Extract Coefficients from Selection Models

Description

This function extracts coefficients from sample selection models

Usage

## S3 method for class 'selection'
coef(object, part = "full", ...)
## S3 method for class 'summary.selection'
coef(object, part = "full", ...)
## S3 method for class 'coef.selection'
print( x, prefix = TRUE,
      digits = max(3, getOption("digits") - 3), ... )

Arguments

Value

coef.selection returns a vector of the estimated coefficients.

coef.summary.selection returns a matrix of the estimated coefficients, their standard errors, t-values, and p-values.

Author(s)

Arne Henningsen, Ott Toomet (otoomet@ut.ee)

See Also

coef, selection, vcov.selection, and selection-methods.

Examples

## Estimate a simple female wage model taking into account the labour
## force participation
   data(Mroz87)
   a <- heckit(lfp ~ huswage + kids5 + mtr + fatheduc + educ + city,
               log(wage) ~ educ + city, data=Mroz87)
## extract all coefficients of the model:
coef( a )

## now extract the coefficients of the outcome model only:
coef( a, part="outcome")

## extract all coefficients, standard errors, t-values
## and p-values of the model:
coef( summary( a ) )

## now extract the coefficients, standard errors, t-values
## and p-values of the outcome model only:
coef( summary( a ), part="outcome")

Fitted Values of Selection Models

Description

Calculate fitted values of sample selection models

Usage

## S3 method for class 'selection'
fitted(object, part = "outcome", ... )

Arguments

Details

If the model was estimated by the 2-step method, the fitted values of the outcome equation are calculated using all regressors of this equation including the inverse Mill's ratios, i.e. the fitted values correspond to the conditional expectations (see predict.selection).

If the model was estimated by the maximum likelihood method, the fitted values of the outcome equation are calculated by disregarding the selection equation, i.e. the fitted values correspond to the unconditional expectations (see predict.selection).

The fitted values of the selection equation are probabilities. If the dependent variable of the outcome equation is binary, also the fitted values of the outcome equation are probabilities.

Value

A numeric vector of the fitted values.

Author(s)

Arne Henningsen

See Also

fitted, selection, residuals.selection, and selection-methods.

2-step Heckman (heckit) estimation

Description

These functions do the actual fitting of tobit-2 (sample selection), tobit-5 (switching regression) and normal-disturbance treatment effect models by the 2-step Heckman (heckit) estimation. They are called by selection or heckit and they are intended for sampleSelection internal use.

Usage

heckit2fit( selection, outcome, data=sys.frame(sys.parent()),
   weights = NULL, inst = NULL,
   printLevel=print.level, print.level = 0,
   maxMethod = "Newton-Raphson" )

heckit5fit( selection, outcome1, outcome2, data = sys.frame(sys.parent()),
   ys = FALSE, yo = FALSE, xs = FALSE, xo = FALSE, mfs = FALSE,
   mfo = FALSE,
   printLevel=print.level, print.level = 0, maxMethod = "Newton-Raphson", ... )

heckitTfit(selection, outcome, data=sys.frame(sys.parent()),
   ys=FALSE, yo=FALSE, xs=FALSE, xo=FALSE, mfs=FALSE, mfo=FALSE,
   printLevel=0, maxMethod="Newton-Raphson", ... )

Arguments

Value

see selection.

Author(s)

Arne Henningsen, Ott Toomet otoomet@ut.ee

References

see selection.

See Also

selection, heckit

Heckit Variance Covariance Matrix

Description

Calculate the asymptotic covariance matrix for the coefficients of a Heckit estimation

Usage

   heckitVcov( xMat, wMat, vcovProbit, rho, delta, sigma,
   saveMemory = TRUE )

Arguments

Details

The formula implemented in heckitVcov is available, e.g., in Greene (2003), last formula on page 785.

Value

the variance covariance matrix of the coefficients.

Author(s)

Arne Henningsen

References

Greene, W. H. (2003) Econometric Analysis, Fifth Edition, Prentice Hall.

