# 7.) Specification: Choosing a Functional Form Flashcards

What usually dictates the form of a regression model?

Theoretical considerations

The basic technique in deciding on a functional form is…

To choose the shape that best exemplifies the expected underlying economic or business principles and then to use the mathematical form that produces that shape.

An estimate of beta naught has at least three components…

- ) The true beta naught
- ) the constant impact of any specification errors (an omitted variable, for example), and
- ) THe of the error term for the correctly specified equation (if not equal to zero)

Suppressing the constant term leads to a violation of the Classical Assumptions. This is because …

Classical Assumption II (that the error term has an expected value of zero) can be met only if the constant term absorbs any nonzero mean that the observations of the error term might have in a given sample.

If you omit the constant term…

then the impact of the constant is forced into the stimates of the other coefficients, causing potential bias.

There are at least the two following reason that the intercept term should not be relied on for purposes of analysis or inference.

- ) The error term is generated, in part, by the omission of a number of marginal independent variables, the mean effect of which is placed in the constant term.
- ) The constant term is the value of the dependent variable when all the independent variables and the error term are zero, but the variables used for economic analysis are usually positive.

An equation is linear in the coefficients only if…

the coefficients (the betas) appear in their simplest form - they are not raised to any powers (other than one), are not multiplied or divided by other coefficients, and do not themselves include some sort of function (like logs or exponents).

Linear regression analysis can be applied to an equation that is nonlinear in the variables as long as…

the equation is linear in the coefficients.

The linear regression model is based on the assumption ..

that the slope of the relationship between the independent variable and the dependent variable is constant.

Since the slope is constant, the elasticity of Y with respect to X…

(the percentage change in the dependent variable cause by a 1-percent increase in the independent variable, holding the other variables I the equation constant be calculated fairly easily.

The double-log form is the most common functional form that is…

nonlinear in the variables while still being linear in the coefficients.

In the a double-log form…

the natural log of Y is dependent variable and the natural log of X is the independent variable.

The double-log form is often used because…

a researcher has specified that the elasticities of the model are constant and the slopes are not.

In a linear model the slopes are constant but..

the elasticities are not.

Only run double log models when…

logged variables are positive.