1.1. Briefly answer these questions:

a.What is the causal link the paper is trying to reveal?

The paper try to reveal the effect of class size on student achievement (Stanford Achievement Test(SAT) and Tennessee Basic Skills First (BSF)).

  1. What would be the ideal experiment to test this causal link?

Kindergarten students and teachers are randomly assigned to different class size:small size, regular size, and regular/aide classes.

c.What is the identification strategy?

The paper used ordinary least squares and two stage least squares models to take into account class size.

  1. What are the assumptions / threats to this identification strategy?

This identification strategy would not be revealing a causal effect because re-randomization was done due to parent’s complaints about their children’s initial assignment. In addition, students switched between small and regular classes because of behavioral problems or parental complaints.These nonrandom transitions could be threats to the experimental results.

2.1. Briefly answer these questions:

  1. What is the causal link the paper is trying to reveal?

The study estimated economic returns to schooling by contrasting the wage rates of identical twins with different schooling levels.

  1. What would be the ideal experiment to test this causal link?

We can construct the experiment by contrasting the wage rates of twins with different education levels.

  1. What is the identificationstrategy?

The study used OLS and generalized least squares. The fixed effects is also used to eliminate the omitted variable bias.

  1. What are the assumptions / threats to this identification strategy? (Answer specifically with reference to the data the authors are using)

The correlation between variables in the Census for the Current Population Survey (CPS) gives the clue of the measurement error in the data, which is threats to the identification strategy.

2.2. Replication analysis b. Reproduce the result from table 3 column 5.

library(haven)
twins <- read_dta("C:/Users/ho643/OneDrive - University of Georgia/UGA/2023 Spring/AAEC8610 Adv Quant Meth Econ/HW/HW4/AshenfelterKrueger1994_twins.dta")
wage_d<-twins$lwage1-twins$lwage2
edu_d<-twins$educ1-twins$educ2
reg<-lm(wage_d~edu_d, data=twins)

summary(reg)
## 
## Call:
## lm(formula = wage_d ~ edu_d, data = twins)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.03115 -0.20909  0.00722  0.34395  1.15740 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.07859    0.04547  -1.728 0.086023 .  
## edu_d        0.09157    0.02371   3.862 0.000168 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5542 on 147 degrees of freedom
## Multiple R-squared:  0.09211,    Adjusted R-squared:  0.08593 
## F-statistic: 14.91 on 1 and 147 DF,  p-value: 0.0001682
  1. Explain how this coefficient should be interpreted.

The results show that the estimate is 0.09157. We can interpret this as the effect of schooling on the wage of 9.2 percent per year complete. As the year of schooling increases by one year, the wage increase by 9.2% on average holding others constant.

  1. Reproduce the result in table 3 column 1.
library(reshape2)
twins2 <- reshape(twins,
          varying = c("educ1", "educ2","lwage1", "lwage2","male1","male2", "white1","white2"),
          idvar= c("famid","age"),
          sep= "",
          timevar = "twin",
          times = c("educ1", "educ2","lwage1", "lwage2","male1","male2", "white1","white2"),
          direction = "long")

twins2$age2 <- ((twins2$age)^2)/100
reg2 <- lm(lwage ~ educ + age + age2 + male + white , data = twins2)

summary (reg2)
## 
## Call:
## lm(formula = lwage ~ educ + age + age2 + male + white, data = twins2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.62602 -0.28748  0.00277  0.28474  2.42317 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.47061    0.42602  -1.105 0.270210    
## educ         0.08387    0.01443   5.814 1.60e-08 ***
## age          0.08782    0.01883   4.663 4.75e-06 ***
## age2        -0.08686    0.02335  -3.720 0.000239 ***
## male         0.20403    0.06302   3.237 0.001345 ** 
## white       -0.41047    0.12668  -3.240 0.001333 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5324 on 292 degrees of freedom
## Multiple R-squared:  0.2724, Adjusted R-squared:  0.2599 
## F-statistic: 21.86 on 5 and 292 DF,  p-value: < 2.2e-16
  1. Explain how the coefficient on education should be interpreted.

The estimates in the regression is 0.08387. Thus we interprete this as he effect of schooling on the wage of 9.2 percent per year complete. As the year of schooling increases by one year, the wage increase by 9.2% on average holding others constant.

  1. Explain how the coefficient on the control variables should be interpreted.

Age: As age increase by one year, the wage increase by 8.8% on average, holding others constant.

Age-Squared: Above certain age, as age increase by one year, the wage decrease by 8.7% on average, holing others constant.

Male: If the twin is male, the wage increase by 20.4% on average compared to women.

White: If the twin is white, the wage decrease by 41% on average compare to other race/ethnicity.