In our professional services firm, we want to understand whether workers that are allowed to decorate their offices become productivity as a result.initially, every office was uniform in decorating style.However, we randomly selected a fraction of workers(treatment group) and allowed them to decorate their offices.The rest had to put up with uniform style(control group). We measured the productivity of everybody both before and after.

a) Write down the population model that will allow you to obtain a differences-in-differences estimator.

b) In your population model, what is the expected productivity of workers in the treatment group before they were allowed to decorate their offices?