Fixed Effects Models and Neighborhood Studies
Vartanian: SW 541
There are a number of ways of using fixed effect models.
 Say you want to examine effects of union membership on particular outcomes. You have a
theoretical reason for believing that people who work at specific plants or factories have
different outcomes than people who work at other plants/factories. You may only have
information on the plant/factory where people work instead of some other set of
characteristics of that plant/factory that will help explain these differences. You may then
simply include a dummy variable for where a person works, which will “difference out”
the effects of working in specific places. Thus, in this type of model, you simply use a
dummy variable.
 You are examining the effects of a number of variables on welfare outcomes. You believe
that states differ widely in the way they treat welfare recipients but don’t have similar data
for the different states. You could then include 49 state dummy variables (with one state
being the reference group, or use 50 state dummies with Washington, D.C. being one of
those dummies and another state being the reference group), which will factor out all
differences between states in your analysis. This again is called a fixed effect model.
 You believe that neighborhood conditions affect outcomes. You have a sample of siblings
and wish to examine how growing up in particular types of neighborhoods affects adult
outcomes. You can examine the difference in neighborhood conditions for the siblings and
their adult outcomes. Difference in neighborhood conditions for the siblings may arise
because of household moves to different neighborhoods or changing neighborhood
conditions for the different siblings. We can then examine the difference in neighborhood
conditions (along with the difference in all independent variable conditions) and the
difference in outcomes.
 You can examine the same individual over repeated time periods and have an individualbased fixed effect model. Thus, instead of looking at siblings, you can look at individuals
over periods of time and see how living in different types of conditions affects outcomes.
Variable such as race will be differenced out because the same individual will have the
same race over time. Only if conditions change for the individual will we have non-zero
data for the independent or dependent (depending on how these are measured) variables for
the individual.
Much of the rest of this handout is taken from Vartanian and Buck (2005), “Childhood and
Adolescent Neighborhood Effects on Adult Income: Using Siblings to Examine Differences in
OLS and Fixed Effect Models”
Fixed effect models help in reducing the effects of omitted variable bias (where omitted variables
show up in the error term, and if correlated with the included variables, produce biased b
coefficients). They may also help in reducing the effects of endogeneity. Endogeneity may occur
when examining non-random processes, and attributing the effects of these non-random processes
to a particular characteristic. For example, when examining neighborhoods, we should examine
the possibility of the simultaneous effects of neighborhood effects on individuals and individual
effects on neighborhoods. Simultaneity refers to the exogenous and endogenous social
interactions that presumably occur between individuals, families and their neighborhoods: the
extent to which people influence their neighborhoods and vice versa (Duncan, Connell &
Klebanov, 1997). These types of transactional relationships are difficult to estimate and thus
present empirical challenges in any neighborhood research (Duncan & Raudenbush, 2001).
Omitted variable bias, also known as unmeasured or unobserved variable bias, occurs
when a study lacks important information primarily due to data set constraints (Leventhal &
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Brooks-Gunn, 2000). Selection bias, or endogeneity, occurs when study participants, instead of
being randomly assigned to neighborhoods, choose them for unmeasured reasons (Duncan, et al.,
1997). The effect, therefore, of the unknown factors that influence residential decisions may be
improperly assumed to be a neighborhood effect. These fixed effects models address issues of
endogeneity that arise because neighborhoods are not randomly assigned, assuming that families
choose neighborhoods for unobserved reasons.
Fixed effects models present interesting options for reduced bias. They are often used with
sibling data such that permanent unobserved family characteristics are held constant during
migration to different neighborhoods and changes in neighborhood characteristics. Some studies
that have compared OLS estimates to fixed effects estimates have found that OLS models tend to
overstate neighborhood effects (Levy & Duncan, 2000; Plotnick & Hoffman, 1999; Weinberg, et
al. 2002). Aaronson (1998), however, found that “measuring the unmeasured” does not necessarily
show evidence that OLS results include upward biases. He finds that estimates for the effects of
the neighborhood poverty rate on educational outcomes are sometimes even larger in the fixed
effects models than in the OLS models. It cannot be assumed, therefore, that neighborhood effects
are routinely overestimated by unobservable variables, rather that there is the potential for both
upward and downward biases.
In this work, OLS and fixed effect models are compared. Statistically speaking, the general form
for determining neighborhood effects in OLS models is:
Yi    1 FPi   2 FIVi  N i   i ,
where FP is the set of permanent family variables, FIV is the set of varying family and individual
variables, N is the set of neighborhood variables, μ is the error term, β1, β2, and γ are the
coefficients for the respective permanent family, varying family and individual, and neighborhood
variables, and α is the intercept.
A fixed effect model is better able to control for differences among families than OLS
models. The fixed effect model takes on the following form:
Yij   j  1 FPj   2 FIVij  N ij   ij ,
where i denotes the individual child and j denotes the child’s family. The constant now takes on
family-specific value. Having a different constant value for each family provides a control for
those factors that are permanent features of families, or that are present in the family for each of
the children being examined but are not explicitly examined in the statistical model. Such
uncontrolled factors in the models may include family values or aspirations for the children of the
family, parental skills not captured by educational variables included in the models, or the
emotional well-being of the parents.
As Levy and Duncan (2000) and others (Aaronson 1998; Plotnick and Hoffman 1999) note,
there are permanent components and variable components to family characteristics. The family
fixed effect gets differenced out (that is, held constant) in fixed effect models. One example is the
effect of parental intelligence. Varying family effects (such as those of income) remain because
such effects will be different for each child. Thus, the fixed effect model does not allow control of
unobserved family variables that vary over children, but does allow control for variables that are
unobserved and are more permanent or the same across children. These unobserved permanent
family variables may bias the comparable OLS estimates.
In fixed effect models, sibling differences in unobserved family characteristics bias the key
coefficients only if such differences affect the dependent variable (in this case, the log of the
family income-to-needs ratio as an adult), and are correlated with sibling differences in the
characteristics of the neighborhood. These unobserved variables among siblings include ability,
ambition, and parental expectations (Aaronson 1998). As Aaronson points out, parents may learn
how to better parent in caring for subsequent children and, thus, may choose better neighborhoods
(e.g., for better schools) with each additional child. Thus, younger children may benefit from this
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parental learning, biasing the estimates. Also, if parents favor one child over another, the family
may move to a neighborhood with better schools and other such characteristics when the favored
child starts attending school. If parents favor that child in other ways (hiring tutors, giving more
homework help) that are unobserved, the effects of all of these factors will be attributed to the
neighborhood conditions. Like Aaronson (1998), the current article includes controls for birth
order of children and, thus, explicitly controls for possible better parenting for subsequent children.
