Omission of a variable in the K-variable regression model. Refer to Eq. (13.3.3), which shows the bias
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Omission of a variable in the K-variable regression model. Refer to Eq. (13.3.3), which shows the bias in omitting the variable X3 from the model Yi = β1+β2X2i + β3X3i + ui . This can be generalized as follows: In the k-variable model Yi = β1 + β2X2i + · · ·+βk Xki + ui , suppose we omit the variable Xk . Then it can be shown that the omitted variable bias of the slope coefficient of included variable Xj is:
E(β̂j ) = βj + βkbkj = 2, 3, . . . , (k − 1)
where bkj is the (partial) slope coefficient of Xj in the auxiliary regression of the excluded variable Xk on all the explanatory variables included in the model.*
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