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Dealing with Endogeneity in Regression Models with Dynamic
Coefficients presents a unified econometric framework for dealing
with the issues of endogeneity in Markov-switching models and
time-varying parameter models. While others have considered
estimation of simultaneous equations models with stochastic
coefficients as a system, this book focuses on the LIML (limited
information maximum likelihood) estimation of a single equation of
interest out of a simultaneous equations model. The control
function approach, which is an econometric method used to correct
for biases that arise as a consequence of selection or endogeneity,
will be the main tool in dealing with the problem of endogeneity
throughout the book. While the approach has been extensively
applied to the sample selection models and disequilibrium models in
the micro-econometrics literature, its application in the
time-series econometrics literature is relatively new. The basic
idea behind the control function is to model the dependence of the
disturbance term on the endogenous variables in a way that allows
us to construct a function such that, conditional on the function,
the endogeneity problem in the regression equation of interest
disappears. The book is organized as follows: Section 2 reviews the
basic issues associated with the control function approach, which
is the main tool for dealing with endogeneity in this article. The
authors investigate these issues within the framework of constant
regression coefficients. Section 3 considers estimation of
Markov-switching models with endogenous regressors. Section 4 deals
with estimation of a Markov-switching model, where regressors are
exogenous or predetermined and the Markov-switching coefficients
are correlated with regression disturbances. Section 5 discusses
the issues of endogeneity within the time-varying parameter models.
Section 6 provides concluding remarks.
Both state-space models and Markov switching models have been
highly productive paths for empirical research in macroeconomics
and finance. This book presents recent advances in econometric
methods that make feasible the estimation of models that have both
features. One approach, in the classical framework, approximates
the likelihood function; the other, in the Bayesian framework, uses
Gibbs-sampling to simulate posterior distributions from data. The
authors present numerous applications of these approaches in
detail: decomposition of time series into trend and cycle, a new
index of coincident economic indicators, approaches to modeling
monetary policy uncertainty, Friedman's "plucking" model of
recessions, the detection of turning points in the business cycle
and the question of whether booms and recessions are
duration-dependent, state-space models with heteroskedastic
disturbances, fads and crashes in financial markets, long-run real
exchange rates, and mean reversion in asset returns.
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