However, other unobserved variables may still affect children differently and may be reflected in
the neighborhoods where they live. In addition, the PSID does not contain enough information to
distinguish between biological and nonbiological siblings in all cases. Thus, fixed effect models
cannot control for these differential and unobservable family factors. Accordingly, caution must be
used in interpreting the estimates from the fixed effect models.
The fixed effect model takes the following form:
Yij  Y. j  ( j   j )  1 ( FPj  FP. j )  B2 ( FIVij  FIV. j )   ( N ij  N . j )  (  ij   . j ) .
The constant and the permanent family factors drop out of the equation. Also in this equation, the
term (FIVij – FIV.j), as well as the other subtractions of .j, indicate that overall mean family values
are subtracted from individual values for both independent and dependent variables. In the current
model, the dependent variable is the log of the average family income-to-needs ratio when the
child becomes an adult and is at least 25 years old. The family income-to-needs ratio is a measure
of income relative to the poverty line that adjusts for family size. The value of this variable is
averaged over all years when the individual is 25 years or older. This fixed effect model is
estimated by regressing the differences in sibling outcomes on the differences in their observed
family, neighborhood, and other variables.
Both OLS regression analysis and the fixed effect models are used to examine the
dependent variable, the log of family income-to-needs as an adult.3 OLS models are used as
comparisons to the fixed effect models to determine whether using OLS modeling produces large
differences in the coefficient estimates for the neighborhood and other variables relative to the
fixed effect models. Bivariate and multivariate models that control for a number of family and
individual factors during childhood are used to determine whether the independent effects of
family-varying variables affect the relationship between neighborhood variables and the dependent
variable. A set of models also controls for a number of adult factors, such as marital status, area of
residence, and family size. The multivariate fixed effect models do not explicitly control for
permanent parental variables, such as level of education for the head of household, race, and
region of residence, because only variables that vary across siblings can have non-zero values.4
****************************************************************************
The Following is taken from The Princeton University Library, Data and Statistics Services
(see the web address below).
Fixed effects regression is the model to use when you want to control for omitted variables that
differ between cases but are constant over time. It lets you use the changes in the variables over
time to estimate the effects of the independent variables on your dependent variable, and is the
main technique used for analysis of panel data.
The command for a linear regression on panel data with fixed effects in Stata is xtreg with the fe
option, used like this:
xtreg dependentvar independentvar1 independentvar2 independentvar3 ... , fe
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If you prefer to use the menus, the command is under Statistics > Cross-sectional time series >
Linear models > Linear regression.
This is equivalent to generating dummy variables for each of your cases and including them in a
standard linear regression to control for these fixed "case effects". It works best when you have
relatively fewer cases and more time periods, as each dummy variable removes one degree of
freedom from your model.
Between Effects
Regression with between effects is the model to use when you want to control for omitted
variables that change over time but are constant between cases. It allows you to use the variation
between cases to estimate the effect of the omitted independent variables on your dependent
variable.
The command for a linear regression on panel data with between effects in Stata is xtreg with the
be option.
Running xtreg with between effects is equivalent to taking the mean of each variable for each case
across time and running a regression on the collapsed dataset of means. As this results in loss of
information, between effects are not used much in practice. Researchers who want to look at time
effects without considering panel effects generally will use a set of time dummy variables, which
is the same as running time fixed effects.
The between effects estimator is mostly important because it is used to produce the random effects
estimator.
Random Effects
If you have reason to believe that some omitted variables may be constant over time but vary
between cases, and others may be fixed between cases but vary over time, then you can include
both types by using random effects. Stata's random-effects estimator is a weighted average of
fixed and between effects.
The command for a linear regression on panel data with random effects in Stata is xtreg with the
re option.
Choosing Between Fixed and Random Effects
The generally accepted way of choosing between fixed and random effects is running a Hausman
test.
Statistically, fixed effects are always a reasonable thing to do with panel data (they always give
consistent results) but they may not be the most efficient model to run. Random effects will give
you better P-values as they are a more efficient estimator, so you should run random effects if it is
statistcally justifiable to do so.
The Hausman test checks a more efficient model against a less efficient but consistent model to
make sure that the more efficient model also gives consistent results.
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To run a Hausman test comparing fixed with random effects in Stata, you need to first estimate the
fixed effects model, save the coefficients so that you can compare them with the results of the next
model, estimate the random effects model, and then do the comparison.
. xtreg dependentvar independentvar1 independentvar2
independentvar3 ... , fe
. estimates store fixed
. xtreg dependentvar independentvar1 independentvar2
independentvar3 ... , re
. estimates store random
. hausman fixed random
The hausman test tests the null hypothesis that the coefficients estimated by the efficient random
effects estimator are the same as the ones estimated by the consistent fixed effects estimator. If
they are (insignificant P-value, Prob>chi2 larger than .05) then it is safe to use random effects. If
you get a significant P-value, however, you should use fixed effects.
Source: http://dss.princeton.edu/online_help/analysis/panel.htm
****************************************************************************
You can also run these models with dummy dependent variables but only when there is variation
within the siblings on their outcomes. All sibling sets that have the same outcomes are not use
because there is no variability in the outcome.
While you can run these models in SAS and SPSS, I find that the easiest way of running fixed
effect models is in STATA. The code for this in stata is the following:
xtreg logefmns femhh move birthord varinc ynghh fipln perafdc hdag unemrate
limited ownhome gotsepdv gotwid gotmarr nevmarr sepdiv widow kds und6 maxage
agesq female yr6872 bigcity urbany city3y suby if count>1, fe i(newid)
xtreg is indicating a fixed effect model (or other similar type of model). The first variable after
xtreg is the dependent variable (the log of fmns). All other variables are independent variables.
On the last line -- if count>1, indicates that the regression should only use cases where there are at
least two family members. Count is a variable I created to indicate the number of brothers and
sisters in the family that lived together throughout their childhood years. At the end of the
statement, fe indicates a fixed effect model and (newid) indicates that observations should be
grouped by a variable I created called newid.
