Econometrics Homework 4 Solutions Computer Question (Optional, no need to hand in) (a) c i may capture some state-specific factor that contributes to higher or low rate of accident or fatality. For example, geographical feature, culture in driving, etc. (b) Pooled OLS with clustered standard errors.. reg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 lnincome age yr1984 yr1997, vce(robust) Linear regression Number of obs = 556 F( 21, 534) = 34.73 R squared = 0.5679 Root MSE =.00337 sb_useage.0045798.0013516 3.39 0.001.0019247.0072349 speed65.0002029.0005631 0.36 0.719.0009033.0013092 speed70.0019266.0005544 3.47 0.001.0008374.0030158 ba08.001981.0003625 5.47 0.000.0026931.001269 drinkage21.0005615.0010652 0.53 0.598.002654.0015309 lnincome.0184.0013082 14.07 0.000.0209698.0158302 age.0000179.0001694 0.11 0.916.0003506.0003148 yr1984.0032855.0015651 2.10 0.036.000211.00636 yr1985.0037588.0016269 2.31 0.021.000563.0069547 yr1986.004711.0016913 2.79 0.006.0013885.0080334 yr1987.0044055.0018591 2.37 0.018.0007534.0080575 yr1988.0048785.0019334 2.52 0.012.0010806.0086764 yr1989.003858.0018718 2.06 0.040.0001809.007535 yr1990.0048058.0019123 2.51 0.012.0010492.0085623 yr1991.0037004.0019337 1.91 0.056.0000981.007499 yr1992.0029305.0019717 1.49 0.138.0009427.0068037 yr1993.003368.0019972 1.69 0.092.0005554.0072914 yr1994.0037277.0020124 1.85 0.065.0002255.0076808 yr1995.0039587.0021007 1.88 0.060.0001679.0080854 yr1996.0044151.0020994 2.10 0.036.0002909.0085393 yr1997.0050835.0021389 2.38 0.018.0008819.0092851 _cons.1957515.0122827 15.94 0.000.1716231.2198799 The seat belt usage here has a positive effect on fatality, which is not as expected. We expect seat belt can save the driver and passengers even when there are accidents. Higher speed limit (the base group has a 55mph limit.) leads to a higher fatality, which make sense, as lower speed can reduce the impact of accidents. A lower blood alchohol limit (missing group is a higher blood alcohol level is 0.1.) is related to a lower fatality, which also makes sense because alcohol reduces the ability of judgement for drivers, which increases number of accidents. A higher legal drinking age is associated to a lower fatality rate, which also makes sense, though the coeffi cient is not significantly different from zero. States with higher income is associated with a lower fatality rate, which makes sense, as richer states may have better roads, or cars better maintained or with better safety measures, or with people driving more carefully. The age effect is not significant and close to zero (it the average age of a state, which has little variation across states). The year dummies 1
generally involves small coeffi cients, and there is no clear trend over the decade. (c) Random Effect Estimator:. *Random effect model. xtreg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 lnincome age yr1984 yr1997, re vce(robust) Random effects GLS regression Number of obs = 556 Group variable: fips Number of groups = 51 R sq: within = 0.7376 Obs per group: min = 8 between = 0.2761 avg = 10.9 overall = 0.4521 max = 15 Wald chi2(21) = 1148.23 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 (Std. Err. adjusted for 51 clusters in fips) fatalityrate Coef. Std. Err. z P> z [95% Conf. Interval] sb_useage.0030776.0015007 2.05 0.040.0060189.0001363 speed65.0009825.0006319 1.55 0.120.002221.000256 speed70.0007266.0004319 1.68 0.092.0001199.0015731 ba08.0011603.0003748 3.10 0.002.0018948.0004257 drinkage21.0007095.000573 1.24 0.216.0018327.0004136 lnincome.0093569.0041158 2.27 0.023.0174237.0012901 age.0002356.0005193 0.45 0.650.0007822.0012534 yr1984.0012335.0011133 1.11 0.268.0009486.0034155 yr1985.0015175.0012717 1.19 0.233.000975.0040099 yr1986.0028411.001364 2.08 0.037.0001677.0055145 yr1987.0036311.001633 2.22 0.026.0004305.0068316 yr1988.0037392.0018478 2.02 0.043.0001176.0073609 yr1989.0025717.0020652 1.25 0.213.0014759.0066194 yr1990.0024855.0021993 1.13 0.258.0018249.006796 yr1991.0016075.0023077 0.70 0.486.0029155.0061305 yr1992.0006467.0024266 0.27 0.790.0041094.0054028 yr1993.0009072.0025183 0.36 0.719.0040286.0058431 yr1994.0010045.0027394 0.37 0.714.0043647.0063737 yr1995.0013854.0029253 0.47 0.636.0043481.0071189 yr1996.0013555.003066 0.44 0.658.0046537.0073647 yr1997.0016532.0032724 0.51 0.613.0047607.008067 _cons.1051933.0374545 2.81 0.005.0317839.1786028 sigma_u.00310665 sigma_e.00161752 rho.78672599 (fraction of variance due to u_i) The most notable change is the coeffi cient on seat belt usage, from positive to negative, and marginally significant. Coeffi cient on speed65 has also become negative, but still insignificant. The effect of age has changed sign, but it is still very small. (d) Fixed Effect Estimator: 2
. xtreg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 lnincome age yr1984 yr1997, fe vce(robust) Fixed effects (within) regression Number of obs = 556 Group variable: fips Number of groups = 51 R sq: within = 0.7506 Obs per group: min = 8 between = 0.1139 avg = 10.9 overall = 0.0338 max = 15 F(21,50) = 52.30 corr(u_i, Xb) = 0.5086 (Std. Err. adjusted for 51 clusters in fips) sb_useage.0037186.0014515 2.56 0.013.0066339.0008032 speed65.0007833.0005801 1.35 0.183.0019484.0003818 speed70.0008042.0004572 1.76 0.085.0001142.0017225 ba08.0008225.0004433 1.86 0.069.0017128.0000678 drinkage21.0011337.0006221 1.82 0.074.0023831.0001158 lnincome.0062643.0066992 0.94 0.354.0071913.01972 age.001318.0006937 1.90 0.063.0000753.0027114 yr1984.0004319.001378 0.31 0.755.0031998.002336 yr1985.0010707.0017641 0.61 0.547.004614.0024726 yr1986.0005777.0020078 0.29 0.775.0046106.0034551 yr1987.0008722.0024939 0.35 0.728.0058813.0041368 yr1988.001885.002877 0.66 0.515.0076636.0038936 yr1989.0041766.0032564 1.28 0.206.0107172.0023641 yr1990.005266.0035402 1.49 0.143.0123767.0018448 yr1991.0066622.0037593 1.77 0.082.0142131.0008886 yr1992.008518.0039855 2.14 0.037.0165232.0005128 yr1993.0089399.004199 2.13 0.038.0173738.000506 yr1994.0096297.0045934 2.10 0.041.0188559.0004035 yr1995.0101123.0048961 2.07 0.044.0199464.0002782 yr1996.0110766.0052089 2.13 0.038.0215389.0006142 yr1997.0116075.0055341 2.10 0.041.0227231.0004919 _cons.0779904.0663611 1.18 0.245.2112805.0552998 sigma_u.00575371 sigma_e.00161752 rho.92675648 (fraction of variance due to u_i) In terms of order of magnitudes, the random effect and fixed effect models are similar and again seatbelt usage has a negative effect on fatality. However, the effect of income now becomes positive and insignificant, while age is positive and significant. (e) Here we test all the time varying variables:. *first generate the means. egen sb_usem=mean(sb_useage), by(fips). egen speed65m=mean(speed65), by(fips). egen speed70m=mean(speed70), by(fips). egen ba08m=mean(ba08), by(fips). egen drinkm=mean(drinkage21), by(fips). egen lnincm=mean(lnincome), by(fips). egen agem=mean(age), by(fips) 3
