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R E VIE W O F E C O N O M I C S T U D IE S
such central sociological concepts as norms and p eer influences to be spu rious phen om ena
explainable by processes operating entirely at the level of the individual. (See, for exam ple,
the Friedm an (1957) criticism of D uesenberry (1949).) Even am ong sociologists, on e still
does not find consensus on the nature of social effects. For example, there has been a
long-running debate about the existence and nature of neighbourhood effects. (See, for
example, Jencks and Mayer (1989).)
Why d o such different perspectives persist? Why d o the social sciences seem unab le
to converge to com mon conclusions abou t the channels through which society affects the
individual? I believe that a large part of the answer is the difficulty of the identification
problem. Empirical analysis of behaviour often cannot distinguish among competing
hypotheses about the nature of social effects.
Econo mists have lon g been c oncerned w ith the identification of end ogenou s effects
channelled through markets, especially with the conditions under which observations of
equilibrium prices and quantities reveal the demand behaviour of consumers and the
sup ply behaviour of firms. But the identification of oth er endogeno us effects has remained
relatively unexamined and poorly understoo d.
This pape r examines the "reflection" problem that arises whe n a researcher observing
the distribution of behaviour in a pop ulatio n tries to infer whether the average behaviour
in som e grou p influences the behaviour of the individuals that comprise the g roup. The
term reflection is appropriate because the problem is similar to that of interpreting the
almost simultaneous movements of a person and his reflection in a mirror. Does the
mirror image cause the person's movements or reflect them? An observer who does not
understand something of optics and hu man behaviour would not be able to tel l.
Although the reflection problem has several aspects, the series of simple findings
reported in this paper collectively develop a theme: Inference on endogenous effects is
not possible unless the researcher has prior information specifying the composition of
reference grou ps. If this information is available, the prospects for inference depe nd
critically on the pop ulatio n relationship between the variables defining reference gro ups
an d thos e directly affecting outc om es. Inferenc e is difficult to im pos sible if these variables
are functionally dependent or statistically independent. The prospects are better if the
variables defining reference grou ps an d those directly affecting outco me s are "moderately"
related in the popu lation.
Section 2 examines the reflection problem in the context of a linear model applied
in m any e mpirical studies of social effects. Section
3
analyzes non-linear models. Section
4 discusses dynam ic models. Section 5 relates conventional consumer dem and analysis
to the work of this paper. Section
concludes by stressing the need for richer data if
the analysis of social effects is to make more progress.
2. A L I N E A R M O D E L
Th e linear model analyze d here gives formal ex pression to three hypothe ses often advanced
to explain the com mon observation that individuals belonging to the sam e group tend to
behave similarly. These hypotheses are:
(a) endogenous effects, wherein the propensity of an individual to behave in some
way varies with the behaviour of the group;
(b ) exogenous (con textual) effects, wherein th e prop ensity of a n individual to behave
in some way varies with the exogenous characteristics of the group,' and
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MA NSKI THE REFLEC TION PROBLEM 533
(c) correlated efects, wherein ind ividu als in th e sam e gro up tend to behave similarly
because they have similar individual characteristics or face sim ilar institutional
environments.
An exam ple may help to clarify the distinction. Consider the high school achievement
of a teenage yo uth. Th ere is a n endog enous effect if, all else equal, individual achievement
tend s to vary with the average achievement of the students in the youth's school, ethnic
group, or other reference group. There is an exogenous effect if achievement tends to
vary w ith, say, the socio-econom ic com position of the reference g roup. There are correlated
effects if yo uths in th e s am e school tend t o achieve similarly because they have similar
family backgrounds or because they are taught by the same teachers.
The three hypo theses have differing policy implications. Consider, for examp le, a n
educational intervention providing tutoring to some of the students in a school but not
to the others. If individual achievement increases with the average achievement of the
students in the school, then an effective tutoring programme not only directly helps the
tutored stud ents but, as their achievement rises, indirectly helps all students in the sch ool,
with a feedba ck to fu rther achievement gains by the tutored students. Ex ogenou s effects
and correlated effects do not generate this "social multiplier".
