8 Suppose that average worker productivity at manufacturing firms (avgprod) depe

Question

8 Suppose that average worker productivity at manufacturing firms (avgprod) depends on two factors average hours of training (avgtrain) and average worker ability (avgabil); avgprod-A, + 1avgtrain + 2avgabil + u. Assume that this equation satisfies the Gauss-Markov assumptions. If grants have been given to firms whose workers have less than average ability, so that avgtrain and avgabil are negatively correlated, what is the likely bias in obtained from the simple regression of avgprodon avgtran?

Explanation / Answer

for the simple regression :

beta1(avgtrain) + beta2(avgabil) + betao + u = avgprod.

now since the relation between training and worker ability is of simple regression so ,

we could use the linear interpolation in the above equation

here betao and u are the constraints that act as the y intercept ,

and , beta1(avgtrain) and beta2(avgabil) are the independent variables and avgprod is the dependent variable.

so [beta1(avgtrain) + beta2(avgabil)] = avgprod - (betao + u)

beta1(avgtrain) = avgprod - (betao + u) - beta2(avgabil)

or beta1 = [avgprod - (betao + u) - beta2(avgabil)]/avgtrain

and for that above equation the Gauss - Markov assumption is valid as well

here the expected value of 'u' is 0 , u represents the error

=> beta1 = [avgprod - (betao) - beta2(avgabil)]/avgtrain

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