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260 Chapter 6 Linear Regression with Multiple Regressors

b. Run a regression of Growth on TradeShare, YearsSchool, Rev_Coups,
Assassinations, and RGDP60. What is the value of the coefficient on
Rev_Coups? Interpret the value of this coefficient. Is it large or small
in a real-world sense?

c. Use the regression to predict the average annual growth rate for a
country that has average values for all regressors.

d. Repeat (c) but now assume that the country’s value for TradeShare is
one standard deviation above the mean.

e. Why is Oil omitted from the regression? What would happen if it
were included?

Appendix

6.1 Derivation of Equation (6.1)

This appendix presents a derivation of the formula for omitted variable bias in Equation (6.1).
Equation (4.30) in Appendix (4.3) states

bn1 + n1 n - X )ui
- . (6.16)
= b1 ia= 1(Xi
n X)2
1 (Xi
n a
i=1

Under the last two assumptions in Key Concept 4.3, (1 > n) g n 1(Xi - X )2 ¡p sX2 and
i=
n ¡p
(1 > n) g i= 1(Xi - X )ui cov(ui, Xi) = rXususX. Substitution of these limits into Equa-

tion (6.16) yields Equation (6.1).

Appendix

6.2 Distribution of the OLS Estimators

When There Are Two Regressors and
Homoskedastic Errors

Although the general formula for the variance of the OLS estimators in multiple regression is
complicated, if there are two regressors (k = 2) and the errors are homoskedastic, then the
formula simplifies enough to provide some insights into the distribution of the OLS estimators.