ps1_iv_card_schholing.Rmd

---
title: "IO & Econometrics workshop - PS1"
author: "Doron Zamir"
output:
  html_document:
    keep_md: yes
    df_print: paged
  pdf_document: default
---
This is a markdown file created using RStudio.

### Using Packeges
I used these packages to create the data:

```{r warning= FALSE, message=FALSE}
library(tidyverse)
library(knitr)
library(magrittr)
library(AER)
library(broom)
```
```{r, include=FALSE}
knitr::opts_chunk$set(warning = FALSE, message = FALSE)
```

## Tidy the Data
### Importing Data
 
I used the data from [David Card's website](https://davidcard.berkeley.edu/data_sets.html) 
The relevant file is `nls.dat` saved in the `Data` directory.

```{r }
data <- read.table("Data/nls.dat") %>% as_data_frame()
head(data)
```
### Changing col names & type

Using variable names from `code_bk.txt'

```{r}
colnames(data) <-(c("id","nearc2","nearc4","nearc4a","nearc4b","ed76","ed66","age76","daded","nodaded","momed","nomomed","weight","momdad14","sinmom14","step14","reg661","reg662","reg663","reg664","reg665","reg666","reg667","reg668","reg669","south66","work76","work78","lwage76","lwage78","famed","black","smsa76r","smsa78r","reg76r","reg78r","reg80r","smsa66r","wage76","wage78","wage80","noint78","noint80","enroll76","enroll78","enroll80","kww","iq","marsta76","marsta78","marsta80","libcrd14"))

data %<>% mutate_if(is_character,suppressWarnings(as.numeric))
head(data)
```
### Creating new Varibales for experiance
$$exp76=age76-ed76-6$$
$$exp762=exp76*exp76$$
```{r}
data <- data %>% mutate(exp76 =  age76-ed76 - 6)
data <- data %>% mutate(exp762 = exp76 ** 2)
```

### Sumaarise Data

```{r}
data_summary <- data[-1] %>%
  summarise_all(list(
    Min = min, 
    Mean = mean, 
    Max = max,
    SD = sd)) %>%
  pivot_longer(everything(),
               names_to = c("Var","Stat"),
               names_sep = "_") %>%
  pivot_wider(names_from = "Stat") %>% column_to_rownames("Var") 
data_summary %>% format(scientific = FALSE, digits = 2,trim = TRUE)  
```

## Plotting


```{r}
data_to_plot <- data %>% 
  mutate(
    black = factor(black,labels = c("no","yes")),
    nearc4=factor(nearc4,labels = c("no","yes")),
         )
```
### Education and lwage

```{r}
data_to_plot %>% ggplot(aes(ed76,lwage78)) +
  geom_point(aes(
    color = nearc4),
    alpha =0.4 ) +
  geom_smooth(method = lm)
```

### Splitting by distance from collage

```{r}
data_to_plot %>% ggplot(aes(ed76,lwage78)) +
  geom_point(aes(
    color = black),
    alpha =0.4 ) +
  geom_smooth(method = lm)+
  facet_grid(cols = vars(nearc4))
```

### Histogram of ed76

```{r}
data_to_plot %>% ggplot(aes(ed76)) + 
  geom_bar(aes(
    fill = black)) + 
  facet_grid(row = vars(nearc4))

```

## Estimating a model
### OLS
$$ lwage78 = \alpha \cdot ed76 + \beta \cdot X  + u$$

I used model #2 from Card's paper 
```{r}
ols_model <- data %>% lm(lwage78~ed76 + exp76 +exp762+smsa76r+ reg76r+smsa66r+              
+reg662+reg663+reg664+reg665+reg666+reg667+reg668+reg669, data = .)
kable(tidy(ols_model))
```

### 2SLS

$$ lwage78 = \alpha \cdot (\delta \cdot nearc4 + v) + \beta \cdot X  + u$$
```{r}
IV_model <- data %>% ivreg(lwage78~ed76 + exp76 +exp762+smsa76r+reg76r+smsa66r+reg662+reg663+reg664+reg665+reg666+reg667+reg668+reg669|exp76 +exp762+smsa76r+reg76r+smsa66r+reg662+reg663+reg664+reg665+reg666+reg667+reg668+reg669 + nearc4, data = .)
kable(tidy(IV_model))
```


I used a standard model of wage as function of education, controlling experince ($ exp^2) and using panel data for race, region of living, etc.

For IV, I used procimity to collage (as card did). It sounds like a reasnble IV as it is corelated with education, but it can fail. 
It can effect wage and earnings in more ways the just throw education: it can effect the quality of education, the enveirmont a perso grows in, etc.