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.
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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 1. Does Hormone Replacement Therapy (X) reduce the risk of heart disease (Y)? A longitudinal study follows 10,000 nurses over time, some who elect to receive HRT, some who do not. The data include measures on whether each individual contracts heart disease. 2. Does having access to cheaper health insurance lead to higher expenditures on health care? A large survey asks respondents how much they are required to pay for a variety of medical procedures: X measures the percent of total medical costs that must be paid by the individual (X ranges from O – insurance provides total coverage – to 100 – there’s no insurance coverage). The survey also asks about total yearly expenditures (both those paid by the individual and those paid by insurance) incurred by each person. 3. Does living in a high poverty neighborhood adversely affect the academic achievement of younger students? The test scores (Y) from students in the 3 rd grade in NYC are linked to information about the neighborhoods in which they reside. In particular, data are available on the fraction of poor (incomes below the poverty line) individuals in each students’ neighborhood (census tract).
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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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