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Q1) Present summary statistics for treatment villages vs. control villages. Specifically, test whether differences in age, education, and gender are statistically different between the treatment and control group.

Q2) Present community summary statistics for treatment villages vs. control villages. Are there any differences? Look at access to electricity, piped water, and distance from the capital. Do a test to see whether differences are statistically different between the treatment and control group.

Q3) Based on your analysis so far, do you think that treatment villages are different from control villages? Why do you think secondary schools were built in treatment villages?

Q4) We are now going to get the naïve diff-in-diff estimate. Please calculate the effect of having a new secondary school built in your village using the two-by-two table of summary statistics that characterizes the diff-in-diff models.

Q5) We will now estimate the treatment effect using a diff-in-diff regression. Write out the regression model and estimate it. Which coefficient shows the causal effect of building new schools? Is it statistically significant (at the 5% level)? How does it compare to your response in Q4?

Q6) What is the main assumption you need to make in the difference-in-difference model in order to interpret the effect you estimate above as causal? (In other words, what is necessary to happen so that you don’t have biased results?) How would you test this assumption? Explain what data you would need and what regression model or graph you would use.

## Summary statistics for treatment villages vs. control villages

Q1) Present summary statistics for treatment villages vs. control villages. Specifically, test whether differences in age, education, and gender are statistically different between the treatment and control group.

Summary statistics for treatment villages vs. control villages

ANOVA

The p-values of the different tests have a p-value < 0.05. Thus we, we reject the null hypothesis that the group has no effect on the two ratings of treatment.  Therefore, age, education, and gender are statistically different between the treatment and control group.

Q2) Present community summary statistics for treatment villages vs. control villages. Are there any differences? Look at access to electricity, piped water, and distance from the capital. Do a test to see whether differences are statistically different between the treatment and control group.

Electricity

The result shows that villages without electricity had statistically significantly lower number of secondary schools (0.268   0.07) compared to villages with electricity (0.3  0.15), t(49) = -0.1975, p = 0.8442.

Piped water

The result shows that villages without piped water had statistically significantly lower number of secondary schools (0.22   0.07) compared to villages with piped water (0.2  0.2), t(49) = 0.1319, p = 0.8956.

The result shows that villages that are very distant from the capital had a statistically significantly lower number of secondary schools (44.4   9.2) compared to villages that are less distant from the capital (69.89  11.7), t(49) = 0.85, p = 0.3.

Q3) Based on your analysis so far, do you think that treatment villages are different from control villages?

Yes, there the treatment villages are different from the control villages in terms of age, gender and education.

Why do you think secondary schools were built in treatment villages?

The secondary schools were built in treatment villages due to the availability of piped water, electricity, and the close proximity to the capital.

Q4) We are now going to get the naïve diff-in-diff estimate. Please calculate the effect of having a new secondary school built in your village using the two-by-two table of summary statistics that characterizes the diff-in-diff models.

From the figure above, it is evident that 342 persons not aged 6 to 16 completed primary school with no secondary school while 18 of those in the cohort 6 to 16 years completed primary school with secondary schools available. Conversely, 674 persons not aged 6 to 16 completed primary school with no secondary school while 165 of those in the cohort 6 to 16 years completed primary school with secondary schools available.

## Community summary statistics test

Q5) We will now estimate the treatment effect using a diff-in-diff regression. Write out the regression model and estimate it. Which coefficient shows the causal effect of building new schools? Is it statistically significant (at the 5% level)? How does it compare to your response in Q4?

For every unit increase in ycohort, we expect 1.812 increase in the log-odds of the dependent variable primary. Consequently, for every unit increase in ycohort with access to secondary school, we expect a 0.865 increase in the log-odds of the dependent variable primary. The coefficients are statistically significant at p = 0.05. The results compares with Q4 as the presence of secondary schools does not significantly affects completion of secondary school.

Q6) What is the main assumption you need to make in the difference-in-difference model in order to interpret the effect you estimate above as causal? (In other words, what is necessary to happen so that you don’t have biased results?)

The main assumptions to interpret the effect estimated as casual the assumptions of exchangeability, positivity and stable unit treatment value assumption must hold. The assumption that is commonly used is parallel trend assumption.

How would you test this assumption?

The parallel trend assumption is tested by ensuring that the absence of treatment, the difference between control and treatment group is constant over time.

Explain what data you would need and what regression model or graph you would use.

A graph is necessary which is plotted by the treatment group against time.

