Question

Assume that you are conducting an experiment. You are interested in whether a treatment ? affects an outcome ?. Assume that ? is binary—individuals either receive the treatment or they do not. For example, assume that ? indicates whether an individual received medicine intended to reduce cholesterol (at the risk of developing side-effects), and ? is a measure of health. (a) Write down a regression model which you can estimate to investigate your research question. Clearly state what each parameter in your model represents. What is the average causal effect of ? (b) Assume that the error term in your linear regression model follows a standard Normal distribution conditional on both values of ?. What is the PDF of ? given ?=1? Given ?=0? Draw these PDFs and label every parameter in your regression model. (c) Assume that you have ? participants in your experiment and that ? is large. With the least squares assumptions in mind, how can you choose which participants receive the treatment ? in order to get a good estimate of the average casual effect of ? on ?? What is the relationship between your suggested method of choosing participants who receive the treatment and the least squares assumptions? (d) Assume that you are not able to implement your method of choosing participants who receive the treatment. Instead, participants can themselves choose whether or not to receive the treatment. What consequences might this have for your estimates? (Hint: Correct answers will discuss bias.)

Answer 1