Say I have the following regression equation:

$$Wage_i = YearsOfEduc_i + Age_i + NumOfSiblings_i + u_i$$

How would I go about peforming a wald test of the hypothesis that for an individual with median Years Of Education, that the marginal effect of age is not affected by the the number of siblings the indiviual has?

How would I form a null hypothesis?


Your model assumes that the number of siblings does not influence the effect of age. So you cannot test your hypothesis with this model.

You could inlcude an interaction term between age and number of siblings. Since, you use a linear model, the marginal effects are just the parameters and you don't need to fix any of the other controll variables. The null hypothesis is just that the parameter for the interaction term is 0. This test is in many statistical software packages reported immediately after that parameter.


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