Question 4 Let\'s say we wanted to evaluate the effectiveness of a water-cleanin

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Question 4 Let's say we wanted to evaluate the effectiveness of a water-cleaning program in Kenya on the health of the country's people. The Kenyan government constructed and delivered free clearn piped water to a quarter of the villages in the country. We have the data for a random sample of individuals in Kenya, and we know if they lived in a village that received free clean water CLEAN-1 if the water is provided by the Kenyan government) or not (CLEAN-0). We also know how many days over the last month each individual in our sample felt sick, S,. The equation we estimated is below. Standard errors are in parentheses 0. S, = 1.5 + 2.5 CLEAN, 50) (1.25) where: SF sick days in the last month for individual i CLEAN,= indicator equaling 1 if the Kenyan government provided clean piped water to the village of individual i a) Interpret A and b) Can you reject the idea that having clean piped water provided by the Kenyan govern- ment has no effect on the number of days a person is sick per month? c) Is the result from b) combined with the sign of unexpected? Why or why not? d) Many times when governments of developing countries spend money on providing free services to a part of their population, they choose to deliver the services to the poorest villages, as they are typically the ones that are in biggest need of the public programs. Given this information, what do you think would happen to your original estimate of the effect of the clean water program on sickness (bigger, smaller, same) from equation 2 if you included into equation [2 a variable WEALTH, which represented the wealth of individual i,? Why? e) Many times when governments of developing countries spend money delivering free ser- vices to certain areas of the country they also must engage in other infrastructure projects (roads, health clinics for government workers, etc.) Also, since new and better infras tructure is now available in these villages, usually non-government organizations (NGOs) and charities that previously had no access to these areas start to provide their services for the first time. Given this information, what do you think would happen to your orig inal estimate of the effect of the clean water program on sickness (bigger, smaller, same) from equation 2 if you included into equation 2, a variable NGO, which represents the number of NGOs currentlv operating in individual is village? Why? f What do you think would happen to your original estimate of the effect of the clean water program on sickness (bigger, smaller, same) from equation 2 if you included into equation 2], a variable MONTH (1 to 12), which represents the month individual i was born Why? g) What is an example of an important variable, excluded from equation [2)? How would it change your original estimate in equation [2 of the effect of the clean water program on sickness?

Explanation / Answer

a. Beta_0 is the intercept in the equation. It tells us the average sich days when clean = 0, i.e. when there is no clean water provided. Beta_2 is the slope coefficient which measures additional sick days if the water is clean, clean = 1

b. H0 : beta1 = 0

Ha : beta1 is not equal to zero

t = (2.5-0)/1.25 = 2 > 1.96 at 5% significance level.

So, we reject the null hypothesis that the clean water has no effect on the days felt sick

c. The result from b is unexpected as the sign of beta1 is positive and we have statistically found from b that it is different from 0. Hence, we expect number of sick days to go up when clean water is provided. This is unexpected.

d. If we include the variable measuring the wealth of the individual, then we expect the number of sick days to go down as the wealth increases, i.e, the slope coefficient is expected to be negative and sickness is expected to go down.

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