Question

Intepret the SATE and the coefficient estimate on treat. Discuss the use of linear regression in experimental research designs. What is the relationship between β and the Sample Average Treatment Effect (SATE)? When would one use regression over the SATE?

Answer 1

Sample Average Treatment Effect (SATE) is a measure used to compare treatments. Let yo(i) be the value of the outcome variable for individual i if they are not given the treatment, and yı(i) be the value of the outcome variable for individual i if they are given the treatment. The treatment effect Bli) for individual i is given by B(i)= y1 (i) – voli). If there are N individuals in a sample, then average treatment effect is given as follows: SATE = 2 80 = (16Yo (3) If one could observe, for each individual, yı(i) and yo(i) in a representative sample of the population, the estimate of SATE is obtained simply by taking the average value of vii)-yoi) across the sample. The problem in SATE is that one cannot observe both yili) and yo(i) for each individual, therefore regression method for estimating SATE is used. Experimental research is any research conducted with a scientific approach, where a set of variables are kept constant while the other set of variables are being measured as the subject of experiment. The estimates of the set of constants can be efficiently obtained by applying linear regression as it uses the method of least square to estimates the coefficients of the variables involved in the experiment. Thus, linear regression is one of the important methods for obtaining the set of constants.