23.11.2023 IV Regression#

Maps#

library(sf)
library(tidyverse)
library(terra)

import the sf dataset

World <- read_sf("data/shape/shapecountries.shp")

plot the shapes

ggplot(World) + 
  geom_sf()

Subsetting on smaller regions with ext(longitude_min, longitude_max, latitude_min, latitdue_max)

world_v <- vect(World)
coords_subset <- ext(5.0, 23, 47, 56)
europe <- crop(world_v, coords_subset)

europe_sf <- st_as_sf(europe)

Plot it again

ggplot(europe_sf) + 
  geom_sf()

IV Regression#

to control for omitted variable which is exogenous with error term

=> OLS does not work

Solution:

  • replace with instrument variable that correlets to explanatory variable

  • IV should be exogenous

  • and relevant in explaining variation

  1. stage:

  • \(x = \gamma + \delta instrument + e\)

  • leads to \(\hat{x} = \hat{\gamma} + \hat{delta} instrument + residual\)

  1. Stage: \(y = a + b \hat{x} + e\)

How to do in R:

library(AER)
load("data/dataset_AJR2001.Rdata")
head(data)

ivreg(logpgp95 ~avexpr | logem4, data = data)

=> R2 is not relevant for IV Regression!