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Say I estimate the following probit model:

$$ins = \Phi(\alpha + \beta_1 age + \beta_2 educ + \beta_3 hg + \beta_4chronic + \beta_5 hisp + \beta_6 lin) + u$$

where:

$ins = 1$ for any individual who has private health insurance, $0$ otherwise.

age = age in years.

educ = years of schooling.

$hg=1$ if health status self-assessed as good, 0 otherwise.

chronic = number of chronic conditions an individual has.

hisp$=1$ if Hispanic, 0 otherwise.

lin = natural log of household income.

I was if I were to perform a Wald test that for an individual with otherwise median characteristics, the marginal effect of age is unaffected by the number of chronic diseases the individual has, how do I derive the null hypothesis? (P.S., I can conduct the wald test quite easily in STATA, but my question is how do I state the null hypothesis?).

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Test for the age*chronic interaction:

$$ins = \Phi(\alpha + \beta_1 age + \beta_2 educ + \beta_3 hg + \beta_4chronic + \beta_5 hisp + \beta_6 lin + \beta_7age*chronic) + u$$

$H_0 : \beta_7 = 0$

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