gmm: Generalized Method of Moments Estimation

Solves problems defined as solutions to moment conditions / estimating equations $E[g(\theta; Z)] = 0$ for some function $g(\theta; Z)$ of the data $Z$. Common examples include $g(\theta) = X(y - X\theta)$ for OLS and $g(\theta) = z(y - X\theta)$ for IV.

Supports both scipy.optimize.minimize and pytorch.minimize to solve the GMM for just- and over-identified problems (with Identity or Optimal weight matrix) and computes HAC-robust standard errors. See OLS and IV examples in example.ipynb.

The scipy optimizer uses an analytic expression for the jacobian of linear moment conditions, while the pytorch.minimize version uses forward-mode autodiff and therefore supports both linear and non-linear moment conditions.

Todo

• Support numerical optimization via pytorch-minimize
• Support Empirical Likelihood and Generalized Empirical Likelihood
• Support Bayesian Bootstrap with exponential(1) weights for inference