ENH: Simulations using Pyvmte (Bernstein Polynomials)

[buddejul]

Implement simulations using Pyvmte. This allows to use Bernstein polynomials.

Simulations with Bernstein Polynomials

For Bernstein polynomials, we need to construct a DGP for every new combination of parameters y1c, y0c, y0nt.
If we take the constant spline approach used for generating data so far, the model will be misspecified.
An approach could look like this:

• Start with constant spline MTRs based on y1c, y0c, y0nt
• Use identification to construct (one) solution set, i.e. MTR functions. Using this implied Bernstein polynomial means we
  • have a DGP that generates y1c, y0c, y0nt,
  • that our model is correctly specified when we impose Bernstein polynomial constraints,
  • and that the parameter will be on the boundary of the identified set.
• Then simulate from this model as usual.