R Programming/Tobit And Selection Models
Tobit (type 1 Tobit)[edit | edit source]
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. 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) #Plot a correlation matrix and scatter plot library(GGally) library(ggplot2) library(ggfortify) ggcorr(DATA) ggpairs(DATA) # M<lm(y~.) library(ggfortify) autoplot(M, label.size = 3) # library(AER) tobit <- tobit(y ~ x,left=0,right=Inf,dist = "gaussian")
Selection models (type 2 tobit or heckit)[edit | edit source]
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 . The command is called
heckit()in honor of James Heckman.
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 | edit source]
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. 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$OUT) summary(lm1)
Correct for sorting bias by running the Gibbs sampler in Sorensen (2007).
fit2 <- stabit2(OUT = xdata$OUT, colleges = "c1", students = "s1", outcome = y ~ c1:s1, selection = ~ -1 + c1:s1, niter=1000 ) summary(fit2)
Truncation[edit | edit source]
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- truncreg package
- DTDA "An R package for analyzing truncated data" pdf.
References[edit | edit source]
- 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.