Sec tion 2.1 specifies the m ode l. Sections 2.2 an d 2.3 analy se the identification
problem , first considering th e general mo del a nd th en a restricted version assuming that
neither exo genous no r correlated effects are present. Section 2.4 shows that, although
the linear mo del sometimes imposes restrictions o n observed beh aviour, the m odel holds
tautologically if the attributes defining reference groups and those directly affecting
outcom es are functionally dep end ent. Section 2.5 draws implications for the problem of
identifying reference groups. Section 2.6 discusses sample inference.
2.1. Model
speciJication
Let each m emb er of a po pula tion be characterized by a value fo r (y, x, z, u) R x R
R~
x R . Here y is a scalar outcom e (e.g. a youth's achievement in high school), are
attributes characterizing a n individual's reference g roup (e.g. a youth's school or ethnic
gr ou p), an d (z, u) are attributes that directly affect y (e.g. socioecono mic status an d
ability). A researcher observes a rand om samp le of realizations of (y, x, z). Realizations
of u are not observed.
Assume that
where ( a , p , y, S, is a parameter vector. It follows that the mean regression of y on
(x, z) h as the l inear form
If 0, the linear regression (2 ) expresses an endoge nous effect: a person's o utco m e y
varies with E(y x), the mean of y among those persons in the reference group defined
by x.' If y 0, the model expresses an exogenous effect: y varies with E ( z x) , the mean
of the exog enous variables z amon g those persons in the reference group. If 6
Z
0, the
mo del expresses correlated effects: persons in reference g roup x tend to behave similarly
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535A N S K I T H E R E F L E C T I O N P R OB L EM
The abil ity to detect some social effect breaks down if ~ z l) is a linear function
of [ I , x, z ]
Unfortuna tely, E z lx ) is a linear function of [ I , x, z] in various situations,
including those stated in the following corollary to Proposition 1.
Corollary In the linear model
2)
with
P
1,
the composite social-effects parameter
P 7 ) / 1 P )
is not ident~jied
f
any of these conditions hold almost everywhere.
a) z
is a function of
x.
b )
E
z x )
does not vary with
x.
c)
E
z x )
is a linear function of
x.
Th e corollary shows th at th e ability to infer the presenc e of social effects depe nds critically
on the ma nne r in which z varies with x. In the context of the linear mo del 2), inference
is possible only if E z x ) varies non-linearly with x an d Var z x )> 0.
2.3.
A pure endogenous-eflects model
Th e outloo k for identification improves if on e has inform ation o n som e parame ter values.
Em pirical studies of end oge nou s effects typically assume that =O; so neither
exogen ous nor correlated effects are present. In this case, 5) reduces to
Inspection of 6) show s the following:
Proposition
2
In the linear model
2)
with parameter restrictions
0
and
/3 1,
the composite parameters a / l - P ) , P q / 1 - P ) , and 7 are identijied if the regressors
[ I , E z x ) , z ] are linearly independent in the population.
The en dogenous-effectsparameter
/3
is not identijied
i 0
or if
E z x )
is a linear
function of
[ I , z].
In particular
/3
is not identijied if any of these conditions hold almost
everywhere:
a) z
is a function of
x.
b) E z x )
does not vary with
x.
d ) E z x ) is a linear function of x. x is a linear function of z.
Fo r exam ple, in a stu dy of scho ol achievem ent, /3 is identified if x is family incom e,
z is ability , ave rage ability ~ z l x )aries non-linearly with income, and achievement
varies with ability i.e. 0). But is not identified if x is ability, family incom e) an d
z is ability con dition a ) ; if x is family inco me , z is ability, an d average ability doe s not
vary with incom e con dition b ); or if x is family income, z is ability, family income ),
and average ability varies linea rly with income condition d ).
2.4. Tautological models
Even wh en its param eters are unid entified , a social-effects mod el may im pose restrictions
on observed behaviour and so have testable implications. There are, however,
specifications of x, z ) that make a mod el hold tautologically. In particular, this is the
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536 REVIEW O F ECON OM IC STUDIES
always consistent with the hypothesis that individual behav iour reflects m ean reference-
group behaviour. For example, if a researcher studying student achievement specifies x
to be (ability, family income) and z to be (ability), he will find that the da ta are consistent
with the hypothesis that reference groups are defined by (ability, family income), that
individual achievement reflects reference-group achievem ent, an d tha t ability has no direct
effect on achievement.
