and Postlewaite (1995), a status is an assignment in each period t of an element X from the set of statuses Xi, whereXi = {mainstream,deviant}.
The two possible status labels used in this model are “mainstream” and “deviant”. A “mainstream” individual is someone who has been cooperative when matched with an-other mainstream individual and has punished when matched with a deviant. Everyone else is a “deviant”. This model could include more status assignments. For example, in some real-world situations, it may be that individuals who are only non-punishers (but follow all other “mainstream” behavior) might be sanctioned to a lesser degree than other opportunistic individuals in the community.11 I have chosen to restrict my model to two status assignments since two is sufficient to address the point that both opportunists and non-punishers might expect to face costs from being sanctioned in future interactions as
10See Fudenberg and Tirole (1991) for a summary of folk theorem results.
11It could possibly also be true that the stigma or punishment from non-punishing is greater than the punishment
well as the benefits they receive from their immediate actions. In future research, it would be interesting and important to compare the results that are generated with additional status assignments with the results derived in this paper since the results from this paper cannot necessarily be generalized to the case with more status assignments.
An individual’s status is then updated in each period according to the transition map-pingτi : XAi = XiXjAi → Xi. The transition mapping for player i specifies his next
period’s status as a function of his current status (Xi), his match’s current status (Xj) and
his action (Ai), whereAi =(C, D, O)is the set of action choices “cooperate”, “deviate”
or “ostracize”, respectively.
The players know the payoff structure of the stage game and they also know the sta-tus label of the player with whom they are matched (i.e. whether he is “mainstream” or “deviant”). This information structure is assumed. We do not model how the information is conveyed.12 Additionally, an individual’s returnwi is not publicly observable, although,
in equilibrium players can deduce something about each other’s returns from observing his/her status. It does not matter in this model whether they know precisely their partners’ returns to trade or not.
3. The social norm and the candidate equilibrium
From the set of strategies of each player there is a particular prescribed social standard of behavior and a transition mapping which together are defined to be the social norm of the game. The social standard of behavior prescribes what action an individual of a given status should follow when matched with a player of a given status. The transition function then maps the actions into the new statuses for the next period. The transition function is denoted byτi and the social standard of behavior for each individual is denoted byαi. Given this
notation the social norm of the game is defined as follows:
τi(Xi, Xj6=i, Ai) =
(
M if (Xi, Xj6=i, Ai)=(M, M, C)or(M, D, O)
D otherwise
αi(Xi, Xj6=i) =
C if(Xi, Xj6=i)=(M, M)
O if(Xi, Xj6=i)=(M, D)
D otherwise
The transition function gives the next period’s status for player i. The social standard of behavior lists the prescribed actions for player i. The transition function and the social stan-dard of behavior for player j are symmetric. The prescribed social stanstan-dard of behavior in this game thus states that an individual should behave cooperatively if he/she has a “mainstream” status and is matched with someone who is also “mainstream”; a “mainstream” individual should ostracize any “deviant” player with whom he is matched, and an individual with a “deviant” status should deviate regardless of opponent’s status. The transition function states that an individual will retain his “mainstream” status if he is currently “mainstream”
and behaves cooperatively when matched with another “mainstream” individual and ostra-cizes when matched with a “deviant”. Otherwise the individual will have a “deviant” status. Incorporated in this social norm is a prescription for third party sanctioning and a prescrip-tion for a metanorm. Axelrod (1986) refers to a norm which prescribes the sancprescrip-tioning of those who do not sanction “deviants” as a “metanorm”.13
In a stationary equilibrium the total payoffs to an individual in the infinitely repeated game will depend on the proportion of individuals of each status. This proportion determines the probability of being punished if you are opportunistic and also the probability of potentially having to punish. In equilibrium these probabilities will depend on the distribution ofw, the return to cooperative trade in the community. Thus the probability of being matched with someone who is deviant is defined asp=(w∗−w)/(w¯−w), wherew∗is the critical return such that in a stationary equilibrium all individuals with returns to trade abovew∗
punish and are not opportunistic and all below are opportunistic and do not punish. In other words, all individuals with returns greater thanw∗are “mainstream”, (p is the cumulative density function atw∗). The solution for the critical returnw∗will be shown shortly.
