clear
cd "E:\Econ 107\LAB7\data"
use seatbelt.dta\[y_{it}=\alpha + \beta x_{it}+u_{it}\]
gen logincome=ln(income)
reg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 logincome age, robustOutputs:
Linear regression Number of obs = 556
F(7, 548) = 90.96
Prob > F = 0.0000
R-squared = 0.5493
Root MSE = .0034
------------------------------------------------------------------------------
| Robust
fatalityrate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sb_useage | .0040684 .0012323 3.30 0.001 .0016478 .0064889
speed65 | .0001479 .0004076 0.36 0.717 -.0006527 .0009486
speed70 | .0024045 .0004721 5.09 0.000 .0014771 .0033319
ba08 | -.0019246 .0003612 -5.33 0.000 -.002634 -.0012151
drinkage21 | .0000799 .0009872 0.08 0.936 -.0018593 .002019
logincome | -.0181444 .001086 -16.71 0.000 -.0202776 -.0160111
age | -7.22e-06 .0001644 -0.04 0.965 -.0003302 .0003158
_cons | .1965469 .0092503 21.25 0.000 .1783766 .2147172
------------------------------------------------------------------------------The estimated coefficient on seat belt usage is positive. This suggests that seat belt usage leads to an increase in the fatality rate.
\[y_{it}=\alpha_i + \beta x_{it}+u_{it}\]
reg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 logincome age i.fips, robustOutputs:
i.fips _Ifips_1-56 (naturally coded; _Ifips_1 omitted)
Linear regression Number of obs = 556
F(57, 498) = 90.12
Prob > F = 0.0000
R-squared = 0.8867
Root MSE = .00179
------------------------------------------------------------------------------
| Robust
fatalityrate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sb_useage | -.0057748 .0013175 -4.38 0.000 -.0083634 -.0031862
speed65 | -.000425 .0003735 -1.14 0.256 -.0011589 .0003089
speed70 | .0012333 .0003169 3.89 0.000 .0006106 .0018559
ba08 | -.0013775 .0003296 -4.18 0.000 -.0020251 -.0007298
drinkage21 | .0007453 .0006444 1.16 0.248 -.0005208 .0020115
logincome | -.0135144 .0016114 -8.39 0.000 -.0166805 -.0103483
age | .0009787 .0004957 1.97 0.049 4.69e-06 .0019527
_Ifips_2 | .0100326 .0035745 2.81 0.005 .0030097 .0170556
_Ifips_4 | .0022479 .0008314 2.70 0.007 .0006144 .0038814
_Ifips_5 | .0012263 .0007868 1.56 0.120 -.0003195 .0027722
_Ifips_6 | .0015822 .0014353 1.10 0.271 -.0012377 .0044021
_Ifips_8 | -.000033 .0011743 -0.03 0.978 -.0023403 .0022742
_Ifips_9 | -.0041954 .0010154 -4.13 0.000 -.0061903 -.0022004
_Ifips_10 | -.0007464 .0010806 -0.69 0.490 -.0028695 .0013766
_Ifips_11 | .0005718 .0013871 0.41 0.680 -.0021535 .003297
_Ifips_12 | .0009356 .001521 0.62 0.539 -.0020527 .003924
_Ifips_13 | -.0006633 .0013075 -0.51 0.612 -.0032322 .0019056
_Ifips_15 | -.0006398 .0012663 -0.51 0.614 -.0031277 .0018481
_Ifips_16 | .0026381 .001335 1.98 0.049 .0000152 .005261
