Using the data BirthWt. xlsx, we want to see if the dependent variable LogBW (log of the weight of the child at birth) is affected by maternal smoking during pregnancy, which is measured by the number of cigarettes the pregnant mother smoked during the pregnancy (CigPerDay) We suspect that this variable CigPerDay may be correlated with the regression error leading to an instrumental variable problem. You can assume the other explanatory variables are uncorrelated with the error. These variable are:
Order: which is the order of birth
Male: Dummy variable taking 1 if child's sex is male,
The potential instrumental variables, which might affect maternal smoking behavior but have no direct influence on birth weight, are years of maternal schooling (MotherEducation), years of paternal schooling (FatherEducation) and family income (FamilyIncome), measured in thousands of US dollars).
Undertake the following steps to look at the potential Instrumental Variable problem:
Run an OLS regression of LogBW on an intercept, CigPerDay, Order and Male. Assuming (possibly incorrectly) that CigPerDay is uncorrelated with the error. Interpret the results of this OLS regression. Does maternal smoking have a negative impact on birth weight?
a- Test for evidence on multicollinearity and heteroscedasticity.
b- Test BetaMotherCigPerDay = -0.0060
c- Jointly test Beta_Male = BetaBirthorder= 0