Global poverty and impact evaluation
Economics 174: Spring 2024 Problem Set 1 This assignment is due Sunday, February 25th by 11:59pm. Note that late submissions will not be accepted. This problem set contains four questions and is worth a total of 100 points. You may work in groups of up to four people total, but you must write up (and understand) your own answers. Do not copy and paste answers or parts of answers from one another. Identical answers will results in zero. Please submit your completed assignment by uploading to bCourses. Your submission should include two components: (1) a list of any other students you worked with, (2) the text of your response (along with any equations, diagrams, etc.). Short questions (40 pts) 1. Explain what is population tax? (2 pts) 2. Is population growth an asset or a liability for development, or both? Explain. (6 pts) 3. What is the poverty gap? What is the drawback of poverty head count ratio. What is the advantage of this measure over the headcount ratio? (6 pts) 4. Consider a country in which 20 percent of the population live on 20 cents per day, 15 percent live on 30 cents per day, 15 percent live on 50 cents per day, 10 percent live on 70 cents per day, 20 percent live on 90 cents per day, and 20 percent live on 1.50 dollars per day. If the poverty line is set at one dollar per day, what is the poverty headcount ratio? What is the poverty gap? What is the poverty severity? (6pts) 5. How should a country target a given welfare budget in order to minimize P0 (area B), or P2 (area A)? (8 pts) area A = area B 1 Economics 174: Spring 2024 Problem Set 1 6. How P0 , P1 , P2 change in graph (a), (b), (c) between situation 1 (black line) and situation 2 (blue line)? (12 points) Long Questions (60 pts) Question 1: Regression (30 pts) A group of researchers wishes to test whether cash transfers to low-income households have any spillovers on local small business owners. Their sample consists of 160 villages across 20 districts in India. The researchers randomly assign 80 villages to control and 80 villages to treatment, stratifying by district. In control villages, no households receive cash transfers. In treatment villages, approximately one fourth of households receive a cash transfer. The researchers conduct surveys with a sample of 10-15 small business owners in each village 3 months 2 Economics 174: Spring 2024 Problem Set 1 after the cash transfers are disbursed. Note that none of the small business owners are also cash transfer recipients. In these surveys, the researchers collect information such as the nature of the business as well as monthly revenues, labor costs, input costs, and profits. The researchers run the following regression: Yivd = α0 + α1 Treatmentv + εivd In this regression, Yivd represents outcomes of interest (revenues, profits) for business owner i in village v in district d, T reatmentv denotes treatment status at the village level. Here is the regression table and results: (Note: The “village wealth index” (VWI) variable combines several indicators of village wealth, constructed so that the index has an average of zero and a standard deviation of one. Positive values indicate a village is wealthier, and the index is measured in standard deviation units.The variable ”Above median business assets” is a dummy variable that takes values 0 and 1. 1 if the business has above median assets and 0 if the business has below median assets) Monthly Revenues Monthly Profits Monthly Revenues Monthly Revenues (1) (2) (3) (4) 180.3*** (58.6) 22.5* (12.4) 280.1*** (81.2) 130.8** (48.7) -105.3** (45.4) 240.4*** (67.3) Treatment Village wealth index Treatment * Village wealth index Above median business assets 110.5* (54.6) -68.3*** (20.6) Treatment * Above median business assets Control Mean Observations 1560 1920 185 1920 1560 1920 1560 1920 (a) (4 pt) Write out the regression equation for results presented in column (3). What’s the variable of interest and coefficient? (b) (6 pts) Columns (1) and (2) below show the results of this analysis. Interpret these results, commenting on the magnitude and significance of the parameters of interest. (c) (5 pts ) What is the 95% confidence interval around the estimated treatment effect in column (1) and (2)? What does this confidence interval tell you? (d) (12 pts) In columns (3) and (4), the researchers want to test whether the cash transfers had differential impacts on business revenues based on individual business owner’s characteristics and village characteristics. Write down the regressions depicted in columns (3) and (4). Interpret each of the parameters in detail. (e) (3 pts) How would you summarize these results? 3 Economics 174: Spring 2024 Problem Set 1 Question 2: Potential Outcomes (30 points) Suppose a state government in India wishes to improve child immunization rates among its rural and lowincome populations. Achieving complete immunization entails several doses of different immunizations (BCG, DPT, polio, measles) requiring repeated visits to a health clinic over the course of many months. As a result, full immunization rates are relatively low among rural and low-income populations in this context. This state government decides to partner with a technology start up that has created a phone-based program to help parents track their child’s immunization history. Parents who sign up for the program receive text message reminders around the time their child is due for the next immunization. Parents can also request a text message summarizing their child’s immunization history and providing information about remaining immunizations at any point. Your research team is working in partnership with the state government to assess whether this program improves immunization rates among rural and low-income populations. To that end, the state government offered this program to parents who gave birth at any of a set of 20 hospitals in the state that participated in the research. Parents could choose whether to sign up for the service at the hospital when their child was born. Your research team is able to collect for each birth: (1) basic information about the household (including monthly household income, monthly consumption, number of adults and children in the household, etc.), (2) whether or not the parents signed up for the text message reminders program, and (3) the child’s full immunization history (specifically, whether the child completed the full set of required immunizations). Suppose that for 40% of births, parents choose to sign up for the program. Of the children born during this year to parents who signed up, complete immunization rates averaged 60%. Of the children born during this year to parents who did not sign up, complete immunization rates averaged 25%. (a) (2 pt) Based on the described setup, what are the outcome of interest (Yi ) and the treatment (Di )? (b) (4 pts) What are the four potential outcomes of interest? For each, include the mathematical expression (something like E[. . . | . . . ]) and a brief statement of what that expression represents. (c) (4 pts) How do these four potential outcomes relate to the outcomes your research team is able to observe? (Which of these are realized outcomes versus which represent counterfactual outcomes?) The government is deciding whether they will automatically offer this service to all parents, instead of requiring parents to sign up for the service. To help make the decision, the Minister of Health asks your research team to report the results of your research after the first year. (d) (4 pts) Simply comparing immunization rates across children whose parents did and did not sign up for the program, what is the program’s apparent impact? Are you confident that this estimate represents the true impact of the text message reminder program on immunization rates? Why or why not? (e) (6 pts) If you are not confident, how would you concisely explain your concerns to the Minister of Health in words? How would you illustrate your concerns mathematically? If you are confident, how would you support the validity of your estimate to the Minister of Health, in words and mathematically? Because the program will be costly to provide to all parents, the Minister of Health decides to fund your research team to conduct additional research before making a decision. Specifically, she would like you to run a randomized evaluation, where for a new sample of 20 hospitals, parents giving birth in 10 hospitals are automatically enrolled in the program, while parents are not offered the program in 10 of the hospitals. (f) (2 pts) Intuitively, how would you expect the estimate of the impact of the program to compare to that from part (d)? (Would it be smaller, larger, the same?) (g) (8 pts) Describe mathematically and in words how this estimate will differ from the estimate in part (d). If the estimate of impact of the program will be the same as in part (d), show why that is so. 4
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