3 Functional Form
The model \(Y = \alpha + \beta X + u\) is linear in two senses: linear in the variable \(X\) and linear in the parameters \(\alpha \) and \(\beta \). Least squares and all the theory of Section 2 need only the second. Any relation that becomes linear in its parameters after the variables are transformed can be estimated by the same formulas, applied to the transformed variables. That covers a great deal of economics: constant growth, constant elasticities, diminishing returns, saturation. This section works through the standard forms, the economic meaning of the coefficient in each, and the question of how to choose between them.
3.1 Time as a regressor
3.2 Constant growth curves
3.3 Transformations of the variables
3.4 The logistic curve
3.5 Choosing the functional form
3.6 Functional form in software
3.7 Practice Problems
3.2 Constant growth curves
3.3 Transformations of the variables
3.4 The logistic curve
3.5 Choosing the functional form
3.6 Functional form in software
3.7 Practice Problems
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