How are players going to make their decisions about what actions to choose in a stationary equilibrium? A player will follow the prescribed behavior for the mainstream individual if the one shot gain from choosing to deviate (and thereby losing their “mainstream” status) is less than the discounted sum of future losses in payoffs, given that some proportion of the population will sanction the player in the future. Thus the following inequalities must be satisfied in equilibrium.
1. “Mainstream” player matched with another “mainstream” player:
bd≤δ
This equation states that the one shot gain from deviating is less than the discounted net present value of following the social norm. On the right-hand side of the inequality in the first set of brackets is the payoff the player would receive from following the social norm in each subsequent period, from this is subtracted what the player would get if he deviated in that period and thus received the payoff for a “deviant” in each subsequent period (the quantity in the second set of brackets).
2. “Mainstream” player matched with a “deviant”:
(wi−ld)−f ≤δ
This equation states that the one shot gain from not punishing the “deviant” is less than the net present value of following the social norm.
13Axelrod (1986) shows that the employment of a metanorm is a key condition for the evolution and maintenance
The first inequality is satisfied if the “mainstream” player prefers to be honest instead of being opportunistic when matched with another “mainstream” player. The second in-equality is satisfied if a “mainstream” player chooses to punish the deviant with whom he is matched.14 In equilibrium, if either of the inequalities does not hold then the individual will be a “deviant”, the other inequality becomes irrelevant. The set of pure strategy equilibrium returnsw∗are determined from solving Eqs. (1) and (2).
Proposition 1. There always exists at least one stable15 equilibrium where everyone de-viates. Two interior equilibria may also exist, one of which will be stable and one of which will not(see Fig. 1).
Proof. In each Eqs. (1) and (2) we solve for the returnsw∗that solve each equation with equality. Eqs. (1) and (2) are both quadratic inw∗(recallp = (w∗−w)/(w¯ −w)) and consequently have two solutions (or roots) each. If the two roots are not real then the only equilibrium is where everyone deviates. The solutions to each equation will be denoted respectively as (w1,w¯1) and (w2,w¯2). The minimum solution for each quadratic equation
(w∗1andw∗2) is stable.16
We will focus most attention on these minimum solutions because they determine the stable interior equilibrium.17 The critical returnw∗, which determines the stable interior equilibrium percentage of individuals who are not mainstream must satisfy two conditions to be the critical equilibrium return to “mainstream” behavior. If these conditions are not met for any return then there is no stable interior equilibrium. The conditions are as follows:
1. w∗is the lowest return such that the inequalities in the two equations hold (i.e.w∗ = max(w∗1, w∗2)).
14The inequalities for the deviant player are satisfied because the deviant player plays his best response. Since
the deviant status is absorbing there is no benefit from doing anything else.
15The equilibrium is defined to be stable when an individual with a returnwijust less than the critical returnw∗
will want to deviate from “mainstream” behavior, and an individual with a returnwijust above the critical return
w∗will want to follow “mainstream” behavior.
16From Eqs. (1) and (2) it is easy to see the stability properties of the equilibrium solutions. Consider Eq.
(2), substitute into the equation the equilibrium percentage of deviants for a given distribution of returns. If an individual’s return to tradewiwas less then the smallest solutionw∗
2for a given distribution of returns, then the
individual would want to deviate (i.e. the inequality would be reversed). Similarly, if the individual’s return to trade was between the smallest solutionw∗
2 and the largest solutionw¯∗2then the individual would not want to
deviate (the inequality in Eq. (2) would hold). Finally if the individual’s return to trade is greater than the largest solutionw¯2∗then the individual will want to deviate (the inequality in the equation would again be reversed).
17The explicit solutions forw∗
2. If, for instance,w∗1=max(w∗1, w∗2)then it must be true that whenp=(w∗−w)/(w¯−w)
is substituted into the non-binding constraint 2 then thew∗2that results is still less than
w∗1.
