Does a mother's smoking affect the birthweight of her child? Using the data file bweight_small, we explore this question. The file bweight contains more observations.

a. Estimate the regression model represented by equation (7.38) for BWEIGHT. Include as explanatory variables MMARRIED, MAGE, PRENATAL1, and FBABY, along with MBSMOKE and interactions between MBSMOKE and the other variables. Use equation (7.40), and the discussion below equation (7.40), to estimate the average treatment effect.

b. Use equation (7.41) to estimate the average treatment effect of mother smoking on infant birthweight, and construct a \(95 \%\) interval estimate for \(\tau_{A T E}\).

c. Calculate the normalized difference equation (7.44) for each of the variables MMARRIED, MAGE, PRENATAL1, and FBABY. Are any of the normalized differences bigger than the rule of thumb threshold of 0.25?

d. Use equation (7.42) to estimate the average treatment effect on the treated, \(\tau_{A T T}\). How much does it differ from your estimate of the population average treatment effect?

e. Use equation (7.43) to estimate the average treatment effect on the population of mothers who are Hispanic \((M H I S P=1)\). How does it compare to the estimated population average treatment effect?

f. Use equation (7.43) to estimate the average treatment effect on the population of mothers who are white \((M W H I T E=1)\). How does this compare to the population average treatment effect estimate?

Data From Equation 7.38, 7.40, 7.41, 7.42, 7.43,7.44:-

Transcribed Image Text:

y = a + Od; + x; +y(d;x;) + e; (7.38)