Q1: The lost boys of Neverland build a few artificial reefs around several of their coastal villages. Artificial reefs are great for marine life and are believed to stimulate tourism. Yet, as any good economist, the lost boys don’t want to take things for granted. They want to know whether the artificial reefs they built indeed helped local businesses. They ask you to do the evaluation. What evaluation approach would you suggest and what data would you ask for/collect?

The evaluation approach that should be used is Diff-in-diff. The data to be used is in the regression model will be the level of business before and after installation of the artificial reefs. The artificial reefs will be the independent variable while the level of business will be the dependent variables.

Q2: Captain Cook is fed up with Peter Pan always outsmarting him and his pirates. He hears that there is a magic box called a “computer” that could give out fighting secrets if his pirates know how to use it. But he doesn’t really know what this computer thing does and whether its secrets are actually useful so he wants to formally test whether these metal boxes are effective in improving the skills of his pirates. He comes to you for help before he buys any computers. What evaluation approach would you suggest and what data would you ask for/collect?

## Naive diff-in-diff estimate

The evaluation approach that should be used for Cook is Instrumental Variable (IV). IV is used in a regression analysis when there is an endogenous variable that is influenced by other variables (Stock & Yogo, 2005). The data needed for this is the level of skills his pirates have before and after the boxes are introduced. Then the skills levels will be regressed against the use of computers.

Q3: As you know, the lost boys can fly if they can generate a certain number of “lovely wonderful thoughts”. Tinker Bell likes the number 33. So she decided that if they generate 33 or more happy thoughts, they can fly. While most lost boys are pretty happy and can easily generate at least 25 happy thoughts, some fall short of the required number and cannot fly. Peter Pan is lobbying for Tinker Bell to get rid of that arbitrary rule and he is gathering evidence to prove that flying is good because it builds self-confidence. He comes to you for help. What evaluation approach would you suggest and what data would you ask for/collect?

The best evaluation approach is the Risk Difference (RD). RD compares two measures frequency through the calculation of their ration and compares them in their absolute difference (Cheung, 2007). The data required is the self-confidence index of the boys, number of happy thoughts generated, and the number of times they have flown. The variables will be tested using a multivariate ANOVA test.

Q4: Peter Pan is trying to recruit some more lost children! He doesn’t have time to go and personally invite every little boy and every little girl but he randomly chooses a few dozen children and visits them at night to tell them all about Neverland. To be fair to everyone, he also opens up the Neverland gates to any boy (and girl!) who wants to join so that even kids who didn’t get a personal visit could join. Now, Peter knows that the children who come to Neverland are happy children but he recently heard about the issue of “selection”. So he is starting to wonder if the children come to Neverland because they are happy or they are happy because they came to Neverland. He comes to you and asks you for help in figuring out whether coming to Neverland actually causes children to be happier. What evaluation approach would you suggest and what data would you ask for/collect?

A diff in diff approach should be used. Diff in diff calculates the effect of a treated explanatory variable on an outcome through the comparison of the average change over time (Villa, 2017). Data that are required the level of happiness of the children coming to Neverland and after coming to Neverland. The data will be tested using a t-test and a regression analysis.

Q5: Captain Cook is also recruiting pirates! In the sea of one thousand islands, he visits 200 islands to recruit from. In addition, he thinks that men who come from rural areas make better pirates, so he only recruits in rural areas and doesn’t take anyone who lives in urban areas. After he completes his recruitment, he brags that his men are the most ferocious of them all (they have a ferocity index of 52). But he doesn’t have proof for that statement and he likes to support his words with facts. So he comes to you to ask for help. What evaluation approach would you suggest and what data would you ask for/collect?

The evaluation approach that should be used in Cook’s scenario is Instrumental Variable (IV). IV is used in a regression analysis when there is an endogenous variable that is influenced by other variables (Newey & Powell 2003). The data to collect is the two groups of pirates who come from the rural areas and the urban areas. Then their ferocity index has to be collected for analysis. The independent data will be the areas they come from while ferocity will be the dependent variables.

Reference:

Cheung, Y. B. (2007). A modified least-squares regression approach to the estimation of risk difference. American journal of epidemiology, 166(11), 1337-1344.

Newey, W. K., & Powell, J. L. (2003). Instrumental variable estimation of nonparametric models. Econometrica, 71(5), 1565-1578.

Stock, J., & Yogo, M. (2005). Asymptotic distributions of instrumental variables statistics with many instruments (Vol. 6). Chapter.

Villa, J. (2017). DIFF: Stata module to perform Differences in Differences estimation.

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