In the context of a controlled experiment, consider the simple linear regression formulation Y_i = ?₀ + ?₁X_i + u_i. Let the Y_i be the outcome, X_i the treatment level when the treatment is binary, and u_i contain all the additional determinants of the outcome. Then calling $\hat \beta _ { 1 }$ a differences estimator A)makes sense since it is the difference between the sample average outcome of the treatment group and the sample average outcome of the control group. B)and $\hat \beta _ { 0 }$ the level estimator is standard terminology in randomized controlled experiments. C)does not make sense, since neither Y nor X are in differences. D)is not quite accurate since it is actually the derivative of Y on X.

Question

Quizplus · Accepted Answer

A differences estimator makes sense in this context because $\hat \beta _ { 1 }$ represents the estimated difference in the outcome variable Y between the treatment group (X=1) and the control group (X=0), which is exactly the effect of the treatment.

In the Context of a Controlled Experiment, Consider the Simple β^1\hat \beta _ { 1 }β^​1​

In the Context of a Controlled Experiment, Consider the Simple $\hat \beta _ { 1 }$