I am looking at the effects of the % of female headed families during childhood on the log of
FMNS as adults.
reg logefmns femhh, cluster(newid)
First, the OLS model:
Regression with robust standard errors
Number of clusters (newid) = 2239
Number of obs
F( 1, 2238)
Prob > F
R-squared
Root MSE
=
=
=
=
=
4627
353.43
0.0000
0.1485
.70634
-----------------------------------------------------------------------------|
Robust
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logefmns |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------femhh | -.0214611
.0011416
-18.80
0.000
-.0236998
-.0192225
_cons |
1.141882
.0225106
50.73
0.000
1.097739
1.186026
------------------------------------------------------------------------------
Next, the Fixed Effects Model.
xtreg logefmns femhh if caunt>1, fe i(newid)
Fixed-effects (within) regression
Group variable (i): newid
Number of obs
Number of groups
=
=
3652
1264
R-sq:
Obs per group: min =
avg =
max =
2
2.9
10
within = 0.0079
between = 0.2380
overall = 0.1596
corr(u_i, Xb)
= 0.3018
F(1,2387)
Prob > F
=
=
18.95
0.0000
-----------------------------------------------------------------------------logefmns |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------femhh | -.0102226
.0023484
-4.35
0.000
-.0148277
-.0056175
_cons |
.9261333
.0451412
20.52
0.000
.8376132
1.014653
-------------+---------------------------------------------------------------sigma_u | .57748155
sigma_e | .56947051
rho | .50698429
(fraction of variance due to u_i)
-----------------------------------------------------------------------------F test that all u_i=0:
F(1263, 2387) =
2.70
Prob > F = 0.0000
The coefficient estimate on the FE model is around ½ of what the OLS model shows. This is in
part due to the fact that the FE model is essentially controlling for the effects of unobserved
“permanent” family variables that exist among siblings.
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Table 2
Coefficient Estimates for OLS and Fixed Effect Bivariate Models for the Natural Log of
Family Income-to-Needs Ratio as an Adult
OLS models:
Female headed families (%)
Households receiving public assistance income (%)
In poverty (%)
Household income < $15,000 a (%)
Household income > $60,000 a (%)
Income above respondent’s income (%)
Income same as respondent’s (%)
Neighborhood index 1
Neighborhood index 2
Splines (% of neighborhood):
Top 10
Top 11-25
Top 26-50
Top 51-75
Top 76-90
Bottom 10
Log of family income-to-needs ratio
N
Number of groups
R2 for neighborhood index models
Fixed effect models:
Female headed families (%)
Households receiving public assistance income (%)
In poverty (%)
Household income < $15,000 a (%)
Household income > $60,000 a (%)
Income above respondent’s income (%)
Income same as respondent’s (%)
Neighborhood index 1
Neighborhood index 2
Splines (% of neighborhood):
Top 10
Top 11-25
Top 26-50
Top 51-75
Top 76-90
Bottom 10
Log of family income-to-needs ratio
N
Number of groups
Average number of observations per group
Within R2 for neighborhood index models
Ages 0-4
-.021 (.002)***
-.031 (.004)***
-.020 (.002)***
-2.667 (.279)***
1.595 (.138)***
-.550 (.097)***
1.536 (.390)***
.136 (.012)***
-.087 (.015)***
Ages 5-8
-.022 (.002)***
-.031 (.002)***
-.022 (.001)***
-2.957 (.206)***
1.722 (.111)***
-1.001 (.084)***
1.768 (.318)***
.154 (.009)***
-.163 (.017)***
Ages 9-13
-.022 (.001)***
-.031 (.002)***
-.022 (.001)***
-2.832 (.171)***
1.712 (.089)***
-1.051 (.070)***
1.677 (.234)***
.157 (.007)***
-.169 (.015)***
Ages 14-18
-.022 (.001)***
-.031 (.002)***
-.023 (.001)***
-2.876 (.152)***
1.787 (.079)***
-1.136 (.060)***
1.159 (.229)***
.164 (.007)***
-.158 (.013)***
-.328 (.132)**
-.195 (.068)**
-.164 (.052)**
-.111 (.048)*
-.187 (.119)
-.067 (.044)
.514 (.033)***
1,660
1,199
.1258
-.265 (.114)**
-.228 (.049)***
-.304 (.042)***
.014 (.047)
-.015 (.108)
-.096 (.031)**
.569 (.027)***
2,683
1,660
.1785
-.098 (.107)
-.351 (.042)***
-.215 (.032)***
-.068 (.035)*
-.222 (.101)*
-.031 (.028)
.549 (.023)***
3,818
2,043
.1886
-.109 (.120)
-.347 (.036)***
-.248 (.032)***
-.008 (.031)
-.242 (.090)**
-.058 (.024)*
.535 (.019)***
4,949
2,319
.2004
-.006 (.011)
-.029 (.013)*
-.005 (.009)
-.745 (1.142)
1.084 (.691)
.806 (.320)**
1.470 (1.395)
.072 (.062)
.067 (.066)
-.001 (.006)
.001 (.007)
.001 (.005)
-.555 (.571)
.543 (.396)
-.421 (.208)*
1.663 (.759)*
.057 (.033)+
-.135 (.042)***
-.010 (.003)**
-.011 (.005)**
-.006 (.003)+
-.665 (.415)
.224 (.277)
-.312 (.146)*
.600 (.534)
.074 (.024)**
-.073 (.031)*
-.010 (.003)***
-.012 (.003)***
-.008 (.003)**
-.576 (.313)+
.622 (.209)**
-.028 (.113)
.496 (.404)
.071 (.018)***
-.026 (.022)
.091 (.719)
-.234 (.239)
-.092 (.140)
.105 (.101)
.467 (.337)
-.468 (.166)**
-.298 (.171)
831
370
2.2
.0068
-.135 (.323)
-.251 (.168)
-.149 (.094)
.010 (.063)
.100 (.188)
.022 (.065)
.281 (.099)**
1,723
700
2.5
.0109
-.230 (.261)
-.038 (.121)
-.027 (.068)
-.076 (.044)+
-.060 (.137)
-.079 (.049)
.079 (.066)
2,795
1020
2.7
.0069
-.061 (.281)
-.181 (.091)*
.005 (.055)
-.018 (.034)
-.145 (.110)
-.094 (.038)**
-.105 (.045)*
3,961
1,331
3.0
.0058
***p <= .001; **p <= .01;*p <= .05; +p <= .10; all for two-tailed tests.
a
Income expressed in 2001 dollars.
Note.—Neighborhood index variables are determined through principal components analysis (see
Appendix table 1). Generally, each coefficient and standard error in the table comes from a
separate regression model. Neighborhood variables run in the same models include the two
neighborhood index variables; income above respondent’s income (%) and same income as
respondent’s (%); and the spline variables.
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Table 3
Coefficient Estimates and Standard Errors for Multivariate Models for the Natural Log of
Family Income-to-Needs Ratio as an Adult
OLS models
Female headed families (%)
Households receiving public assistance income
(%)
In poverty (%)
Household income < $15,000 a (%)
Household income > $60,000 a (%)
Income above respondent’s income (%)
Income same as respondent’s (%)
Neighborhood index 1
Neighborhood index 2
Splines (% of neighborhood):
Top 10
Top 11-25
Top 26-50
Top 51-75
Top 76-90
Bottom 10
Log of family income-to-needs ratio
N
Number of groups
R2 for neighborhood index models
Fixed effect models
Female headed families (%)
Households receiving public assistance income
(%)
In poverty (%)
Household income< $15,000 a (%)
Household income> $60,000 a (%)
Income above respondent’s income (%)
Income same as respondent’s (%)
Neighborhood index 1
Neighborhood index 2
Splines (% of neighborhood):
Top 10
Top 11-25
Top 26-50
Top 51-75
Top 76-90
Bottom 10
Log of family income-to-needs ratio
N
Number of groups
Average number of observations per group
Within R2 for neighborhood index models
Ages 0-4
-.002 (.003)
Ages 5-8
-.001 (.002)
Ages 9-13
-.003 (.002)+
Ages 14-18
-.005 (.001)***
-.009 (.004)*
-.003 (.003)
-.643 (.342)+
.378 (.170)*
.214 (.114)+
-.102 (.397)
.023 (.016)
.024 (.019)
-.005 (.003)+
-.003 (.002)+
-.646 (.246)**
.335 (.137)**
-.103 (.100)
.591 (.311)+
.038 (.012)***
-.046 (.017)**
-.004 (.002)
-.004 (.001)**
-.444 (.187)*
.311 (.112)**
-.222 (.083)**
.581 (.244)*
.042 (.010)***
-.064 (.016)***
-.006 (.002)***
-.005 (.001)***
-.555 (.166)***
.442 (.098)***
-.255 (.070)***
.184 (.228)
.049 (.009)***
-.049 (.013)***
-.163 (.130)
-.021 (.062)
.008 (.054)
-.082 (.044)+
.056 (.119)
-.059 (.045)
.177 (.073)**
1,660
1,199
.2423
-.098 (.111)
-.050 (.049)
-.078 (.041)+
.018 (.041)
.101 (.101)
-.048 (.031)
.296 (.043)***
2,683
1,660
.2811
.004 (.115)
-.137 (.041)***
-.013 (.033)
-.052 (.031)+
-.085 (.091)
.015 (.027)
.259 (.034)***
3,818
2,043
.2842
.033 (.128)
-.096 (.036)**
-.069 (.029)*
.018 (.028)
-.049 (.083)
-.032 (.023)
.292 (.029)***
4,949
2,319
.2990
-.004 (.013)
.001 (.006)
-.007 (.004)+
-.006 (.003)*
-.030 (.015)*
-.010 (.009)
-1.912 (1.244)
1.124 (.738)
1.103 (.517)*
1.656 (1.639)
.109 (.066)+
.018 (.078)
.002 (.007)
.001 (.005)
-.810 (.615)
.483 (.416)
-.269 (.292)
1.671 (.875)+
.059 (.036)+
-.118 (.044)**
-.006 (.005)
-.007 (.004)*
-.903 (.437)*
.061 (.296)
-.332 (.193)+
.412 (.613)
.064 (.026)*
-.066 (.033)*
-.008 (.004)*
-.008 (.003)***
-.768 (.326)*
.399 (.219)+
-.063 (.132)
-.018 (.461)
.054 (.019)**
-.010 (.023)
.333 (.728)
-.141 (.250)
-.111 (.146)
.136 (.102)
.461 (.360)
-.541 (.177)**
-.379 (.202)+
831
370
2.2
.0780
-.215 (.331)
-.183 (.172)
-.124 (.096)
.018 (.064)
.121 (.191)
-.007 (.066)
.284 (.120)*
1,723
700
2.5
.0524
-.280 (.266)
-.013 (.124)
-.011 (.069)
-.082 (.044)+
-.040 (.139)
-.068 (.051)
.170 (.081)*
2,795
1020
2.7
.0313
.058 (.288)
-.121 (.093)
.015 (.055)
-.019 (.034)
-.162 (.110)
-.068 (.040)+
.008 (.060)
3,961
1,331
3.0
.0273
Source: Panel Study of Income Dynamics and the 1970, 1980, and 1990 Census.
***p <= .001; **p <= .01; *p <= .05; +p <= .10; all for two-tailed tests.
a
Income expressed in 2001 dollars.
Note.—All models control for the full set of control variables (see the first two columns of
Appendix tables 3 to 6 for a full list of variables included in each of the models). Neighborhood
index variables are determined through principal components analysis (see Appendix table 1).
Generally, each coefficient and standard error in the table comes from a separate regression model.
Neighborhood variables run in the same models include the two neighborhood index variables;
income above respondent’s income (%) and same income as respondent’s (%); and the spline
variables.
