e 8

E 8.4

_cons -.1222363 .6626687 -0.18 0.854 -1.447324 1.202852 yearsschool .2429753 .083702 2.90 0.005 .0756027 .4103478 tradeshare 1.897823 .9360473 2.03 0.047 .0260808 3.769565 growth Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 207.80816 63 3.29854222 Root MSE = 1.691 Adj R-squared = 0.1331 Residual 174.431689 61 2.85953588 R-squared = 0.1606 Model 33.3764711 2 16.6882356 Prob > F = 0.0048 F( 2, 61) = 5.84 Source SS df MS Number of obs = 64

. reg growth tradeshare yearsschool

_cons -.185739 .5642853 -0.33 0.743 -1.314097 .9426191 lnschool 1.016292 .2230901 4.56 0.000 .5701953 1.462388 tradeshare 1.748979 .8599768 2.03 0.046 .0293486 3.468609 growth Coef. Std. Err. t P>|t| [95% Conf. Interval]


. reg growth tradeshare lnschool

_cons 11.74591 2.919804 4.02 0.000 5.901285 17.59053 lnrgdp60 -1.621135 .3985046 -4.07 0.000 -2.418829 -.8234416assasinati~s .2277195 .4336512 0.53 0.602 -.6403278 1.095767 rev_coups -2.299537 1.004465 -2.29 0.026 -4.310193 -.2888815 lnschool 2.161291 .3626545 5.96 0.000 1.435359 2.887223 tradeshare 1.10353 .8331579 1.32 0.191 -.5642167 2.771277 growth Coef. Std. Err. t P>|t| [95% Conf. Interval]


. reg growth tradeshare lnschool rev_coups assasinations lnrgdp60

_cons 10.48423 3.038863 3.45 0.001 4.399009 16.56945tradesh_sc~l -.3304394 .2399308 -1.38 0.174 -.8108925 .1500138 lnrgdp60 -1.488327 .4070466 -3.66 0.001 -2.303424 -.6732302assasinati~s .1168864 .4377972 0.27 0.790 -.7597874 .9935603 rev_coups -2.315257 .9968542 -2.32 0.024 -4.311424 -.3190912 lnschool 2.487355 .4307764 5.77 0.000 1.62474 3.34997 tradeshare 2.23006 1.163038 1.92 0.060 -.0988828 4.559003 growth Coef. Std. Err. t P>|t| [95% Conf. Interval]


. reg growth tradeshare lnschool rev_coups assasinations lnrgdp60 tradesh_school

_cons 12.92906 3.098466 4.17 0.000 6.722087 19.13603 lnrgdp60 -1.584348 .4079428 -3.88 0.000 -2.401556 -.7671405assasinati~s .1021111 .4435059 0.23 0.819 -.7863379 .99056 rev_coups -2.035454 1.025946 -1.98 0.052 -4.09067 .0197616 lnschool 2.133188 .3669534 5.81 0.000 1.398092 2.868284 trade_3 -2.759737 9.249787 -0.30 0.767 -21.28929 15.76981 trade_2 8.48788 17.43506 0.49 0.628 -26.43874 43.4145 tradeshare -5.701947 9.75512 -0.58 0.561 -25.2438 13.83991 growth Coef. Std. Err. t P>|t| [95% Conf. Interval]


. reg growth tradeshare trade_2 trade_3 lnschool rev_coups assasinations lnrgdp60

a)

The relationship doesn’t look linear. Regression (2) is better because it take the natural log of years school.

-20

24

68

gro

wth

0 2 4 6 8 10yearsschool

-20

24

68

-2 -1 0 1 2lnschool

growth Fitted values

-20

24

68

0 2 4 6 8 10yearsschool

growth Fitted values

b) Regression 1: (-.122 + 1.898 + (.243*6)) – (-.122 + 1.898 + (.243*4)) = 0.4857Regression 2: (-.186 + 1.749 + (1.016*ln[6])) – (-.186 + 1.749 + (1.016*ln[4])) = 0.412

c) Assassination: T-test= ((0.2277195-0)/0.4336512) = 0.53 -> not statistically significant at 10% level!Rev_coups: T-test = ((-2.299537-0)/1.004465) = -2.29 -> statistically significant at the 5% level!

d) TradeShare x Yearsschool: T-test = ((-0.3304394-0)/0.2399308) = 3.45 -> not statistically significant at the 10% level. This means that the effect of TradeShare on Growth doesn’t depend on the level of education in the country.

e) No, there is no evidence of a nonlinear relationship between TradeShare and Growth because TradeShare^2 & TradeShare^3 are not statistically significant at the 10% level.

