### E1: Nonlinear Least Squares with Cobb-Douglas Production Function

Problem Statement In economics, a production function relates the output of a production process to the inputs. The Cobbâ€“Douglas (C-D) production function, a particular functional form of the production function, is used widely to represent the technological relationship between the amounts of two or more inputs, physical capital and labor, and the amount of output...

### E2: Nonlinear Least Squares with Constant Elasticity of Substitution Production Function

Problem Statement In this example, we estimate the unknown parameters of Constant Elasticity of Substitution (CES) production functions with either additive or multiplicative error terms using Mizon (1977). The CES production function is a neoclassical production function that displays constant elasticity of substitution. In other words, the production technology has a constant percentage change in...

### E3: Maximum Likelihood Estimation with Probit Model (Binary Dependent Variable Case)

Problem statement In statistics, a probit model (binary dependent variable case) is a type of regression in which the dependent variable can take only two values (0/1), for example, married or not married. The name comes from probability and unit. The purpose of the model is to estimate the probability that an observation with particular...

### E4: Maximum Likelihood Estimation with Logit Model (Binary Dependent Variable Case)

Problem Statement Similar to the probit model we introduced in Example 3, a logit (or logistic regression) model is a type of regression where the dependent variable is categorical. It could be binary or multinomial; in the latter case, the dependent variable of multinomial logit could either be ordered or unordered. On the other hand,...