Econometrics 1. Consider the regression model of: murderrate t = 0 + 1 policebud

Question

Econometrics

1. Consider the regression model of:

murderratet = 0 + 1policebudgett + t

where murderratet is the annual murder rate in Fresno in year t, policebudgett is the annual police budget in Bakersfield. The data set available has one observation for each of the last 40 years.

(a) What assumptions must hold for OLS to give an unbiased estimate of the 1,the structural effect of increasing the police budget on the murder rate?

****Which of these assumptions (of part a) is most likely violated if policebudgett, depends onmurderratet-1?

(b) What assumptions must hold for OLS to give a consistent estimate of the 1, the structural effect of increasing the police budget on the murder rate?

*******Which of these assumptions (of part b) is most likely violated if policebudgett, depends onmurderratet-1?

Explanation / Answer

Consider the regression model of:

murderratet = 0 + 1policebudgett + t

Where, murederrate is dependent variable and police budget is independent variable.

Assumptions must hold for OLS to give an unbiased estimate of the 1:

i) (Xi , Yi); i = 1, ..., n is a random sample of size n from the population.

ii) j and k such that Xj Xk .

If all the Xi in the sample take the same value, the slope parameter 1 cannot be identified

iii) The average value of the error term is 0.

iv) Conditional mean is 0.

If these four assumptions are verified then E(0^) = 0 and E(1^) = 1

The OLS estimators are unbiased estimators of the parameters.

Assumptions must hold for OLS to give a consistent estimate of the 1,

Assumptions:

If these assumptions are met, OLS gives us an unbiased and consistent estimate of 1, the slope and 0, the intercept of regression.

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