f) Regression 3: [11.74 + (1.104*1) + 2.161 – 2.300 + 0.228 – 1.621] – [11.74 + (1.104*0.5) + 2.161 – 2.300 + 0.228 – 1.621] = 0.552

Regression 5: [12.929 + (-5.702*1) + (8.488*1^2) + (-2.760*1^3) + 2.133 + 0.102 – 1.584] – [12.929 + (-5.702*0.5) + (8.488*0.5^2) + (-2.760*0.5^3) + 2.133 + 0.102 – 1.584] = 1.1

E11.1

a)

i) Prob = 0.2423 SE = 0.428/√10000 = 0.004

female 10000 .5637 .4959505 0 1 hispanic 10000 .1134 .317097 0 1 black 10000 .0769 .266446 0 1 colgrad 10000 .1972 .3979045 0 1 colsome 10000 .2802 .4491193 0 1 hsgrad 10000 .3266 .468993 0 1 hsdrop 10000 .0912 .2879077 0 1 age 10000 38.6932 12.11378 18 88 smkban 10000 .6098 .4878194 0 1 smoker 10000 .2423 .4284963 0 1 Variable Obs Mean Std. Dev. Min Max

. sum smoker smkban age hsdrop hsgrad colsome colgrad black hispanic female

ii) Prob = 0.2120 SE = 0.409/ √6098 = 0.005

female 6098 .6093801 .4879293 0 1 hispanic 6098 .1046245 .306094 0 1 black 6098 .0783864 .2688006 0 1 colgrad 6098 .2243358 .4171784 0 1 colsome 6098 .2856674 .4517688 0 1 hsgrad 6098 .2974746 .4571846 0 1 hsdrop 6098 .069039 .2535413 0 1 age 6098 39.08101 11.84533 18 88 smkban 6098 1 0 1 1 smoker 6098 .2120367 .4087842 0 1 Variable Obs Mean Std. Dev. Min Max

. sum if smkban == 1

iii)Prob = 0.2896 SE = 0.454/√3902 = 0.007

female 3902 .4923116 .500005 0 1 hispanic 3902 .1271143 .3331437 0 1 black 3902 .0745771 .2627415 0 1 colgrad 3902 .1547924 .361753 0 1 colsome 3902 .2716556 .4448702 0 1 hsgrad 3902 .3721169 .4834313 0 1 hsdrop 3902 .1258329 .3317035 0 1 age 3902 38.08713 12.49925 18 81 smkban 3902 0 0 0 0 smoker 3902 .2895951 .4536326 0 1 Variable Obs Mean Std. Dev. Min Max

. sum if smkban == 0

b) The difference in the probabilities of smoking between workers affected by a workplace smoking ban and workers not affected by a workplace smoking ban is :- Prob: (0.2896 – 0.2120) = 0.0776

SE = √0.0052+0.0072=0.0086 T-test= ((0.078-0) / 0.0086) = 9.02

The difference is statistically significant at the 1% level.

c)

_cons -.0141099 .043282 -0.33 0.744 -.0989514 .0707316 female -.0332569 .008536 -3.90 0.000 -.0499891 -.0165247 hispanic -.1048159 .013926 -7.53 0.000 -.1321137 -.0775182 black -.0275658 .0157286 -1.75 0.080 -.0583969 .0032654 colgrad .0447983 .0160142 2.80 0.005 .0134072 .0761893 colsome .1642968 .0153841 10.68 0.000 .1341409 .1944527 hsgrad .2327012 .0150941 15.42 0.000 .2031138 .2622886 hsdrop .3227142 .019846 16.26 0.000 .283812 .3616164 age_2 -.0001318 .0000233 -5.65 0.000 -.0001775 -.0000861 age .0096744 .0019815 4.88 0.000 .0057902 .0135586 smkban -.0472399 .0087179 -5.42 0.000 -.0643288 -.030151 smoker Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 1835.9071 9999 .183609071 Root MSE = .41631 Adj R-squared = 0.0560 Residual 1731.27299 9989 .173317949 R-squared = 0.0570 Model 104.634106 10 10.4634106 Prob > F = 0.0000 F( 10, 9989) = 60.37 Source SS df MS Number of obs = 10000

. reg smoker smkban age age_2 hsdrop hsgrad colsome colgrad black hispanic female

The smoking ban coefficient is -0.0472 which is less than that in part (b). The reason for that is omitted variable bias in part (b), where smkban can be correlated with the other variables.

d) H0: b_smkban = 0 H1: b_smkban ≠ 0 T-test = ((-0.04723 – 0)/0.0087) = -5.42Result: Reject the null.

e) F-test ¿(0.0570−0.0106)/ 4

(1−0.0570)/(10000−10−1) = 122.876

Yes, because all variables coefficients are statistically significant at the 5% level at least.

f) Yes there is a nonlinear relationship between age and probability smoking.

