Berndt–Hall–Hall–Hausman algorithm

BHHH is an optimization algorithm in econometrics. It is an acronym of the four authors: Berndt, B. Hall, R. Hall, and Jerry Hausman.

Usage

If a nonlinear model is fitted to the data one often needs to estimate coefficients through optimization. In general $\beta _{k+1}=\beta _{k}-\lambda _{k}A_{k}{\frac {\delta Q}{\delta \beta }}(\beta _{k})$, where $\beta _{k}$ is the coefficient at step k, $\lambda _{k}$ is a parameter, Q is the objective function (the negative of the likelihood function) and $A_{k}=\left[1/N\sum _{i=1}^{N}{\frac {\delta \ln f}{\delta \beta }}(\beta _{k}){\frac {\delta \ln f}{\beta }}(\beta _{k})'\right]^{-1}$ in the case of BHHH. In other cases, e.g. Newton-Raphson, $A_{k}$ can have other forms.

Literature

- Berndt, E., B. Hall, R. Hall, and J. Hausman, (1974), “Estimation and Inference in Nonlinear Structural Models”, Annals of Social Measurement, Vol. 3, 653-665. - Luenberger, D. (1972), Introduction to Linear and Nonlinear Programming, Addison Wesley, Reading Massacusetts. - Gill, P., W. Murray, and M. Wright, (1981), Practical Optimization, Harcourt Brace and Company, London