Add identification diagnostics to estimation functions

[janosg]

Problem

In empirical applications we often have weakly identified parameters. This can have two sources:

1. The criterion function for the estimation problem is flat
2. Two or more parameters are not separately identified

The first problem manifests itself in large standard errors, the second in strong correlations between parameters.

Desired solution

Ideally, the results of estimate_ml and estimate_msm contain some information on the most weakly identified parameters. Moreover, the functions should raise a warning if it detects a strong identification problem.

Open questions

• How large does a standard error need to be (maybe relative to the absolute value of the estimate) in order to classify a parameter as weekly identified?
• How large does the absolute value of correlations need to be in order to classify two parameters as collinear?
• Are there formal tests for this?
• How should we format the output to make it readable? Should it be a report or a plot of a filtered correlation matrix?

[janosg]

It looks like the test we need already exists: https://arxiv.org/pdf/1907.13093.pdf