_Ifips_17 | -.0013855 .0009304 -1.49 0.137 -.0032136 .0004425
_Ifips_18 | -.0040948 .0007695 -5.32 0.000 -.0056067 -.0025829
_Ifips_19 | -.0026051 .0008317 -3.13 0.002 -.0042391 -.0009711
_Ifips_20 | -.0017657 .0006931 -2.55 0.011 -.0031275 -.0004039
_Ifips_21 | -.0021878 .0006634 -3.30 0.001 -.0034913 -.0008844
_Ifips_22 | .0024998 .0011649 2.15 0.032 .000211 .0047885
_Ifips_23 | -.0059608 .0007634 -7.81 0.000 -.0074608 -.0044609
_Ifips_24 | -.0008352 .0010262 -0.81 0.416 -.0028514 .0011811
_Ifips_25 | -.0079672 .0008881 -8.97 0.000 -.0097121 -.0062223
_Ifips_26 | -.0018792 .0008739 -2.15 0.032 -.0035963 -.0001621
_Ifips_27 | -.0057477 .000932 -6.17 0.000 -.0075787 -.0039166
_Ifips_28 | .0038804 .0007906 4.91 0.000 .002327 .0054337
_Ifips_29 | -.0013953 .0008173 -1.71 0.088 -.003001 .0002105
_Ifips_30 | .0012472 .0008788 1.42 0.156 -.0004795 .0029738
_Ifips_31 | -.0041884 .0007177 -5.84 0.000 -.0055986 -.0027782
_Ifips_32 | .0066381 .0011669 5.69 0.000 .0043455 .0089308
_Ifips_33 | -.0041284 .0010376 -3.98 0.000 -.006167 -.0020898
_Ifips_34 | -.0046699 .0009803 -4.76 0.000 -.0065961 -.0027438
_Ifips_35 | .0046203 .0013391 3.45 0.001 .0019893 .0072512
_Ifips_36 | -.0006631 .0008814 -0.75 0.452 -.0023947 .0010685
_Ifips_37 | .0014575 .0008867 1.64 0.101 -.0002846 .0031996
_Ifips_38 | -.0093883 .0008365 -11.22 0.000 -.0110318 -.0077448
_Ifips_39 | -.00464 .0007117 -6.52 0.000 -.0060384 -.0032416
_Ifips_40 | -.0054662 .0006977 -7.83 0.000 -.006837 -.0040953
_Ifips_41 | .0000348 .0008248 0.04 0.966 -.0015856 .0016553
_Ifips_42 | -.003881 .0009815 -3.95 0.000 -.0058093 -.0019527
_Ifips_44 | -.011189 .0010029 -11.16 0.000 -.0131595 -.0092186
_Ifips_45 | .0026997 .0009462 2.85 0.005 .0008407 .0045588
_Ifips_46 | -.0028029 .0007661 -3.66 0.000 -.0043081 -.0012978
_Ifips_47 | .0011872 .0006062 1.96 0.051 -3.95e-06 .0023783
_Ifips_48 | .0006296 .0015091 0.42 0.677 -.0023354 .0035945
_Ifips_49 | .0003764 .0027246 0.14 0.890 -.0049768 .0057296
_Ifips_50 | -.0031505 .0008039 -3.92 0.000 -.00473 -.001571
_Ifips_51 | -.00316 .0009348 -3.38 0.001 -.0049966 -.0013234
_Ifips_53 | -.0036127 .0009087 -3.98 0.000 -.005398 -.0018273
_Ifips_54 | -.0016792 .0014689 -1.14 0.254 -.0045652 .0012069
_Ifips_55 | -.0051829 .0006722 -7.71 0.000 -.0065036 -.0038621
_Ifips_56 | .0007427 .0013262 0.56 0.576 -.001863 .0033483
_cons | .1223864 .0118767 10.30 0.000 .0990518 .1457211
------------------------------------------------------------------------------Another method to estimate robust standard error:
reg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 logincome age i.fips, cluster(fips)Outputs:
i.fips _Ifips_1-56 (naturally coded; _Ifips_1 omitted)
Linear regression Number of obs = 556
F(6, 50) = .
Prob > F = .