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Table 4
Coefficient Estimates and Standard Errors for Multivariate Models for the Natural Log of
Family Income-to-Needs Ratio as an Adult, with Adult Variables Included
OLS models
Female headed families (%)
Households receiving public assistance income
(%)
In poverty (%)
Household income < $15,000 a (%)
Household income > $60,000 a (%)
Income above respondent’s income (%)
Income same as respondent’s (%)
Neighborhood index 1
Neighborhood index 2
Splines (% of neighborhood):
Top 10
Top 11-25
Top 26-50
Top 51-75
Top 76-90
Bottom 10
Log of family income-to-needs ratio
N
Number of groups
R2 for neighborhood index models
Fixed effect models
Female headed families (%)
Households receiving public assistance income
(%)
In poverty (%)
Household income < $15,000 a (%)
Household income > $60,000 a (%)
Income above respondent’s income (%)
Income same as respondent’s (%)
Neighborhood index 1
Neighborhood index 2
Splines (% of neighborhood):
Top 10
Top 11-25
Top 26-50
Top 51-75
Top 76-90
Bottom 10
Log of family income-to-needs ratio
N
Number of groups
Average number of observations per group
Within R2 for neighborhood index models
Ages 0-4
-.001 (.003)
Ages 5-8
.001 (.002)
Ages 9-13
-.002 (.001)
Ages 14-18
-.004 (.001)***
-.008 (.003)*
-.002 (.002)
-.494 (.303)+
.336 (.149)*
.170 (.102)+
-.183 (.355)
.018 (.014)
.023 (.017)
-.002 (.002)
-.002 (.002)
-.341 (.212)
.195 (.117)+
-.081 (.084)
.289 (.266)
.018 (.010)+
-.027 (.015)+
-.001 (.002)
-.003 (.001)*
-.320 (.155)*
.233 (.093)**
-.157 (.068)*
.292 (.203)
.028 (.008)***
-.040 (.013)**
-.004 (.002)*
-.004 (.001)***
-.409 (.143)**
.334 (.082)***
-.178 (.057)**
-.009 (.190)
.034 (.007)***
-.028 (.011)**
-.175 (.108)+
-.003 (.056)
.005 (.051)
-.043 (.040)
.070 (.101)
-.067 (.040)+
.152 (.068)*
1,660
1,199
.3800
-.027 (.093)
-.035 (.041)
-.060 (.036)+
.036 (.035)
.132 (.084)
-.042 (.025)+
.231 (.037)***
2,683
1,660
.4373
.039 (.092)
-.087 (.034)**
-.013 (.028)
-.027 (.027)
-.067 (.077)
.012 (.022)
.192 (.030)***
3,818
2,043
.4436
.025 (.102)
-.050 (.030)+
-.062 (.025)**
.005 (.024)
-.033 (.070)
-.017 (.019)
.224 (.024)***
4,949
2,319
.4671
-.005 (.012)
.004 (.006)
-.008 (.004)*
-.006 (.003)*
-.031 (.014)*
-.009 (.009)
-1.098 (1.187)
.920 (.701)
.795 (.500)
.513 (1.574)
.069 (.063)
.067 (.070)
.004 (.007)
.002 (.005)
-.503 (.566)
.347 (.383)
-.160 (.268)
.970 (.809)
.027 (.033)
-.071 (.041)+
-.007 (.005)
-.008 (.003)**
-1.003 (.395)**
.244 (.268)
-.078 (.175)
.530 (.555)
.064 (.024)**
-.039 (.030)
-.005 (.003)
-.006 (.002)**
-.515 (.295)+
.321 (.198)+
-.037 (.120)
.062 (.416)
.040 (.018)*
-.010 (.021)
.518 (.696)
-.079 (.238)
-.086 (.138)
.119 (.097)
.577 (.341)+
-.556 (.168)***
-.292 (.193)
831
370
2.2
.1938
-.114 (.303)
-.081 (.159)
-.141 (.088)
.028 (.059)
.250 (.177)
-.017 (.061)
.217 (.111)*
1,723
700
2.5
.2137
-.257 (.240)
-.036 (.112)
-.021 (.063)
-.060 (.040)
-.147 (.125)
-.044 (.046)
.132 (.073)+
2,795
1020
2.7
.2173
.050 (.260)
-.121 (.084)
-.001 (.050)
-.028 (.031)
-.164 (.100)+
-.023 (.036)
-.015 (.055)
3,961
1,331
3.0
.2090
Source: Panel Study of Income Dynamics and the 1970, 1980, and 1990 Census.
***p <= .001; **p <= .01; *p <= .05; +p <= .10; all for two-tailed tests.
a
Income expressed in 2001 dollars.
Note.—All models control for the full set of control variables (see the last two columns of
Appendix tables 3 to 6 for a full list of variables included in each of the models).
Neighborhood index variables are determined through principal components analysis (see
Appendix table 1). Generally, each coefficient and standard error in the table comes from a
separate regression model. Neighborhood variables run in the same models include the two
neighborhood index variables; income above respondent’s income (%) and same income as
respondent’s (%); and the spline variables.
