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Suppose that I am interested in the effect of income on consumption by gender:

$$consumption_i = \alpha_i + \beta_1income_i + \beta_2 male_i + \beta_3 (income * male)_i + \varepsilon_i$$

In this two-way interaction model, $\beta_1$ shows the effect of income on consumption for women and $\beta_1 + \beta_3$ shows the effect of income on consumption for men.

Suppose that I am further interested in the effect of income on consumption by gender and education:

$$consumption_i = \alpha_i + \beta_1 income_i + \beta_2 male_i + \beta_3 (income * male)_i + \beta_4 college_i + \beta_5 (income * college)_i + \beta_6 (male * college)_i + \beta_7 (income * male * college)_i + \varepsilon_i $$

My understanding is that:
The effect of income on consumption for women without a college education is $\beta_1$
The effect of income on consumption for men without a college education is $\beta_1 + \beta_3$
The effect of income on consumption for women with a college education is $\beta_1 + \beta_5$

(a) Is the above correct?
(b) What is the effect of income on consumption for men with a college education?

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1 Answer 1

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a) Yes

b) The effect of income on consumption for men with a college education would be $\beta_1 + \beta_3 + \beta_5 + \beta_7$

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