N. Brooks J. of Economic Behavior Org. 44 2001 249–267 263
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: b
i
= a
i
− γ ¯s + u
1
1 An individual’s deviant behavior b
i
is determined by a factor a
i
, which encompasses all of the observable and unobservable idiosyncratic fixed components that influence behavior;
the sanctioning received from peer ¯s and the error term u
1
which is randomly distributed. The coefficient on a
i
is normalized to 1. s
i
= − δ
1
a
i
− δ
2
¯ a + u
2
2 An individual’s decision to sanction s
i
is negatively affected by the same individual specific factor a
i
, a group specific factor ¯a, and the error term u
2
. The group specific factor ¯a is the aggregate of the individual specific factor a
i
. Thus the group specific factor includes all the observable and unobservable aggregated fixed characteristics that can affect
behavior. Factors that may be represented in ¯a include the aggregation of the preferences and aggregated family characteristics such as level of discipline and the amount of church-going.
¯ b = ¯
a − γ ¯s + U
1
3 ¯
S = −δ
1
+ δ
2
¯ a + U
2
4
20
In particular, better data on the sanctioning behavior of individuals would improve the analysis.
21
This assumes the community is at the stable interior equilibrium.
264 N. Brooks J. of Economic Behavior Org. 44 2001 249–267
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 a
i
are likely to affect b
i
and s
i
and hence ¯ b and ¯s. Given this limitation, the system
of four structural equations is used to derive the following reduced form equation that can be estimated:
s
i
= − δ
1
b
i
+ δ
1
γ δ
1
+ δ
2
− δ
2
1 + γ δ
1
+ δ
2
¯ b + δ
1
u
1
+ u
2
− δ
1
+ δ
2
γ U
2
+ U
1
1 + γ δ
1
+ δ
2
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 δ
2
0. Although it will not be possible to identify completely the coefficients γ and δ
2
, 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 b
i
and u
1
. To obtain unbiased estimates it is necessary to instrument for b
i
and ¯ b using instruments that are correlated to
b
i
and ¯ b but not to the error term. Given that the error term u
1
is serially uncorrelated, data for b
i
and ¯ b 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. b
i
= 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. s
i
= 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
b
i
and ¯ b. In the second stage the reduced form equation is estimated. It is assumed that the
22
There is not as much variance in the responses to variable s
i
as would be preferred. The predominant response is yes. An affirmative response could indicate a desire to help one’s friends as well as to punish them. This issue
suggests significant limitations of the data set. Unfortunately, better data is not currently available. Consequently, I will remind you, my primary goal with this data is simply to demonstrate how the theoretical model enables the
development of the structural model which does not have the omitted variable bias problem.
N. Brooks J. of Economic Behavior Org. 44 2001 249–267 265
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 b
i
− 0.1257
− 2.43
N = 1291, adj. R
2
= 0.06
The null hypotheses that all the coefficients equal zero γ = δ
1
= δ
2
or more importantly the null hypotheses that the two coefficients supporting our theory on sanctioning are both
zero γ = δ
2
= 0 can be rejected from the above equation, although the parameter
estimates for b
i
and ¯ b 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 δ
1
6= 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 δ
2
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 δ
2
≥ 0, controlling for the individual factor a
i
, 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 a
i
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 a
i
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.
23
Like most survey data, particularly with categorical responses, measurement error is also likely to be a problem. The instrumenting also corrects for measurement error.
24
It is unlikely that γ 0 as this would imply that sanctioning would encourage deviant behavior. Consequently, it is improbable that δ
2
= 0.
266 N. Brooks J. of Economic Behavior Org. 44 2001 249–267
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 a
i
and ¯a 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
