Descriptive of Newborn Babies and Their Parents, Cigprice as Instrumental Variable for Packs - Statistics Project Example

QUАNTITАTIVЕ АSSIGNMЕNT, МАЕ306 Trimester 2 2013 Q1. 1.1 Descriptive Statistics 1.1.1 Weight of Newborn Babies The mean of weight of newborn babies (bwght) is 118.6996 and the standard deviation is 20.3540. The median weight of newborn babies is 120. The maximum weight of newborn babies is 271 while the minimum is 23. The distribution for the data in this variable is relatively normal; the skewness value of about -0.1459 is not significant. The variable has 1388 observations. 1.1.2 Male The mode for the variable male (if the child is male) is 1, meaning most of the children are male. The data is normally distributed; the skewness value of about -0.0836 is not significant. The variable has 1388 observations. 1.1.3 Parity The median birth order of the children (parity) is 1. The mode (most prevalent) birth order of the children is also 1. The maximum birth order is 6. The variable has 1388 observations. 1.1.4 Family Income The average family income (faminc) is about $29,026.66 with a standard deviation of $18,739.28. However, the median family income is about $27,500.00. The maximum family income is approximately $65,000 while the minimum family income is approximately $500. The data for the variable family income has a relatively normal distribution even with the skewness value of about 0.6176. The variable has 1388 observations. 1.1.5 Average Number of Packs of Cigarettes Smoked per Day The mean average number of packs of cigarettes smoked per day during pregnancy (packs) is about 0.1044 packs with a standard deviation of 298.63. The maximum number of packs smoked per day by a pregnant mother is 2.5 packs while the minimum is zero, which means some of the respondents did not smoke at all during pregnancy. The data for the variable packs is positively skewed with skewness value of about 3.5604. The variable has 1388 observations. Table 1 Descriptive Statistics FAMINC BWGHT PARITY MALE PACKS  Mean  29.02666  118.6996  - -  0.104359  Median  27.50000  120.0000  1.000000 -  0.000000  Maximum  65.00000  271.0000  6.000000 -  2.500000  Minimum  0.500000  23.00000  1.000000 -  0.000000  Std. Dev.  18.73928  20.35396  - -  0.298634  Skewness  0.617620 -0.145866  1.629925 -0.083647  3.560448  Observations  1388  1388  1388  1388  1388 1.2 Model Estimation The following model estimate the effects of family income (faminc), birth order of this child (parity), male (if the child is male), and the average number of packs of cigarettes smoked per day during pregnancy (packs) on the weight of newborn babies (bwght): log(bwght)=4.6756+0.02624male+0.0147parity+18.050log(faminc)-0.0837packs ± 0.0603 Each coefficient including the constant is statistically significant (P0.05) also suggest that there is no heteroskedasticity. The sample has no autocorrelation (Durbin-Watson statistic =1.931302); a Durbin-Watson statistic of 2.0 implies non-existence of autocorrelation. 