Part 1: Paper using randomized data: Impact of Class Size on Learning

What is the identification strategy?

Randomly distributing students and teachers to different class sizes.

What are the assumptions?

The size of class assigned to a student doesn’t impact parent’s behavior – shifting their kid’s school or classes, for instance.

Part 2: Using Twins for Identification: Economic Returns to Schooling

What is the identification strategy?

To rule out correlations related to ability and other genetic and family confounders, the paper focuses on outcomes of monozygotic twins.

What are the assumptions?

How family characteristics are related with other characteristics of twins is assumed to be the same for each twin.

Replication analysis

library(haven)
library(stargazer)
library(reshape)
#Loading data
data <- read_dta("D:/downloads/AshenfelterKrueger1994_twins.dta")

Table 3 Column 5

ed_dif <- data$educ1-data$educ2 #First difference for education
wage_dif <- data$lwage1-data$lwage2 #First difference for wage
reg1 <- lm(wage_dif ~ ed_dif, data=data) #running regression

#Regression results
stargazer(reg1, title="Table 3", align=TRUE, type="text", 
          dep.var.labels=c("First difference (v)"), 
          covariate.labels = c("Own education"))
## 
## Table 3
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                        First difference (v)    
## -----------------------------------------------
## Own education                0.092***          
##                               (0.024)          
##                                                
## Constant                      -0.079*          
##                               (0.045)          
##                                                
## -----------------------------------------------
## Observations                    149            
## R2                             0.092           
## Adjusted R2                    0.086           
## Residual Std. Error      0.554 (df = 147)      
## F Statistic           14.914*** (df = 1; 147)  
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

Interpretation

The impact of difference in schooling on difference in wages is 9.2%

Table 3 Column1

#Wage
wage_comb <- cbind(data$lwage1, data$lwage2)
wage <- melt(wage_comb) #reshaping wage
wage <- wage$value

#Education
educ_comb <- cbind(data$educ1, data$educ2)
educ <- melt(educ_comb) 
educ <- educ$value

#Age
age_comb <- cbind(data$age, data$age)
age <- melt(age_comb)
age <- age$value

#Age squared
agesq <- (age^2)/100

#Male
male_comb <- cbind(data$male1,data$male2)
male <- melt(male_comb)
male <- male$value

#White
white_comb <- cbind(data$white1,data$white2)
white <- melt(white_comb)
white <- white$value

data2 <- cbind(wage, educ, age, agesq, male, white) #combining into a new data
data3 <- data.frame(data2) 
#Running regression and printing table
reg2 <- lm(wage ~ educ+age+agesq+male+white, data=data3)

stargazer(reg2, reg1, title="Table 3", align=TRUE, type="text", 
          dep.var.labels=c("OLS (i)", "First difference (v)"), 
          covariate.labels = c("Own education", "Age", "Age squared / 100",
                               "Male", "White")) #regression table
## 
## Table 3
## ===================================================================
##                                   Dependent variable:              
##                     -----------------------------------------------
##                             OLS (i)          First difference (v)  
##                               (1)                     (2)          
## -------------------------------------------------------------------
## Own education              0.084***                                
##                             (0.014)                                
##                                                                    
## Age                        0.088***                                
##                             (0.019)                                
##                                                                    
## Age squared / 100          -0.087***                               
##                             (0.023)                                
##                                                                    
## Male                       0.204***                                
##                             (0.063)                                
##                                                                    
## White                      -0.410***                               
##                             (0.127)                                
##                                                                    
## ed_dif                                             0.092***        
##                                                     (0.024)        
##                                                                    
## Constant                    -0.471                  -0.079*        
##                             (0.426)                 (0.045)        
##                                                                    
## -------------------------------------------------------------------
## Observations                  298                     149          
## R2                           0.272                   0.092         
## Adjusted R2                  0.260                   0.086         
## Residual Std. Error    0.532 (df = 292)        0.554 (df = 147)    
## F Statistic         21.860*** (df = 5; 292) 14.914*** (df = 1; 147)
## ===================================================================
## Note:                                   *p<0.1; **p<0.05; ***p<0.01

Interpretation of the coefficient on education

An additional year of schooling increases wage on average by 8.4%

Interpretation of coefficients on other control variables

An additional year increase in age leads to a higher wage on average by 8.8%. On average, wage of male is higher than female by 20.4%. On average, wage of white people is lower than non–whites by 41%