.2.2

2.2

4.2

6F

itted

va

lues

20 30 40 50 60 70ages

E 11.2a)

_cons -1.734926 .152582 -11.37 0.000 -2.033982 -1.435871 female -.1117313 .0288205 -3.88 0.000 -.1682183 -.0552442 hispanic -.3382743 .0477535 -7.08 0.000 -.4318694 -.2446792 black -.0842789 .0526498 -1.60 0.109 -.1874705 .0189127 colgrad .2346839 .0650598 3.61 0.000 .107169 .3621988 colsome .6771192 .0609347 11.11 0.000 .5576893 .7965491 hsgrad .8826708 .059778 14.77 0.000 .7655081 .9998336 hsdrop 1.14161 .0720428 15.85 0.000 1.000409 1.282812 age_2 -.0004675 .0000828 -5.65 0.000 -.0006299 -.0003052 age .0345114 .0069362 4.98 0.000 .0209167 .048106 smkban -.15863 .0289964 -5.47 0.000 -.2154619 -.1017981 smoker Coef. Std. Err. z P>|z| [95% Conf. Interval]

Log likelihood = -5235.8679 Pseudo R2 = 0.0544 Prob > chi2 = 0.0000 LR chi2(10) = 602.60Probit regression Number of obs = 10000

Iteration 3: log likelihood = -5235.8679 Iteration 2: log likelihood = -5235.868 Iteration 1: log likelihood = -5238.7464 Iteration 0: log likelihood = -5537.1662

. probit smoker smkban age age_2 hsdrop hsgrad colsom colgrad black hispanic female

b) H0: b_smkban= 0 H1: b_smkban≠ 0T-Test= (-.15863-0) / (.0289964) = -5.47 p-value= 0.000Reject the null. The T-stat for smkban using the linear probability model is -5.47.

c) F-test ¿(0.0544−0.0096)/4

(1−0.0544)/(10000−10−1) = 118.31

Reject the null. All variables are statistically significant. This resulted as in E11.1(e).

d) Mr. A’s Z= (-.159*0) + (.0345*20) + (-.000467*202) + (1.142*1) + (.883*0) + (.677*0) + (.235*0) + (-.0842*0) + (-.338*0) + (-.112*0) – 1.735 =0.0898 -> Prob= 46.81% . Mr. A has a 46.81% probability being a smoker in no smoking ban workplace.Mr. A’s Z= (-.159*1) + (.0345*20) + (-.000467*202) + (1.1416*1) + (.883*0) + (.677*0) + (.235*0) + (-.0842*0) + (-.338*0) + (-.112*0) – 1.735 = - 0.2483 -> Prob= 40.13%. Mr. A has a 40.13% probability being a smoker in a smoking ban workplace.The effect of having smoking ban made Mr. A 6.68% less chance being a smoker.

e) Ms. B’s Z= (-.159*0) + (.0345*40) +(-.000467*402) +(1.142*0) + (.883*0) + (.677*0) + (.235*1) + (-.0842*1) + ( -.338*0) + (-.112*1) – 1.735 = -1.079 -> Prob = 14.23% Ms. B has a 14.23% probability being a smoker.Ms. B’s Z= (-.159*1) + (.0345*40) +(-.000467*402) +(1.142*0) + (.883*0) + (.677*0) + (.235*1) + (-.0842*1) + ( -.338*0) + (-.112*1) – 1.735 = -1.238 -> Prob = 10.93% Ms. B has a 14.23% probability being a smoker.The effect of having smoking ban made Ms. B 3.3% less chance being a smoker.

f) Mr. A = (-.0472*0) + (.00967*20) + (-.000132*202) + (.3227*1) + (.2327*0) + (.1643*0) + (.0448*0) + (-.02757*0) + (-.1048*0) + (-.0332*0) – 0.0141 = 0.4492 -> Mr. A has a 44.92% probability being a smoker in no smoking ban workplace.Mr. A = (-.0472*1) + (.00967*20) + (-.000132*202) + (.3227*1) + (.2327*0) + (.1643*0) + (.0448*0) + (-.02757*0) + (-.1048*0) + (-.0332*0) – 0.0141 = 0.402 -> Mr. A has a 40.20% probability being a smoker in a smoking ban workplace.The effect of having smoking ban made Mr. A 4.72% less chance being a smoker.

