Interpreting coefficients when there are dummy variables present

[Amy Moore]

Hi,

I had a question about interpreting coefficients on Stata. I have a continuous variable, call it x, which has values ranging from -2 to 2. I have also created a dummy variable which equals one when x < - 1, and a separate dummy variable which equals one when x > 1. If I run an OLS of my dependent variable on x and the two dummy variables, how would I interpret the coefficient on x? I.e., would it be capturing the effect of - 1 <= x <= 1 (the values not already captured by the dummies) or is it still capturing the effect of x as a whole (i.e., the values between -2 and 2)?

I hope my explanation isn't too confusing.

Best,
Amy

[Clyde Schechter]

The model you describe makes your dependent variable a piecewise linear function of x, with jumps at -1 and 1, and with the same slope on all three segments of the relationship. The coefficient of x is the slope of all of those segments. So in that sense, it is the effect of x "as a whole," but the coefficient of x does not express the jumps that occur: those are expressed by the coefficients of the two "dummy" variables. The graph shows the kind of relationship being modeled here: