# P1.T2.219. Omitted variable bias

Discussion in 'Today's Daily Questions' started by David Harper CFA FRM, Feb 28, 2012.

1. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

AIMs: Define, interpret, and discuss methods for addressing omitted variable bias. Distinguish between simple and multiple regression. Define and interpret the slope coefficient in a multiple regression.

Questions:﻿

219.1. We regress a stock's returns against a market index according to the following OLS model: Return(i) = B(0) + B(1)*Index(i) + u(i). However, our regression is guilty of omitted variable bias. If our regression indeed suffers from omitted variable bias, which of the following is MOST likely true?

a. The OLS assumption that E[u(i) | X(i)] = 0 is incorrect
b. The OLS assumption that [X(i), Y(i)], i = 1, ..., n are i.i.d. random draws is incorrect
c. The OLS assumption the large outliers are unlikely is incorrect
d. The assumption of no perfect multicollinearity is incorrect

219.2. Our multiple regression model regresses a (dependent) credit score against two (independent) regressors, Leverage and CashFlow. This multivariate OLS model is given by: Score(i) = B(0) + B(1)*Leverage(i) + B(2)*CashFlow(i) + u(i). Next, we omit CashFlow and only use a single regressor according to: Score(i) = B'(0) + B'(1)*Leverage(i) + u(i). Under which of the following conditions will there be omitted variable bias?

a. If Score(i) and Leverage(i) are correlated
b. If Leverage(i) and CashFlow(i) are correlated
c. If CashFlow(i) is a dummy variable
d. If Score(i) is independent of CashFlow(i)

219.3. Data were collected from a random sample of 220 home sales from a community in 2003. Let 'Price' denote the selling price (in $1000), 'BDR' denote the number of bedrooms, 'Bath' denote the number of bathrooms, 'Hsize' denote the size of the house (in square feet), 'Lsize' denote the lot size (in square feet), 'Age' denote the age of the house (in years), and 'Poor' denote a binary variable that is equal to 1 if the condition of the house is reported as “ poor.” An estimated regression yields Price = 119.2 + 0.485*BDR + 23.4*Bath + 0.156*HSize + 0.002*LSize + 0.090*Age - 48.8*Poor Suppose that a homeowner adds a new bathroom to her house, which increases the size of the house by 100 square feet. What is the expected increase in the value of the house? [Source: S&W Question 6.5.b.] a. Zero b.$17,500
c. $28,350 d.$39,000