The stable interior equilibrium critical returnw∗is the value forwthat is the maximum of the two minimum solutions of each equation. In other words,w∗determines the equilibrium percentage of individuals for whom both constraints are satisfied (they are “mainstream”). One of the inequalities will hold with equality and one will not, the binding one will be determined by the values of the other parameters. The returnw∗characterizes the equilib-rium condition for which all players with returns abovew∗will cooperate and ostracize (both inequalities hold). Any player with a returnwi > w∗does not have a strategy that
unilaterally improves his/her discounted payoff for the game over the strategy dictated by the prescribed social norm. The stable interior equilibrium defined by the critical returnw∗
determines a distribution of statuses described by p, the proportion of individuals with a “deviant” status.
As just mentioned, the critical returnw∗associated with the stable interior equilibrium is also the equilibrium that gives us the smallest proportion of deviants. Fig. 1 illustrates a graph of critical returnsw∗for a given set of parameters and varying values ofw¯. As you can see, for most values ofw¯ there are three equilibrium solutions. The smallest interior equilibrium is stable, the larger interior equilibrium solution is unstable and the third equilibrium is where everyone deviates, as depicted by the ray from the origin in Fig. 1.
It is important to note that in order to support a stable interior equilibrium a critical mass of individuals who are “mainstream” is required. If the upper bound on the distribution of the returns to trade in the community is below a certain level it becomes impossible to support the interior equilibrium and everyone will be “deviant”. For instance, in Fig. 1, ifw <¯ 40 then the only equilibrium is for every one to deviate. This implies a possible discontinuity in the proportion of individuals who are “deviant” in the set of stable stationary equilibria.
Even if the distribution of returns to trade improves (i.e. the upper bound onwincreases) it will not necessarily be possible to support the interior equilibrium unless there is some coordination among the individuals, since of course no single individual would have an incentive to unilaterally return to cooperative behavior when everyone else is deviating. This might help explain why we might see two neighborhoods with similar economic characteristics but very different behavior patterns.
4. Comparative statics
This section considers what happens to the stable interior equilibrium when there are small changes in the distribution of returns to cooperative behaviorwi.
Proposition 2. Ifw¯ increases then the equilibriumw∗decreases at a decreasing rate, all else constant.
Proof. The derivative of the equilibrium solution ofw∗ (as given in footnote 17) with respect tow¯ is negative while the second derivative is positive.
Figs. 1 and 2, which give the percentage of deviants in equilibrium, illustrate this rela-tionship for a given set of parameters. This implies that as the distribution of returns to trade gets worse more individuals will choose to be “deviant” and at an increasing rate.
In these graphs, the lower bound on the distribution of the returns to trade has been as-sumed to be zero. This implies that asw¯is increasing both the average return and the variance of the returns are increasing. It is important to separate these two effects to determine which effect is driving the comparative static results.
Proposition 3. If the averagewidecreases, ceteris paribus, then the equilibrium percentage
of deviant behavior will increase at an increasing rate. If the variance of the returns is increased holding the average constant, then the equilibrium percentage of deviant behavior will increase at a decreasing rate.
Proof. To hold the variance constant substitutew = ¯w−variance into the equilibrium solution ofw∗as given in footnote 17. The derivative of this with respect tow¯ is negative while the second derivative is positive.
Similarly, to hold the average return constant substitutew=2(averagewi)− ¯winto the
equilibrium solution ofw∗. The derivative of this with respect tow¯ is positive while the second derivative is negative.
When the average return in the community increases the interior stable equilibrium critical returnw∗decreases and thus the equilibrium percentage of deviants also decreases. It is important to note that the equilibrium percentage of deviants decreases non-linearly, thus there will be a lower overall level of deviance if instead of having one community with a high average return and one community with a low average return there are two communities with an average return in the middle. If the variance of the returns increases the equilibrium percentage of deviants increases at a decreasing rate.
