
           library(AER)
           data(CollegeDistance)


           # compute the correlation
           
           # perform the first stage regression and compute the fraction of explained variation
          
           # regress `log(wage)` on `education` and save the result to `wage_mod_1`
           
           # regress `log(wage)` on `education` and controls and save the result to `wage_mod_2`
           
           # obtain robust coefficient summaries on both models


           # compute the correlation
           cor(CollegeDistance$distance, CollegeDistance$education)
           
           # perform the first stage regression and compute the fraction of explained variation
           R2 <- summary(lm(education ~ distance, data = CollegeDistance))$r.squared  
           
           # estimate the IV regression of `log(wage)` on `education` using distance as the instrument and save the result to `wage_mod_iv1`
           wage_mod_iv1 <- ivreg(log(wage) ~ education | distance, data = CollegeDistance)           
           
           # perform TSLS regression of `log(wage)` on `education` and controls using distance as the instrument and save the result to `wage_mod_iv2`
           wage_mod_iv2 <- ivreg(log(wage) ~ unemp + ethnicity + gender + urban + education | . - education + distance, data = CollegeDistance) 
           
           # obtain robust coefficient summaries on both models
           coeftest(wage_mod_iv1, vcov. = vcovHC, type = "HC1")
           coeftest(wage_mod_iv2, vcov. = vcovHC, type = "HC1")


            test_output_contains("cor(CollegeDistance$distance, CollegeDistance$education)")
            
            test_object("R2")
             
            test_or({
            
              f <- ex() %>% override_solution("attach(CollegeDistance); wage_mod_iv1 <- ivreg(log(wage) ~ education | distance); wage_mod_iv2 <- ivreg(log(wage) ~ unemp + ethnicity + gender + urban + education | . - education + distance); coeftest(wage_mod_iv1, vcov. = vcovHC, type = \"HC1\"); coeftest(wage_mod_iv2, vcov. = vcovHC, type = \"HC1\")")
              
              f %>% check_function("ivreg", index = 1) %>% check_arg("formula") %>% check_equal()
              f %>% check_function("ivreg", index = 2) %>% check_arg("formula") %>% check_equal()
              
              f %>% check_object("wage_mod_iv1")
              f %>% check_object("wage_mod_iv2")

              f %>% check_function("coeftest", index = 1) %>%  check_arg("vcov.") %>% check_equal()
              f %>% check_function("coeftest", index = 2) %>%  check_arg("vcov.") %>% check_equal()
            
            },{
            
              f <- ex() %>% override_solution("wage_mod_iv1 <- ivreg(log(CollegeDistance$wage) ~ CollegeDistance$education | CollegeDistance$distance); wage_mod_iv2 <- ivreg(log(CollegeDistance$wage) ~ CollegeDistance$unemp + CollegeDistance$ethnicity + CollegeDistance$gender + CollegeDistance$urban + CollegeDistance$education | . - CollegeDistance$education + CollegeDistance$distance); coeftest(wage_mod_iv1, vcov. = vcovHC, type = \"HC1\"); coeftest(wage_mod_iv2, vcov. = vcovHC, type = \"HC1\")")
              
              f %>% check_function("ivreg", index = 1) %>% check_arg("formula") %>% check_equal()
              f %>% check_function("ivreg", index = 2) %>% check_arg("formula") %>% check_equal()
              
              f %>% check_object("wage_mod_iv1")
              f %>% check_object("wage_mod_iv2")

              f %>% check_function("coeftest", index = 1) %>%  check_arg("vcov.") %>% check_equal()
              f %>% check_function("coeftest", index = 2) %>%  check_arg("vcov.") %>% check_equal()
            
            },{
            
           test_function("ivreg", index = 1, args = "formula")
           test_function("ivreg", index = 2, args = "formula")
           test_function("coeftest", index = 1, args = c("x", "vcov."))
           test_function("coeftest", index = 2, args = c("x", "vcov."))
            
            }) 
             
           success_msg("Nice! In the multiple regression model the estimated coefficient on education is positive, of reasonable size and highly significant when education is instrumented by college distance. ")