Sufficient number of observation for an estimation

Estimation ML/Bayesian estimation
1

Hi, my question is how much observation is sufficient for an estimation?

I estimated 3 models and want to find the favorable model that has the largest log data density.
However, for robustness, I estimated them again with imposing the following estimation option,
“first_obs=1,nobs=58”, “first_obs=1,nobs=57” and “first_obs=1,nobs=56”.
And I got consistent results.

However, when I estimate with
“first_obs=2,nobs=58”, “first_obs=3,nobs=58” and “first_obs=4,nobs=58”,
results become slightly different.

My interpretation is that the first few observations are relatively important than the last few ones.
But if I could have more observations, results do not change.
Is there common knowledge about sufficient number of observations for DSGE estimation?

2

In Bayesian estimation, the data is the data. You have to take it as given. Usually, the more data the better, because you want to use the information from the data to infer the parameters of the model or even identify the best model from the model space. Unfortunately, you can only use the data that you have.
The only caveat is: you are assuming that the data are generated by the model with the parameters. If your first observations are outliers (in the sense of coming from a different model/distribution) or a structural break happens, you should not use them. If you do not suspect something like this, your first observations seem to be simply informative.