3 intro Linear Regression Model
Y= Y(X1,X2) = m(X1, X2) + u
what is m(X1,X2)
it is the conditional mean functiob. m is an unknown function that is the same for all units of observations (etc classrooms).
we assume that u is balanced
and = 0.
m(X1,X2) = E[Y| X1=x1, X2=x2]
how is the treatment effect formula with the conditional mean function (CMF)
treatment effect = m(D+1,X2) - m(D, X2) written as the difference between the to m-funtions
adding a confoubding variable to the regression model is also called:
controlling for "X2" by adding a controll variable (X2) to our regression model
what does the parametric assumtion say?
it is a functional form assumption and we assume that the shape of m is linear and can wright the reg. model with Beta/coefficients
what is the interpretation for causal effect, dvs vad är treatment effect?
treatment effect = the marginal effect of one more unit, and is therefore independent on the levels of x1 and x2 and the baseline treatment intensity (contol group, D) applied with ceteris paribus