D:\106750786.doc
9
Variable
Neigh Index 1
Neigh Index 2
# OF MOVES
Child Order
INCOME VARIANCE
HD/WF BEFORE AGE 18
FAM INCOME-TO-NEEDS
% OF YRS WITH AFDC
AGE OF THE HEAD
CNTY UNEM RATE
HD PHYS/EMOT LIMIT
HOME OWNERSHIP
gotsepdv
gotwid
gotmarr
nevmarr
sepdiv
widow
# OF KIDS
Children Under 6 (dummy)
MAX AGE OF R
Max Age of R Squared
FEMALE
HS DROPOUT
HS GRADUATE
SOME COLLEGE
AFAM
OTHRACE
SOUTH
BIG CITY (500,00+)
CITY2 (100,000-499,999)
CITY3 (50,000-99,999)
CITY4 (25,000-49,999)
Started HH as a wife (dummy)
% YRS MARRIED
FAMILY SIZE
HS DROPOUT
HS GRADUATE
SOME COLLEGE
STUDENT AFTER AGE 25
County/State Unemploy Rate
SOUTH AS AN ADULT
LIVE IN SMSA
yr6872
yr7377
yr7882
yr8387
_cons
N
# of groups
Avg obs per group
R2/Within R2
Appendix Table 3
Full Models, Ages 0 to 4
Ages 0-4
No Adult Variables
Includes Adult Variables
OLS
Fixed Effect
OLS
Fixed Effect
.035 (.015)*
.009 (.018)
-.046 (.014)***
.012 (.020)
.000 (.000)
-.403 (.124)***
.062 (.020)**
-.290 (.110)**
-.005 (.003)
-.002 (.010)
.022 (.041)
.045 (.051)
-.253 (.081)**
-.138 (.198)
.114 (.072)
.046 (.152)
-.097 (.113)
-.251 (.155)
-.023 (.017)
(dropped) (.000)
.104 (.115)
-.001 (.002)
-.027 (.033)
-.230 (.051)***
-.170 (.046)***
-.130 (.049)**
-.278 (.058)***
-.079 (.109)
-.002 (.039)
.058 (.054)
.037 (.043)
-.030 (.056)
.135 (.063)*
.112 (.048)*
.041 (.059)
-.042 (.039)
-.024 (.048)
.000 (.000)
-.350 (.203)+
-.233 (.192)
-.469 (.293)
.018 (.012)
.015 (.034)
-.019 (.088)
-.063 (.094)
-.161 (.139)
-.580 (.782)
.167 (.148)
-.432 (.316)
-.137 (.264)
-.293 (1.045)
.014 (.066)
(dropped) (.000)
.066 (.207)
.000 (.003)
-.068 (.055)
-.010 (.051)
…
.003 (.088)
…
-1.009 (1.726)
1491
-1.095 (3.108)
748
333
2.2
.1028
.2917
-.046 (.196)
.013 (.161)
.047 (.195)
-.090 (.235)
.022 (.014)
.014 (.017)
-.020 (.012)+
-.008 (.017)
.000 (.000)
-.216 (.120)
.059 (.021)**
-.215 (.095)*
-.004 (.003)
.012 (.009)
.041 (.034)
.043 (.043)
-.161 (.069)*
-.145 (.178)
.076 (.060)
.061 (.116)
-.049 (.099)
-.114 (.103)
.000 (.014)
(dropped) (.000)
-.031 (.103)
.001 (.002)
.014 (.037)
-.061 (.048)
-.086 (.040)*
-.071 (.043)+
-.083 (.053)
-.013 (.086)
.047 (.043)
.086 (.047)+
.037 (.039)
-.002 (.050)
.112 (.054)*
.004 (.045)
.789 (.053)***
-.192 (.019)***
-.350 (.046)***
-.282 (.039)***
-.159 (.038)***
.097 (.083)
-.096 (.015)***
-.068 (.041)+
.067 (.034)*
-.013 (.047)
…
…
…
1.561 (1.539)
1491
.4771
.051 (.043)
.064 (.049)
-.022 (.035)
-.033 (.043)
.000 (.000)
-.210 (.184)
-.042 (.053)
-.243 (.258)
.022 (.011)*
.016 (.030)
-.079 (.080)
-.012 (.083)
-.206 (.124)+
.000 (.711)
.170 (.130)
-.269 (.280)
-.251 (.237)
.206 (.952)
.072 (.056)
(dropped) (.000)
-.131 (.187)
.003 (.003)
-.057 (.060)
-.039 (.176)
.054 (.143)
.100 (.176)
-.137 (.212)
.006 (.084)
.648 (.092)***
-.151 (.032)***
-.337 (.085)***
-.230 (.084)**
-.254 (.084)**
.074 (.142)
-.019 (.034)
-.219 (.095)*
.241 (.062)***
-.011 (.080)
…
…
…
1.881 (2.784)
748
333
2.2
.264
***: p<=.001; **:p<=.01;*:p<=.05; +:p<=.10
D:\106750786.doc
10
Variable
Neigh Index 1
Neigh Index 2
# OF MOVES
Child Order
INCOME VARIANCE
HD/WF BEFORE AGE 18
FAM INCOME-TO-NEEDS
% OF YRS WITH AFDC
AGE OF THE HEAD
CNTY UNEM RATE
HD PHYS/EMOT LIMIT
HOME OWNERSHIP
Gotsepdv
Gotwid
Gotmarr
Nevmarr (all years)
Sepdiv (all years)
Widow (all years)
# OF KIDS
Children Under 6 (dummy)
MAX AGE OF R
Max Age of R Squared
FEMALE
HS DROPOUT
HS GRADUATE
SOME COLLEGE
AFAM
OTHRACE
South
BIG CITY (500,00+)
CITY2 (100,000-499,999)
CITY3 (50,000-99,999)
CITY4 (25,000-49,999)
Started HH as a wife (dummy)
% of YRS MARRIED
FAMILY SIZE
HS DROPOUT
HS GRADUATE
SOME COLLEGE
STUDENT AFTER AGE 25
County/State Unemploy Rate
Live in South as Adult
Live in SMSA as Adult
yr6872
yr7377
yr7882
yr8387
_cons
N
# of groups
Avg obs per group
R2/Within R2
Appendix Table 4: Full Models, Ages 5 to 8
Ages 5 to 8
No Adult Variables
Adult Variables Included
OLS
Fixed Effect
OLS
Fixed Effect
.055 (.013)***
-.026 (.017)
-.057 (.016)***
-.001 (.015)
.000 (.000)
-.303 (.084)***
.046 (.012)***
-.252 (.082)**
-.002 (.002)
.007 (.008)
-.083 (.034)*
.027 (.039)
-.049 (.086)
-.197 (.199)
-.061 (.068)
.115 (.124)
.031 (.086)
-.146 (.156)
