I derived the mean squared errors (MSE) of a consistent estimator for two models: restricted and unrestricted. In addition, I showed that both has the same rate of convergence (that is, the asymptotic expressions for the MSE's are equal).
When I do Monte Carlo simulations I observe that the MSEs slowly become closer as the sample size increases. This was expected since both are asymptotically equal. But for $n=500$ (the sample size), they are still far from each other. Someone more experienced than me asked if it isn't suggesting that I commited errors on the theoretical derivations.
I'm thinking myself that if there were some big flaw in theory, both MSE shouldn't get closer with $n$. The fact that for a finite sample size, the MSEs are still far from each other means nothing for the asymptotic theory.
I want to generate an estimator from the MSE of the unrestricted model. As the MSE of the restricted model is simpler, and both MSE's are asymptotically equivalent, it makes sense to consider the restricted MSE. As commented above, this strategy may result in poor finite sample performance (with asymptotic justification though).
My question is: do you see anything wrong with my ideas?
Thanks in advance!