Ms. B = (-.0472*0) + (.00967*40) + (-.000132*402) + (.3227*0) + (.2327*0) + (.1643*0) + (.0448*1) + (-.02757*1) + (-.1048*0) + (-.0333*1) – 0.01454 = -> Mr. A has a 14.54% probability being a smokerMs. B = (-.0472*1) + (.00967*40) + (-.000132*402) + (.3227*0) + (.2327*0) + (.1643*0) + (.0448*1) + (-.02757*1) + (-.1048*0) + (-.0333*1) – 0.0982 = -> Mr. A has a 9.82% probability being a smoker

The effect of having smoking ban made Ms. B 4.72% less chance being a smoker.

g) Yes they differ. In the linear model, the coefficient of smkban affects the probability of an individual smoking and it doesn’t dependent on the other characteristics of the individual. In the Probit model, the coefficient of smkban affects the probability of smoking and it depends on individual characteristics. The probit model makes more sense because it takes into consideration all other variables that are being regressed on. As in the real world-sense, I thing that the result I had to the difference is large, because a smoking ban is not going to affect this percentage of smokers.

h) Yes, this depends on the individuals’ preference if he (a smoker) would seek a job with no smoking ban workplace. Or an individual that doesn’t care to be in a smoking environment. Or an individual who don’t smoke and hate smoking are (smoking ban workplace).

E11.3

a)

insured 7731 .8167119 .3869275 0 1 Variable Obs Mean Std. Dev. Min Max

. sum insured if selfemp==0


. sum insured if selfemp==1


. sum insured

If insured: Prob: 0.801 SE=0.399/√8802=0.0043

If insure and self-employed: Prob: 0.689 SE=0.463/√1071=0.0141

If insured and not self-employed: Prob: 0.817 SE=0.390/√7731=0.0044

T-stat= 0.1277/√(0.01412+0.00442) = 8.70 >Tcritical

The difference of being insured between self-employed and not self-employed is 12.8% which is large in the real world sense. The difference is statistically significant at the 1% level.

b)

_cons .7654478 .039234 19.51 0.000 .6885399 .8423557 race_wht .0239444 .0123463 1.94 0.052 -.0002573 .0481461 race_ot -.0232437 .0230079 -1.01 0.312 -.0683445 .0218571 race_bl (omitted) reg_we -.0368839 .0123842 -2.98 0.003 -.0611599 -.0126079 reg_so -.0335534 .0112929 -2.97 0.003 -.0556901 -.0114166 reg_mw .0163843 .0122499 1.34 0.181 -.0076285 .040397 reg_ne (omitted) familysz -.0163237 .0027848 -5.86 0.000 -.0217825 -.0108649 married .1372416 .009238 14.86 0.000 .119133 .1553502 deg_oth -.0708897 .0350051 -2.03 0.043 -.1395079 -.0022714 deg_phd (omitted) deg_ma -.0241882 .0357559 -0.68 0.499 -.094278 .0459017 deg_ba -.0443334 .0332854 -1.33 0.183 -.1095805 .0209137 deg_hs -.1085053 .0324613 -3.34 0.001 -.172137 -.0448736 deg_ged -.2124028 .0372987 -5.69 0.000 -.2855169 -.1392887 deg_nd -.3681424 .0339496 -10.84 0.000 -.4346915 -.3015933 age .0037415 .0003885 9.63 0.000 .0029799 .0045031 selfemp -.1781373 .0122893 -14.50 0.000 -.2022271 -.1540474 insured Coef. Std. Err. t P>|t| [95% Conf. Interval]


note: race_bl omitted because of collinearitynote: reg_ne omitted because of collinearitynote: deg_phd omitted because of collinearity> e race_bl race_ot race_wht. reg insured selfemp age deg_nd deg_ged deg_hs deg_ba deg_ma deg_phd deg_oth married familysz reg_ne reg_mw reg_so reg_w

Yes, the self-employed are 17.81% less likely to have health insurance. This number is larger than 12.8% ( part(a) ).

c)

