Question

A researcher wants to investigate the impact of providing pain killers to rickshaw drivers (n=350) in India on their alcohol consumption. In an RCT experiment, she runs this model where Pain_Killer is 1 if given free pain killers or 0 otherwise and Alcohol_Cons_i is amount of daily alcohol consimption for each rickshaw driver.

Alcohol_Cons_i = B₀ + B₁Pain-Killer+u_i

_{Is there anything "Wrong" with this equation?}

Answer 1

There is nothing wrong with the equation. But, the description of the dummy variable must be clearly defined . The interpretation of the dummy may differ person to person. For example, Dummy =1 when "free" pain killers are given. This also means that Dummy = 0 when paid pain killers are provided.

Secondly, the definition of population also needs to be defined clearly. Suppose a sample is taken in which many drivers do not consumer alcohol. Then in this case, dummy variable i.e. pain killer will show biased results. Thus a sample/samples must be obtained of rickshaw drivers who consume alcohol.

Thirdly, in the above equation only one variable is considered. In RCT experiment we try to keep all the possible factors other than the interested factor (in this case; pain killer) constant. Thus, we need to incorporate other factors like age, income etc. in the regression equation. If we don't take other factors in the regression equation, the coefficient of the dummy variable i.e.pain killer will remain biased.