4 All the variables (faminc, parity, male, and packs) have a non-linear effect on the birth weight of newborn babies. First, the scatter plot of each variable against bwght illustrates a non-linear relationship. Additionally, the correlation coefficients (r) representing each of the relationship between bwght and each variable are close to zero, implying non-existence of linear relationship. Figure 4.1 Correlation Matrix LOG(BWGHT) MALE PARITY LOG(FAMINC) PACKS LOG(BWGHT)  1.000000  0.064068  0.051516  0.099241 -0.140674 5 By inspecting the graph of the residual against packs, one would expect that packs is correlated with u(error term). The plot implies a pattern (the plots are not random) suggesting that the variable pack may be correlated with the error term. Figure 5.1 6 The average cigarette price in each woman’s state of residence (cigprice) is likely to satisfy the properties of a good instrumental variable for packs. A visual inspection of a scatter plot of packs versus cigprice (figure 6.1a) as well as the correlation coefficient (r= 0.0097) suggest existence of a weak correlation between packs and cigprice. Therefore, the requirement of correlation between the stochastic variable and the candidate instrument is met. Additionally, it seems there no correlation between cigprice and the error term as shown by the scatterplot of cigprice and the residues (figure 6.1b), which is also a satisfaction of the second property of a good instrumental variable. in general, therefore, cigprice is a good instrumental variable for packs. (a) (b) Figure 6.1 Motheduc, nonetheless, is not a good instrumental variable for packs because it has very weak, if any, correlation with the stochastic variable packs, and it is likely that motheduc is correlated (although weak) with the error term as illustrated by the scatter plots in figure 6.2. (a) (b) 6.2 7 Estimation using 2SLs, where cigprice is an instrumental variable for packs: log(bwght) = 4.1792 + 0.0884male + 0.1466parity + 72.4780log(faminc) + 0.6976packs ± 3.217865 A number of important differences in OLS and 2SLs estimates in equation (1) are evident. First, the effects of the coefficients on the bwght (weight of the newborn babies) changes significantly. The values of the constant and the coefficient for male decreases under 2SLs but the values of the coefficients for parity, log(faminc), packs and the value for error term increases packs. The coefficients of male, parity, log(faminc), and packs that were significant under OLS (P0.05) when 2SLs is applied. In addition, although the model is statistically significant (P0.05) even as the percentage of the changes in bwght accounted for by the regressors increases when 2SLs is applied. 8 The results of the Hausman test test shows the existence of endogeneity (P>0.05). 9 The first-stage regression for packs: log(bwght) = 4.1792 + 0.0884male + 0.1466parity + 72.4780log(faminc) + 0.6976packs ± 3.217865. The instrument cigprice is weak; The instrument is insignificant (P>0.05). 10 Estimation of the reduced form for packs: packs = 0.200233 - 0.004178 male + 0.018063 parity - 0.052142 log(faminc) + 0.000284cigprice(-1). The cigprice is not significant in the model (P>0.05). Therefore, cigprice is not a good instrument for packs and should not be used to in identify equation(1) as an instrument of packs. It means the answer from question 7 above is not valid. Appendix 1.0 1.1 FAMINC BWGHT PARITY MALE PACKS  Mean  29.02666  118.6996  1.632565  0.520893  0.104359  Median  27.50000  120.0000  1.000000  1.000000  0.000000  Maximum  65.00000  271.0000  6.000000  1.000000  2.500000  Minimum  0.500000  23.00000  1.000000  0.000000  0.000000  Std. Dev.  