ECMT 676 Assignment #1 March 18, and x. are unknown? - Run the following regression: directly? What if μ1

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Sheryl Nelson
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1 ECMT 676 Assignment #1 March 18, (Average Partial Effect) (, ) = β + β + β + β + β E y x x x x x x x a. Average Partial Effect(APE) of x1 and x - APE of x 1 : - APE of x : (, ) E y x x = β + β = β + β μ α1 1 E E[ 1 3x] 1 3 x1 (, ) E y x x β + β + β = β + β μ + β μ α 1 E = E[ 3x1 4x x b. Rewrite the regression function in terms of α 1 and α - Let β1 = α1 β3μ and β = α β3μ1 β4μ (, ) ( ) ( ) E y x x = β + α β μ x + α β μ β μ x + β x x + β x = α + α x + α x + β x x + β x ( )( ) ( ) = β0 + α1x1+ αx + β3 x1 μ1 x μ μ1μ + β4 x μ μ = and x1, xare de-mean variables. - where α0 ( β0 β3μ1μ β4μ) c. How to estimate α1 and α directly? What if μ1 and μ are unknown? - Run the following regression: y == α + α x + α x + β x x + β x + u If the population mean is unknown, replace it with sample mean: ˆ μ ˆ 1, μ d. Use NLS80.RAW (1) y = β + β x + β x + β x x + β x +u educ exper educ_exper

2 exper_sq _cons () y == α + α x + α x + β x x + β x + u educ exper educ_exper_dm exper_sq_dm _cons Estimates for β3 and β4 are identical in both regressions. - In Equation, we have smaller std. error for coefficient of x 1 and x 4.11 (Unobserved variable: Ability) a. KWW and IQ as proxies for ability Variable eq1 eq eq exper tenure married south urban black educ iq kww _cons If we consider individual's ability in wage equation, the return on education decreases. b. Joint Significance of KWW and IQ - Null-Hyopothesis H : 0 0 β = β = KWW IQ - F(,95)=8.1 (Prob>F=0.0003) : Reject H at 1% significance level

3 c. Wage differential between nonblacks and blacks? - The wage differential between nonblacks and blacks does not disappear after controlling KWW and IQ (eq 3) - Blacks earn less wage by 13% on average. d. Add the interactions: educ(iq-100), educ(kww-kww) exper tenure married south urban black educ iq kww educ_iq_dm educ_kww_dm _cons Null-Hyopothesis H0 : β ( 100) = β = 0 educ IQ educ( KWW KWW ) - F =4.48 (Prob>F=0.0116): Reject H0 at 5% significance level - Coefficient for IQ is no longer significant, and KWW has a negative effect on wage. - Coefficient for educ(iq-100) is not significant, and we could drop out the variable. e. Use KWW as IV for IQ, and use IQ as IV for KWW use IQ as IV for KWW kww exper tenure married south urban black

4 educ _cons Instrumented: kww Instruments: exper tenure married south urban black educ iq use KWW as IV for IQ iq exper tenure married south urban black educ _cons Instrumented: iq Instruments: exper tenure married south urban black educ kww 4.1 (Effect of Job Training Grant) a. Effects of Job training grants log scrap = β + β grant+ β union + γq + u ( ) Hypothesis: The average scrap rate should be lower among firms received a grant - Use log(scarp₁) as a proxy variable for unobserved productivity factor q q= θ0 + θ1log( scrap 1) +v

5 Variable eq1 eq eq3 eq grant lscrap_ union _cons After controlling union variable, job-training grants is more effective (Attendance and Student s performance) a. Effects of attending lecture on performance atndrte frosh soph _cons % increase in attendance rate has positive effect on final exam score by b. Causal effect of attendance? - Some Unobservable variables, like students ability, affect the final score. - Causal effect of attendance (β₁) could be biased. c. Use prigpa and ACT as proxy for student ability atndrte frosh soph prigpa

6 ACT _cons Including proxy varibles decrease the marginal effect from atndrte by (- 38%) d. Significance of dummy variables frosh, soph - Whether the student is a freshmen or not is a significant factor in (c) - β₃ becomes more significant (t-value is -1.79) e. Add the squres of prigpa and ACT to the equation. - H0: β3=β0=0: Reject the null F=11.77 atndrte frosh soph prigpa prigpa_sq ACT ACT_sq _cons f. To test for a nonlinear effect of antdrte, add its square to the equation from (e) atndrte atndrte_sq.87e frosh soph prigpa prigpa_sq ACT ACT_sq _cons t-value for β is only atndrte² has no effect on test score - atndrte and atndrte² is jointly significant, since F= 3.83 and its p-value 0.0

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