Ecmt 675: Econometrics I

Transcription

1 Ecmt 675: Econometrics I Assignment 7 Problem 1 a. reg hours lwage educ age kidslt6 kidsge6 nwifeinc, r Linear regression Number of obs = 428 F( 6, 421) = 3.93 Prob > F = R-squared = Root MSE = hours Coef. Std. Err. t P> t [95% Conf. Interval] lwage educ age kidslt kidsge nwifeinc _cons ivreg hours (lwage=exper expersq) educ age kidslt6 kidsge6 nwifeinc, r Instrumental variables (2SLS) regression Number of obs = 428 F( 6, 421) = 2.53 Prob > F = R-squared =. Root MSE = hours Coef. Std. Err. t P> t [95% Conf. Interval] lwage educ age kidslt kidsge nwifeinc

2 _cons Instrumented: lwage Instruments: educ age kidslt6 kidsge6 nwifeinc exper expersq We can find that the coefficient on lwage is positive in 2SLS regression. b. reg lwage hours educ exper expersq, r Linear regression Number of obs = 428 F( 4, 423) = R-squared = Root MSE =.6659 lwage Coef. Std. Err. t P> t [95% Conf. Interval] hours educ exper expersq _cons ivreg lwage (hours=age kidslt6 kidsge6 nwifeinc) educ exper expersq, r Instrumental variables (2SLS) regression Number of obs = 428 F( 4, 423) = R-squared = Root MSE = lwage Coef. Std. Err. t P> t [95% Conf. Interval] hours educ exper expersq _cons Instrumented: hours Instruments: educ exper expersq age kidslt6 kidsge6 nwifeinc c. reg hours lwage educ exper expersq, r 2

3 Linear regression Number of obs = 428 F( 4, 423) = R-squared = Root MSE = hours Coef. Std. Err. t P> t [95% Conf. Interval] lwage educ exper expersq _cons ivreg hours (lwage=age kidslt6 kidsge6 nwifeinc) educ exper expersq, r Instrumental variables (2SLS) regression Number of obs = 428 F( 4, 423) = 6.12 Prob > F = R-squared =. Root MSE = hours Coef. Std. Err. t P> t [95% Conf. Interval] lwage educ exper expersq _cons Instrumented: lwage Instruments: educ exper expersq age kidslt6 kidsge6 nwifeinc We can see the coefficients are not significant because those exogenous variables would not seem to appear in the reduced model. d (9.9) a.. reg3 (hours lwage educ age kidslt6 kidsge6 nwifeinc) (lwage hours educ exper expersq) Three-stage least-squares regression Equation Obs Parms RMSE "R-sq" chi2 P hours

4 lwage Coef. Std. Err. z P> z [95% Conf. Interval] hours lwage educ age kidslt kidsge nwifeinc _cons lwage hours educ exper expersq _cons Endogenous variables: hours lwage Exogenous variables: educ age kidslt6 kidsge6 nwifeinc exper expersq d (9.9) b.. gen educ_exog=educ. reg3 (hours lwage educ_exog age kidslt6 kidsge6 nwifeinc) (lwage hours educ exper expersq) (educ motheduc fatheduc huseduc) Three-stage least-squares regression Equation Obs Parms RMSE "R-sq" chi2 P hours lwage educ Coef. Std. Err. z P> z [95% Conf. Interval] hours lwage educ_exog age kidslt kidsge nwifeinc _cons lwage 4

5 hours educ exper expersq _cons educ motheduc fatheduc huseduc _cons Endogenous variables: hours lwage educ Exogenous variables: educ_exog age kidslt6 kidsge6 nwifeinc exper expersq motheduc fatheduc huseduc Problem 2 (9.8) a.. reg educ2 nearc4_exper nearc4_expersq nearc4_black nearc4_south nearc4_reg661 nearc4_reg662 nearc4_reg663 nearc4_reg664 nearc4_reg665 nearc4_reg666 nearc4_reg667 nearc4_reg668 nearc4_smsa66 nearc4_smsa, r Linear regression Number of obs = 3010 F( 14, 2995) = R-squared = Root MSE = educ2 Coef. Std. Err. t P> t [95% Conf. Interval] nearc4_exper nearc4_exp~q nearc4_black nearc4_south nearc4_r~ nearc4_r~ nearc4_r~ nearc4_r~ nearc4_r~ nearc4_r~ nearc4_r~ nearc4_r~ nearc4_sm~ nearc4_smsa _cons test nearc4_exper nearc4_expersq nearc4_black nearc4_south nearc4_reg661 nearc4_reg662 nearc4_reg663 nearc4_reg664 nearc4_reg665 nearc4_reg666 nearc4_reg667 nearc4_reg668 nearc4_smsa66 nearc4_smsa 5