R-squared = 0.8867
Root MSE = .00179
(Std. Err. adjusted for 51 clusters in fips)
------------------------------------------------------------------------------
| Robust
fatalityrate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sb_useage | -.0057748 .001751 -3.30 0.002 -.0092919 -.0022577
speed65 | -.000425 .0004778 -0.89 0.378 -.0013847 .0005346
speed70 | .0012333 .0003654 3.38 0.001 .0004994 .0019671
ba08 | -.0013775 .0003935 -3.50 0.001 -.0021677 -.0005872
drinkage21 | .0007453 .0007536 0.99 0.327 -.0007684 .002259
logincome | -.0135144 .0025018 -5.40 0.000 -.0185394 -.0084894
age | .0009787 .0007826 1.25 0.217 -.0005933 .0025507
_Ifips_2 | .0100326 .0046542 2.16 0.036 .0006843 .0193809
_Ifips_4 | .0022479 .0006823 3.29 0.002 .0008774 .0036184
_Ifips_5 | .0012263 .0006766 1.81 0.076 -.0001327 .0025854
_Ifips_6 | .0015822 .0019286 0.82 0.416 -.0022914 .0054559
_Ifips_8 | -.000033 .0015549 -0.02 0.983 -.0031561 .0030901
_Ifips_9 | -.0041954 .0011113 -3.78 0.000 -.0064274 -.0019633
_Ifips_10 | -.0007464 .0008742 -0.85 0.397 -.0025023 .0010095
_Ifips_11 | .0005718 .0010655 0.54 0.594 -.0015683 .0027118
_Ifips_12 | .0009356 .0021564 0.43 0.666 -.0033956 .0052668
_Ifips_13 | -.0006633 .0016197 -0.41 0.684 -.0039166 .00259
_Ifips_15 | -.0006398 .0012935 -0.49 0.623 -.0032378 .0019582
_Ifips_16 | .0026381 .001448 1.82 0.074 -.0002703 .0055466
_Ifips_17 | -.0013855 .0009078 -1.53 0.133 -.0032089 .0004378
_Ifips_18 | -.0040948 .0004523 -9.05 0.000 -.0050033 -.0031863
_Ifips_19 | -.0026051 .0007147 -3.65 0.001 -.0040406 -.0011697
_Ifips_20 | -.0017657 .000348 -5.07 0.000 -.0024647 -.0010667
_Ifips_21 | -.0021878 .0001678 -13.04 0.000 -.0025249 -.0018508
_Ifips_22 | .0024998 .0013779 1.81 0.076 -.0002678 .0052673
_Ifips_23 | -.0059608 .0006398 -9.32 0.000 -.0072458 -.0046758
_Ifips_24 | -.0008352 .0011347 -0.74 0.465 -.0031142 .0014439
_Ifips_25 | -.0079672 .0009074 -8.78 0.000 -.0097898 -.0061445
_Ifips_26 | -.0018792 .0008724 -2.15 0.036 -.0036314 -.000127
_Ifips_27 | -.0057477 .0009287 -6.19 0.000 -.0076131 -.0038822
_Ifips_28 | .0038804 .0007184 5.40 0.000 .0024374 .0053233
_Ifips_29 | -.0013953 .0003414 -4.09 0.000 -.0020809 -.0007096
_Ifips_30 | .0012472 .0003392 3.68 0.001 .0005659 .0019284
_Ifips_31 | -.0041884 .0002797 -14.97 0.000 -.0047502 -.0036266
_Ifips_32 | .0066381 .0010135 6.55 0.000 .0046025 .0086737
_Ifips_33 | -.0041284 .001072 -3.85 0.000 -.0062816 -.0019752
_Ifips_34 | -.0046699 .0009271 -5.04 0.000 -.0065321 -.0028077
_Ifips_35 | .0046203 .0016093 2.87 0.006 .0013878 .0078527
_Ifips_36 | -.0006631 .0006996 -0.95 0.348 -.0020682 .0007421
_Ifips_37 | .0014575 .0003775 3.86 0.000 .0006994 .0022157
_Ifips_38 | -.0093883 .0004502 -20.86 0.000 -.0102925 -.0084841
_Ifips_39 | -.00464 .0003533 -13.14 0.000 -.0053495 -.0039305
_Ifips_40 | -.0054662 .0002129 -25.67 0.000 -.0058939 -.0050385
