3.5 Functional Forms
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3.5 Functional Forms The functional form of a model is an empirical issue Theory only explains the relation among variables Can we decide between models, relying on the measures that we have studies so far, when two models share the same dep. var. but one with the variable “transformed”? NO!

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3.5 Functional Forms

The functional form of a model is an empirical issue

Theory only explains the relation among variables

Can we decide between models, relying on the measures that we have studies so far, when two models share the same dep. var. but one with the variable “transformed”?

NO!

Example: Y ≠ log(Y)

The researcher should consider the relevance of the X’s and theory, the signs of the coefficients, etc.


3.5 Functional Forms

In some situations it is more suitable to re-express the model (elasticities, semi-elasticities)

So far, coefficients informed us about the absolute change (on average) on Y, to unit changes in X’s

Different functional forms for models:

  • lin-lin  absolute changes  β: ∆y to ∆x

  • log-lin semi-elasticities  100*β: ∆%y to ∆x

  • lin-log  semi-elasticities  β/100: ∆y to ∆%x

  • log-log  elasticities  β: ∆%y to ∆%x

  • reciprocal

  • polynomial


3.6 Dummy variables

Also, qualitative, binary, dichotomic

Example: gender, race, religion, marital status, etc.

“women, ceteris paribus, earn less than men”

Values: 0 – 1

With one variable, two categories (ex. M – W). The use of 0 & 1 has no effect on the estimation. Remember: if considering two variables here  Multicollinearity

With ‘m’ categories of same quality we have ‘m-1’ dummies (ex. level of studies)

Also: seasonal analysis, interaction with other variables, dependent variable (Logit, Probit)


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