8. (20 points) Let mort be the infant mortality rate at hospitals. A model to es

Question

8. (20 points) Let mort be the infant mortality rate at hospitals. A model to estimate
the effect of per capital government health expenditures on infant mortality is:
mort = 0 + 1 log(expend) + 2 log (beds) + 3 poverty + u,
where expend measures per capital government health expenditures (in real U.S.
dollars), beds is the number of beds at a hospital, and poverty is the percentage of
mothers at the hospital who live in poverty.
a. Let welfare be the percentage of mothers at the hospital who receive welfare
payments from the government. Would the percentage of mothers who receive
welfare payments be a good proxy variable for poverty? Explain.

b. The following table contains OLS estimates (SE) for two different models.
Interpret coefficient estimates in Models 1 and 2.

Independent variables Model 1         Model 2
Log (expend)        -12.12 (4.32)     -4.57 (2.68)
Log (beds)            -3.34 (0.514)     -1.62 (0.58)
welfare                           -                 -0.884 (0.292)
Intercept                25.61 (6.93)       17.32 (15.86)
Observations         1828                  1828
R-squared              0.0727               0.1517

c. Explain why the effect of expenditures on reducing infant mortality is much lower
in Model 2 than in Model 1. Is the effect of expenditures in Model 2 statistically
greater than zero?

d. Are infant mortality rates on average lower at larger hospitals, other factors
being equal?

e. What do you make of the increase in R-squared from Model 1 to Model 2?

Explanation / Answer

a)

No the percentage of mothers who receive welfare payments cannot be good proxy variable for the poverty as poverty is the defined as percentage of mothers who lives in poverty and welfare as percentage of mothers who receives welfare payments from the government. There can be cases where a mother who doesn’t live in poverty can receive the welfare payments from the government.

b)

Welfare is provided by the government as a part of government expenditure. There is strong correlation between government expenditure and the welfare.

Model 1 has only expenditure as the independent variable whereas model 2 has both welfare and the expenditure as independent variable. Thus model 1 has higher coefficient as expenditure whereas model 2 has its coefficient divided between expenditure and the welfare. The effect of expenditure in model 2 is lower because some of the effect in reducing mortality is also defined by the variable welfare, which is a part of government expenditure itself.

d)

yes infant mortality rates on average lower at larger hospitals, other factors being constant as the variable bed is one of the significant determinant of the mortality rates. The number of beds is in the larger hospital is expected to be more than the number of beds in the smaller hospital.

e)

Increase in R-square from model 1 to model 2 implies that the variance in the mortality rate is more explained by the model 2 than the model 1. The model 1 can only explain 7.27% of the infant mortality rate where as the model 2 can explain approx. 15% of the infant mortality rate. Thus model 2 is better predictor than the model 1

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