This paper examines the properties of various approximation methods fo
r solving stochastic dynamic programs in structural estimation problem
s. The problem addressed is evaluating the expected value of the maxim
um of available choices. The paper shows that approximating this by th
e maximum of expected values frequently has poor properties. It also s
hows that choosing a convenient distributional assumptions for the err
ors and then solving exactly conditional on the distributional assumpt
ion leads to small approximation errors even if the distribution is mi
sspecified.