the work is in the files
Please fill in your group members and IDs. Name 1: Student ID 1: Name 2: Student ID 2: Name 3: Student ID 3: Name 4: Student ID 4: ARE/ECN 115A Spring 2020 Problem Set 2: Inequality, Human Development, and Health Subsidies Due: April 28, 2020 11:59pm Instructions: All of the data for this problem set can be found in the Problem Set 2 folder in Canvas (files/folder/Problem Sets/SQ 2020). Note that the space for each answer is restricted, so your answer may be cut off if it exceeds the length of the designed box. Please check your answer carefully before submitting. Submission comes in two steps: 1. Gradescope: Your group will turn in a PDF of the problem set on Gradescope as a group. Indicate members in your group on Gradescope. 2. Canvas: Each member of the group will submit an Excel file for Question 1&2 of the problem set on Canvas (Under Assignment tab/Problem Set 2) individually on Canvas. Failure to do so would lead to a 10-point deduction to your individual grade. Please fill out the “SQ2020_PS2_template” Excel file (use two decimal spaces for display) and copy each of the two figures described below into the worksheet that has a title matching the figure number. Problem 1: Lorenz curves and Gini coefficients Using the KwaZulu-Natal Income Dynamics Study (KIDS) survey, we will examine the evolution of inequality in South Africa between 1993 and 2004. (Use the data provided in the “SQ2020_PS2_template” Excel file under the worksheet titled “Q1_Lorenz and Gini_n” in the folder for Problem Set 2. DO NOT use the data from the Problem Set 1 since it is a different version. All the numbers are reported in real values of 2000. Thus, there is no need to use any CPI conversions.) (a) Plot the Lorenz curves for per-capita expenditures for 1993, 1998 and 2004 in Excel. Put the three Lorenz curves on a single graph. While there are multiples ways to generate the Lorenz curves, we would like you to divide your sample into ten deciles of per-capita expenditures (so that you have 11 points on the horizontal axis). Please fill out the following table first, which will help you plot the Lorenz curve for each year in Excel. Please insert final graph AS AN IMAGE (screenshot is allowed) under this question AND copy it into the worksheet titled “Figure 1A” in the Excel template. (Use two decimal spaces for display along the axes) Income Decile Percent of Population Cumulative percent of Population Cumulative Percent of Income 1993 Cumulative Percent of Income 1998 Cumulative Percent of Income 2004 0 0.00% 0.00% 0.00% 0.00% 0.00% 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (b) Based on your Lorenz curves, briefly explain what you conclude about the evolution of inequality in South Africa. (c) Will your answer to (a) change if all the income numbers become 10 times larger than the original ones? Briefly explain. (d) Will your answer to (a) change if we add 100 to all the income numbers? Briefly explain. (e) Use the covariance formula to calculate the Gini coefficient and report the Gini coefficients for 1993, 1998 and 2004 in the table below.[footnoteRef:1] (Use two decimal spaces for display) [1: See Chapter 5 of Taylor and Lybbert (page 121) for instructions on calculating the Gini coefficient in Excel.] The Evolution of Inequality in South Africa 1993 1998 2004 Gini Coefficient (f) Based on your Gini coefficients, briefly explain what you conclude about the evolution of inequality in South Africa. Problem 2: Human Development Index This question asks you to empirically explore the strength of the relationship between income per capita and measurement of human development. To answer this question, use the Human Development Report Data in the second worksheet of the SQ2020_PS2_template. This file contains data from 2017 for 189 countries and comes from the United Nations Development Program country-level data sets. To calculate the indexes, use the minimum and maximum values for Gross National Income (GNI), life expectancy at birth (LE), mean years of schooling (MYSA), and expected years of schooling (EYSC) that are provided in the Excel spreadsheet. (a) In your Excel file, calculate Human Development Index (HDI) for all countries and fill in the table below. (Use two decimal spaces for display) Country Singapore United States Malaysia Kenya Haiti (b) Generate the scatter plot for human development (HDI) vs. income (GNI) per capita with HDI on the vertical axis and GNI per capita on the horizontal axis (for all countries). Add a logarithmic trend-line through the data points. Please insert the final graph AS AN IMAGE (screenshot is allowed) under this question AND copy it into the Excel worksheet titled “Figure 2B” in the Excel template. (c) In a few sentences, discuss the relationship between income per capita and HDI. Do you conclude that higher income per capita leads to better performance in terms of the human development indicator? Is the relationship strong? Do you notice any outliers? Problem 3: Targeting Health Subsidies Pascaline Dupas, Vivian Hoffmann, Michael Kremer, and Alix Peterson Zwane did a Randomized Controlled Trial (RCT) on ways of delivering chlorine tablets to treat water. They designed this experiment to address two issues that some public health systems have faced. First, they want to test whether those who need the product do receive it under each delivery mechanism: if there are people who aren’t receiving it who should, this is called overexclusion. Secondly, they want to test if people who receive the tablets waste them by not using them correctly, which is called overinclusion. Both of these issues could happen under the same delivery mechanism. These issues of “targeting” are also crucial in distributing other health goods, such as insecticide-treated bednets which help prevent malaria. You have been asked by a policymaker in Kenya to evaluate the best way to distribute bednets, accounting for the trade-offs between overexclusion and overinclusion. (a) In two sentences or less, why should the policymaker care if there is overexclusion in the provision of treated bednets (that is, if those who need bednets do not receive them)? (b) In two sentences or less, why should they care if there is overinclusion (that is, if recipients don’t use them correctly)? Having read this paper in your development economics class, you decide to run a similar experiment which compares (i) partially subsidized (50% subsidy) bednets available for immediate purchase at enrollment (“Cost Sharing”), (ii) totally free bednets available immediately at enrollment (“Free Delivery”), and (iii) vouchers for free bednets which the household can redeem at a local shop (“Vouchers”). 900 households from the target population were randomly assigned to one of the three experimental conditions (300 per treatment arm). You then visit households on unannounced days to see whether households are correctly using their treated bednets. The following table reports take-up and bednets usage at the later visit by treatment arm: Treatment Arm Take-up: Correct Bednet Usage Mean Unconditional Mean Cost Sharing Purchased bednet .178 .107 Free Delivery Accepted bednet .995 .787 Vouchers Redeemed voucher for bednet .862 .753 (c) Calculate the rate of overinclusion and overexclusion for each treatment arm, and write them in the table below. To calculate the rate of overinclusion, find the share of people who received a bednet who did not use it correctly (takeup – usage rates). To calculate the rate of overexclusion, use the rate of correct bednet usage among those in the free delivery arm as the comparison point – that is, what share of people who would have used the bednet correctly if given it for free are not using it under this treatment arm (subtract the usage rate from the rate under free delivery)? (Use three decimal spaces for Display. No need to convert decimals to percents.) Treatment Arm Overinclusion Overexclusion Cost Sharing Free Delivery Vouchers Given the results of your study, the policymaker is trying to decide whether to provide bednets via free delivery or vouchers to their population of 1000 households. They have read Dupas et al’s paper and so want to use the inequality she provides. That is, they will prefer free delivery to vouchers if the following equation holds: Let denote free delivery of bednets while denotes vouchers. The policymaker has told you that their valuation of each additional household using bednets correctly is $50 (). Furthermore, the cost of each bednet, regardless of distribution mechanism, is $7 (). (d) Given your findings about the number of households using bednets correctly under each policy ( and ), as well as the number of bednets distributed under each policy ( and ), should you recommend a policy of free bednet distribution or vouchers? How does this compare to the recommendation made by Pascaline Dupas and her coauthors about chlorine tablets? Please show your work on the calculations and briefly explain. 3