_Ifips_41 | .0000348 .0003693 0.09 0.925 -.000707 .0007767
_Ifips_42 | -.003881 .0012139 -3.20 0.002 -.0063191 -.0014429
_Ifips_44 | -.011189 .0010421 -10.74 0.000 -.0132822 -.0090959
_Ifips_45 | .0026997 .0005788 4.66 0.000 .0015372 .0038623
_Ifips_46 | -.0028029 .0003933 -7.13 0.000 -.0035929 -.002013
_Ifips_47 | .0011872 .0003186 3.73 0.000 .0005472 .0018272
_Ifips_48 | .0006296 .0021336 0.30 0.769 -.0036558 .0049149
_Ifips_49 | .0003764 .0041335 0.09 0.928 -.0079259 .0086787
_Ifips_50 | -.0031505 .0005095 -6.18 0.000 -.0041738 -.0021272
_Ifips_51 | -.00316 .0010105 -3.13 0.003 -.0051896 -.0011305
_Ifips_53 | -.0036127 .0010083 -3.58 0.001 -.005638 -.0015874
_Ifips_54 | -.0016792 .0015892 -1.06 0.296 -.0048711 .0015128
_Ifips_55 | -.0051829 .0004405 -11.77 0.000 -.0060676 -.0042981
_Ifips_56 | .0007427 .0014742 0.50 0.617 -.0022184 .0037037
_cons | .1223864 .0193546 6.32 0.000 .0835116 .1612613
------------------------------------------------------------------------------If we do not need the estimated value of each \(\alpha_i\):
areg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 logincome age, cluster(fips) absorb(fips)Outputs:
Linear regression, absorbing indicators Number of obs = 556
F( 7, 50) = 87.90
Prob > F = 0.0000
R-squared = 0.8867
Adj R-squared = 0.8737
Root MSE = 0.0018
(Std. Err. adjusted for 51 clusters in fips)
------------------------------------------------------------------------------
| Robust
fatalityrate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sb_useage | -.0057748 .001751 -3.30 0.002 -.0092919 -.0022577
speed65 | -.000425 .0004778 -0.89 0.378 -.0013847 .0005346
speed70 | .0012333 .0003654 3.38 0.001 .0004994 .0019671
ba08 | -.0013775 .0003935 -3.50 0.001 -.0021677 -.0005872
drinkage21 | .0007453 .0007536 0.99 0.327 -.0007684 .002259
logincome | -.0135144 .0025018 -5.40 0.000 -.0185394 -.0084894
age | .0009787 .0007826 1.25 0.217 -.0005933 .0025507
_cons | .1209958 .0193262 6.26 0.000 .082178 .1598137
-------------+----------------------------------------------------------------
fips | absorbed (51 categories)The results change when state effects are included. The coefficient on seat belt usage is now negative and the coefficient is statistically significant. The estimated value of sb_useage is 0.0057.
States with more dangerous driving conditions (and a higher fatality rate) also have more people wearing seat belts. Thus (1) suffers from omitted variable bias.
\[y_{it}=\alpha_i + \alpha_t + \beta x_{it}+u_{it}\]
reg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 logincome age i.fips i.year, cluster(fips)Outputs:
i.fips _Ifips_1-56 (naturally coded; _Ifips_1 omitted)
i.year _Iyear_1983-1997 (naturally coded; _Iyear_1983 omitted)
Linear regression Number of obs = 556
F(20, 50) = .
Prob > F = .