Lee, L., G. Maddala and R. Trost (1980) Asymetric covariance matrices of two-stage probit and two-stage tobit methods for simultaneous equations models with selectivity. Econometrica, 48, p. 491-503.

See Also

heckit.

Inverse Mill's Ratio of probit models

Description

Calculates the 'Inverse Mill's Ratios' of univariate and bivariate probit models.

Usage

   invMillsRatio( x, all = FALSE )

Arguments

Details

The formula to calculate the inverse Mill's ratios for univariate probit models is taken from Greene (2003, p. 785), whereas the formulas for bivariate probit models are derived in Henning and Henningsen (2005).

Value

A data frame that contains the Inverse Mill's Ratios (IMR) and the delta values (see Greene, 2003, p. 784).

If a univariate probit estimation is provided, the variables IMR1 and IMR0 are the Inverse Mill's Ratios to correct for a sample selection bias of y = 1 and y = 0, respectively. Accordingly, 'delta1' and 'delta0' are the corresponding delta values.

If a bivariate probit estimation is provided, the variables IMRa1, IMRa0, IMRb1, and IMRb0 are the Inverse Mills Ratios to correct for a sample selection bias of y = 1 and y = 0 in equations 'a' and 'b', respectively. Accordingly, 'deltaa1', 'deltaa0', 'deltab1' and 'deltab0' are the corresponding delta values.

Author(s)

Arne Henningsen

References

Greene, W. H. (2003) Econometric Analysis, Fifth Edition, Prentice Hall.

Henning, C.H.C.A and A. Henningsen (2005) Modeling Price Response of Farm Households in Imperfect Labor Markets in Poland: Incorporating Transaction Costs and Heterogeneity into a Farm Household Approach. Unpublished, University of Kiel, Germany.

Examples

## Wooldridge( 2003 ): example 17.5, page 590
data(Mroz87)
myProbit <- glm( lfp ~ nwifeinc + educ + exper + I( exper^2 ) + age +
   kids5 + kids618, family = binomial( link = "probit" ), data=Mroz87 )
Mroz87$IMR <- invMillsRatio( myProbit )$IMR1
myHeckit <- lm( log( wage ) ~ educ + exper + I( exper^2 ) + IMR,
   data = Mroz87[ Mroz87$lfp == 1, ] )

# using NO labor force participation as endogenous variable
Mroz87$nolfp <- 1 - Mroz87$lfp
myProbit2 <- glm( nolfp ~ nwifeinc + educ + exper + I( exper^2 ) + age +
   kids5 + kids618, family = binomial( link = "probit" ), data=Mroz87 )
all.equal( invMillsRatio( myProbit )$IMR1, invMillsRatio( myProbit2 )$IMR0 )
   # should be true

# example for bivariate probit
library( "mvtnorm" )
library( "VGAM" )

nObs <- 1000

# error terms (trivariate normal)
sigma <- symMatrix( c( 2, 0.7, 1.2, 1, 0.5, 1 ) )
myData <- as.data.frame( rmvnorm( nObs, c( 0, 0, 0 ), sigma ) )
names( myData ) <- c( "e0", "e1", "e2" )

# exogenous variables (indepently normal)
myData$x0 <- rnorm( nObs )
myData$x1 <- rnorm( nObs )
myData$x2 <- rnorm( nObs )

# endogenous variables
myData$y0 <-   -1.5 + 0.8 * myData$x1 + myData$e0
myData$y1 <- (  0.3 + 0.4 * myData$x1 + 0.3 * myData$x2 + myData$e1 ) > 0
myData$y2 <- ( -0.1 + 0.6 * myData$x1 + 0.7 * myData$x2 + myData$e2 ) > 0

# bivariate probit (using rhobit transformation)
bProbit <- vglm( cbind( y1, y2 ) ~ x1 + x2, family = binom2.rho,
   data = myData )
summary( bProbit )

# bivariate probit (NOT using rhobit transformation)
bProbit2 <- vglm( cbind( y1, y2 ) ~ x1 + x2, family = binom2.rho(
   lrho = "identitylink" ), data = myData )
summary( bProbit2 )

