simualte_bartik.R

library(lfe)
library(stargazer)

set.seed(6152011)

# Number of cities                                                                                                       
L <- 1000

# Number of industries                                                                                                        
K <- 3

# National growth rates by industry                                                                                     
g.raw <- runif(K)
g.k <- g.raw/sum(g.raw)

CreateCity <- function(g.k, eta.s){
    #  Give each city some industry shares                                                                                 
    K <- length(g.k)
    z.raw <- runif(K)
    z <- z.raw / sum(z.raw)
    # Give each city some idiosyncratic growth by industry                                                                        
    g.kl.tilde <- g.raw/sum(g.raw)
    # Change in employement is inner product of the national + idiosyncratic component with industry share               
    x <- (g.kl.tilde + g.k) %*% z
    # Bartik instrument (national growth & city industry share inner product)                                                                                                      
    B <- g.k %*% z
    # Realized change in wage                                                                                                 
    y <- (1/eta.s) * x + rnorm(1,0,1/10)
    list("y" = y, "B" = B, "x" = x)
}

# Create a city data frame                                                                                                    
city.data <- rep(CreateCity(g.k, 1), L)
df <- data.frame(matrix(unlist(city.data), ncol = 3))
colnames(df) <- c("y", "B", "x")

# Estimates                                                                                                                   
m.ols <- felm(y ~ x | 0 | 0 | 0, data = df)
m.iv <- felm(y ~ 1 | 0 | (x ~ B) | 0, data = df)
stargazer(m, m.iv, type = "text")