_cons .6488858 .0593874 10.93 0.000 .5324725 .765299 race_wht .0251474 .0123508 2.04 0.042 .0009368 .0493579 race_ot -.0224865 .0230021 -0.98 0.328 -.067576 .0226029 race_bl (omitted) reg_we -.0370427 .0123803 -2.99 0.003 -.0613109 -.0127744 reg_so -.0331834 .0112901 -2.94 0.003 -.0553145 -.0110522 reg_mw .0168325 .0122471 1.37 0.169 -.0071747 .0408396 reg_ne (omitted) familysz -.0168734 .0027918 -6.04 0.000 -.0223459 -.0114008 married .1334348 .009349 14.27 0.000 .1151085 .1517611 deg_oth -.0714988 .0349943 -2.04 0.041 -.1400957 -.0029018 deg_phd (omitted) deg_ma -.0255385 .0357477 -0.71 0.475 -.0956125 .0445354 deg_ba -.0454383 .033277 -1.37 0.172 -.110669 .0197925 deg_hs -.1070808 .0324551 -3.30 0.001 -.1707003 -.0434612 deg_ged -.2113906 .0372883 -5.67 0.000 -.2844844 -.1382968 deg_nd -.3647937 .0339625 -10.74 0.000 -.4313681 -.2982192 age_2 -.0000819 .0000313 -2.61 0.009 -.0001433 -.0000205 age .0102347 .0025143 4.07 0.000 .0053061 .0151633 selfemp -.1783847 .0122856 -14.52 0.000 -.2024672 -.1543021 insured Coef. Std. Err. t P>|t| [95% Conf. Interval]


note: race_bl omitted because of collinearitynote: reg_ne omitted because of collinearitynote: deg_phd omitted because of collinearity> reg_we race_bl race_ot race_wht. reg insured selfemp age age_2 deg_nd deg_ged deg_hs deg_ba deg_ma deg_phd deg_oth married familysz reg_ne reg_mw reg_so

A one year increase in age results in 1.02% increase in the probability of being insured, but this diminishes with the increase in age, because the coefficient of age squared is negative (nonlinearity).

d)

_cons .6468352 .0595049 10.87 0.000 .5301917 .7634786 race_wht .0251717 .0123514 2.04 0.042 .0009601 .0493833 race_ot -.0223941 .0230036 -0.97 0.330 -.0674865 .0226982 race_bl (omitted) reg_we -.0371866 .0123835 -3.00 0.003 -.0614612 -.0129121 reg_so -.0332493 .0112911 -2.94 0.003 -.0553826 -.0111161 reg_mw .0167853 .0122479 1.37 0.171 -.0072234 .040794 reg_ne (omitted) familysz -.0168893 .002792 -6.05 0.000 -.0223624 -.0114163 married .1334253 .0093494 14.27 0.000 .1150982 .1517524 deg_oth -.0717762 .0349992 -2.05 0.040 -.1403828 -.0031695 deg_phd (omitted) deg_ma -.0258137 .0357526 -0.72 0.470 -.0958971 .0442698 deg_ba -.0457082 .0332819 -1.37 0.170 -.1109485 .0195321 deg_hs -.1072068 .0324572 -3.30 0.001 -.1708304 -.0435832 deg_ged -.211561 .037291 -5.67 0.000 -.2846602 -.1384619 deg_nd -.3647788 .0339638 -10.74 0.000 -.4313558 -.2982017 selfempage .000683 .0012321 0.55 0.579 -.0017322 .0030982 age_2 -.0000853 .0000319 -2.67 0.008 -.0001479 -.0000227 age .0104365 .0025406 4.11 0.000 .0054563 .0154167 selfemp -.2079321 .0546982 -3.80 0.000 -.3151533 -.1007109 insured Coef. Std. Err. t P>|t| [95% Conf. Interval]


note: race_bl omitted because of collinearitynote: reg_ne omitted because of collinearitynote: deg_phd omitted because of collinearity> g_mw reg_so reg_we race_bl race_ot race_wht. reg insured selfemp age age_2 selfempage deg_nd deg_ged deg_hs deg_ba deg_ma deg_phd deg_oth married familysz reg_ne re

Adding an interpretation between Age and Self-employed (selfempage), doesn’t affect because it is statistically insignificant i.e. not different from zero.

e)

selfemp 8173 .1228435 .3282776 0 1 Variable Obs Mean Std. Dev. Min Max

. sum selfemp if healthy == 1


. sum selfemp if healthy == 0

The probabilities are very close, yet the self-employed have a higher probability being healthy than wage earners.


. sum selfemp if healthy == 1/age >=40


. sum selfemp if healthy == 0/age >=40


. sum selfemp if healthy == 1/age <=40


. sum selfemp if healthy == 0/age <=40

This shows that it doesn’t matter for the young workers and old workers, the effects are the same for ages below and above 40.Yes there is a potential of a two-way causality because the individual may choose not to be self-employed in order to be insured, or choose to be self-employed because he thinks he is healthy, etc.

e 8

Documents

workplace

smoking ban

squared adj

collinearity

nonlinear

statistically

sum selfemp

degphd omitted