Introducing brotools
Lesser known purrr tricks
Make ggplot2 purrr
How to use jailbreakr
Lesser known dplyr tricks
Functional programming and unit testing for data munging with R available on Leanpub
My free book has a cover!
Work on lists of datasets instead of individual datasets by using functional programming
Method of Simulated Moments with R
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Nonlinear Gmm with R - Example with a logistic regression
Simulated Maximum Likelihood with R
Bootstrapping standard errors for difference-in-differences estimation with R
Careful with tryCatch
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Export R output to a file
I've started writing a 'book': Functional programming and unit testing for data munging with R
Introduction to programming econometrics with R
Merge a list of datasets together
Object Oriented Programming with R: An example with a Cournot duopoly
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Read a lot of datasets at once with R
Unit testing with R
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Using R as a Computer Algebra System with Ryacas

This document details section *12.5.6. Unobserved Heterogeneity Example*. The original source code giving the results from table 12.3 are available from the authors' site here and written for Stata. This is an attempt to translate the code to R.

Consult the original source code if you want to read the authors' comments. If you want the R source code without all the commentaries, grab it here. This is not guaranteed to work, nor to be correct. It could set your pet on fire and/or eat your first born. Use at your own risk. I may, or may not, expand this example. Corrections, constructive criticism are welcome.

The model is the same as the one described here, so I won't go into details. The moment condition used is \( E[(y_i-\theta-u_i)]=0 \), so we can replace the expectation operator by the empirical mean:

\[ \dfrac{1}{N} \sum_{i=1}^N(y_i - \theta - E[u_i])=0 \]

Supposing that \( E[\overline{u}] \) is unknown, we can instead use the method of simulated moments for \( \theta \) defined by:

\[ \dfrac{1}{N} \sum_{i=1}^N(y_i - \theta - \dfrac{1}{S} \sum_{s=1}^S u_i^s)=0 \]

You can consult the original source code to see how the authors simulated the data. To get the same results, and verify that I didn't make mistakes I prefer importing their data directly from their website.

```
data <- read.table("http://cameron.econ.ucdavis.edu/mmabook/mma12p2mslmsm.asc")
u <- data[, 1]
e <- data[, 2]
y <- data[, 3]
numobs <- length(u)
simreps <- 10000
```

In the code below, we simulate the equation defined above:

```
usim <- -log(-log(runif(simreps)))
esim <- rnorm(simreps, 0, 1)
isim <- 0
while (isim < simreps) {
usim = usim - log(-log(runif(simreps)))
esim = esim + rnorm(simreps, 0, 1)
isim = isim + 1
}
usimbar = usim/simreps
esimbar = esim/simreps
theta = y - usimbar - esimbar
theta_msm <- mean(theta)
approx_sterror <- sd(theta)/sqrt(simreps)
```

These steps yield the following results:

```
## Theta MSM= 1.188 Approximate Standard Error= 0.01676
```