II. Empirical Exercise: Instrumental Variables Regression

Using the "broiler" dataset, which is described in the lecture notes. Run the R program ("Broiler Program") provided to you on canvas.

In this question, you construct a table that is similar to the table "Estimating the slope of

the Demand Curve for Broiler Chicken" in the Week 5 Lecture Notes, i.e. Column (1) is a short regression of quantity on price only, Column (2) is a long regression of quantity on price and some control variables (to be selected by you), Column (3) is the instrumental variables regression.

(a) In constructing the results in Columns (2) and (3), write down your reasoning for each variable you would like to include in the regression model for quantity demanded in addition to price.

(b) Explain why the slope of the regression of quantity on price (column (1) of your table) is positive.

(c) Explain in detail the difference between the coefficient on PCHICK in columns (1) and (2). Perform any additional regressions you may need to answer this question.

(d) What are the instruments used to compute the coefficients in instrumental variable re- gression (Column (3))? Write down the R command used to obtain the IV estimates and explain in detail how the two stage least squares procedure is performed.

(e) Discuss how the inclusion of additional variables in the quantity equation affects the plausibility of the validity condition of the instruments you used in the previous question.

(f) For each of the columns in your table, test whether the coefficient on PCHICK is significant or not.

(g) Now estimate the first-stage regression of the IV estimation procedure. Are the coeffi- cients on the instruments significant? Which of the assumptions of instrumental variables does this test? What are the implications of those results on your analysis?

(h) Now suppose that PBEEF is also endogenous, how would you adjust your IV strategy? Describe which variables would be included in the first and second stage regression. Perform the IV estimation using the data accordingly. Report the estimation results in a table similar to the one you replicated in (a).