Conversely, specify x to be a function of z, say x x (z ). Then E [y x( z), z] E ( y Iz).
So the semi-linear model
holds w ith
3
y 0 and g (z ) E ( y 12); the only testable restriction of the l inear
model (2) is i ts assumption that g ( . ) is a l inear function. Continuing the school achieve-
ment example, a researcher who specifies x to be (family income) and z to be (ability,
family income) will find that th e da ta are consistent with the hypo thesis that social forces
d o no t affect achievement.
2.5. Identifying reference groups
So far, I have presumed that researchers know how individuals form reference groups
an d that individuals correctly perceive the mean outcom es experienced by their sup pos ed
reference group s. There is substantial reason to question these assum ptions. Researchers
studying social effects rarely offer empirical evidence to support their reference-group
specifications. Th e prevailing practice is simply to assum e that ind ividua ls are influenced
by E ( y x ) a nd E ( z Ix) , for some specif ied x . ~ ne of the few s tudies that does a t tempt
to justify its specification of reference g roup s is Woittiez an d K aptey n (1991). They use
individuals' responses to questions abo ut their social environments as evidence o n their
reference grou ps.
If researchers do not know how individuals form reference groups and perceive
reference-group outcom es, then it is reasonable to ask whether observed behavior can be
used to infer these unknow ns. The findings reported in S ection 2.4 imply that this is not
possible. Any specification of a functionally depen den t pair (x, z) is consistent with
observed behaviou r. The con clusion to be d raw n is that info rmed specification of reference
groups is a necessary prelude to analysis of social effects.
2.6. Sample inference
Although our primary concern is with identification, a discussion of sample inference is
warranted.
Em pirical studies of social effects have generally assum ed that there are no correlated
effects and only one of the two types of social effects. Studies of exogenous effects have
typically a pplie d a two-stage m ethod to estimate (y, 7 ). In the first stage, one uses the
sample data on (z,
x
to estimate E ( z x ) non-parame trically; typically x is discrete and
the estimate of
E
(z lx) is a cell-average. In the second stage, one estimates (y, 7 ) by
f inding the leas t squares fit of y to [ I , ~ , ( z l x ) , ], where ~ , ( z l x ) s the f irs t-stage
estim ate of ~ ( z l x ) . ee, for example, Coleman et al. (1966), Sewell and Armer (1966),
Hauser (1970), Crane (1991) or Mayer (1991).
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537ANSKI THE REFLECTION PROBLEM
Studies of endogenous effects have also applied a two-stage method to estimate
(p, q ) , but in the guise of a spatial correlation model
Here Y
=
(y,,
i
=
1 ,
N )
is the
N
1 vector of sample realizations of y and WiN is a
specified 1x N weighting vector; the components of WiN are non-negative and sum to
one. The disturbances
u
are usually assumed to be normally distributed, independent of
x, and the model is estimated by maximum likelihood. See, for example, Cliff and Ord
(1981), Doreian (1981), or Case (1991).
Equation (7) states that the behaviour of each person in the sample varies with a
weighted average of the behaviours of the other sample members. Thus, the spatial
correlation model assumes that an endogenous effect is present within the researcher's
sample rather than within the population from which the sample was drawn. This makes
sense in studies of small-group interactions, where the sample is composed of clusters
of friends, co-workers, or household members; see, for example, Duncan, Haller, and
Portes (1968) or Erbring and Young (1979). But it does not make sense in studies of
neighbourhood and other large-group social effects, where the sample members are
randomly chosen individuals. Taken at face value, equation (7) implies that the sample
members know who each other are and choose their outcomes only after having been
selected into the sample.
The spatial correlation model does make sense in studies of large-group interactions
if interpreted as a two-stage method for estimating a pure endogenous-effects model. In
the first stage, one uses the sample data on (y, x ) to estimate E (y Ix) non-parametrically,
and in the second stage, one estimates (p , q ) by finding the least-squares fit of y to
[I , x) , z ] where
x ) is the first-stage estimate of E (y x). Many non-
parametric estimates of E(y x i) are weighted averages of the form EN(y xi )= W.NY,
with WiN determining the specific estimate; see Hardle (1990). Hence, estimates of (P, q )
reported in the spatial correlation literature can be interpreted as estimates of pure
endogenous-effects models.