R-squared = 0.9098
Root MSE = .00162
(Std. Err. adjusted for 51 clusters in fips)
------------------------------------------------------------------------------
| Robust
fatalityrate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sb_useage | -.0037186 .0015246 -2.44 0.018 -.0067808 -.0006563
speed65 | -.0007833 .0006093 -1.29 0.205 -.0020071 .0004405
speed70 | .0008042 .0004803 1.67 0.100 -.0001605 .0017688
ba08 | -.0008225 .0004656 -1.77 0.083 -.0017577 .0001127
drinkage21 | -.0011337 .0006534 -1.74 0.089 -.0024461 .0001787
logincome | .0062643 .0070367 0.89 0.378 -.0078693 .0203979
age | .001318 .0007287 1.81 0.076 -.0001455 .0027816
_Ifips_2 | .006243 .0042864 1.46 0.152 -.0023666 .0148526
_Ifips_4 | .0010385 .0007334 1.42 0.163 -.0004346 .0025115
_Ifips_5 | .0019924 .0006749 2.95 0.005 .0006367 .003348
_Ifips_6 | -.0046545 .0026128 -1.78 0.081 -.0099023 .0005934
_Ifips_8 | -.0046086 .0020453 -2.25 0.029 -.0087167 -.0005005
_Ifips_9 | -.0158628 .0036944 -4.29 0.000 -.0232833 -.0084423
_Ifips_10 | -.0073367 .0022963 -3.19 0.002 -.011949 -.0027243
_Ifips_11 | -.0108581 .0039561 -2.74 0.008 -.0188042 -.002912
_Ifips_12 | -.0047175 .0027592 -1.71 0.094 -.0102595 .0008244
_Ifips_13 | -.002997 .0015928 -1.88 0.066 -.0061962 .0002022
_Ifips_15 | -.007201 .0018451 -3.90 0.000 -.0109069 -.003495
_Ifips_16 | .003059 .0013709 2.23 0.030 .0003055 .0058125
_Ifips_17 | -.0073873 .0020735 -3.56 0.001 -.011552 -.0032226
_Ifips_18 | -.006817 .0008814 -7.73 0.000 -.0085874 -.0050466
_Ifips_19 | -.0057302 .0010414 -5.50 0.000 -.0078219 -.0036385
_Ifips_20 | -.0054187 .0012191 -4.44 0.000 -.0078674 -.00297
_Ifips_21 | -.0014577 .0002027 -7.19 0.000 -.0018648 -.0010506
_Ifips_22 | .0031179 .0013502 2.31 0.025 .0004059 .0058298
_Ifips_23 | -.0081397 .00105 -7.75 0.000 -.0102486 -.0060307
_Ifips_24 | -.0083354 .0025522 -3.27 0.002 -.0134617 -.003209
_Ifips_25 | -.0163695 .0029061 -5.63 0.000 -.0222066 -.0105324
_Ifips_26 | -.0060909 .0015497 -3.93 0.000 -.0092036 -.0029783
_Ifips_27 | -.0107385 .0017307 -6.20 0.000 -.0142148 -.0072622
_Ifips_28 | .0076234 .0012895 5.91 0.000 .0050335 .0102134
_Ifips_29 | -.004406 .0010682 -4.12 0.000 -.0065515 -.0022604
_Ifips_30 | .0008326 .0003791 2.20 0.033 .0000712 .0015939
_Ifips_31 | -.0069169 .0009749 -7.09 0.000 -.0088751 -.0049586
_Ifips_32 | .0012562 .0019356 0.65 0.519 -.0026315 .005144
_Ifips_33 | -.0107429 .0023232 -4.62 0.000 -.0154091 -.0060768
_Ifips_34 | -.0146688 .0031854 -4.61 0.000 -.0210669 -.0082708
_Ifips_35 | .005655 .0015416 3.67 0.001 .0025586 .0087514
_Ifips_36 | -.0093885 .0026295 -3.57 0.001 -.01467 -.004107
_Ifips_37 | -.0012724 .0007679 -1.66 0.104 -.0028147 .00027
_Ifips_38 | -.0090427 .0003947 -22.91 0.000 -.0098356 -.0082499
_Ifips_39 | -.008499 .0011757 -7.23 0.000 -.0108605 -.0061375
_Ifips_40 | -.0057419 .0002094 -27.42 0.000 -.0061625 -.0053214
