Question

The cost of attending your college has once again gone up. Although you have been told that education is a good investment in human capital, which carries a return of roughly 10% a year, you (and your parents) are not pleased. One of the administrators at your university/college does not make the situation better by telling you that you pay more because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data randomly for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual rankings. Next you perform the following regression Cost7,711.17+2,985.20x Reputation-0.21x Size (1,058.63) (564.58) (0.12) + 9,406.79x Dpriv - 718.38x Dlibart 2,871.51x Dreligion (3,754.85) (1,123.92) (1,107.86) R=072 where Cost is Tuition, Fees, Room and Board in dollars, Reputation is the index used in U.S News and World Report (based on a survey of university presidents and chief academic officers), which ranges from 1 ("marginal") to 5 ("distinguished"), Size is the number of undergraduate students, and Dpriv, Dlibart, and Dreligion are binary variables indicating whether the institution is private, a liberal arts college, and has a religious affiliation. The numbers in parentheses are heteroskedasticity-robust standard errors. Eliminating the Size and Dlibart variables from your regression, the estimation regression Cost 5,950.35+ 3,798.84x Reputation12,135.70x Dpriv-2,583.31x Dreligion; (1,272.35) (690.49) (975.51) (1,081.57) R-0.72 Why do you think that the effect of attending a private institution has increased now?

Answer 1

Private institutions are smaller, on average, and some of these are liberal arts colleges. Both of these variables had negative coefficients. This is due to omitted variable bias. The ρχυ is negative, because 1. Correlation between private and size is negative (private turns to 1, size decreases) 2. Correlation between cost and size is negative (as size increases, cost decreases) The bias-inducing term is positive, which means the estimated coefficient on private now is being estimated “plus some stuff" The term is too high because of the omitted variable of size messing everything up!