*******Please use R language in coding and do all parts.

This exercise analyzes the data from a recent paper that studies whether additional government revenues affect political corruption or the quality of politicians. The paper can be found at:

Brollo, Fernanda, et al. ["The political resource curse."](https://doi.org/10.1257/aer.103.5.1759) *The American Economic Review* 103.5 (2013): 1759-1796.

The authors argue that a "political resource curse" exists - that an increase in non-tax government revenues leads to more corruption and lowers the quality of politicians. First, with a larger budget size, incumbent politicians are more able to grab political rent without being noticed by the electorate. Second, a larger budget attracts challengers with poorer quality so that incumbents' misbehavior is punished less frequently.

The authors wish to identify the causal effect of additional federal transfers on corruption and candidate quality. Their theory states that additional non-tax revenues cause corruption, so they use transfers (the *treatment*) from the federal government to municipal governments as exogenous increases in non-tax revenues. The authors ask whether or not larger transfers lead to corruption, so the outcome is the occurrence of bad administration or overt corruption. Since corruption is a somewhat vague concept, the authors use two measurements to make sure that their results do not depend on a particular definition of corruption. To avoid this, the authors use two *separate* definitions of corruption to avoid this - 'narrow' corruption includes severe irregularities in audit reports, while 'broad' corruption is a looser interpretation "which includes irregularities [in audit reports] that could also be interpreted as bad administration rather than as overt corruption" (p. 1774).

The data can be found in `corruption.csv` in the `data` folder. Each row in the dataset is a Brazilian municipality that is found to be corrupt or not.

-------------------------------- ---------------------------------------------------------- Name Description -------------------------------- ---------------------------------------------------------- `broad` Whether any irregularity (this might include bad administration rather than corruption) was found or not. `narrow` Whether any severe irregularity that is more likely to be visible to voters was found or not. `fpm` The FPM transfers, in $100,000 at 2000 prices. `pop` Population estimates. `pop_cat` Population category with respect to FPM cutoffs. -------------------------------------------------------------------------------------------

## Question 1 Read in the data below for all municipalities in the authors' dataset. Then, create three regressions. Regress the *broad* measure of corruption on:

1. the measure of federal transfers 2. the measure of federal transfers and population. 3. the measure of federal transfers, population, and the population category (as a factor).

Then, repeat this analysis for the *narrow* measure of corruption (so you will have six regressions in total). Interpret the coefficients from the regressions. Can the coefficients be interpreted causally in these models? Explain why or why not.

# Your code here

- **Answer**:

## Question 2

The authors use a Regression Discontinuity (RD) design.

1. What do the authors use as the *forcing variable* and outcome variable? 2. Discuss why the authors can't simply compare all "treated" and "non-treated" municipalities. 3. Then, discuss how the RD design addresses this problem. What is one weakness of the RD design?

- **Answer**:

## Question 3

First, let's perform a simple RD analysis to test whether the Brazilian government used the population cut points correctly, so transfers were different for municipalities just below and above the cut points utilized. One of the population thresholds used for FPM transfers was 10188. This means that villages with a population slightly above 10188 received different amounts of transfers to villages slightly below this population. For this analysis, we will use all villages within 500 people of this cutoff. Specifically, this means to take two separate subsets: one subset of villages with populations larger but less than 500 larger than 10188 and another subset of villages with populations smaller but less than 500 smaller than 10188.

1. plot showing the relationship between population and fpm transfers for these villages. Please add a dotted vertical line to show the location of the cutoff (10188) on the x-axis. 2. Additionally, fit two regressions and visualize them on the plot: one showing the relationship between population and FPM transfers for the subset of villages *above* the cutoff and another showing the relationship between population and FPM transfers for the subset of villages *below* the cutoff.

```{r} # Your code here

```

- **Answer**:

## Question 4

What does the plot you just created tell you about how population and federal transfers are related? Do you see a difference between the amount of the federal transfers near the cut point?

Additionally, consider this: in real world settings, you often see "noncompliance" with different kinds of treatments. For example, patients may not take the medication their doctors prescribe. Do you see evidence of similar noncompliance in this setting, where the "patient" is the different Brazilian municipalities and the "doctor" in the federal government?

Would noncompliance like this be a problem for the RDD analysis based on using the population thresholds?

- **Answer**:

## Question 5

Now, we will perform a Regression Discontinuity analysis by taking observations that are close to *any* of the cutoffs.

In this question, we will be comparing rates of corruption for villages just above and below a series of population thresholds for different federal transfer amounts. Recall from the article that the amount of federal transfers to municipalities should change (discontinuously) at several population cut points (see Table 1 of the article).

To begin, create a subset of the data that contains observations within 500 people of the population cuttoffs: $\{10188, 13584, 16980, 23772, 30564, 37356, 44148\}$. We want to include all municipalities that have populations within 500 people above or below any of these cutoffs (the R 'OR' operator, `|`, may be useful here).

Next, using that subset for municipalities within the 500 +/- range of the cutoffs, create an indicator variable to show whether each remaining observation is above or below the nearest cutoff point. For example, a municipality with a population of 10,180 would be "0", a 10,200 would "1", a 13,500 would be "0", and a 13,600 would be "1" and so on.

You should now have a subset of data with the columns for "broad", "narrow" and the 0/1 indicator variable, where the a "1" indicates the population is just above the nearest cut off point and a "0" indicates the population is just below the nearest cut off point.

Now, use `lm()` to compare the rates of broad and narrow corruption for municipalities just above and just below these thresholds. Explain your interpretation of the coefficient for the indicator variable. Does this evidence support the "political resource curse" hypothesis?

Finally, earlier in question 1, you performed a simple analysis that regressed measures of corruption on federal transfers. Between what you did in question 1 and what you just did in question 5, is one of the results more convincing? If so, which one?

```{r} # Your code here ```

- **Answer**:

Please use R language in coding.

https://drive.google.com/file/d/1zCJdS0jT42HanjI5QpG_0BvUlX5BF6-d/view?usp=sharing here is the data