. xtreg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 lnincome age yr1984 yr1997 sb_usem agem, re vce(robust) Random effects GLS regression Number of obs = 556 Group variable: fips Number of groups = 51 R sq: within = 0.7506 Obs per group: min = 8 between = 0.5441 avg = 10.9 overall = 0.6206 max = 15 Wald chi2(28) = 1293.30 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 (Std. Err. adjusted for 51 clusters in fips) fatalityrate Coef. Std. Err. z P> z [95% Conf. Interval] sb_useage.0036794.0014634 2.51 0.012.0065476.0008111 speed65.0007732.0005808 1.33 0.183.0019117.0003652 speed70.0008026.000459 1.75 0.080.000097.0017022 ba08.0008184.0004446 1.84 0.066.0016897.0000529 drinkage21.0011352.0006323 1.80 0.073.0023745.000104 lnincome.0062112.0063844 0.97 0.331.006302.0187243 age.001349.00068 1.98 0.047.0000162.0026817 yr1984.0004117.0013856 0.30 0.766.0031274.002304 yr1985.0010593.0017642 0.60 0.548.0045171.0023984 yr1986.0005755.0019916 0.29 0.773.004479.003328 yr1987.000891.0024551 0.36 0.717.0057029.0039209 yr1988.0019024.0028145 0.68 0.499.0074186.0036139 yr1989.0042006.0031721 1.32 0.185.0104178.0020165 yr1990.005289.0034377 1.54 0.124.0120268.0014488 yr1991.0066889.0036448 1.84 0.066.0138325.0004547 yr1992.008548.0038626 2.21 0.027.0161184.0009775 yr1993.0089729.0040654 2.21 0.027.016941.0010048 yr1994.0096658.0044412 2.18 0.030.0183704.0009613 yr1995.0101516.004732 2.15 0.032.0194262.0008771 yr1996.0111185.0050303 2.21 0.027.0209777.0012592 yr1997.0116522.0053424 2.18 0.029.0221232.0011812 sb_usem.0136737.0037679 3.63 0.000.0062888.0210586 speed65m.0027627.0021271 1.30 0.194.0014062.0069316 speed70m.0056357.005749 0.98 0.327.005632.0169034 ba08m.0029648.0018393 1.61 0.107.0065697.0006401 drinkm.0006738.0041371 0.16 0.871.0074347.0087823 lnincm.0239093.0061603 3.88 0.000.0359833.0118353 agem.0014076.0006089 2.31 0.021.002601.0002142 _cons.1948447.0346721 5.62 0.000.1268887.2628007 sigma_u.00307437 sigma_e.00161752 rho.78319974 (fraction of variance due to u_i). test sb_usem speed65m speed70m ba08m drinkm lnincm agem ( 1) sb_usem = 0 ( 2) speed65m = 0 ( 3) speed70m = 0 ( 4) ba08m = 0 ( 5) drinkm = 0 ( 6) lnincm = 0 ( 7) agem = 0 chi2( 7) = 37.07 Prob > chi2 = 0.0000 So, we reject the null that c i and regressors are uncorrelated, and we should use fixed effect. (f) Here I use the fixed effect specification. 4
( 1) yr1984 = 0 ( 2) yr1985 = 0 ( 3) yr1986 = 0 ( 4) yr1987 = 0 ( 5) yr1988 = 0 ( 6) yr1989 = 0 ( 7) yr1990 = 0 ( 8) yr1991 = 0 ( 9) yr1992 = 0 (10) yr1993 = 0 (11) yr1994 = 0 (12) yr1995 = 0 (13) yr1996 = 0 (14) yr1997 = 0 F( 14, 50) = 9.82 So we reject the null that there is no time effect. (g). reg d.fatalityrate d.sb_useage d.speed65 d.speed70 d.ba08 d.drinkage21 d.lnincome d.age yr1984 yr1997, vce(robust) noc Linear regression Number of obs = 497 F( 21, 476) = 6.30 R squared = 0.2343 Root MSE =.00174 D. sb_useage D1..0026035.0012698 