Using interaction terms compared to separate group regressions

[Jaweriah Abdullah]

i have a question regarding interactions compared to running separate regressions.
I have a data on consumption expenditure at the intra hosuehold level. Using this information I categorise family members into boys, girls, men and women. Now I want to see the impact of a certain government policy on the consumption expenditure of these separate family members.
My question is that should I run a regression with interaction terms of the Policy variable with the Member variable. and then estimate the marginal effects and compare the marginal effects for the different family members.

xtreg Consumption_exp Policy i.Members Policy*i.Members Controls,   fe cluster (household) robust
margins, dydx(Policy) at(Members=(1(1)4))

or should I estimate separate regression for these family members

forvalues i=1/4 {
xtreg Consumption_exp Policy Controls if member==`i',   fe cluster (household) robust
    est store `var'_`i'
    }

[Clyde Schechter]

The problem with the separate regressions approach is that you won't have the machinery you want to then make the comparisons between the marginal effects in the different household members.

Using the first approach gives you that machinery. But you need to use it correctly:

xtreg Consumption_exp  i.Policy##i.Members Controls, fe cluster(household)
margins Members, dydx(Policy)

Now, there is another issue you need to address. If you did separate regressions, the effects of the "control variables" (more properly called covariates) would differ across the types of household members. But the single regression code, as written, constrains them to be the same. So you need to decide whether you want to constrain those covariate effects or not. If you don't want the covariate effects to be the same across all types of household members, then the code for the regression would be:

xtreg Consumption_exp  i.Policy##(i.Members Controls), fe cluster(household)

Note that when you write out the actual variables that you are here summarizing as Controls, you will need to prefix each of them with an i. or c. according to whether they are discrete or continuous variables. Using this approach, the single regression with interaction will give exactly the same effects as you would get with the four separate regressions.

[Jaweriah Abdullah]

Clyde Schechter Thank you for your reply. My objective is to compare the impact of the policy on different family members.
The covariates included in the regression are household size, remittances and rainfall.
Would the correct regression then be

 
 xtreg Consumption_exp  i.Policy##i.Members Controls, fe cluster(household)

[Clyde Schechter]

Well, I am no economist, and you really should consult one about this modeling issue. But as an informed layperson, my intuition is that remittances would have a larger impact on the consumption expenditures of adults than children. So I think I would do this as:

xtreg Consumption_exp i.Policy##(i.Members c.remittances) rainfall household_size, fe cluster(household)

(I have put c. before remittances on the assumption that this is a continuous variable reflecting amount of remittances. If it is just a yes-no or other categorical variable, then replace c. with i. My intuition is that rainfall and household size might affect the personal consumption to the same extent irrespective of sex or adult vs child distinctions. So I have left them outside the interaction. But, again, this is well outside my area of expertise and you really should ask somebody who is knowledgeable in this area. It's not a statistical or Stata issue: it's a substantive question.

[Jaweriah Abdullah]

Clyde Schechter thank you for reply.
I get the point you have raised that the impact of some covariates can vary across family members and will account for it. Thanks again!

[Clyde Schechter]

Wait, I got it wrong in #4. The issue is that the remittances would affect different household members differently. So the code should have been:

xtreg Consumption_exp (i.Policy c.remittances)##i.Members rainfall household_size, fe cluster(household)

Sorry about that!

[Jaweriah Abdullah]

Clyde Schechter
SP covariates that can impact household members differentially should be interacted with the member variable.

[Clyde Schechter]

That's right.