Note that point estimates can be obtained for unidentified models. If condition a, b,
or d of Proposition
holds, then E (y lx) is a linear function of [ I , z]. But the estimate
EN(y x) typically is linearly independent of [I, z ] . So the two-stage procedure typically
produces an estimate for
p even when this parameter is unidentified.'
3. NON-LINEAR ENDOGENOUS-EFFECTS MODELS
How do the findings reported in Section fare when the social-effects model is not
necessarily linear? This section examines two situations. Section 3.1 assumes that one
7 . It is necessary to point out that empirical studies reporting two-stage estimates of social-effects models
have routinely misreported the sampling distribution of their estimates. The practice in two-stage estimation
of exogenous-effects models has been to treat the first-stage estimate E , z l x ) as if it were E z x ) rather than
an estimate thereof. The literature on spatial correlation models has presumed that equation 7 ) holds as stated
and has not specified how the weights
W
should change with
N.
Two-stage estimation of social-effects models is similar to other semi-parametric two-stage estimation
problems whose asymptotic properties have been studied recently. Ahn and Manski
1 9 9 3 ) ,
Ichimura and Lee
1 9 9 1 ) , and others have analyzed the asymptotic behaviour of various estimators whose first stage is non-
parametric regression and whose second stage is parametric estimation conditional on the first-stage estimate.
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538 REVIEW O F ECONOMIC STUDIES
doesnotknowtheformoftheregressionandsoanalysessocialeffectsnon-parametrically.
Section3.2 assumesthat the regression isamemberofaspecified non-linear familyof
functions.Tokeeptheanalysisrelativelysimple,Irestrictattentiontopureendogenous-
effectsmodels.
3.1. Non-parametricanalysis
Assumethat,forsomeunknownfunction R1
x
R K R1,
This non-parametric endogenous-effects model, with the implied social equilibrium
equation
dropsthelinearityassumptionimposedinSection2.3.
Inthisnon-parametricsetting,onemeasuresendogenouseffectsdirectlyratherthan
throughaparameter. Thatis,onefixeszandaskshow E(y
) ,z]varieswithE ( ~ ).
Let6E R~ and(e,, el)E R2.Thenthecontrast
measurestheeffectat6ofexogenouslychangingmeanreference-groupbehaviour from
e, toel . Intheabsenceoffunctionalformassumptions,
, ) isidentifiedonthesupport
of [ E ( ~ x),z]. The contrast T(e l,e,, 5)isidentifiedif andonly if (e l, 6)and (e,, 5)
arebothonthesupportof [E(yIx),z].
To say more requires that one z].haracterize the support of [ ~ ( ~ l x ) , Useful
conditionsensuringthatcontrastsareidentifiedseemhardtoobtain. Ontheotherhand,
I canshowthat contrastsaregenerically notidentifiedifxandzareeitherfunctionally
dependentorstatisticallyindependent.
Proposition
3 In thenon-parametric endogenous-efects model (8), no contrasts of
theform (10) areidentijed
i
anyof theseconditionshold,almost everywhere:
(e) zisafunction of xandthesocialequilibriumequation (9)hasauniquesolution.
(f) z is statistically independentof x and thesocialequilibrium equation (9) hasa
uniquesolution.
(g) x isafunction of z.
ProoJ: IfE (y
x)isafunctionofz,( el , 6)and(e,, 6)cannotbothbeonthesupport
of (x,z). Sono contrasts areidentified. Conditions e,J andg all implythat E (y lx)
isa functionof z.
(e) Let6
E
RK.Thedistributionofxconditionalontheevent[z
=
51
isconcentrated
onthesetX(6)= [x:z(x)= 61; hence, the distributionof E(y x)conditional
ontheevent[z= 61isconcentratedon[ E (y x),x
E
X([)]. Forx
E
X(6),P(z x)
has all itsmass at thepoint
5
Hence, forX E X ( ~ ) , quation (9)reduces to
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MANSKI THE REFLECTION PROBLEM 539
(f) Statistical independence means that
~ ( z l x ) = P ( z ) .
Hence
( 9 )
reduces to
E ( y
x ) = f
E
( y
x ) , z ] d P ( z ) . So
E ( y
x ) solves the same equation for each
value of x. The uniqueness assumption then implies that E ( y x ) is constant for
all values of x.
