Some aspects of statistical inference for econometrics

Abstract

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 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.