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Date of Award

Spring 2022

Degree Name

Bachelor of Science



First Advisor

Prof. Mark Stater


There is variation throughout econometric literature regarding the relationship between the two broad classical estimator classes, M and GMM. An M estimator minimizes a sample mean, whereas a GMM estimator minimizes a quadratic form in a sample mean. Instrumental Variables is an example of a GMM estimator. Many nonlinear estimation techniques, such as maximum likelihood and nonlinear least squares, are understood to be M estimators. Ordinary Least Squares (OLS) is an example of both. Some economists (Peracchi 1990, Greene 2003) have proven that all M estimators are GMM. This thesis further explores the relationship between the estimators by evaluating the extent to which GMM estimators are M. Many authors of journal articles claim that all GMM are M estimators, but this containment seems to be defined in a broader framework than the textbook definitions. In fact, some authors have proposed opposing claims saying that this containment is not universally true (Hansen 2022). Most of the claims regarding the containment of GMM within M are not backed by proofs or counterexamples, thus leaving the true relationship between M and GMM unclear. This thesis seeks to clarify the true extent to which M and GMM are related and the potential implications of the equality or inequality of the estimators.


Senior thesis completed at Trinity College, Hartford CT for the degree of Bachelor of Science in Economics. Full text access is limited to the campus community.