-.024 (.014)+
(dropped) (.000)
.111 (.061)+
-.001 (.001)
-.258 (.044)***
-.119 (.039)**
-.100 (.044)*
-.300 (.047)***
-.023 (.099)
.058 (.035)+
.034 (.044)
.016 (.039)
-.079 (.047)+
.052 (.056)
.055 (.036)
-.114 (.035)**
.025 (.029)
-.050 (.027)+
.000 (.000)
.022 (.124)
-.004 (.041)
.194 (.161)
.003 (.007)
-.005 (.018)
-.060 (.055)
-.014 (.060)
-.060 (.131)
-.591 (.276)*
-.052 (.130)
-.798 (.277)**
-.052 (.145)
-.049 (.256)
-.004 (.033)
(dropped) (.000)
.176 (.080)*
-.002 (.001)+
-.029 (.037)
-.104 (.146)
-.180 (.149)
-.471 (.194)*
-.062 (.194)
-.042 (.061)
-.010 (.049)
-.241 (.112)*
-.134 (.079)+
-1.132 (.963)
2473
1543
-2.091 (1.313)
1581
650
2.2
.0666
.3153
.034 (.011)**
-.016 (.014)
-.039 (.013)**
-.008 (.012)
.000 (.000)
-.067 (.077)
.035 (.012)**
-.177 (.066)**
-.003 (.002)
.014 (.007)*
-.025 (.029)
.013 (.032)
-.022 (.072)
-.270 (.161)+
.002 (.059)
.033 (.098)
-.020 (.071)
-.094 (.117)
-.002 (.011)
(dropped) (.000)
.023 (.053)
.000 (.001)
.025 (.029)
-.101 (.039)**
-.064 (.033)+
-.066 (.038)+
-.135 (.040)***
.029 (.084)
.096 (.041)*
.092 (.038)*
.036 (.035)
-.041 (.043)
.031 (.047)
-.067 (.032)*
.909 (.044)***
-.201 (.015)***
-.411 (.035)***
-.285 (.030)***
-.154 (.029)***
.099 (.061)
-.084 (.012)***
-.086 (.037)*
.066 (.028)*
-.083 (.057)
-.051 (.045)
.040 (.032)
-.083 (.031)**
.003 (.026)
-.035 (.024)
.000 (.000)
.157 (.109)
-.009 (.036)
.259 (.142)+
.001 (.006)
-.007 (.016)
-.047 (.049)
-.027 (.053)
-.084 (.115)
-.518 (.243)*
-.005 (.114)
-.612 (.244)**
-.151 (.128)
-.193 (.225)
-.006 (.029)
(dropped) (.000)
.058 (.071)
-.001 (.001)
-.016 (.039)
.814 (.847)
2473
1543
.233 (1.174)
1581
650
2.4
.2728
.5098
.023 (.129)
-.124 (.132)
-.328 (.171)+
-.178 (.172)
-.034 (.052)
.784 (.061)***
-.136 (.020)***
-.289 (.055)***
-.159 (.050)**
-.114 (.053)*
.117 (.085)
-.062 (.020)**
-.152 (.071)*
.134 (.043)**
-.261 (.101)**
-.161 (.071)*
***: p<=.001; **:p<=.01;*:p<=.05; +:p<=.10
D:\106750786.doc
11
Variable
Neigh Index 1
Neigh Index 2
# OF MOVES
Child Order
INCOME VARIANCE
HD/WF BEFORE AGE 18
FAM INCOME-TO-NEEDS
% OF YRS WITH AFDC
AGE OF THE HEAD
CNTY UNEM RATE
HD PHYS/EMOT LIMIT
HOME OWNERSHIP
Gotsepdv
Gotwid
Gotmarr
Nevmarr (all years)
Sepdiv (all years)
Widow (all years)
# OF KIDS
Children Under 6 (dummy)
MAX AGE OF R
Max Age of R Squared
FEMALE
HS DROPOUT
HS GRADUATE
SOME COLLEGE
AFAM
OTHRACE
South
BIG CITY (pop. 500,00+)
CITY2 (100,000-499,999)
CITY3 (50,000-99,999)
CITY4 (25,000-49,999)
Started HH as a wife (dummy)
% YRS MARRIED
FAMILY SIZE
HS DROPOUT
HS GRADUATE
SOME COLLEGE
STUDENT AFTER AGE 25
County/State Unemploy Rate
Live in the South as Adult
Live in SMSA as Adult
yr6872
yr7377
yr7882
yr8387
_cons
N
# of groups/clusters
Avg obs per group
R2/Within R2
Appendix Table 5: Full Models, Ages 9 to 13
Ages 9 to 13
No Adult Variables
Adult Variables Included
OLS
Fixed Effect
OLS
Fixed Effect
.048 (.011)***
-.059 (.016)***
-.051 (.012)***
-.012 (.012)
.000 (.000)
-.239 (.079)**
.033 (.011)**
-.182 (.069)**
-.001 (.002)
-.007 (.007)
-.029 (.031)
.035 (.039)
-.039 (.061)
-.070 (.080)
-.070 (.050)
.091 (.099)
.003 (.066)
-.019 (.105)
-.023 (.012)+
.033 (.028)
.064 (.044)
-.001 (.001)
-.043 (.024)+
-.265 (.038)***
-.165 (.037)***
-.085 (.038)*
-.318 (.041)***
.016 (.074)
.032 (.030)
.064 (.038)+
.020 (.034)
-.020 (.042)
.063 (.044)
.068 (.024)**
-.058 (.030)*
.014 (.023)
-.025 (.020)
.000 (.000)
.004 (.107)
.040 (.030)
.124 (.128)
.010 (.005)+
-.010 (.015)
-.115 (.047)*
-.031 (.056)
.073 (.083)
.277 (.167)+
.032 (.090)
.056 (.213)
-.039 (.102)
.214 (.201)
.052 (.023)*
-.004 (.041)
.117 (.053)*
-.001 (.001)+
-.043 (.030)
-.107 (.065)+
-.041 (.060)
-.015 (.050)
-.090 (.119)
-.020 (.099)
-.021 (.080)
-.264 (.715)
3215
1831
-1.925 (.892)*
2248
866
2.6
.044
.3286
-.087 (.117)
-.018 (.104)
-.105 (.130)
.145 (.132)
.035 (.009)***
-.040 (.013)***
-.029 (.011)**
-.012 (.010)
.000 (.000)
-.033 (.071)
.028 (.009)**
-.088 (.056)
.000 (.002)
.002 (.006)
-.013 (.026)
-.018 (.033)
.004 (.049)
-.004 (.076)
-.047 (.042)
.104 (.075)
.012 (.054)
-.019 (.083)
-.004 (.010)
.046 (.023)*
.022 (.039)
.000 (.001)
.024 (.025)
-.109 (.033)***
-.092 (.031)***
