MATHEMATICS

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. For simplicity, assume that each household has a single member. The household data file called “Mexico Household Data” is available on SmartSite.  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 transfersfor 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. Below, report and briefly explain what each one means.

 

a.   The Poverty Headcount Index:

b.  The Total Poverty Gap (not the index):

c.   The Squared Poverty Gap Index:

 

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 andthose 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.       Income difference:

b.      Is this difference statistically significant?  How do you know?

c.       Is this difference economically significant?  Briefly support your answer.

 

5.      Compute the Gini index for recipient and non-recipient households. It would be easiest to use the Gini index formula from page 121 of the Taylor &Lybbert text. (Round-off to two decimal places)

 

a.       Gini index for recipients:

b.      Gini index for non-recipients:

 

6.      Construct two Lorenz curves, one for recipients and another for non-recipients. First, group the households into four income categories as defined below. Complete the table, and then graph the two Lorenz curves in one graph (using excel). Do not forget to include the point [0,0] in your graphs. When completing the table, round to 1 decimal (i.e. 3.2%).

 

Recipients
Income Category Cumulative % of Households Cumulative % of Income
1 25%  
2 50%  
3 75%  
4 100%  

 

Non-Recipients
Income Category Cumulative % of Households Cumulative % of Income
1 25%  
2 50%  
3 75%  
4 100%  

 

 

 


[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.

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