Application questions.

Read carefully the following and answer all the questions. The information is provided in the

table below. State all the relevant formulas and all your calculations.

You are part of a World Bank mission to the country of Tatooine created with the objective of evalu-

ating two policy policy programs in terms of their eect on household income per person. The rst one is

an agricultural training program targeted to the population that is concentrated in the most fertile region

of the country. The second program is a subsidy designed to incentivize engagement in activities related

machinery production and repair among the population that lives in the infertile regions of the country. It

is known that educational attainment levels, family composition and other sociodemographic variables vary

according to the region inhabited. That is, the sociodemographic variables are dierent between the most

fertile and the most infertile regions.

Due to budgetary constraints, none of the programs was able to cover its target population in full. Taking

advantage of this limitation, the policy makers decided to randomize the assignment of the programs across

its target populations.

The rst program was designed as follows. Those that were selected into the treatment group received

a semester long training program on how to take advantage of the characteristics of the land they owned.

That is, they were introduced to the type of crops that have the highest yields and that can be produced in

the region, the dierent production processes that can be implemented due to the geological characteristics

and so on. The population that is part of the control group did not received any training.

The second program consisted on a xed subsidy to the employers in the manufacturing and repair service

sector per local worker employed. This means that on a monthly basis, employers told the government how

many local employees they have in the payroll, the government veried the information, and transferred an

amount kL to the employer, where k is the subsidy amount, and L the number of local employees hired.

Both programs have been instrumented over the last two years.

Table 1) shows the average household income of the control and treatment group of each intervention both at the moment the programs were

started, and at the moment you arrived to evaluate them. The table also shows the size of each group.

What condition, or conditions, need to hold in order for the randomization to have been correctly

implemented?.

Assume that condition, or conditions, hold. Your task is to evaluate if, at the end of the day, the

program had an eect on the household income per capita of the treated population with respect to

those in the control group. Calculate the ATE of each program on the nal level of household income

per capita, assuming that all the individuals are compliers.

Evaluate if the eect is statistically dierent from zero at the usual condence levels. For this case,

the standard errors have to be calculated following the formula:

Table 1: Outcomes Agricultural Program Manufacturing Program Pre-treatment Pre-treatment Treatment Control Treatment Control 7,100 7,103 5,600 5,599 n=2,000 n=2,000 n=1,700 n=1,700 Post-treatment Post-Treatment Treatment Control Treatment Control 9,000 9,200 8,000 7,300 n=2,000 n=2,000 n=1,700 n=1,700 OT SE= + o Table 1: Outcomes Agricultural Program Manufacturing Program Pre-treatment Pre-treatment Treatment Control Treatment Control 7,100 7,103 5,600 5,599 n=2,000 n=2,000 n=1,700 n=1,700 Post-treatment Post-Treatment Treatment Control Treatment Control 9,000 9,200 8,000 7,300 n=2,000 n=2,000 n=1,700 n=1,700 OT SE= + o