Exam 14: Instrumental Variables for Simultaneous Equations, Endogenous Independent Variables, and Measurement Error

Suppose that in an effort to explain the demand for pineapples,you collect a weekly time series data set with 780 total observations and you propose the following demand and supply equations for pineapples =+++ =+++ a)With a graph,explain estimating the demand equation alone would yield biased estimates. b)Explain why this specification can be viewed as a simultaneous equation.Be as specific as possible. c)Now with a similar graph explain how the supply shifter,rain,helps identify the demand equation. d)Describe,using rain as an instrumental variable,how to estimate the demand equation for pineapples. e)Describe,using income as an instrumental variable,how to estimate the supply equation for pineapples. f)Why would this sample size be a concern for using instrumental variables in this circumstance?

The second-stage in an instrumental variable approach to controlling for endogenous independent variables is to

The second-stage in an instrumental variable approach to identify simultaneous equations is to

The second-stage in an instrumental variable approach to control for measurement error in an independent variable is

Endogeneity of an independent variable presents a challenge because

Suppose you are interested in testing whether athletes receive better grades in high school but you are considered that the decision to compete in athletics is endogenous because athletes tend to have higher levels of motivation which results in the performing better at school work but cannot be measured and included as an independent variable in the regression.After collecting data for a sample of 32,416 high school seniors,you estimate the following instrumental variable model Second-Stage: = 1.253+ 0.29 Athletıc \nobreakspace\nobreakspaceicıpatio+ 0.02- 0.076 (0.034) (0.08) (0.002) (1.382) First-Stage: Athletıc \nobreakspace\nobreakspaceicıpatio= 0.03+ .213+ 0.006+ 0.15 (0.002) (0.014) (0.001) (0.05) a)Which of the two models is the regression model you are interested in estimating? Why is it not appropriate to estimate this model using OLS? b)What two attributes does height need to have to make it a valid instrument? Do you think these hold in this circumstance? c)Explain the intuition behind the first stage model. d)Comment on the results above. e)Why is it necessary to have such a large sample size when estimating an instrumental variable model? Explain.