Omitted Variable Bias: The Simple Case - Hedibert

Omitted Variable Bias: The Simple Case1 / 8 IngredientesSuppose that we omit a Variable that actually belongs in thetrue (or population) is often called the problem of excluding a relevantvariable or under-specifying the problem generally causes the OLS estimators to the bias caused by omitting an important variableis an example of misspecification / 8 Let us begin assuming that the true population model isy= 0+ 1x1+ 2x2+uand that this model satisfies Assumptions interest: 1, the partial effect :yis log of hourly wage,x1is education, andx2is a measure of innate ability. To get an unbiased estimatorof 1, we should run a regression ofyonx1andx2(whichgives unbiased estimators of 0, 1and 2).However, due to our ignorance or data unavailability, weestimate the model by / 8In other words, we perform a Simple regression ofyonx1only, obtaining the equation y= 0+ 1x1We use the symbol rather than to emphasize that 1comes from an underspecified / 8We can derive the algebraic relationship 1= 1+ 2 where 1and 2are the slope estimators (if we could havethem) from th

It is easy to see that Bias( ~ 1) = 0 when 1 2 = 0 The omitted variable x 2 is not in the \true" model. 2 ~ = 0 Recall that ~ is the slope from the simple regression x i2 on x i1 i= 1;:::;n; which is directly related to the correlation between x

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  Variable, Bias, Omitted, Omitted variable bias, Omitted variable

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