# inverse Mills Ratios
imr  <- invMillsRatio( bProbit )
imr2 <- invMillsRatio( bProbit2 )
all.equal( imr, imr2, tolerance = .Machine$double.eps ^ 0.25)

# tests
# E[ e0 | y1* > 0 & y2* > 0 ]
mean( myData$e0[ myData$y1 & myData$y2 ] )
mean( sigma[1,2] * imr$IMR11a + sigma[1,3] * imr$IMR11b, na.rm = TRUE )
# E[ e0 | y1* > 0 & y2* <= 0 ]
mean( myData$e0[ myData$y1 & !myData$y2 ] )
mean( sigma[1,2] * imr$IMR10a + sigma[1,3] * imr$IMR10b, na.rm = TRUE )
# E[ e0 | y1* <= 0 & y2* > 0 ]
mean( myData$e0[ !myData$y1 & myData$y2 ] )
mean( sigma[1,2] * imr$IMR01a + sigma[1,3] * imr$IMR01b, na.rm = TRUE )
# E[ e0 | y1* <= 0 & y2* <= 0 ]
mean( myData$e0[ !myData$y1 & !myData$y2 ] )
mean( sigma[1,2] * imr$IMR00a + sigma[1,3] * imr$IMR00b, na.rm = TRUE )
# E[ e0 | y1* > 0 ]
mean( myData$e0[ myData$y1 ] )
mean( sigma[1,2] * imr$IMR1X, na.rm = TRUE )
# E[ e0 | y1* <= 0 ]
mean( myData$e0[ !myData$y1 ] )
mean( sigma[1,2] * imr$IMR0X, na.rm = TRUE )
# E[ e0 | y2* > 0 ]
mean( myData$e0[ myData$y2 ] )
mean( sigma[1,3] * imr$IMRX1, na.rm = TRUE )
# E[ e0 | y2* <= 0 ]
mean( myData$e0[ !myData$y2 ] )
mean( sigma[1,3] * imr$IMRX0, na.rm = TRUE )

# estimation for y1* > 0 and y2* > 0
selection <- myData$y1 & myData$y2
# OLS estimation
ols11 <- lm( y0 ~ x1, data = myData, subset = selection )
summary( ols11 )
# heckman type estimation
heckit11 <- lm( y0 ~ x1 + IMR11a + IMR11b, data = cbind( myData, imr ),
   subset = selection )
summary( heckit11 )

# estimation for y1* > 0 and y2* <= 0
selection <- myData$y1 & !myData$y2
# OLS estimation
ols10 <- lm( y0 ~ x1, data = myData, subset = selection )
summary( ols10 )
# heckman type estimation
heckit10 <- lm( y0 ~ x1 + IMR10a + IMR10b, data = cbind( myData, imr ),
   subset = selection )
summary( heckit10 )

# estimation for y1* <= 0 and y2* > 0
selection <- !myData$y1 & myData$y2
# OLS estimation
ols01 <- lm( y0 ~ x1, data = myData, subset = selection )
summary( ols01 )
# heckman type estimation
heckit01 <- lm( y0 ~ x1 + IMR01a + IMR01b, data = cbind( myData, imr ),
   subset = selection )
summary( heckit01 )

# estimation for y1* <= 0 and y2* <= 0
selection <- !myData$y1 & !myData$y2
# OLS estimation
ols00 <- lm( y0 ~ x1, data = myData, subset = selection )
summary( ols00 )
# heckman type estimation
heckit00 <- lm( y0 ~ x1 + IMR00a + IMR00b, data = cbind( myData, imr ),
   subset = selection )
summary( heckit00 )

# estimation for y1* > 0
selection <- myData$y1
# OLS estimation
ols1X <- lm( y0 ~ x1, data = myData, subset = selection )
summary( ols1X )
# heckman type estimation
heckit1X <- lm( y0 ~ x1 + IMR1X, data = cbind( myData, imr ),
   subset = selection )
summary( heckit1X )

