Including an interaction term vs running a regression with a portion of the dataset

[Santiago Valdivieso]

I ran an ordered probit regression with the following equation:

(Eq.1) Y = B0 + B1 X1 + B2 Not_Poor + Other controls

Where Y is a categorical variable, X1 is a continous variable and Not_Poor is dichotomous variable that takes the value of 1 if an individual is not poor and 0 otherwise.

I got and insignificant B1. Theory suggest, however, that relationship between X1 and Y should be stronger among the poor. To test this, I have contemplated two methods.

A) Keeping only the poor individuals of my dataset (i.e., running the line "keep if Not_Poor==0") and running Eq.1 again.

B) Adding an interaction term between X1 and Not_Poor as follows: Y = B0 + B1 X1 + B2 Not_Poor + B3 (Not_Poor * X1) + Controls.

In both cases, B1 is the effect of X1 on Y among the poor. However, I find that B1 is non-significant with method A and significant with method B.

My questions are:

i) What could explain this discrepancy?
ii) Under which circumstances should method A be prefered to method B and viceversa?

Thank you in advance!

[Carlo Lazzaro]

Santiago:
1) different regression specifications give back different coefficients; no wonder about that;
2) the approach B is the way to go, as interaction gives you an idea of the effect of X1 on rich and poor, something that you cannot get with approach A.

[Santiago Valdivieso]

Thanks Carlo Lazzaro !