18.73928  20.35396  0.894027  0.499743  0.298634  Skewness  0.617620 -0.145866  1.629925 -0.083647  3.560448  Kurtosis  2.473396  6.147639  5.933811  1.006997  17.93397  Jarque-Bera  104.2811  577.9134  1112.359  231.3362  15830.76  Probability  0.000000  0.000000  0.000000  0.000000  0.000000  Sum  40289.00  164755.0  2266.000  723.0000  144.8500  Sum Sq. Dev.  487060.0  574611.7  1108.608  346.3941  123.6961  Observations  1388  1388  1388  1388  1388 1.2 Dependent Variable: LOG(BWGHT) Method: Least Squares Date: 09/29/13 Time: 16:36 Sample: 1 1388 Included observations: 1388 Variable Coefficient Std. Error t-Statistic Prob.   C 4.675618 0.021881 213.6812 0.0000 MALE 0.026241 0.010089 2.600832 0.0094 PARITY 0.014729 0.005665 2.600231 0.0094 LOG(FAMINC) 0.018050 0.005584 3.232601 0.0013 PACKS -0.083728 0.017121 -4.890393 0.0000 R-squared 0.035038     Mean dependent var 4.760031 Adjusted R-squared 0.032247     S.D. dependent var 0.190662 S.E. of regression 0.187563     Akaike info criterion -0.505810 Sum squared resid 48.65368     Schwarz criterion -0.486950 Log likelihood 356.0321     Hannan-Quinn criter. -0.498757 F-statistic 12.55439     Durbin-Watson stat 1.931302 Prob(F-statistic) 0.000000 2.0 2.1 Dependent Variable: LOG(BWGHT) Method: Least Squares Date: 09/29/13 Time: 17:14 Sample: 1 1388 Included observations: 1387 Variable Coefficient Std. Error t-Statistic Prob.   MALE 0.279908 0.039412 7.102068 0.0000 PARITY 0.324386 0.020833 15.57089 0.0000 LOG(FAMINC) 0.216119 0.023411 9.231443 0.0000 PACKS 0.511012 0.066764 7.653960 0.0000 MOTHEDUC 0.251747 0.006290 40.02084 0.0000 R-squared -14.168290     Mean dependent var 4.760094 Adjusted R-squared -14.212193     S.D. dependent var 0.190717 S.E. of regression 0.743848     Akaike info criterion 2.249639 Sum squared resid 764.6747     Schwarz criterion 2.268510 Log likelihood -1555.125     Hannan-Quinn criter. 2.256697 Durbin-Watson stat 1.900895 2.2 Dependent Variable: LOG(BWGHT) Method: Least Squares Date: 09/29/13 Time: 17:50 Sample: 1 1388 Included observations: 1191 Variable Coefficient Std. Error t-Statistic Prob.   C 4.675889 0.037493 124.7129 0.0000 MALE 0.033601 0.010737 3.129422 0.0018 PARITY 0.016445 0.006149 2.674333 0.0076 LOG(FAMINC) 0.016037 0.008405 1.907997 0.0566 PACKS -0.101457 0.020583 -4.929124 0.0000 MOTHEDUC -0.003389 0.002980 -1.137328 0.2556 FATHEDUC 0.003683 0.002614 1.409005 0.1591 R-squared 0.042026     Mean dependent var 4.767536 Adjusted R-squared 0.037172     S.D. dependent var 0.188013 S.E. of regression 0.184485     Akaike info criterion -0.536634 Sum squared resid 40.29723     Schwarz criterion -0.506762 Log likelihood 326.5655     Hannan-Quinn criter. -0.525377 F-statistic 8.656993     Durbin-Watson stat 1.976307 Prob(F-statistic) 0.000000 3.0 3.1 Figure 1. Scatter plot of residue versus the fitted values (bwghtf) Heteroskedasticity Test: White F-statistic 0.434372     Prob. F(13,1374) 0.9577 Obs*R-squared 5.681028     Prob. Chi-Square(13) 0.9570 Scaled explained SS 32.57738     Prob. Chi-Square(13) 0.0020 Heteroskedasticity Test: Breusch-Pagan-Godfrey F-statistic 0.282681     Prob. F(4,1383) 0.8893 Obs*R-squared 1.133884     Prob. Chi-Square(4) 0.8889 Scaled explained SS 6.502162     Prob. Chi-Square(4) 0.1647 4.0 4.1 LOG(BWGHT) MALE PARITY LOG(FAMINC) PACKS LOG(BWGHT)  1.000000  0.064068  0.051516  0.099241 -0.140674 