Asymptotic Approximations and Finite Sample Performance in Econometrics----------------For approximately 30 years most econometric estimator evaluation was based on first order asymptotic normal approximations. However, in the past 5 years econometricians have realized that these approximations provide a poor guide to actual finite sample estimator performance in the weak instrument/many instrument situation. Higher order approximations of different types have proven useful to analyzing different estimation situations that commonly arise in applied research. My talk will discuss different estimators and how they perform in given applied situations. I will also discuss new estimators that have been invented to treat situations where "optimal" first order estimators do not perform well. I will point to areas of future research where these advanced techniques may be useful.