_Ifips_41 | -.0039604 .001228 -3.23 0.002 -.006427 -.0014939
_Ifips_42 | -.0095413 .0020478 -4.66 0.000 -.0136544 -.0054281
_Ifips_44 | -.0162439 .0019085 -8.51 0.000 -.0200773 -.0124105
_Ifips_45 | .0028703 .0005825 4.93 0.000 .0017002 .0040403
_Ifips_46 | -.0026968 .0003757 -7.18 0.000 -.0034514 -.0019422
_Ifips_47 | -.0009243 .0007277 -1.27 0.210 -.0023859 .0005373
_Ifips_48 | -.0013714 .0020247 -0.68 0.501 -.0054381 .0026953
_Ifips_49 | .0027227 .0038473 0.71 0.482 -.0050048 .0104502
_Ifips_50 | -.0062963 .001069 -5.89 0.000 -.0084435 -.0041491
_Ifips_51 | -.0088905 .001912 -4.65 0.000 -.0127308 -.0050502
_Ifips_53 | -.0086983 .0017761 -4.90 0.000 -.0122657 -.0051309
_Ifips_54 | -.0009197 .0014567 -0.63 0.531 -.0038455 .0020061
_Ifips_55 | -.008633 .00109 -7.92 0.000 -.0108223 -.0064437
_Ifips_56 | -.0010498 .0014509 -0.72 0.473 -.0039641 .0018645
_Iyear_1984 | -.0004319 .0014475 -0.30 0.767 -.0033392 .0024754
_Iyear_1985 | -.0010707 .001853 -0.58 0.566 -.0047925 .0026512
_Iyear_1986 | -.0005777 .002109 -0.27 0.785 -.0048138 .0036583
_Iyear_1987 | -.0008722 .0026195 -0.33 0.741 -.0061336 .0043892
_Iyear_1988 | -.001885 .0030219 -0.62 0.536 -.0079547 .0041847
_Iyear_1989 | -.0041766 .0034205 -1.22 0.228 -.0110468 .0026936
_Iyear_1990 | -.005266 .0037186 -1.42 0.163 -.012735 .0022031
_Iyear_1991 | -.0066622 .0039487 -1.69 0.098 -.0145935 .001269
_Iyear_1992 | -.008518 .0041863 -2.03 0.047 -.0169265 -.0001095
_Iyear_1993 | -.0089399 .0044105 -2.03 0.048 -.0177988 -.0000811
_Iyear_1994 | -.0096297 .0048249 -2.00 0.051 -.0193207 .0000613
_Iyear_1995 | -.0101123 .0051428 -1.97 0.055 -.0204419 .0002172
_Iyear_1996 | -.0110766 .0054713 -2.02 0.048 -.022066 -.0000871
_Iyear_1997 | -.0116075 .0058129 -2.00 0.051 -.0232831 .0000681
_cons | -.0730503 .0686829 -1.06 0.293 -.2110039 .0649033
------------------------------------------------------------------------------
Tidier version:
areg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 logincome age i.year, cluster(fips) absorb(fips)Outputs:
i.year _Iyear_1983-1997 (naturally coded; _Iyear_1983 omitted)
Linear regression, absorbing indicators Number of obs = 556
F( 21, 50) = 47.41
Prob > F = 0.0000
R-squared = 0.9098
Adj R-squared = 0.8966
Root MSE = 0.0016
(Std. Err. adjusted for 51 clusters in fips)
------------------------------------------------------------------------------
| Robust
fatalityrate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sb_useage | -.0037186 .0015246 -2.44 0.018 -.0067808 -.0006563
speed65 | -.0007833 .0006093 -1.29 0.205 -.0020071 .0004405
speed70 | .0008042 .0004803 1.67 0.100 -.0001605 .0017688
ba08 | -.0008225 .0004656 -1.77 0.083 -.0017577 .0001127
drinkage21 | -.0011337 .0006534 -1.74 0.089 -.0024461 .0001787
logincome | .0062643 .0070367 0.89 0.378 -.0078693 .0203979
age | .001318 .0007287 1.81 0.076 -.0001455 .0027816