These comparative static results of the stable interior equilibrium illustrate two points. First, the equilibrium percentage of deviant behavior decreases in response to a increase in the average return to trade. This is consistent with evidence of the negative effect on behavior of concentrated poverty. Of particular interest is the non-linearity of this relationship, which implies that the overall level of deviance can be reduced if different neighborhoods have a more equal income distribution. The second result illustrates the increase in the equilibrium percentage of deviant behavior due to an increase in the mean preserving spread of returns. This implies that the equilibrium level of deviant behavior is a function of income inequality.
5. Discussion of theoretical results
The purpose of this model is to demonstrate the important effect that community economic conditions have on the ability of a community to generate adherence to socially efficient norms. Individuals who might typically be inclined to follow “mainstream” behavior will not do so given limited returns to cooperating and/or a large percentage of fellow deviants who are costly to ostracize. There are two important externalities. The first is that deviant behavior has a social cost, second the overall cost of sanctioning is a function of the distribution of statuses in the community.
prefer to deviate. This equilibrium is stable so even if the distribution of returns improves, no individual will have an incentive to be cooperative. This results potentially limits the effectiveness of income redistribution implied by the first two results.
This analysis is simplistic in that we are only considering the case of heterogeneous returns to cooperative behaviorwi. It may be important to analyze the case of heterogeneous returns
to deviant behavior. It may be that some individuals while having a low return to cooperative behavior may have an even lower return to deviant behavior.
Merton (1957) discussed how the “absence of realistic opportunities for advancement results in a marked tendency toward deviant behavior”.18 Wilson (1987, 1996) conjectures that a likely cause of the pathological social patterns of the urban poor result in part from the absence of a middle class or stable working class in the post-industrial inner city. These groups not only reinforced societal norms but they maintained social institutions such as churches, shops, etc. He also points out that high rates of neighborhood poverty are less likely to create problem of social organization if residents are working in the mainstream labor market. This model illustrates a mechanism that is consistent with these conjectures and consistent with the observations that increases in deviant behavior have been observed in areas with increasing concentrated poverty.
6. Empirical issues and estimation
Empirical research on neighborhood effects has hit a dead-end recently as economists have discovered the difficulties of trying to correctly estimate neighborhood effects given that the neighborhood choice is at least partially endogenous. Manski’s 1993 paper on the “reflection problem” explains that because of the endogeneity of the neighborhood choice it is difficult if not impossible to discern in an econometric analysis of individual behavior whether a significant coefficient on a neighborhood characteristic implies that this variable is influencing the individual or merely capturing something about the average characteristics of the community. Economists, as mentioned in Section 1, have tried to control for the individual characteristics that might influence neighborhood choice by either trying to eliminate the individual fixed effects using panel data or by trying to control for every possible individual background variable. Unfortunately, both of these approaches suffer from an omitted variable bias problem. The problem with the panel data approach is that there may be unobservable factors influencing both the decision to move to a different neighborhood and the choice of the new neighborhood that will cause omitted variable bias. The problem with the second approach of trying to control directly for every possible background variable is that it is impossible to control for many of these background variables because they are unobservable and thus also cause omitted variable bias. Another difficulty with trying to measure neighborhood effects using US data is that confidentiality restrictions limit the amount of neighborhood information available for micro level data.19 While this empirical analysis would, no doubt, be strengthened by the availability of better data
18See Merton (1957, p. 145).
19The panel study of income dynamics (PSID), the national longitudinal survey of youth (NLSY) and the national
sources,20 it demonstrates how a theoretical model enables the development of a testable structural empirical model which is purged of omitted variable bias arising from the potential endogeneity of the neighborhood choice.
In Section 7 of this paper, a reduced form equation which is derived from structural equations developed from the theoretical model presented earlier will be estimated. This empirical work will test the validity of the theoretical mechanism itself, not the comparative statics results of the model. It is important to test the model itself in that it will allow us to differentiate between a pure sorting model and the model of neighborhood effects. In a pure sorting model, such as the model developed by Tiebout (1956), individuals who behave in a similar way may also have other similar characteristics or preferences that may make them tend to choose to live in the same neighborhoods. In this model individuals efficiently sort themselves and neighbors do not influence each other. In the model of neighborhood effects developed in the previous chapter, an individual’s behavioral choice is instead influenced by his neighbors through their use of sanctioning. The difficulty in differentiating between a pure sorting model and a model with neighborhood effects is what Manski is calling the “reflection problem”.
