Lecture 07

# Lecture 07 - PAM 3300 Regression Analysis Omitted Variable...

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PAM 3300: Regression Analysis

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Omitted Variable Bias In an OLS regression of Y on X, b OLS measures the ‘true’ partial effect of X on Y ( β ) only if X is uncorrelated with the omitted variables that also affect Y (d ε /dX = 0). In observational studies, this is unlikely to be true and so in general, b OLS will be biased. b ols = dY dX = " + #\$ Effect of X on Z Effect of Z on Y If we know something about the signs of the effect of omitted variables on Y ( δ ) and the relationship between X and the omitted variables ( π ) then we can ‘sign the bias’: guess whether it is positive or negative.
OVB - some examples For each of the following examples, think about what biases, if any, might be important in interpreting the results of a simple regression of Y on X. Is the simple regression likely to capture the causal effect of X on Y? What omitted variables do you think are important? What are the signs of the biases, if any, due to omitting each variable (what are you assuming in signing the bias)? On net, can you say whether the simple bivariate regression is likely to overestimate or underestimate the true causal effect (I.e., is the bias positive or negative)?

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OVB - examples (cont.) 4. Does regular exercise reduce the prevalence of obesity? A survey asks a large

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• Fall '08
• MATSUDAIRA
• Regression Analysis, bOLS, Adj R-squared Root, R-squared Root MSE, R-squared Adj R-squared

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