-.033 (.033)
-.150 (.035)***
.059 (.060)
.032 (.034)
.097 (.032)**
.048 (.029)+
.009 (.039)
.028 (.039)
-.047 (.028)+
.894 (.039)***
-.189 (.013)***
-.444 (.033)***
-.284 (.026)***
-.183 (.025)***
.081 (.052)
-.074 (.010)***
-.040 (.033)
.043 (.025)+
-.156 (.059)**
-.128 (.055)*
-.097 (.046)*
.071 (.021)***
-.044 (.026)+
.016 (.020)
-.023 (.018)
.000 (.000)
.076 (.094)
.026 (.026)
.186 (.112)+
.011 (.005)*
-.018 (.013)
-.112 (.041)**
-.012 (.049)
.087 (.072)
.220 (.147)
.036 (.079)
.272 (.186)
-.008 (.089)
.184 (.175)
.044 (.021)*
.017 (.036)
.066 (.047)
-.001 (.001)
-.017 (.032)
.911 (.637)
3215
1831
-.063 (.071)
2248
866
2.6
.2899
.5160
-.045 (.102)
.028 (.091)
-.035 (.114)
.073 (.115)
-.022 (.042)
.806 (.050)***
-.136 (.016)***
-.300 (.044)***
-.170 (.038)***
-.125 (.041)**
.027 (.066)
-.067 (.015)***
-.127 (.057)*
.163 (.037)***
-.136 (.107)
-.086 (.089)
-.045 (.102)
***: p<=.001; **:p<=.01;*:p<=.05; +:p<=.10
D:\106750786.doc
12
Variable
Neigh Index 1
Neigh Index 2
# OF MOVES
Child Order
INCOME VARIANCE
HD/WF BEFORE AGE 18
FAM INCOME-TO-NEEDS
% OF YRS WITH AFDC
AGE OF THE HEAD
CNTY UNEM RATE
HD PHYS/EMOT LIMIT
HOME OWNERSHIP
Gotsepdv
Gotwid
Gotmarr
Nevmarr (all years)
Sepdiv (all years)
Widow (all years)
# OF KIDS
Children Under 6 (dummy)
MAX AGE OF R
Max Age of R Squared
FEMALE
HS DROPOUT
HS GRADUATE
SOME COLLEGE
AFAM
OTHRACE
South
BIG CITY (pop. 500,00+)
CITY2 (100,000-499,999)
CITY3 (50,000-99,999)
CITY4 (25,000-49,999)
Started HH as a wife (dummy)
% YRS MARRIED
FAMILY SIZE
HS DROPOUT
HS GRADUATE
SOME COLLEGE
STUDENT AFTER AGE 25
County/State Unemploy Rate
Live in South as Adult
Live in SMSA as Adult
yr6872
yr7377
yr7882
yr8387
_cons
N
# of groups/clusters
Avg obs per group
R2/Within R2
Appendix Table 6: Full Models, Ages 14 to 18
Ages 14 to 18
No Adult Variables
Adult Variables Included
OLS
Fixed Effect
OLS
Fixed Effect
.055 (.008)***
-.052 (.012)***
-.065 (.013)***
-.020 (.010)*
.000 (.000)***
-.183 (.061)**
.046 (.007)***
-.124 (.062)*
-.002 (.002)
-.005 (.005)
-.039 (.026)
.016 (.035)
-.028 (.050)
.054 (.075)
-.101 (.047)*
.082 (.088)
.030 (.057)
-.019 (.061)
-.015 (.009)+
-.030 (.031)
.063 (.023)**
-.001 (.000)*
-.034 (.020)+
-.236 (.030)***
-.087 (.033)**
-.045 (.032)
-.284 (.033)***
.016 (.058)
.020 (.027)
.059 (.034)+
.006 (.029)
.003 (.036)
.090 (.041)*
.042 (.018)*
-.020 (.021)
.017 (.019)
-.020 (.017)
.000 (.000)
-.077 (.089)
.013 (.018)
.022 (.090)
.001 (.003)
.004 (.011)
.038 (.038)
.045 (.049)
.023 (.068)
.016 (.110)
-.090 (.066)
-.101 (.162)
.033 (.074)
.066 (.116)
.005 (.019)
-.026 (.036)
.049 (.030)
-.001 (.000)
-.038 (.024)
-.039 (.056)
-.066 (.053)
-.007 (.052)
.014 (.043)
-.272 (.392)
4626
2238
.009 (.119)
-.026 (.105)
.027 (.093)
.039 (.076)
-.461 (.542)
3652
1264
2.9
.0268
.3289
.041 (.090)
.063 (.089)
.081 (.097)
.026 (.112)
.042 (.007)***
-.033 (.010)***
-.032 (.010)**
-.010 (.008)
.000 (.000)***
.011 (.053)
.036 (.006)***
-.071 (.050)
-.002 (.001)
.004 (.004)
-.033 (.021)
-.039 (.029)
-.046 (.040)
.101 (.069)
-.040 (.037)
.076 (.076)
-.002 (.046)
-.013 (.046)
.003 (.007)
-.004 (.028)
.044 (.020)*
.000 (.000)
.035 (.021)+
-.096 (.026)***
-.029 (.028)
-.001 (.025)
-.129 (.027)***
.074 (.043)+
.029 (.031)
.088 (.029)**
.018 (.026)
-.008 (.032)
.067 (.033)*
-.047 (.023)*
.917 (.030)***
-.190 (.010)***
-.451 (.027)***
-.275 (.021)***
-.187 (.023)***
.050 (.041)
-.061 (.008)***
-.048 (.029)+
.054 (.020)**
-.130 (.053)*
-.157 (.049)**
-.136 (.048)**
-.079 (.041)*
.532 (.342)
4626
2238
.5146
.033 (.016)*
-.014 (.019)
.010 (.017)
-.016 (.015)
.000 (.000)
-.007 (.079)
.006 (.016)
.035 (.080)
-.001 (.003)
-.009 (.010)
.012 (.034)
.017 (.043)
.011 (.060)
.028 (.098)
-.074 (.058)
-.088 (.144)
.043 (.066)
.034 (.103)
.006 (.017)
-.020 (.032)
.051 (.027)+
-.001 (.000)
.032 (.027)
.055 (.080)
.047 (.079)
.065 (.087)
.100 (.100)
-.061 (.034)+
.835 (.041)***
-.154 (.012)***
-.324 (.036)***
-.187 (.031)***
-.156 (.034)***
-.063 (.055)
-.086 (.012)***
-.105 (.048)*
.072 (.030)*
-.059 (.108)
-.087 (.096)
-.061 (.085)
-.047 (.069)
.405 (.490)
3652
1264
2.9
.2338
***: p<=.001; **:p<=.01;*:p<=.05; +:p<=.10
D:\106750786.doc
13