Breusch, Trevor Stanley
Description
This thesis is concerned with examining relationships among the
various asymptotic hypothesis testing principles in econometric settings
and with developing applications of the Lagrange multiplier (LM)
procedure to econometric problems. For a wide range of hypothesis
testing situations, particularly those associated with detecting misspecification
errors in regression models, it is argued that the LM
method is most useful. The LM test, which is asymptotically equivalent
to the likelihood...[Show more] ratio test in regular problems, is frequently less
demanding computationally than other procedures that might be applied
in the same circumstances. In addition, the LM statistic sometimes
corresponds to a criterion which is familiar to the econometrician but
which has been previously motivated by other considerations. The LM
testing principle provides a convenient framework in which such existing
tests can be extended and new tests can be developed.
Chapter 1 sketches the theoretical setting that is applicable to
many statistical problems in econometrics and highlights a number of
aspects of the various testing principles, for reference in later chapters
Tests of coefficient restrictions in linear regression models are considered
in Chapter 2, including an examination of a systematic numerical
inequality relationship among the criteria. Chapter 3 is concerned with
the LM test in its various guises and with applicability of the LM
method to diverse econometric situations. Specific applications are
considered in greater detail in Chapters 4 through 6: in Chapter 4 the
LM method is applied to testing for autocorrelation in dynamic single
equation linear models; in Chapter 5 the ideas of the preceding chapter
are extended to simultaneous equations systems, and in Chapter 6 a test
against a wide class of heteroscedastic disturbance formulations is developed. Since the theoretical properties of the LM test derive
mainly from asymptotic considerations, questions regarding the validity
of asymptotic results to practical situations with finite sample sizes
remain open. A Monte Carlo simulation study, comparing the LM test
for heteroscedasticity with other asymptotically equivalent tests, is
presented in Chapter 7.
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