CHAPTER 14: NONLINEAR REGRESSION MODELS

ü  Intrinsically Linear and Intrinsically Nonlinear Regression Models

·         Cobb-Douglas production function

·         Constant elasticity of substitution

ü  Estimation of Linear and Nonlinear Regression Models

Exponential regression model – used to measure the growth of a variable, such as a population, GDP, or money supply.

Nonlinear least squares – OLS applied to nonlinear regression model.

ü  Approaches to Estimating Nonlinear Regression Models

·         Direct Search or Trial-and-Error or Derivative-Free Method

·         Direct Optimization

We differentiate the error sum of squares with respect to each unknown coefficient, or parameter, set the resulting equation to zero, and solve the resulting normal equations simultaneously.

-          Method of sleepest descent

·         Iterative Linearization Method

In this method we linearize a nonlinear equation around some initial values of the parameters. The linearized equation is then estimated by OLS and the initially chosen values are adjusted. These adjusted values are used to relinearize the model, and again we estimate it by OLS and readjust the estimated values. This process is continued until there is no substantial change in the estimated values from the last couple of iterations.

-          Taylor Series Expansion

Ø  Gauss-Newton iterative method

Ø  Newton-Raphson iterative method