You are interviewing for the position of junior analyst at a global macro hedge fund. The managing director (MD) interviewing you outlines the following scenario: You are tasked with studying the relation between stock market returns and GDP growth for multiple countries and must use a binary variable in your regression model to categorize countries by stock market type, emerging (1) or developed (0) markets. He provides three choices, saying the following:
Identify the new variable and its function.
Slope dummy: It allows for a change in slope to classify countries into weak stock performance countries and strong stock performance countries.
Intercept dummy: It allows for a change in intercept to classify countries by their stock market development status.
Interaction term: It allows for a change in intercept to classify countries into low-GDP growth and high-GDP growth countries.
and difference in mean returns between the two equals b2, so b2 is a shift in the intercept because b2 is a fixed amount. The intercept in emerging markets is b0+b2 and the slope is b1. The intercept in developed markets is b0 (because b2*0 is 0) and the slope is still b1.
This would mean that #2 doesn’t sound quite right (3 sounds better in the poorly defined scenario above), unless an interaction is fit between GDP growth and market type
E(Y) = b0 + b1x1 + b2x2 + b3x1*x2
Using substitution and a similar process as above we can see the slope for emerging markets and developed markets is actually different as is the intercept. The slope is only different when there is interaction between a quantitative and qualitative variable (or in the case of quantitative by quantitative interaction). For example, the intercept is b0 and slope is b1 for developed markets; the intercept is (b0+b2) and the slope is (b1+b3) for emerging markets (by plugging in the 1 and 0 appropriately and rearranging).
I suggest to post the question as written with answers because the verbiage is not clear.