MALE  0.064068  1.000000 -0.013465 -0.044251 -0.000490 PARITY  0.051516 -0.013465  1.000000 -0.088097  0.068383 LOG(FAMINC)  0.099241 -0.044251 -0.088097  1.000000 -0.163616 PACKS -0.140674 -0.000490  0.068383 -0.163616  1.000000 LOG(BWGHT) MALE PARITY LOG(FAMINC) PACKS LOG(BWGHT)  1.000000  0.064068  0.051516  0.099241 -0.140674 MALE  0.064068  1.000000 -0.013465 -0.044251 -0.000490 PARITY  0.051516 -0.013465  1.000000 -0.088097  0.068383 LOG(FAMINC)  0.099241 -0.044251 -0.088097  1.000000 -0.163616 PACKS -0.140674 -0.000490  0.068383 -0.163616  1.000000 5.0 Figure 5.1 6.0 (a) (b) Figure 6.1 (a) (b) 6.2 7.0 Dependent Variable: LOG(BWGHT) Method: Two-Stage Least Squares Date: 09/30/13 Time: 07:45 Sample (adjusted): 2 1388 Included observations: 1387 after adjustments Instrument list: MALE(-1) PARITY(-1) LOG(FAMINC)(-1) CIGPRICE Variable Coefficient Std. Error t-Statistic Prob.   C 4.179208 0.586532 7.125284 0.0000 MALE 0.088403 0.446658 0.197922 0.8431 PARITY 0.146587 0.243883 0.601054 0.5479 LOG(FAMINC) 0.072478 0.094981 0.763079 0.4455 PACKS 0.697584 1.845811 0.377928 0.7055 R-squared -1.903497     Mean dependent var 4.760081 Adjusted R-squared -1.911901     S.D. dependent var 0.190722 S.E. of regression 0.325454     Sum squared resid 146.3816 F-statistic 1.463930     Durbin-Watson stat 1.906329 Prob(F-statistic) 0.210824     Second-Stage SSR 49.79537 8.0 Estimation Command: ========================= TSLS LOG(BWGHT) C MALE PARITY LOG(FAMINC) PACKS @ MALE(-1) PARITY(-1) LOG(FAMINC)(-1) CIGPRICE Estimation Equation: ========================= LOG(BWGHT) = C(1) + C(2)*MALE + C(3)*PARITY + C(4)*LOG(FAMINC) + C(5)*PACKS Substituted Coefficients: ========================= LOG(BWGHT) = 4.17920804871 + 0.0884032150072*MALE + 0.146586901071*PARITY + 0.072477803545*LOG(FAMINC) + 0.697583557787*PACKS 9.0 Dependent Variable: PACKS Method: Least Squares Date: 09/30/13 Time: 09:45 Sample: 1 1388 Included observations: 1388 Variable Coefficient Std. Error t-Statistic Prob.   C 0.137408 0.104001 1.321219 0.1866 MALE -0.004726 0.015854 -0.298105 0.7657 PARITY 0.018149 0.008880 2.043784 0.0412 LOG(FAMINC) -0.052637 0.008699 -6.050876 0.0000 CIGPRICE 0.000777 0.000776 1.000900 0.3171 R-squared 0.030454     Mean dependent var 0.104359 Adjusted R-squared 0.027650     S.D. dependent var 0.298634 S.E. of regression 0.294477     Akaike info criterion 0.396363 Sum squared resid 119.9291     Schwarz criterion 0.415223 Log likelihood -270.0760     Hannan-Quinn criter. 0.403417 F-statistic 10.86023     Durbin-Watson stat 1.944888 Prob(F-statistic) 0.000000 10.0 Dependent Variable: PACKS Method: Least Squares Date: 09/30/13 Time: 09:51 Sample (adjusted): 2 1388 Included observations: 1387 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   C 0.200233 0.104029 1.924777 0.0545 MALE -0.004178 0.015872 -0.263210 0.7924 PARITY 0.018063 0.008887 2.032382 0.0423 LOG(FAMINC) -0.052142 0.008708 -5.987568 0.0000 CIGPRICE(-1) 0.000284 0.000778 0.364834 0.7153 R-squared 0.029867     Mean dependent var 0.104434 Adjusted R-squared 0.027059     S.D. dependent var 0.298729 S.E. of regression 0.294660     Akaike info criterion 0.397606 Sum squared resid 119.9911     Schwarz criterion 0.416477 Log likelihood -270.7398     Hannan-Quinn criter. 0.404664 F-statistic 10.63681     Durbin-Watson stat 1.945395 Prob(F-statistic) 0.000000 Read More