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Unformatted text preview: pact on Y, like in this example, β will have a positive bias (more discussion later). Example 2: Suppose a researcher is interested in the effect of class attendance on GPA, and plans to estimate the following model: colGPA = α + β skipped + u, where colGPA is college GPA, and skipped is the number of classes skipped per week. The researcher believes that a component of u is the students’ inherent laziness. OLS estimate of β will be biased, and in particular, the negative impact will be
Given Assumptions 14, OLS estimators of α , β are unbiased. Example 1: Suppose the true population model is Y = α + β X + u , but you forget to include the constant term in the regression, so you estimate Y = β X + u. It can be n n i =1 i =1 shown that the OLS estimator for β in this case is β = ∑ xi yi / ∑ xi2 . Is it biased? It is biased (how to prove?) if in the true model α ≠ 0 , and it is unbiased if in t...
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