15.1 Delta Method

  • approximate the mean and variance of a function of random variables using a first-order Taylor approximation
  • A semi-parametric method
  • Alternative approaches:
    • Analytically derive a probability function for the margin

    • Simulation/Bootstrapping

  • Resources:

Let \(G(\beta)\) be a function of the parameters \(\beta\), then

\[ var(G(\beta)) \approx \nabla G(\beta) cov (\beta) \nabla G(\beta)' \]


  • \(\nabla G(\beta)\) = the gradient of the partial derivatives of \(G(\beta)\) (also known as the Jacobian)