Article: Krueger (1999) Experimental Estimates of Education Production Functions QJE 114 (2): 497-532
The paper is trying to estimate the impacts of classroom resources (specifically classroom size) on education outcomes (test scores).
Ideal experiment to test this would be to conduct a randomized control trial experiment where a large enough sample of randomly selected students are put to classrooms of varying student sizes. Calculating the average of the means of the wage differences between two adjacent groups would give us the causal estimate.
Randomization is used so that a student’s assignment to their classroom size is not correlated to any confounding variable. Doing so, one can claim that endogeneity issue is removed and the estimate is unbiased.
The identification strategy solely rests on the benefits of randomization. The study is as good as the randomization. The threat is that it is not a completely controlled environment in that students can freely enter and leave the treated classes. If, for instance, a new student entering a small class comes from a better school with smaller class size, this would underestimate the impacts of the class size on outcome variables.
Article: Ashenfelter and Krueger (1994) Estimates of the Economic Return to Schooling from a New Sample of Twins AER 84(5): 1157-1173
The paper is trying to estimate the wage impacts of going to school for one more year.
Ideal experiment to test this would be to conduct a randomized control trial experiment where a large enough sample of randomly selected individuals are sent to school for varying number of years. Calculating the average of the means of the wage differences between two adjacent groups (by number of school) would give us the causal estimate.
The identification strategy used in the paper is to compare the wages between identical twins. Since they are genetically identical and have similar family backgrounds, the difference in the wages could be attributed to the difference in education.
A crucial assumption to this identification strategy, as said above, is that monozygotic twins are genetically identical and have similar family backgrounds. A threat to this strategy is that although they have similar innate biological and family characteristics, their tastes and preferences could be different, leading to different number of years of schooling and thus, different wages.
library(haven)
library(stargazer)data <- read_dta("AshenfelterKrueger1994_twins.dta")
data$diff1=data$educ1-data$educ2
data$diff2=data$lwage1-data$lwage2
reg1<-lm(diff2~diff1,data=data)
stargazer(reg1, type = "text")##
## ===============================================
## Dependent variable:
## ---------------------------
## diff2
## -----------------------------------------------
## diff1 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<0.01We can interpret the coefficient as: one more year of education leads to an increase in wage by 9.2 percent on average.
l <- reshape(data,
varying=c("educ1", "lwage1", "male1","white1", "educ2","lwage2","male2","white2"),
v.names=c("educ","lwage","male","white"),
timevar = "twin",
times = c("T1", "T2"),
idvar=c("famid","age"),
direction = "l")
l.sort <- l[order(l$famid),]
#Help for -reshape- command taken from https://stats.oarc.ucla.edu/r/faq/how-can-i-reshape-my-data-in-r/
l$age2<-l$age^2/100
reg2<-lm(lwage~educ+age+age2+male+white, data=l)
stargazer(reg2, type = "text")##
## ===============================================
## Dependent variable:
## ---------------------------
## lwage
## -----------------------------------------------
## educ 0.084***
## (0.014)
##
## age 0.088***
## (0.019)
##
## age2 -0.087***
## (0.023)
##
## male 0.204***
## (0.063)
##
## white -0.410***
## (0.127)
##
## Constant -0.471
## (0.426)
##
## -----------------------------------------------
## Observations 298
## R2 0.272
## Adjusted R2 0.260
## Residual Std. Error 0.532 (df = 292)
## F Statistic 21.860*** (df = 5; 292)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01We can interpret the coefficient on education as: One more year of school will lead to an 8.4 percent increase in wage on average.
Wages increase but then drops after a certain point. Male individuals earn 20.4 percent more than female individuals on average. White individuals earn 41 percent lower than non-white individuals.