Econometrics - Casual Inference and IV

Extract

[...] This question shall be done on R. However, we have first to install and load the necessary packages and then create the plot : install.packages("ggplot2") library(ggplot2) ggplot(df, aes(x=educ, y=log(wage))) + geom_point(alpha=0.5) + # scatter points with transparency for better visualization labs(title="Scatter plot of log(wage) vs educ", # plot title x="Education (Years)", # x-axis label y="Log(Wage)") + # y-axis label theme_minimal() # minimal theme for neat visualization Heteroskedasticity arises when the error variance in a regression model isn't consistently distributed across observations. [...]

[...] We'll be using the Two-Stage Least Squares (2SLS) to estimate the causal effect of education on income using `nearc4` as an instrument for `educ`. controls c("exper", "I(exper^2)", "black", "south", "smsa", "reg662", "reg663", "reg664", "reg665", "reg666", "reg667", "reg668", "reg669") form5 as.formula(paste0("log(wage) ~ educ + paste(controls, collapse = " + " paste(c(controls, "nearc4"), collapse = " + est5 ivreg(form5, data = df) Upon executing the IV regression via `est5`, one can juxtapose the `educ` coefficient from `est1` (OLS) against that of `est5` (2SLS). [...]

[...] Econometrics - Casual Inference and IV Question 1 This question should be done on by setting the working directory and loading the data. By running the following code, the descriptive table will appear : selected_vars c("wage", "educ", "exper", "black", "smsa", "south", "nearc4")] n_obs nrow(selected_vars) mean_vals sapply(selected_vars, mean, na.rm = TRUE) sd_vals sapply(selected_vars, sd, na.rm = TRUE) min_vals sapply(selected_vars, min, na.rm = TRUE) max_vals sapply(selected_vars, max, na.rm = TRUE) descriptive_table data.frame(Variable = names(selected_vars), Observations = rep(n_obs, length(selected_vars)), Mean = mean_vals, SD = sd_vals, Min = min_vals, Max = max_vals) print(descriptive_table) The means will indicate if the average wage seem reasonable for the time period and the average education level in terms of years. [...]

[...] Here, if an individual's inherent ability (partially depicted by is simultaneously linked with both `educ` and `log(wage)`, its exclusion can introduce bias. The use of `nearc4` as an instrument is valuable, but its efficacy is contingent on it being uncorrelated with the omitted entity The regression shall be run as the following: estIQ lm(IQ ~ nearc4 + exper + I(exper^2) + black + south + smsa + reg662 + reg663 + reg664 + reg665 + reg666 + reg667 + reg668 + reg669, data=df) summary(estIQ) Regarding our case, the 2 following options should be evaluated: A statistically significant coefficient for `nearc4` implies a connection between proximity to a 4-year college and `IQ`. [...]

[...] This allows us to discern the influence of accounting for IQ on the projected education return. A decline in the `educ` coefficient upon including IQ implies that the earlier observed educational return might have been partially driven by individual capability. The following code shall be executed: est2 lm(log(wage) ~ educ + exper + exper_sq + black + south + smsa + reg662 + reg663 + reg664 + reg665 + reg666 + reg667 + reg668 + reg669 + IQ, data=df) The following reasons are in favor of using nearc4 as an Instrument: If one's proximity to a 4-year college sways their educational choices (owing to convenience), it demonstrates instrument relevance since it's affecting the predictor. [...]