(g) Let
x
=
x ( z ) .
Then
E C y x ( z ) ]
is a function of
z .
A useful way to think about the proposition is to imagine that f ( . ,
.
is really linear
with p
#
but, not knowing this, one proceeds non-parametrically. The linear model has
a unique social equilibrium so conditions e, f, and g all apply. Taken together, the
conditions say that non-parametric identification of endogenous effects is precluded if
the attributes defining reference groups and those directly affecting outcomes are func-
tionally dependent or statistically independent. Non-parametric study of social effects
remains conceivable only if x and z are "moderately related" random variables.
The prospects for identification may improve iff( is non-linear in a manner that
generates multiple social equilibria. In this case, condition
g
remains in effect but
e
and
do not apply. When there are multiple equilibria,
E ( y x )
may fluctuate from one
equilibrium value to another and so may not be a function of
z.
3.2. Binary response models
Perhaps the most familiar non-linear parametric models with endogenous effects are
binary response models. Let y be a binary random variable and assume that
where H ( . ) is a specified continuous, strictly increasing distribution function.
For
example, if
H ( . )
is the logistic distribution, we have a logit model with social effects.
Models of form
1 1 )
have been estimated by two-stage methods. The usual approach
is to estimate P ( y = 1 Ix ) non-parametrically and then estimate
p ,
y by maximizing the
quasi-likelihood in which P N ( y=
1
l x ) takes the place of P ( y = 1 l x ) . Examples include
Case and Katz ( 1 9 9 1 ) and Gamoran and Mare ( 1 9 8 9 ) . multinomial response model
estimated in this manner appears in Manski and Wise (1983 , Chapter 6 ) .
The literature has not addressed the coherency and identification of model
1 1 )
but
I can settle the coherency question here. The model is coherent if there is a solution to
the social equilibrium equation
P ( y = l I x ) = H [ a + P P ( y = l I ~ ) + z ~ ] d ~ ( z \ x ) .
( 1 2 )
If
p =
0,
E ( y Ix) =
so there is a unique solution to
( 1 2 ) .
If
p <
0,
H ( a ~ ~ ) d ~ ( z l x )
the right-hand side of
( 1 2 ) decreases strictly and continuously from H ( a
~ ~ ) d ~ ( z l
to H ( a
/3 z t V ) d ~ ( z) as E ( y x ) rises from 0 to 1. Meanwhile, the left-hand side
increases strictly and continuously from 0 to
1 .
Hence the left- and right-hand sides cross
at a unique value of
E ( y x ) .
Finally, let
P
>
0. In this case, a solution exists because the right-hand side of
( 1 2 )
increases strictly and continuously from
H ( a
z 1 7 7 ) d p ( z x )
to
H ( a P z t 7 ) d P ( z x )
as E ( y x ) rises from 0 to
1 .
Meanwhile, the left-hand side traverses the larger interval
[O,
1 1 .
Hence, the left-hand side must cross the right-hand side from below at some value
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540 REVIEW OF ECONOMIC STUDIES
not appear possible to determine the number of equilibria without imposing additional
structure. The conditions under which the parameters a ,
P 7
are identified have not
been established.
4 .
DYNAMIC MODELS
The models posed thus far assume contemporaneous effects. It may well be more realistic
to assume some lag in the transmission of these effects. Some authors, including Alessie
and Kapteyn ( 1 9 9 1 ) and Borjas ( 1 9 9 1 ) ,have estimated the following dynamic version of
the linear model 2):
E,(Y
x,
2
a
+
PEr-1 (y x ) E , - I ( z X ) ' Y x r f 6 ~ ~ ' 7 ,
( 1 3 )
where E, and E , - , denote expectations taken at periods t and t - 1 . The idea is that
non-social forces act contemporaneously but social forces act on the individual with a lag.
If
{ ~ ( z l x ) ,
< p
<
1,
the dynamic process
( 1 3 )
has a
, z )
are time-invariant and
- 1
unique stable temporal equilibrium of the form ( 3 ) . If one observes the process in temporal
equilibrium, the identification analysis of Section 2 holds without modification. On the
other hand, if one observes the process out of equilibrium, the recursive structure of ( 1 3 )
opens new possibilities for identification.
