A friend is trying to estimate clothing demand for low- income Canadians. Using

Question

A friend is trying to estimate clothing demand for low- income Canadians. Using a predefined poverty line, he has separated his sample into low- and high-income Canadian. Then, using a Probit model to collect the inverse Mills ratio (IMR), he regresses a dummy for above/ below the poverty line on: age, age squared, country of birth, family size, education level, gender, occupation, marital status, and province of residence. He wants to estimate clothing expenditure on: age, age squared, country of birth, family size, gender, a dummy for being employed, the poverty line dummy, and IMR. He tells you that he knows this procedure does not work if the same repressors are used in each stage, but notes that he has used fewer variables in the second equation and that a couple of these are not found in the first equation. He asks you “Am I violating rules by doing this (i.e. are my equations different enough)”? Are there some tests I can use to find out? What advice would you offer him?

Explanation / Answer

The advice I would give the friend that he is on the right track as in the second equation he is using fewer variables to predict the dependent variable. There is no violation of any rule here as redundant variables are being eliminated to make the regression euation more robust in terms of the number of variables used to predict the dependent variable.

He can use the t and F tests on the coefficients of the independent variables to test how significant they are in predicting the dependent variable. Greater the significane of the coefficients and greater the coeff of determintion of the regression equation, the greater is its predicting power in the model.

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