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Unformatted text preview: , ( xi , yi ), for i = 1, 2,..., n , from the population model. Thus we can write the sample model as yi = α + β xi + ui for i = 1, 2,..., n . Only a random sample from the population is representative of the
population and can capture the population relationship. Figure: random sample vs nonrandom sample 12 Assumption 3: there is variation in X, i.e., X is not a constant in the sample (a constant is not informative! See figure below) Figure: What would happen if X is a constant? Suppose only observe wages for people who have 16 years of schooling… Assumption 4: mean independence or conditional mean zero: E (u | X ) = 0 Assumption 4 is crucial for unbiased estimates. E (u | X ) = 0 implies that u and
X are uncorrelated (What does this mean?). o One (frequently seen) way Assumption 4 can be violated is when X and u are correlated. If X and u are correlated, meaning they vary together, so E (u | X ) ≠ 0 , and hence the OLS estimator is biased. Example 1: Y = α + β X + u , where Y...
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