# estimation for y1* <= 0
selection <- !myData$y1
# OLS estimation
ols0X <- lm( y0 ~ x1, data = myData, subset = selection )
summary( ols0X )
# heckman type estimation
heckit0X <- lm( y0 ~ x1 + IMR0X, data = cbind( myData, imr ),
   subset = selection )
summary( heckit0X )

# estimation for y2* > 0
selection <- myData$y2
# OLS estimation
olsX1 <- lm( y0 ~ x1, data = myData, subset = selection )
summary( olsX1 )
# heckman type estimation
heckitX1 <- lm( y0 ~ x1 + IMRX1, data = cbind( myData, imr ),
   subset = selection )
summary( heckitX1 )

# estimation for y2* <= 0
selection <- !myData$y2
# OLS estimation
olsX0 <- lm( y0 ~ x1, data = myData, subset = selection )
summary( olsX0 )
# heckman type estimation
heckitX0 <- lm( y0 ~ x1 + IMRX0, data = cbind( myData, imr ),
   subset = selection )
summary( heckitX0 )

Calculates linear predictors for different models

Description

Calculates the (unobservable) linear predictors for probability models.

Usage

linearPredictors(x, ...)

## S3 method for class 'probit'
linearPredictors( x, ... )

Arguments

Details

It is a generic function with a method for 'probit'.

Value

A matrix with nrow equal to the number of observations and one column: the linear predictors for observations

Author(s)

Ott Toomet otoomet@ut.ee, Arne Henningsen

See Also

probit and probit-methods.

Examples

data(Mroz87)
Mroz87$kids  <- ( Mroz87$kids5 + Mroz87$kids618 > 0 )
a <- probit(lfp ~ kids + educ + hushrs + huseduc + huswage + mtr +
 motheduc, data=Mroz87)
b <- linearPredictors(a)
cor(Mroz87$lfp, b) # should be positive and highly significant

Data of Binary Choice Models

Description

Return the variables used for estimating a binary choice model

Usage

## S3 method for class 'binaryChoice'
model.frame( formula, ... )

Arguments

Value

A data.frame containing all variables used for the estimation.

Author(s)

Arne Henningsen, Ott Toomet otoomet@ut.ee

See Also

binaryChoice, probit, model.frame, model.matrix.binaryChoice, and probit-methods.

Data of Selection Models

Description

Return the variables used for estimating a sample selection model

Usage

## S3 method for class 'selection'
model.frame(formula, ... )

Arguments

Value

A data.frame containing all variables used for the estimation. The “terms” attribute contains the terms for the selection equation.

Author(s)

Arne Henningsen

See Also

model.frame, selection, model.matrix.selection, and selection-methods.

Design Matrix of Binary Choice Models

Description

Create design matrix of binary choice models

Usage

## S3 method for class 'binaryChoice'
model.matrix( object, ... )

Arguments

Value

The design matrix of binary choice models.

Author(s)

Arne Henningsen, Ott Toomet otoomet@ut.ee

See Also

binaryChoice, probit, model.matrix, model.frame.binaryChoice, and probit-methods.

Design Matrix of Selection Models

Description

Create design matrix of sample selection models

Usage

## S3 method for class 'selection'
model.matrix(object, part = "outcome", ... )

Arguments

Value

If argument part is "selection", the design matrix of the selection equation is returned.

If argument part is "outcome", the design matrix of the outcome equation (tobit-2 or treatment model) or a list of two outcome matrices (tobit-5 model) is returned. All unobserved outcomes, including the corresponding explanatory variables are set to NA, even in case where valid values were supplied for estimation.

Author(s)

Arne Henningsen

See Also

model.matrix, selection, model.frame.selection, and selection-methods.

U.S. Women's Labor Force Participation

Description

The Mroz87 data frame contains data about 753 married women. These data are collected within the "Panel Study of Income Dynamics" (PSID). Of the 753 observations, the first 428 are for women with positive hours worked in 1975, while the remaining 325 observations are for women who did not work for pay in 1975. A more complete discussion of the data is found in Mroz (1987), Appendix 1.

