makeData <- function(){
    id <- rep(1:100, each=10)
    a <- rep(rnorm(100), each=10)
    x <- rnorm(1000) + a
    u <- 2*rnorm(1000) + 2*a
    y <- x + u
    return(data.frame(y=y,x=x,id=id))
}
crossSectionEst <- function(){
    i <- seq(5, 95, 10)
    m <- sapply(
        1:1000,
        function(x){
            df <- makeData()
            df.cs <- df[i,1:2]
            est <- summary(lm(df.cs))$coefficients[2]
            return(est)
        }
    )
    return(mean(m))
}
print(crossSectionEst())

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