One should not, however, conclude that dynamic models solve the problem of
identifying social effects. To exploit the recursive structure of ( 1 3 ) , a researcher must
maintain the hypothesis that the transmission of social effects really follows the assumed
temporal pattern. But empirical studies typically provide no evidence for any particular
timing. Some authors assume that individuals are influenced by the behaviour of their
contemporaries, some assume a time lag of a few years, while others assume that social
effects operate across generations.
5.
DEMAND ANALYSIS
In Section 1, I noted that mainstream economic demand models embody an endogenous
social effect: individual demand for a product varies with price, which is partly determined
by aggregate demand in the relevant market. This section elaborates.
Let y denote a consumer's demand for a given product. Let x denote the market in
which the consumer operates; different values of
x
may, for example, refer to different
geographic areas or to different time periods. Let p ( x ) be the market equilibrium price
in market x. Then a conventional model of consumer demand assumes that, conditioning
on consumer attributes, the market in which a consumer operates affects demand only
through the price prevailing in that market. A common empirical formulation is
E ( Y Ix, z ) D [ p ( x ) , l7
( 1 4 )
where z are consumer attributes observed by the researcher and where D ( . , . is mean
demand conditional on ( x , z .
Market equilibrium models assume that the price p ( x ) is determined by aggregate
demand in market
x
and by supply conditions in this market. Let the population of
consumers living in market x have size m ( x ) . Then ~ ( ~ l x )s per capita demand in
market x and ~ ( y I x ) m ( x )s aggregate demand. Let s ( x ) denote the relevant supply
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MANSKI THE REFLECTION PROBLEM
Equations (14) and (15) imply that
This is an endogenous effects model of a type distinct from (8). Conditional on z, y
varies with x only through ~ ( y lx)m(x), s(x)]x) in (8) but varies with x through [ ~ ( y
in (16). Equation (16) reduces to (8) if m ( . ) and s ( . ) do not vary with x; that is, if the
population of consumers has the same size in all markets and if supply conditions are
homogeneous across markets. In this case, the variation of price across markets derives
entirely from variation in the distribution p(z x) of consumer attributes. The findings of
Sections 2 and then apply to the problem of identifying the consumer demand function.
6. CONCLUSION
This paper has analyzed the problem of identifying endogenous social effects from
observations of the distribution of behaviour in a population. We have found that there
may be realistic prospects for inference on endogenous effects if the attributes defining
reference groups and those directly affecting outcomes are moderately related. On the
other hand, the prospects are poor to nil if these attributes are either functionally dependent
or are statistically independent. Moreover, observations of behaviour cannot be used to
identify individuals reference groups.
The only ways to improve the prospects for identification are to develop tighter
theory or to collect richer data.
I have no thoughts to offer on tighter theory but I see
much that we can do to collect richer data. The analysis of this paper has presumed that
inferences are based only on observed behaviour. Empirical evidence may also be obtained
from controlled experiments and from subjective data, the statements people make about
why they behave as they do. (Jones (1984) surveys some experiments conducted by social
psychologists.) Given that identification based on observed behaviour alone is so tenuous,
experimental and subjective data will have to play an important role in future efforts to
learn about social effects.
Acknowledgement: This research is supported by National Science Foundation Grant SES-8808276 and
by National Institute of Child Health and Human Development grant lROl HD25842 HLB. I have benefitted
from discussions with numerous colleagues and from the comments of the reviewers.
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Disadvantaged Youth (Working Paper No. 3705, National Bureau of Economic Research, Cambridge,
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You have printed the following article:
Identification of Endogenous Social Effects: The Reflection Problem
Charles F. Manski
The Review of Economic Studies, Vol. 60, No. 3. (Jul., 1993), pp. 531-542.
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[Footnotes]
1 Neighborhood Context and College Plans
William H. Sewell; J. Michael Armer
American Sociological Review, Vol. 31, No. 2. (Apr., 1966), pp. 159-168.
Stable URL:http://links.jstor.org/sici?sici=0003-1224%28196604%2931%3A2%3C159%3ANCACP%3E2.0.CO%3B2-C
1The Epidemic Theory of Ghettos and Neighborhood Effects on Dropping Out and Teenage
Childbearing
Jonathan Crane
The American Journal of Sociology, Vol. 96, No. 5. (Mar., 1991), pp. 1226-1259.