Usage

data(Mroz87)

Format

This data frame contains the following columns:

lfp

Dummy variable for labor-force participation.

hours

Wife's hours of work in 1975.

kids5

Number of children 5 years old or younger.

kids618

Number of children 6 to 18 years old.

age

Wife's age.

educ

Wife's educational attainment, in years.

wage

Wife's average hourly earnings, in 1975 dollars.

repwage

Wife's wage reported at the time of the 1976 interview.

hushrs

Husband's hours worked in 1975.

husage

Husband's age.

huseduc

Husband's educational attainment, in years.

huswage

Husband's wage, in 1975 dollars.

faminc

Family income, in 1975 dollars.

mtr

Marginal tax rate facing the wife.

motheduc

Wife's mother's educational attainment, in years.

fatheduc

Wife's father's educational attainment, in years.

unem

Unemployment rate in county of residence, in percentage points.

city

Dummy variable = 1 if live in large city, else 0.

exper

Actual years of wife's previous labor market experience.

nwifeinc

Non-wife income.

wifecoll

Dummy variable for wife's college attendance.

huscoll

Dummy variable for husband's college attendance.

Source

Mroz, T. A. (1987) The sensitivity of an empirical model of married women's hours of work to economic and statistical assumptions. Econometrica 55, 765–799.

PSID Staff, The Panel Study of Income Dynamics, Institute for Social ResearchPanel Study of Income Dynamics, University of Michigan, https://psidonline.isr.umich.edu.

Examples

## Wooldridge( 2003 ): example 17.5, page 590
data( Mroz87 )
# Two-step estimation
summary( heckit( lfp ~ nwifeinc + educ + exper + I( exper^2 ) + age +
   kids5 + kids618, log( wage ) ~ educ + exper + I( exper^2 ), Mroz87,
   method = "2step" ) )

National Longitudinal Survey of Young Working Women

Description

The nlswork data frame contains data about 4711 young working women who had an age of 14–26 years in 1968. These data are collected within the "National Longitudinal Survey" over the years 1968-1988 (with gaps). There are 28534 observations in total.

Usage

data(nlswork)

Format

This data frame contains the following columns:

idcode

NLS ID.

year

interview year.

birth_yr

birth year.

age

age in current year.

race

1=white, 2=black, 3=other.

msp

1 if married, spouse present.

nev_mar

1 if never married.

grade

current grade completed.

collgrad

1 if college graduate.

not_smsa

1 if not SMSA.

c_city

1 if central city.

south

1 if south.

ind_code

industry of employment.

occ_code

occupation.

union

1 if union.

wks_ue

weeks unemployed last year.

ttl_exp

total work experience.

tenure

job tenure, in years.

hours

usual hours worked.

wks_work

weeks worked last year.

ln_wage

ln(wage/GNP deflator).

Details

Two different versions of this data set are available on the internet. They are slighly different: The variable wks_work (weeks worked last year) is 101 in this version (from Stata), but NA in the version provided by the Boston College for the observation with idcode = 1 and year = 83. Moreover, this variable is NA in this version (from Stata), but 104 in the version provided by the Boston College for the observation with idcode = 2 and year = 87.

Source

Datasets for Stata Longitudinal/Panel-Data Reference Manual, Release 10: National Longitudinal Survey. Young Women 14-26 years of age in 1968, https://www.stata-press.com/data/r10/nlswork.dta.

References

Boston College, National Longitudinal Survey. Young Women 14-26 years of age in 1968, https://fmwww.bc.edu/ec-p/data/stata/nlswork.dta.

Examples

data( "nlswork" )
summary( nlswork )

## Not run: 
library( "plm" )
nlswork <- plm.data( nlswork, c( "idcode", "year" ) )
plmResult <- plm( ln_wage ~ union + age + grade + not_smsa + south + occ_code,
   data = nlswork, model = "random" )
summary( plmResult )

## End(Not run)

Predict method for fitted probit models

Description

Calculate predicted values for fitted probit models.

