The rise of endogeneity in multilevel models: A theoretical assessment of the role of stratification

• Date: 01 September 2014
• Author: Tarek Mostafa
• Published date: 01 September 2014
• DOI: http://doi.org/10.1111/ijet.12041

doi: 10.1111/ijet.12041

The rise of endogeneity in multilevel models: A theoretical

assessment of the role of stratification

Tarek Mostafa∗

This paper studies the role of stratification in the rise of endogeneity bias in multilevel models.

The theory is illustrated using educational stratification and its implications on the estimation

of multilevel education production functions. Educational stratification results from the func-

tioning of the education market; it transforms a continuum of student characteristics into a

continuum of tuition fees. These fees enter students’ utility functions and determine the school

they attend and its quality. In other words, student characteristics are the major determinants

of school quality and the two are correlated. In this paper,I analyze how these correlations arise

and what their implications are for multilevel estimation of education production functions. The

major problem posed by such correlations is cross-level endogeneity bias. The theory developed

in this paper can be extended to anyeconomic phenomenon that exhibits stratification or nesting

of smaller units within larger units (employees within firms, residents within neighborhoods,

etc.).

Key wor ds stratification, endogeneity bias, multilevel models, education production functions

JEL classification I20, C02, D70

Accepted 30 January 2014

1 Introduction

The efficiency of multilevel models is threatened by the existence of endogeneity bias resulting from

omitted variables. Endogeneity bias arises when unobserved or omitted variables, which affect the

outcome, are correlated with one or more of the independent variables included. The presence

of such bias in the estimation of panel data models has been recognized for a long time, and

econometricians such as Mundlak (1978) and Maddala (1987) have provided different solutions to

tackle it. However, the study of endogeneity has not been extended to other similar structures such

as multilevel models. Note that panel models and multilevel models bear some similarity since, in

the former, time observations are nested within the same individual and, in the latter,individuals are

nested within larger units (students nested within schools, residents within neighborhoods, etc.).

Multilevel models—also known as hierarchical models, nested models, or mixed models—are

concerned with phenomena where observations are nested within larger units. They have been used

in a variety of contexts such as longitudinal models (e.g., individuals observed at different points in

time), organizational research (e.g., individuals nested within firms), spatial and urban economics

(e.g., residents nested within neighborhoods or regions), educational research (e.g., students nested

within schools), and biometric, environmental, and ecological studies.

∗Centre for Longitudinal Studies Institute of Education, University of London, London, UK. Email: t.mostafa@ioe.ac.uk

International Journal of Economic Theory 10 (2014) 263–274 © IAET 263

International Journal of Economic Theory