2.05 0.041.0050986.0001084 speed65 D1..0004715.0005128 0.92 0.358.0005361.0014792 speed70 D1..0000269.0003734 0.07 0.943.0007068.0007606 ba08 D1..0002792.0003967 0.70 0.482.0010587.0005003 drinkage21 D1..0010048.0005709 1.76 0.079.0021266.000117 lnincome D1..0112131.0061541 1.82 0.069.0008795.0233056 age D1..0018264.0012464 1.47 0.143.0006227.0042755 yr1984.0014063.0011957 1.18 0.240.0037559.0009432 yr1985.0019675.0006068 3.24 0.001.0031598.0007752 yr1986.0001575.000565 0.28 0.781.0009528.0012677 yr1987.0016881.0006983 2.42 0.016.0030603.0003159 yr1988.0017077.0005591 3.05 0.002.0028062.0006092 yr1989.002627.0005816 4.52 0.000.0037699.0014842 yr1990.0016663.0004864 3.43 0.001.002622.0007105 yr1991.001701.0003556 4.78 0.000.0023998.0010022 yr1992.0022125.0004291 5.16 0.000.0030556.0013694 yr1993.0007109.0003267 2.18 0.030.0013528.0000689 yr1994.0010295.0003975 2.59 0.010.0018106.0002485 yr1995.0005935.0003941 1.51 0.133.0013679.0001808 yr1996.0012865.0004066 3.16 0.002.0020856.0004875 yr1997.0008694.0003739 2.33 0.020.0016041.0001347 5
. *use difference in year dummies too. reg d.fatalityrate d.sb_useage d.speed65 d.speed70 d.ba08 d.drinkage21 d.lnincome d.age d.yr1984 d.yr1985 d.yr1986 d.y > r1987 d.yr1988 d.yr1989 d.yr1990 d.yr1991 d.yr1992 d.yr1993 d.yr1994 d.yr1995 d.yr1996 d.yr1997, vce(robust) noc Linear regression Number of obs = 497 F( 21, 476) = 6.30 R squared = 0.2343 Root MSE =.00174 D. sb_useage D1..0026035.0012698 2.05 0.041.0050986.0001084 speed65 D1..0004715.0005128 0.92 0.358.0005361.0014792 speed70 D1..0000269.0003734 0.07 0.943.0007068.0007606 ba08 D1..0002792.0003967 0.70 0.482.0010587.0005003 drinkage21 D1..0010048.0005709 1.76 0.079.0021266.000117 lnincome D1..0112131.0061541 1.82 0.069.0008795.0233056 age D1..0018264.0012464 1.47 0.143.0006227.0042755 yr1984 D1..0014063.0011957 1.18 0.240.0037559.0009432 yr1985 D1..0033738.0014915 2.26 0.024.0063046.0004431 yr1986 D1..0032164.0018058 1.78 0.076.0067647.0003319 yr1987 D1..0049045.0021944 2.23 0.026.0092165.0005925 yr1988 D1..0066122.0025908 2.55 0.011.011703.0015213 yr1989 D1..0092392.0030107 3.07 0.002.015155.0033234 yr1990 D1..0109055.0033457 3.26 0.001.0174798.0043312 yr1991 D1..0126065.0035386 3.56 0.000.0195597.0056533 yr1992 D1..014819.0038478 3.85 0.000.0223798.0072582 yr1993 D1..0155298.0040818 3.80 0.000.0235503.0075093 yr1994 D1..0165594.0043401 3.82 0.000.0250875.0080313 yr1995 D1..0171529.0046398 3.70 0.000.0262699.0080359 yr1996 D1..0184395.0049572 3.72 0.000.0281802.0086987 yr1997 D1..0193089.0052399 3.68 0.000.0296051.0090127 The result is similar to Fixed effect estimator. (h) Using FE or FD estimator, it is found that seat belt, lower speed limit, lower alcohol allowance, higher minimum drinking age can reduce fatality rate. (i) Using fixed effect estimates, this means we increase sb_usage from 0.52 to 0.90, the fatality rate then decreases by (0.90 0.52)(.0037186) = 1.413 1 10 3. If there are 50000 million miles travelled per year, then the number of death reduced is 1.413 1 10 3 50000 71. This question is taken from Stock and Watson textbook. It comes from the paper Cohen and Einav (2003) "The Effect of Mandatory Seat Belt Laws on Driving Behavior and Traffi c Fatality" The Review of Economics and Statistics, 85(4): 828-843. 6