# R Programming/Tobit And Selection Models

## Tobit (type 1 Tobit)[edit]

In this section, we look at simple tobit model where the outcome variable is observed only if it is above or below a given threshold.

`tobit()`in the**AER**package^{[1]}. This is a wrapper for`survreg()`.

```
N <- 1000
u <- rnorm(N)
x <- - 1 + rnorm(N)
ystar <- 1 + x + u
y <- ystar*(ystar > 0)
hist(y)
ols <- lm(y ~ x)
summary(ols)
library(AER)
tobit <- tobit(y ~ x,left=0,right=Inf,dist = "gaussian")
```

## Selection models (type 2 tobit or heckit)[edit]

In this section we look at endogenous selection process. The outcome y is observe only if d is equal to one with d a binary variable which is correlated with the error term of y.

`heckit()`and`selection()`in**sampleSelection**^{[2]}. The command is called`heckit()`

in honor of James Heckman^{[3]}.

```
N <- 1000
u <- rnorm(N)
v <- rnorm(N)
x <- - 1 + rnorm(N)
z <- 1 + rnorm(N)
d <- (1 + x + z + u + v> 0)
ystar <- 1 + x + u
y <- ystar*(d == 1)
hist(y)
ols <- lm(y ~ x)
summary(ols)
library(sampleSelection)
heckit.ml <- heckit(selection = d ~ x + z, outcome = y ~ x, method = "ml")
summary(heckit.ml)
heckit.2step <- heckit(selection = d ~ x + z, outcome = y ~ x, method = "2step")
summary(heckit.2step)
```

## Multi-index selection models[edit]

In this section we look at endogenous selection processes in matching markets. Matching is concerned with who transacts with whom, and how. For example, which students attend which college. The outcome y is observed only for equilibrium student-college pairs (or matches). These matches are indicated with d equal to one with d a binary variable which is correlated with the error term of y.

`stabit()`and`stabit2()`in**matchingMarkets**.^{[4]}^{[5]}The command is called`stabit()`

in reference to the application in stable matching markets.

Simulate two-sided matching data for 20 markets (`m=20`) with 100 students (`nStudents=100`) per market and 20 colleges with quotas of 5 students, each (`nSlots=rep(5,20)`). True parameters in selection and outcome equations are all equal to 1.

```
library(matchingMarkets)
xdata <- stabsim2(m=20, nStudents=100, nSlots=rep(5,20),
colleges = "c1",
students = "s1",
outcome = ~ c1:s1 + eta + nu,
selection = ~ -1 + c1:s1 + eta
)
```

Observe the bias from sorting between students and colleges.

```
lm1 <- lm(y ~ c1:s1, data=xdata$OUT)
summary(lm1)
```

Correct for sorting bias by running the Gibbs sampler in Sorensen (2007).^{[6]}

```
fit2 <- stabit2(OUT = xdata$OUT,
colleges = "c1",
students = "s1",
outcome = y ~ c1:s1,
selection = ~ -1 + c1:s1,
niter=1000
)
summary(fit2)
```

## Truncation[edit]

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**truncreg**package- DTDA "An R package for analyzing truncated data" pdf.

## References[edit]

- ↑ Christian Kleiber and Achim Zeileis (2008). Applied Econometrics with R. New York: Springer-Verlag. ISBN 978-0-387-77316-2. URL http://CRAN.R-project.org/package=AER
- ↑ Sample Selection Models in R: Package sampleSelection http://www.jstatsoft.org/v27/i07
- ↑ James Heckman "Sample selection bias as a specification error", Econometrica: Journal of the econometric society, 1979
- ↑ Klein, T. (2015). "Analysis of Stable Matchings in R: Package matchingMarkets".
*Vignette to R Package matchingMarkets*. http://cran.at.r-project.org/web/packages/matchingMarkets/vignettes/matching.pdf. - ↑ "matchingMarkets: Analysis of Stable Matchings".
*R Project*. http://cran.at.r-project.org/web/packages/matchingMarkets/index.html. - ↑ Sorensen, M. (2007). "How Smart is Smart Money? A Two-Sided Matching Model of Venture Capital".
*Journal of Finance***62**(6): 2725-2762.