- Problem 2. Suppose you wish to study the effect of box-office gross (total value of tickets sold) on the rating of a movie. Let us assume you collected 1,000 movies and for each movie i you defined a variable Y, such that Y; = 1 if and only if movie i is on the current top 250 movie list (say for example, the list from douban.com). In addition, you also defined a variable X, which is equal to the box-office gross of movie i. (a) A simple OLS regression of Y; on X, is usually considered a bad idea in this case, why? (b) Suppose, in addition, you wish to check whether or not the movie is domes- tic will make a difference in this effect (the effect of box-office gross on the rating) and you further defined a new variable Z, such that Z; if and only if movie i is do- mestic. Describe how you would study this problem (be specific about the model you will be using, the estimation method and the testing procedure if necessary). Econometrics: Problem Set 4 2 1 a Suppose instead of a binary indicator, you decided to try the actual rating of a movie as a measure. Assume Y, now contains five different ratings: 1, 2, 3, 4, 5. (c) A simple OLS regression of Y, on X, is still considered a bad idea in this case, why? (d) How would you study the effect of box-office gross on the rating of a movie using the new data? Be specific about the model you use. (e) Propose a quantity that would be a correct measure of this effect based on your model in (d). - Problem 2. Suppose you wish to study the effect of box-office gross (total value of tickets sold) on the rating of a movie. Let us assume you collected 1,000 movies and for each movie i you defined a variable Y, such that Y; = 1 if and only if movie i is on the current top 250 movie list (say for example, the list from douban.com). In addition, you also defined a variable X, which is equal to the box-office gross of movie i. (a) A simple OLS regression of Y; on X, is usually considered a bad idea in this case, why? (b) Suppose, in addition, you wish to check whether or not the movie is domes- tic will make a difference in this effect (the effect of box-office gross on the rating) and you further defined a new variable Z, such that Z; if and only if movie i is do- mestic. Describe how you would study this problem (be specific about the model you will be using, the estimation method and the testing procedure if necessary). Econometrics: Problem Set 4 2 1 a Suppose instead of a binary indicator, you decided to try the actual rating of a movie as a measure. Assume Y, now contains five different ratings: 1, 2, 3, 4, 5. (c) A simple OLS regression of Y, on X, is still considered a bad idea in this case, why? (d) How would you study the effect of box-office gross on the rating of a movie using the new data? Be specific about the model you use. (e) Propose a quantity that would be a correct measure of this effect based on your model in (d)