7. Results of the estimation
7.1. The model
The predictions that the theoretical model suggests are that individuals will sanction less if their peers are more delinquent and that individuals will be less delinquent if they are sanctioned.21 The structural equations are consequently as follows:
bi =ai−γs¯+u1 (1)
An individual’s deviant behavior biis determined by a factor ai, which encompasses all
of the observable and unobservable idiosyncratic fixed components that influence behavior; the sanctioning received from peers¯and the error term u1which is randomly distributed. The coefficient on aiis normalized to 1.
si = −δ1ai−δ2a¯+u2 (2)
An individual’s decision to sanction si is negatively affected by the same individual
specific factor ai, a group specific factora¯, and the error term u2. The group specific factora¯ is the aggregate of the individual specific factor ai. Thus the group specific factor
includes all the observable and unobservable aggregated fixed characteristics that can affect behavior. Factors that may be represented ina¯include the aggregation of the preferences and aggregated family characteristics such as level of discipline and the amount of church-going.
¯
b= ¯a−γs¯+U1 (3)
¯
S= −(δ1+δ2)a¯+U2 (4)
These equations are derived by aggregating the Eqs. (1) and (2) above over the community. The first of these two aggregate structural equations state that a community’s level of deviant behavior is determined by the individuals’ idiosyncratic characteristics that effect behavior, the level of sanctioning in the community and the aggregated randomly distributed error term. The second equation states that the level of sanctioning in the community is a negative function of the individuals’ characteristics that influence deviant behavior.
These four equations cannot be estimated individually because the unobservable compo-nents of ai are likely to affect biand siand henceb¯ands¯. Given this limitation, the system
of four structural equations is used to derive the following reduced form equation that can be estimated:
si = −δ1bi+
(δ1γ (δ1+δ2)−δ2) 1+γ (δ1+δ2)
¯
b+δ1u1+u2−(δ1+δ2)
(γ U2+U1) 1+γ (δ1+δ2)
(5)
The theoretical predictions on the coefficients imply that sanctioning inhibits bad behavior (γ > 0) and that individuals are less likely to sanction if their peers are bad (δ2 > 0). Although it will not be possible to identify completely the coefficientsγandδ2, we will be able to see if the results are consistent with the theory.
It is clear from examining the compound error term that the coefficients on the right-hand side variables will be biased due to the correlation between bi and u1. To obtain unbiased estimates it is necessary to instrument for bi andb¯using instruments that are correlated to
bi andb¯but not to the error term. Given that the error term u1is serially uncorrelated, data for biandb¯from adjacent years will be proper instruments.
7.2. The data and the results
The data come from the National Youth Survey which interviewed 1725 youths in 1976 and then tried to interview all of them each year through the early 1980s. This data set asks young people a variety of questions about their behaviors and the behaviors of their peers. The questions that were used to estimate this reduced form equation were the following:
1. bi =how many times in the last year have you stolen something worth less that $5.00
(1=never through 9=2– 3 times a day).
2. b¯ = how many of your friends have stolen something worth less than $5.00 (1 = none through 5=all).
