Assignment 5 13.04.32 - ECONOMETRICS 30C00200 Fall 2013 EXERCISES 5 DATE 14.10.2013 NAME STUDENT NUMBER Pham Quoc Bao 362683 Mark here the problems you

# Assignment 5 13.04.32 - ECONOMETRICS 30C00200 Fall 2013...

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ECONOMETRICS 30C00200 Fall 2013 EXERCISES 5 DATE 14.10.2013 NAME STUDENT NUMBER Pham Quoc Bao 362683 Mark here the problems you have done 1 2 3 4 5 x x x x x x x x x x x x
Problem 1: Since we have identified that there is a variable regarding the ability of worker omitted, therefore, its effect is left within the error term u. The true model should be: Log(wage) = βo + ´ β 1train + ´ β 2educ + ´ β 3exper + ´ β 4abil + v (1) The error term in the omitted model: u = ´ β 4abil + v Moreover, the omitted variable is also correlated with the dummy variable “train” => the estimated coefficient β1 from the omitted model can be derived as: β1 = ´ β 1 + ´ β 4δ1 where ´ β 1 and ´ β 4 are unbiased coefficient that can be obtained from the true model (1) and δ1 can be obtain from the regression of the variable “abil” on other explanatory variables(in this case, δ1 is the slope of “train” in the regression of “abil” on other explanatory variables) E( β1) = E( ´ β 1 + ´ β 4 δ 1 ¿ = E ( ´ β 1 ) + E ( ´ β 4 ) δ 1 = ´ β 1 + ´ β 4 δ 1 => This implies the bias of β1 is ´ β 4 δ 1 Problem 2: a/ (1) EARNINGS = -12.62 + 2.365 S (2) EARNINGS = -20.53 + 1.77S + 0.31ASVABC The estimate coefficient for S in the second model is smaller than that of the first model because there is correlation between S and ASVABC. Therefore, when ASVABC is omitted in the first model, part of its effect has been transferred to the estimate coefficient of S. ASVABC can be a proxy variable for S (Schooling) since there is a positive correlation between them i.e. a good score on cognitive tests may demonstrate a high schooling.

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