Quality & Quantity 38: 185–203, 2004.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
Nested Unobserved Heterogeneity not Orthogonal
Johns Hopkins University, E-mail: firstname.lastname@example.org
Abstract. Many social phenomena are of a nested nature and recorded in hierarchical data, e.g., re-
peated observations of siblings (individual level) within families (context level). In these phenomena,
unobserved heterogeneity can occur at both levels and may be correlated with the regressors. This
article addresses nested unobserved heterogeneity not orthogonal to the regressors, which is rarely
discussed in the methodology literature. The article extends the econometric one-factor ﬁxed-effects
approach to handle nested ﬁxed effects. F tests for model comparisons are used to test whether the
total heterogeneity exists and whether the total heterogeneity consists solely of contextual heterogen-
eity. It then introduces methods to decompose the two levels of heterogeneity and provides formal
tests for each level and their relative importance, which are developed from classical ANOVA. To
provide a stronger test for time-varying context-speciﬁc heterogeneity, the article develops an estim-
ator using the difference-in-differences method. An empirical example of a study on child behavior
problems is used to illustrate the methods introduced in the article.
Key words: nested unobserved heterogeneity, correlated errors, ﬁxed effects, F tests, difference in
differences, hierarchical data
Many social phenomena are of a nested nature and recorded in hierarchical data.
Examples include repeated observations of siblings (the individual level) within
families (the context level) and repeated observations of students within schools.
The hierarchical data consist of three levels: (1) repeated observations of an indi-
vidual, (2) multiple individuals of a family, and (3) multiple families. Two levels
of unobserved heterogeneity are possible: (1) unobserved differences between in-
dividuals, which are constant for repeated observations of an individual, referred
to as individual-speciﬁc unobserved heterogeneity and (2) unobserved differences
between families, which are constant for individuals within a particular family, re-
ferred to as context-speciﬁc unobserved heterogeneity. The problem of modeling a
hierarchical-structured phenomenon that contains nested heterogeneity at both the
individual and context levels is called a nested unobserved heterogeneity problem.
An earlier version of this paper was presented at the American Sociological Association, Meth-
odology Section Winter Meetings, Duke University, March 1999. This research was supported by a
grant from the National Institute of Child and Human Development (R01HD34293).