3. Diﬂs in Diﬁ's When presenting the ﬁxed effects model for a binary treatment we focused on

the following situation: Yit = ﬁlTit + 02' + U11 Now assume the model is the following: Ya = 1811121 +ai +O€t + Uit This modiﬁes the original setup to allow for time ﬁxed effects. This can be very important if we

imagine there are aggregate changes in Y over time. We will still assume there are two time periods,

0 and 1. Moreover, we will still assume that at time 0, Tit = 0 for everyone. Please answer the following questions: (a) Consider the following set—up: at time 0, all students are in the same sized class, but in time 1 some students may choose to take a smaller class and some may take a larger class. This is essentially the example from class. Why might including at be important in this example?

(b) Take the difference over time of Y and write the differenced regression. (c) Once the equation has been differenced, there is only one observation per individual. Since the

time ﬁxed effects do not vary over individuals, What is the role of the time ﬁxed effects in the differenced regression? How does this setup compare to that in class.