03 Jun Question For problems 1–5 you will use data from the 2008 Me
Question
For problems 1–5 you will use data from the 2008 Mexico National Rural Household Survey to study
poverty in rural Mexico.1 You may assume that the data were generated from a simple random sample in
which the population of interest is all households in rural Mexico. The household data file called
“Mexico Household Data” is available on StartSmite. This data set contains the following variables for
the 1,437 sampled households: ID: The household identifying code. Yi: The household’s income in
2007, excluding government transfers. Ti: The amount of income transferred from the government to
household i.
1. What is your estimate of average household income excluding government transfers for rural Mexico
in 2007? In answering this question, report the following:
a. The sample mean, : ______
b. The sample variance, : ______
c. The variance of the sample mean, : ______
d. The standard error of the sample mean, : ______
e. The 95% confidence interval of the sample mean, 95% C.I.: _________
2. In the year of the survey, the per-capita food poverty line in rural Mexico was 7,596 pesos. Based on
this food poverty line, calculate the poverty headcount index and total poverty gap. For simplicity,
assume each household has a single member. Below, report and briefly explain what each one means.
a. The Poverty Headcount Index:
b. The Total Poverty Gap:
Mexico has two main government programs that transfer income to rural households. The first is
PROCAMPO, which pays a fixed amount per acre to farmers who grew basic grains prior to the North
American Free Trade Agreement (NAFTA). The goal of PROCAMPO was to replace pre-NAFTA output
price supports which were no longer allowed under NAFTA. The second is OPORTUNIDADES, a
welfare program that gives payments to poor women provided that their children are enrolled in schools
and receive health check-ups. Let’s call the households that received some transfers Recipients and those
that received no transfers Non-Recipients.
3. Fill in the table below, where now denotes household income including government transfers.
Recipients
Non-Recipients
95% C.I.
4. What is the difference in income including transfers between recipient and non-recipient households?
a. Difference:
1 These data were collected jointly by Ed Taylor from UCD and the Colegio de México. In order to reduce costs, the researchers used a stratified random sample in which first villages within each region and then approximately 20 households per village were randomly selected.
b. Is this difference statistically significant? How do you know?
c. Is this difference economically significant? Briefly support your answer.
Can you conclude that the difference in income across the Recipients and Non-Recipients that you
found above was caused by the government’s transfer programs? Briefly discuss why or why not.
5. Questions 6 asks you to explore more deeply various measures of income inequality in the context of two
hypothetical countries.
Consider a society (Society A) in which incomes take values in $1,000 increments between $1,000
and $10,000. An equal proportion of the society’s population (10%) occupies each of the ten income
classes. In other words, the income distribution for this society is as follows:
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