Stable URL:
http://links.jstor.org/sici?sici=0002-9602%28199103%2996%3A5%3C1226%3ATETOGA%3E2.0.CO%3B2-5
2 Effects of Peer, Faculty, and Parental Influences on Students' Persistence
Barbara J. Bank; Ricky L. Slavings; Bruce J. Biddle
Sociology of Education, Vol. 63, No. 3. (Jul., 1990), pp. 208-225.
Stable URL:
http://links.jstor.org/sici?sici=0038-0407%28199007%2963%3A3%3C208%3AEOPFAP%3E2.0.CO%3B2-S
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2 Habit Formation, Interdependent Preferences and Demographic Effects in the Almost IdealDemand System
Rob Alessie; Arie Kapteyn
The Economic Journal, Vol. 101, No. 406. (May, 1991), pp. 404-419.
Stable URL:
http://links.jstor.org/sici?sici=0013-0133%28199105%29101%3A406%3C404%3AHFIPAD%3E2.0.CO%3B2-0
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A Theory of Social Custom, of Which Unemployment May be One Consequence
George A. Akerlof
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http://links.jstor.org/sici?sici=0033-5533%28198006%2994%3A4%3C749%3AATOSCO%3E2.0.CO%3B2-N
Habit Formation, Interdependent Preferences and Demographic Effects in the Almost IdealDemand System
Rob Alessie; Arie Kapteyn
The Economic Journal, Vol. 101, No. 406. (May, 1991), pp. 404-419.
Stable URL:
http://links.jstor.org/sici?sici=0013-0133%28199105%29101%3A406%3C404%3AHFIPAD%3E2.0.CO%3B2-0
Effects of Peer, Faculty, and Parental Influences on Students' Persistence
Barbara J. Bank; Ricky L. Slavings; Bruce J. Biddle
Sociology of Education, Vol. 63, No. 3. (Jul., 1990), pp. 208-225.
Stable URL:
http://links.jstor.org/sici?sici=0038-0407%28199007%2963%3A3%3C208%3AEOPFAP%3E2.0.CO%3B2-S
Spatial Patterns in Household Demand
Anne C. Case
Econometrica, Vol. 59, No. 4. (Jul., 1991), pp. 953-965.
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The Epidemic Theory of Ghettos and Neighborhood Effects on Dropping Out and TeenageChildbearing
Jonathan Crane
The American Journal of Sociology, Vol. 96, No. 5. (Mar., 1991), pp. 1226-1259.
Stable URL:
http://links.jstor.org/sici?sici=0002-9602%28199103%2996%3A5%3C1226%3ATETOGA%3E2.0.CO%3B2-5
Peer Influences on Aspirations: A ReinterpretationOtis Dudley Duncan; Archibald O. Haller; Alejandro Portes
The American Journal of Sociology, Vol. 74, No. 2. (Sep., 1968), pp. 119-137.
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http://links.jstor.org/sici?sici=0002-9602%28196809%2974%3A2%3C119%3APIOAAR%3E2.0.CO%3B2-9
Secondary School Tracking and Educational Inequality: Compensation, Reinforcement, orNeutrality?
Adam Gamoran; Robert D. Mare
The American Journal of Sociology, Vol. 94, No. 5. (Mar., 1989), pp. 1146-1183.
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Context and Consex: A Cautionary Tale
Robert M. Hauser
The American Journal of Sociology, Vol. 75, No. 4, Part 2: Status and Achievement in the U.S.:1969. (Jan., 1970), pp. 645-664.
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http://links.jstor.org/sici?sici=0002-9602%28197001%2975%3A4%3C645%3ACACACT%3E2.0.CO%3B2-A
Tied Transfers and Paternalistic Preferences
Robert A. Pollak The American Economic Review, Vol. 78, No. 2, Papers and Proceedings of the One-HundredthAnnual Meeting of the American Economic Association. (May, 1988), pp. 240-244.
Stable URL:
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Neighborhood Context and College Plans
William H. Sewell; J. Michael Armer
American Sociological Review, Vol. 31, No. 2. (Apr., 1966), pp. 159-168.
Stable URL:
http://links.jstor.org/sici?sici=0003-1224%28196604%2931%3A2%3C159%3ANCACP%3E2.0.CO%3B2-C
http://www.jstor.org
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