This book presents a modern review of some of the main topics in
panel data econometrics. It deals with linear static and dynamic models,
and it is aimed at a readership of graduate students and applied researchers.
Parts of the book can be used in a graduate course on panel data econometrics,
and as a reference source for practitioners. Many applications are discussed
in detail. Some of the methodological issues are explained through applications,
which are closely interwoven with the rest of the text and should be regarded
as an integral part of the discourse.
The book has two main concerns. One is the analysis of models with non-exogenous
explanatory variables. This includes strictly exogenous variables that are
correlated with unobserved individual effects, variables subject to measurement
error, and variables that are predetermined or endogenous relative to time-varying
errors. The other concern is dynamic modelling and, more specifically, the
problem of distinguishing empirically between dynamic responses and unobserved
heterogeneity in panel data analysis. Error components, covariance structures,
autoregressive models, models with general predetermined variables, and optimal
instruments are systematically covered.
For the most part the book adopts a generalized method of moments (GMM)
approach, and makes frequent use of instrumental variable arguments, although
likelihood approaches are also presented when available. Many topics are
discussed from short and long panel perspectives, but there is an emphasis
in the econometrics of micro panels, which is reflected in both the organization
of the material and the choice of topics. The central parts of the book provide
a synthesis, and unified perspective, of a vast literature on dynamic panel
data that has had a significant impact on econometric practice.
autoregressive models, covariance structures, error
components, generalized method of moments, individual effects, measurement
error, optimal instruments, panel data, predetermined variables, unobserved
I Static Models
2 Unobserved Heterogeneity
Chapter 2 begins by introducing the problem of unobserved heterogeneity
in regression analysis and how the availability of panel data helps to
solve it. Correlated effects are motivated as an instance of endogenous
regressors, and compared with other approaches to endogeneity in econometrics.
Within-group or fixed effects estimation is discussed and motivated from
short and long panel perspectives in least squares and likelihood contexts.
The implications of heteroskedasticity and serial correlation for valid
inference and optimal estimation are considered, as well as extensions
to non-linear models with additive effects, including small and long T
robust standard errors, and minimum distance methods.
endogenous regressors, fixed effects, heteroskedasticity,
minimum distance, optimal estimation, robust standard errors, serial correlation,
unobserved heterogeneity bias, within-group estimation.
3 Error Components
This chapter is devoted to error component models. These are initially
motivated from an interest in distinguishing permanent from transitory components
of variation in such areas as the analysis of wage inequality and mobility.
Next, they are regarded as a special case of the unobserved heterogeneity
model in which the effects are uncorrelated with the regressors. Tests of
these restrictions and extensions to models with a subset of uncorrelated
regressors are discussed. Finally, nonparametric estimation of the error
component distributions is considered.
error components models, models with information in
levels, nonparametric estimation, tests of uncorrelated effects, wage inequality
4 Error in Variables
The last chapter in Part I deals with error in variables in panel data.
The central theme here is that regressions in levels and deviations may
not only differ because of unobserved heterogeneity but also as a result
of magnification of measurement error bias in the regressors in changes.
Conditions under which panel data provides internal instrumental variables
are discussed and a firm money demand illustration provided.
error in variables, internal instrumental variables,
firm money demand, measurement error bias, regressions in levels and deviations.
II Time Series Models with
5 Covariance Structures for Dynamic Error Components
Part II deals with time series models with error components. Chapter
5 opens up with an informal discussion of the problem of distinguishing
between unobserved heterogeneity and individual dynamics in short panels.
Next, modelling strategies of time effects, moving average models, and inference
from covariance structures are considered. Then an illustration is provided
by considering tests of the permanent income hypothesis from household panel
covariance structures, moving average models, permanent
income hypothesis, time effects, time series with error components.
6 Autoregressive Models with Individual Effects
Chapter 6 considers the specification and estimation of autoregressive
models with heterogeneous intercepts. Within-group biases in short panels
are discussed. Fixed T consistent estimation from GMM and likelihood perspectives
is considered. The discussion clarifies the impact of assumptions about
initial conditions and heteroskedasticity on estimation. Particular attention
is paid to unit roots and to estimation under mean stationarity. The chapter
concludes with a detailed tutorial on the estimation and testing of VAR
models using firm-level panel data.
autoregressive models, firm-level panel data, initial
conditions, mean stationarity, time series heteroskedasticity, unit roots,
VAR models, within-group biases.
III Dynamics and Predeterminedness
7 Models with both Strictly Exogenous and Lagged Dependent
The subject of Part III is dynamics and predeterminedness. Chapter 7
deals with models with both strictly exogenous and lagged dependent variables
allowing for autocorrelation of unknown form. In contrast to the autoregressive
models of Part II, here lagged dependent variables appear in a structural
role. Their effects are identified regardless of the form of serial correlation
thanks to the availability of strictly exogenous regressors. Estimation is
discussed from short and long panel perspectives in GMM and likelihood contexts.
A model of cigarette addiction is used as an illustration.
autocorrelation of unknown form, cigarette addiction,
lagged dependent variables, short and long panels, strictly exogenous regressors.
8 Predetermined Variables
Chapter 8 deals with models in which the errors are mean independent
of current and lagged values of certain conditioning variables, but not with
their future values. Partial adjustment, Euler equations, and cross-country
growth are discussed as examples. Alternative approaches to estimation
from small and large T perspectives are considered. Special attention is
given to estimators that use information on the levels of the variables.
Such topics as the irrelevance of filtering and optimal instruments with
sequential moment conditions are also considered.
cross-country growth, Euler equations, information
on the levels of the variables, irrelevance of filtering, partial adjustment,
optimal instruments, predetermined variables, sequential moment conditions.
A Generalized Method of Moments Estimation
Part IV contains two additional chapters that review the main results
in the theory of generalized method of moments estimation and optimal instrumental
variables. The purpose of these chapters is to make the book reasonably
self-contained. The first one begins by introducing method of moments estimation
problems, followed by a general formulation of GMM estimation and testing,
using 2SLS and 3SLS as examples. The chapter deals with consistency, asymptotic
normality, asymptotic variance estimation, optimal weight matrix, and Sargan
tests of overidentifying restrictions.
asymptotic variance estimation, generalized method
of moments, moments estimation problems, overidentifying restrictions,
B Optimal Instruments in Conditional Models
This chapter considers models defined by conditional moment restrictions.
The focus of the discussion is in finding the optimal instruments for each
type of model that is considered. The problem is first solved for the linear
regression model, which is the most familiar context, and then the same
procedure is used for increasingly more complex models.
conditional moment restrictions, conditional models,
linear regression, optimal instruments.