_Iyear_1984 | -.0004319 .0014475 -0.30 0.767 -.0033392 .0024754
_Iyear_1985 | -.0010707 .001853 -0.58 0.566 -.0047925 .0026512
_Iyear_1986 | -.0005777 .002109 -0.27 0.785 -.0048138 .0036583
_Iyear_1987 | -.0008722 .0026195 -0.33 0.741 -.0061336 .0043892
_Iyear_1988 | -.001885 .0030219 -0.62 0.536 -.0079547 .0041847
_Iyear_1989 | -.0041766 .0034205 -1.22 0.228 -.0110468 .0026936
_Iyear_1990 | -.005266 .0037186 -1.42 0.163 -.012735 .0022031
_Iyear_1991 | -.0066622 .0039487 -1.69 0.098 -.0145935 .001269
_Iyear_1992 | -.008518 .0041863 -2.03 0.047 -.0169265 -.0001095
_Iyear_1993 | -.0089399 .0044105 -2.03 0.048 -.0177988 -.0000811
_Iyear_1994 | -.0096297 .0048249 -2.00 0.051 -.0193207 .0000613
_Iyear_1995 | -.0101123 .0051428 -1.97 0.055 -.0204419 .0002172
_Iyear_1996 | -.0110766 .0054713 -2.02 0.048 -.022066 -.0000871
_Iyear_1997 | -.0116075 .0058129 -2.00 0.051 -.0232831 .0000681
_cons | -.0779904 .0697046 -1.12 0.269 -.2179962 .0620155
-------------+----------------------------------------------------------------
fips | absorbed (51 categories)Test effect:
reg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 logincome age i.year i.fips, cluster(fips)
testparm i.yearOutputs:
( 1) 1984.year = 0
( 2) 1985.year = 0
( 3) 1986.year = 0
( 4) 1987.year = 0
( 5) 1988.year = 0
( 6) 1989.year = 0
( 7) 1990.year = 0
( 8) 1991.year = 0
( 9) 1992.year = 0
(10) 1993.year = 0
(11) 1994.year = 0
(12) 1995.year = 0
(13) 1996.year = 0
(14) 1997.year = 0
F( 14, 50) = 8.90
Prob > F = 0.0000i.year _Iyear_1983-1997 (naturally coded; _Iyear_1983 omitted)
Linear regression, absorbing indicators Number of obs = 556
F( 21, 50) = 47.41
Prob > F = 0.0000
R-squared = 0.9098
Adj R-squared = 0.8966
Root MSE = 0.0016
(Std. Err. adjusted for 51 clusters in fips)
------------------------------------------------------------------------------
| Robust
fatalityrate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sb_useage | -.0037186 .0015246 -2.44 0.018 -.0067808 -.0006563
speed65 | -.0007833 .0006093 -1.29 0.205 -.0020071 .0004405
speed70 | .0008042 .0004803 1.67 0.100 -.0001605 .0017688
ba08 | -.0008225 .0004656 -1.77 0.083 -.0017577 .0001127
drinkage21 | -.0011337 .0006534 -1.74 0.089 -.0024461 .0001787
logincome | .0062643 .0070367 0.89 0.378 -.0078693 .0203979
age | .001318 .0007287 1.81 0.076 -.0001455 .0027816
-------------+----------------------------------------------------------------
fips | absorbed (51 categories)\[fatality~rate=-0.00372\times sb~useage+...\]
A 38% increase in seat belt usage from 0.52 to 0.90 is estimated to lower the fatality rate by \(0.00372\times 0.38=0.0014\) fatalities per million traffic miles. The average number of traffic miles per year per state in the sample is 41,447. For a state with the average number of traffic miles, the number of fatalities prevented is \(0.0014\times 41,447=58\) fatalities.
