Consider a simple model to estimate the effect of personal computer (PC) ownersh
ID: 1186592 • Letter: C
Question
Consider a simple model to estimate the effect of personal computer (PC) ownership on college grade point average (GPA), GPA = beta 0 + beta 1PC + u where PC is a binary variable indicating PC ownership. Why might PC ownership be correlated with the error term u? Would such a correlation present problems for the use of OLS estimation? Explain why PC is likely to be related to parent's income. Would parent's income be a good Instrumental Variable for PC? Why or why not? Suppose that, four years ago, the university gave computers to one - half of the new incoming students on a randomly selected basis. Explain how you would use this information to construct an instrumental variable for PC. Explain how you could use the instrumental variable from iv) above to test for the endogeneity of PC in this simple model.Explanation / Answer
1.Because its a linear equation, the error in one term gets propogated to other
if suppose its u1 instead of u then then corresponding gpa may be high or low and people evaluate the ownership to be useful.but if by chance if GPA decreases,people will fault the ownership
2.Yes
in these frameworks in which the linear regression model can be cast in order to make the OLS technique applicable. Each of these settings produces the same formulas and same results, the only difference is the interpretation and the assumptions which have to be imposed in order for the method to give meaningful results. The choice of the applicable framework depends mostly on the nature of data at hand, and on the inference task which has to be performed.
3.Because if the parents have some spare cash to buy their children they would gift them a PC and the value wold be 1,rather for poor parents who have other things to ponder upon,they couldn't afford the PC,hence the parents income would be a Instrumental factor
4.The dataset would become half of the initial and now PC value would be set to one and OLS technique would be applied to judge the usage and GPA criteria
5. since pc is set to 1,Test is used to determine whether or not one of the explanatory variables in a regression suffers from endogeneity (omitted variable biased, measurement error, or reverse causality). Estimating the returns to GPA in the form of PC can be overestimated if one does not take into account that there can be omitted variables such as unobserved ability that can be inflating the education coefficient in the regression.