# Matching Lab

## Data and R Libraries
This exercise and problem set 4 both use the `lalonde` dataset from the following paper:

> Dehejia, R. H. and Wahba, S. 1999. [Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs](https://www-jstor-org.proxy.library.cornell.edu/stable/2669919?). Journal of the American Statistical Association 94(448):1053--1062.

The paper compares methods for observational causal inference to recover an average causal effect that was already known from a randomized experiment. You do not need to read the paper; we will just use the study's data as an illustration. We'll load the data into R with the first code block.

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library("tidyverse")
library("MatchIt")
data("lalonde") # this step loads the data
```

To learn about the data, type `?lalonde` in your R console.



### 2.1.  Using `matchit()` to conduct a matching

For this part, we assume that three variables comprise a sufficient adjustment set: `race`, `married`, and `nodegree`. We use `matchit` with:

- a formula `treat ~ race + married + nodegree`
- `method = "exact"` to conduct exact matching, which matches two units only if they are identical along `race`, `married`, and `nodegree`
- `data = lalonde` since we are using the `lalonde` data
-  `estimand = "ATT"` since we are targeting the average treatment effect on the treated (ATT)

We then use the `summary()` function to see how many control units and how many treatment units were matched. 

```{r}
exact <- matchit(treat ~ race + married + nodegree + re74, 
                 data = lalonde, 
                 method = "exact",  
                 estimand = "ATT")

summary(exact)
```

```{r}

#coarsened exact matching
matched_set <- matchit(treat ~ race + married + nodegree + re74, 
                 data = lalonde, 
                 method = "cem",  
                 estimand = "ATT")

summary(matched_set)

# Mahalanobis
matched_set <- matchit(treat ~ race + married + nodegree + re74, 
                 data = lalonde, 
                 distance = "mahalanobis",  
                 estimand = "ATT")

summary(matched_set)


# Propensity Score
matched_set <- matchit(treat ~ race + married + nodegree + re74, 
                 data = lalonde, 
                 method = "nearest",
                 distance = "glm",
                 estimand = "ATT")
summary(matched_set)
plot(matched_set, type = "jitter")
plot(matched_set, type = "density")
```


### 2.2. Effect estimate

Here, we estimate a linear regression model using the match data from 2.1 using the `lm()` function with the formula `re78 ~ treat + race + married + nodegree`. We pass weights that come from the matching. Notice that for this piece, we have passed the matched data `match.data(exact)`. The coefficient in front of the variable `treat` in the linear regression is our estimated effect.

```{r}
fit <- lm(re78 ~ treat + race + married + nodegree + re74,
          data = match.data(matched_set),
          w = weights)
print(round(coef(fit)["treat"],2))
```