6 ( 1) ( 2) nearc4_exper = 0 nearc4_expersq = 0 ( 3) nearc4_black = 0 ( 4) nearc4_south = 0 ( 5) nearc4_reg661 = 0 ( 6) ( 7) nearc4_reg662 = 0 nearc4_reg663 = 0 ( 8) nearc4_reg664 = 0 ( 9) (10) nearc4_reg665 = 0 nearc4_reg666 = 0 (11) nearc4_reg667 = 0 (12) nearc4_reg668 = 0 (13) nearc4_smsa66 = 0 (14) nearc4_smsa = 0 F( 14, 2995) = Prob > F = Significant!. ivreg lwage (educ educ2=nearc4_exper nearc4_expersq nearc4_black nearc4_south nearc4_reg661-nearc4_reg668 nearc4_smsa66 nearc4_smsa) exper expersq black south smsa smsa66 reg661-reg668, r Instrumental variables (2SLS) regression Number of obs = 3010 F( 16, 2993) = R-squared = Root MSE = lwage Coef. Std. Err. t P> t [95% Conf. Interval] educ educ exper expersq black south smsa smsa reg reg reg663 reg reg665 reg reg reg _cons Instrumented: educ educ2 6

7 Instruments: exper expersq black south smsa smsa66 reg661 reg662 reg663 reg664 reg665 reg666 reg667 reg668 nearc4_exper nearc4_expersq nearc4_black nearc4_south nearc4_reg661 nearc4_reg662 nearc4_reg663 nearc4_reg664 nearc4_reg665 nearc4_reg666 nearc4_reg667 nearc4_reg668 nearc4_smsa66 nearc4_smsa. test educ2 ( 1) educ2 = 0 F( 1, 2993) = 2.38 Prob > F = We can see that educ2 is not significant; therefore, we can omit it. b. If educ is the endogenous variable, black educ is also the endogenous variable. However, black is exogenous here; therefore, we can use black z j as the instrumental variables for black educ. black z j are correlated with black educ; also,black z j are the exogenous variables. c.. ivreg lwage (educ black_educ=nearc4 black_educ_hat) black exper expersq smsa smsa66 south reg661-reg668, r Instrumental variables (2SLS) regression Number of obs = 3010 F( 16, 2993) = R-squared = Root MSE = lwage Coef. Std. Err. t P> t [95% Conf. Interval] educ black_educ black exper expersq smsa smsa south reg reg

8 reg663 reg reg reg666 reg reg _cons Instrumented: educ black_educ Instruments: black exper expersq smsa smsa66 south reg661 reg662 reg663 reg664 reg665 reg666 reg667 reg668 nearc4 black_educ_hat We can find that the coefficient on black educ becomes more significant than that in Example 6.2. d. Intuitively, if we have larger F-value in the first stage regression, then we would get more efficient 2SLS estimators. We also can find that the first stage regression is more significant when we use black educ ˆ as the IV. Problem 3 (9.10) a. No, if we estimate the first equation by 2SLS using all exogenous variables (z) as IVs, it means that in the first stage regression we put all the exogenous variables into the regression model. Therefore, we don t impose any restrictions in the second equation. b. If each equation is just identified, 2SLS equation by equation is identical to 3SLS. In this problem, we can easily check that the second equation is overidentified. Therefore, they are not the same. 8

9 c. In 3SLS, we would have more restrictions. If those restrictions are correct, then 3SLS estimators are more efficient. However, if those restrictions are not correct, then we would get the inconsistent estimators. In 2SLS, we always get the consistent estimators. Therefore, we would say that 2SLS is more robust than 3SLS. Problem 4 (10.1) a. Because the investment is likely to be affected by macroeconomic factors over time. b. Something like average country economic climate in different country i. c Larger marginal tax rates might cause less investment; therefore, we expect that δ 1 should be negative. d Because c i might be correlated with the tax rate (tax it ); therefore, we need to use Fixed Effect Model to do that. e Because the natural disaster can not be determined by any factor, the variable disaster is strictly exogenous. However, the government might look at the levels of past investment in determining future tax policy, especially if there 9

10 is a target level of tax revenue they are trying to achieve. Therefore, the variable tax it would not be strictly exogenous. Problem 5 (10.2) a. ln(wage i2 )=θ 1 + θ 2 + z i2 γ + δ 1 female i + δ 2 female i + c i + u i2 t =2 ln(wage i1 )=θ 1 + z i1 γ + δ 1 female i + c i + u i1 t =1 Δln(wage i )=θ 2 +Δz i γ + δ 2 female i +Δu i E[ u it female i,z i1,z i2,c i ]=0 E[ Δu i female i, Δz i ]=0 Therefore, we can get the consistent estimators ˆθ 2,ˆγ, and ˆδ 2. b. θ 2 measures the growth in wage for men over the period. However, δ 2 measures the difference in wage growth rates between women and men. c As shown in part a. d Let Δln(wage i )=θ 2 +Δz i γ + δ 2 female i +Δu i = x i β +Δu i It s easy to show that ˆβ is consistent if E[ Δu i female i, Δz i ]=0 10