Contents
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)
Multiindex selection modelsEdit
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 studentcollege 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 twosided 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)
TruncationEdit

This section is a stub. You can help Wikibooks by expanding it. 
 truncreg package
 DTDA "An R package for analyzing truncated data" pdf.
ReferencesEdit
 ↑ Christian Kleiber and Achim Zeileis (2008). Applied Econometrics with R. New York: SpringerVerlag. ISBN 9780387773162. URL http://CRAN.Rproject.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.rproject.org/web/packages/matchingMarkets/vignettes/matching.pdf.
 ↑ "matchingMarkets: Analysis of Stable Matchings". R Project. http://cran.at.rproject.org/web/packages/matchingMarkets/index.html.
 ↑ Sorensen, M. (2007). "How Smart is Smart Money? A TwoSided Matching Model of Venture Capital". Journal of Finance 62 (6): 27252762.