The Asymptotic Risk of the Least Squares Averaging Estimator Bruce E. Hansen University of Wisconsin y www.ssc.wisc.edu/~bhansen May 15, 2008 Preliminary Abstract This paper examines the asymptotic risk of least-squares averaging estimators in a local as- ymptotic framework. We nd a close connection between Hansens (2007) MMA estimator and the positive-part James-Stein estimator, and use this connection to show that the asymptotic risk of the MMA estimator is uniformly smaller than the unrestricted least-squares estimator when the di/erence in the number of regressors between sub-models is four or larger. Research supported by the National Science Foundation. y Department of Economics, 1180 Observatory Drive, University of Wisconsin, Madison, WI 53706.