3. si = if you found your friends were getting into trouble, would you try to stop these
activities (3=yes,2=maybe,1=no).22
A two stage least squares procedure was used to estimate the reduced form equation. In the first stage instrumental variable estimation was used to obtain instrumented values for
bi andb¯. In the second stage the reduced form equation is estimated. It is assumed that the
22There is not as much variance in the responses to variable s
ias would be preferred. The predominant response
distribution of the underlying latent variables are continuous, so the instrumental variables estimates should be unbiased and efficient. The year used for the regression was 1978. Data for the year before and after 1978 were used as instruments for the two right-hand side variables to correct for the bias.23
The parameter results of the regression are as follows:
Variable Parameter t-statistic
Intercept 3.1660 61.52
¯
b −0.1698 −2.50
bi −0.1257 −2.43
N =1291, adj.R2=0.06
The null hypotheses that all the coefficients equal zero (γ =δ1=δ2) or more importantly the null hypotheses that the two coefficients supporting our theory on sanctioning are both zero (γ = δ2 = 0) can be rejected from the above equation, although the parameter estimates for bi andb¯ are small. It is also true from our regression result that since the
coefficient on an individual’s characteristics in the individual sanctioning equation is not equal to zero (δ16=0) then if the coefficient on the effect of sanctioning in the individual’s behavioral choice equation is greater than or equal to zero (γ ≥0)24 then this implies that the coefficient on the effect of peer characteristics on sanctioning in the sanctioning choice equations is strictly greater than zero (δ2 > 0). So, although it is impossible to use the parameter estimates from our reduced form equation to go back and completely solve for the coefficients in the structural equations with precision, with these composite coefficients it is possible to make inferences about the signs of the coefficients in the structural equations that are consistent with the theoretical predictions that individuals will sanction less when more of their peers are deviating (δ2≥0), controlling for the individual factor ai, and that
an individual’s behavioral decision is affected by the sanctioning they receive (γ ≥0). In summary, these results allow us to reject the hypothesis that there is a pure sorting model; and moreover, the results are consistent with the model of social norm enforcement developed in the previous sections.
Most importantly, though, in the theoretically derived reduced form equation that was estimated the individual factors ai and a¯ were completely eliminated. Thus all of the
estimates are unbiased and consistent. We have consequently shown that it is possible to correct for the potential endogeneity in the explanatory variables by eliminating the variables (ai and a¯) that could be correlated with the dependent variable and the
ex-planatory variables. By developing a structural model from the theory we have seen that we are able to eliminate these omitted variables from our estimated equation and thus obtain true estimates of the effect of our explanatory variables on the dependent variables.
23Like most survey data, particularly with categorical responses, measurement error is also likely to be a problem.
The instrumenting also corrects for measurement error.
24It is unlikely thatγ <0 as this would imply that sanctioning would encourage deviant behavior. Consequently,
There are four main mechanisms that social scientists have suggested to explain neigh-borhood effects. The survey by Jencks and Meyer (1990) explores much of the empirical literature exploring these mechanisms. The results of these papers are somewhat question-able given that they have not solved the identification issues. Manski (1993) discusses in his work on the “reflection problem”. These theories are: (1) the epidemic theory which states that individuals will imitate their peers; (2) the collective socialization theory that suggests the importance of role models; (3) institutional models which discuss the importance of school quality, police commitment to the neighborhood, etc; (4) the relative deprivation theory that states that individuals will feel bad if their peers are much more successful then they are. In this paper, these theories are not necessarily contradicted, in fact the individual and group specific factors ai anda¯ potentially embody these relationships, but by
elimi-nating the individual and group specific factors from the estimated equation we have been able to control for these effects. Thus in rejecting the null hypothesis we have found that even if these other mechanisms are valid (e.g. individuals mimic their peers) their behavior will also be affected by the sanctioning they receive. To truly determine the importance of these other theories in explaining neighborhood effects it is important to develop a theore-tical model for each of the mechanisms as I did for the mechanism in this paper. Without the theoretical model the endogeneity of the neighborhood choice will lead to biased and consequently inconclusive proof of the theory.
8. Discussion of empirical results
This empirical work illustrates how a theoretical model can help researchers begin to move beyond the stalemate in the empirical research on neighborhood effects as explained in Manski (1993). His main points are that developing a better theoretical foundation for the estimation and obtaining better data are the keys to accurate estimation of endogenous social effects. It is very important to first identify and explicitly model the mechanism through which neighborhood characteristics will influence individual behavior. The the-oretical model can then be used to derive a structural model to estimate in which the endogenous social effects are identifiable. Problems with limitations on data are still an important issue for researchers. With more careful modeling of the underlying mecha-nisms determining the social effects and better data to allow the testing of these mech-anisms the “reflection problem” can be addressed. This paper has demonstrated both of these points by showing that consistent estimates of endogenous social effects can be ob-tained from a structural model, but that the limitations on data have prevented precise estimates.
Acknowledgements
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