730 Microeconometrics: Methods and Developments
14.7 Data issues 763
14.7.1 Sampling schemes 763
14.7.2 Missing data 765
14.7.3 Measurement error 766
14.8 Conclusion 767
14.1 Introduction
Applied microeconometrics primarily applies regression methods to cross-
section and longitudinal economics-related data. Most often the goal is to obtain
estimates of one or more marginal effects. A stereotypical example is estimation
of the effect on earnings of a one-year increase in education. A simple approach is
ordinary least squares (OLS) estimation of a linear cross-section regression of log-
earnings on years of schooling and other control variables. Potential complications
include nonlinearity (with implications for estimation and statistical inference);
endogeneity of the regressor schooling (that is chosen by the individual); unob-
served individual heterogeneity (the marginal effect even after controlling for
regressors may differ across individuals); and missing or mismeasured data.
In this chapter I survey various methods to deal with these complications. Some
of these methods have already become well established and command little current
theoretical research. Other methods, especially those that are currently active areas
of research, may or may not ultimately become part of the toolkit. An impetus
for many of these methods is increased computing power and data availability,
discussed in the next chapter in this volume, by Jacho-Chávez and Trivedi.
The survey presumes the basic theory for least squares (LS), maximum likelihood
(ML) and instrumental variables (IV) estimation of nonlinear cross-section mod-
els and linear panel data models, methods well established by the late 1970s.
Section 14.2 presents a summary of identification that includes more recent
semiparametric identification and partial identification. Section 14.3 presents esti-
mation methods that enable the use of richer models, notably generalized methods
of moments (GMM), empirical likelihood, simulation-based methods (classical and
Bayesian), quantile regression, and semiparametric estimation. Even when more
basic LS, ML and IV estimators are used, there have been considerable develop-
ments in statistical inference, most notably the use of robust standard errors and
bootstrap methods. These are presented in section 14.4. Section 14.5 presents a
wide range of methods that have been developed to obtain marginal effects that
can be given a causative interpretation, even when observational data are used. A
fundamental change in thinking is the use of the potential outcomes framework
and quasi-experimental approaches to tease out causation. Section 14.6 discusses
methods to control for unobserved heterogeneity. Section 14.7 presents adjust-
ments to standard methods that incorporate the practical data complications of
survey sampling schemes, missing data, and measurement error.
The following notation is used. The typical observation is theith, with scalar
dependent variableyi,k×1 regressor vectorxi, and, where relevant,m×1 instru-
ment vectorzi. Unless otherwise noted independence overiis assumed. At times