areg sb_useage primary secondary speed65 speed70 ba08 drinkage logincome age i.year, cluster(fips) absorb(fips)Outputs:
Linear regression, absorbing indicators Number of obs = 556
F( 22, 50) = 456.16
Prob > F = 0.0000
R-squared = 0.9016
Adj R-squared = 0.8869
Root MSE = 0.0572
(Std. Err. adjusted for 51 clusters in fips)
------------------------------------------------------------------------------
| Robust
sb_useage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
primary | .2055968 .0243489 8.44 0.000 .1566907 .254503
secondary | .1085184 .0140858 7.70 0.000 .0802262 .1368106
speed65 | .0228485 .0215529 1.06 0.294 -.0204417 .0661388
speed70 | .0120424 .0216313 0.56 0.580 -.0314054 .0554902
ba08 | .0037584 .018507 0.20 0.840 -.033414 .0409307
drinkage21 | .0107149 .0285425 0.38 0.709 -.0466144 .0680442
logincome | .0582708 .269387 0.22 0.830 -.482809 .5993506
age | .0138232 .0243016 0.57 0.572 -.034988 .0626345
|
year |
1984 | .0041178 .0299885 0.14 0.891 -.0561159 .0643514
1985 | .0575169 .0452117 1.27 0.209 -.0332935 .1483273
1986 | .1073527 .0579004 1.85 0.070 -.0089437 .223649
1987 | .1240647 .0810099 1.53 0.132 -.0386485 .2867779
1988 | .1390924 .1025384 1.36 0.181 -.0668621 .3450468
1989 | .1702325 .1186812 1.43 0.158 -.0681457 .4086106
1990 | .1897753 .1358066 1.40 0.168 -.0830004 .462551
1991 | .2370697 .143986 1.65 0.106 -.0521347 .5262741
1992 | .2633971 .1598977 1.65 0.106 -.057767 .5845612
1993 | .2824192 .1717693 1.64 0.106 -.0625896 .6274279
1994 | .2983722 .1826111 1.63 0.109 -.0684131 .6651575
1995 | .2959081 .1946357 1.52 0.135 -.0950292 .6868454
1996 | .2875641 .2086531 1.38 0.174 -.1315281 .7066562
1997 | .2977352 .2209318 1.35 0.184 -.1460193 .7414896
|
_cons | -.893022 2.775641 -0.32 0.749 -6.46806 4.682016
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fips | absorbed (51 categories)The coefficients on primary and secondary are positive and significant. Primary enforcement is estimated to increase seat belt usage by 20.6% and secondary enforcement is estimated to increase seat belt usage by 10.9%.
\[sb~usage = 0.206\times primary+0.109\times secondary+...\]
New Jersey changed from secondary enforcement to primary enforcement, which means:
\[primary:0\rightarrow 1,secondary: 1\rightarrow 0\]
\[\Delta sb~usage = 0.206-0.109=0.094\]
This is predicted to reduce the fatality rate by \(0.00372\times 0.094= 0.00035\) fatalities per million traffic miles.
\[\Delta fatality~rate=-0.00372\times \Delta sb~useage=0.00372\times 0.094= 0.00035\]
The data set shows that there were 63,000 million traffic miles in 1997 in New Jersey. Assuming the same number of traffic miles in 2000 yields \(0.00035\times 63,000=22\) lives saved