Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Exercise 12

Suppose that Y t is the monthly value of the number of new home construction projects started in the United States. Because of the weather, Y t has a pronounced seasonal pattern; for example, housing starts are low in January and high in June. Let
, denote the average value of housing starts in January and denote the average values in the other months. Show that the values of can be estimated from the OLS regression
where Feb t is a binary variable equal to 1 if t is February, Mar t is a binary variable
equal to 1 if t is March, and so forth. Show that ß 0 + ß 2 =
and so forth.