Usage

   ## S3 method for class 'probit'
predict( object, newdata = NULL, type = "link", ... )

Arguments

Value

A numeric vector of the predicted values.

Author(s)

Arne Henningsen and the R Core Team (the code of predict.probit is partly based on the code of predict.lm and predict.glm).

See Also

probit, predict, predict.glm, residuals.probit, and probit-methods.

Examples

## female labour force participation probability
data( "Mroz87" )
m <- probit( lfp ~ kids5 + kids618 + educ + hushrs +
   huseduc + huswage + mtr + motheduc, data=Mroz87 )
predict( m )                            # equal to linearPredictors(m)
predict( m, type = "response" )         # equal to fitted(m)
predict( m, newdata = Mroz87[ 3:9, ] )  # equal to linearPredictors(m)[3:9]
predict( m, newdata = Mroz87[ 3:9, ], type = "response" ) # equal to fitted(m)[3:9]

Predict method for fitted sample selection models

Description

Calculate predicted values for sample selection models fitted with function selection.

Usage

   ## S3 method for class 'selection'
predict( object, newdata = NULL,
   part = ifelse( type %in% c( "unconditional", "conditional" ),
      "outcome", "selection" ),
   type = "unconditional", ... )

Arguments

Value

In most cases, a numeric vector of the predicted values is returned. However, there are three exceptions: (i) when predicting the unconditional expectations of a Tobit-5 model, a matrix with two columns is returned, where the two columns correspond to the two outcome equations (E[yo1] and E[yo2]); (ii) when predicting the conditional expectations of a Tobit-2 model, a matrix with two columns is returned, where the first column returns the expectations conditional on the observation being not selected (E[yo|ys=0]), while the second column returns the expectations conditional on the observation being selected (E[yo|ys=1]); (iii) when predicting the conditional expectations of a Tobit-5 model, a matrix with four columns is returned, where the first two columns return the conditional expectations of the first outcome equation (E[yo1|ys=0] and E[yo1|ys=1]) and the last two columns return the conditional expectations of the second outcome equation (E[yo2|ys=0] and E[yo2|ys=1]).

Author(s)

Arne Henningsen and ‘fg nu’ (the code is partly based on the code posted by ‘fg nu’ at https://stackoverflow.com/questions/14005788/predict-function-for-heckman-model)

See Also

selection, predict, predict.probit, residuals.selection, and selection-methods.

Examples

## Greene( 2003 ): example 22.8, page 786
data( Mroz87 )
Mroz87$kids  <- ( Mroz87$kids5 + Mroz87$kids618 > 0 )

# ML estimation
m <- selection( lfp ~ age + I( age^2 ) + faminc + kids + educ,
   wage ~ exper + I( exper^2 ) + educ + city, Mroz87 )
   
predict( m )
predict( m, type = "conditional" ) 
predict( m, type = "link" ) 
predict( m, type = "response" ) 
predict( m, newdata = Mroz87[ 3:9, ] ) 

Binary choice models.

Description

Binary Choice models. These models are estimated by binaryChoice, intended to be called by wrappers like probit.

Usage

probit(formula, weights = NULL, ...)
binaryChoice(formula, subset, na.action, start = NULL, data = sys.frame(sys.parent()),
             x=FALSE, y = FALSE, model = FALSE, method="ML",
userLogLik=NULL,
             cdfLower, cdfUpper=function(x) 1 - cdfLower(x),
logCdfLower=NULL, logCdfUpper=NULL,
pdf, logPdf=NULL, gradPdf,
maxMethod="Newton-Raphson",
             ... )

Arguments

Details

The dependent variable for the binary choice models must have exactly two levels (e.g. '0' and '1', 'FALSE' and 'TRUE', or 'no' and 'yes'). Internally, the first level is always coded '0' ('failure') and the second level as '1' ('success'), no matter of the actual value. However, by default the levels are ordered alphabetically and this makes puts '1' after '0', 'TRUE' after 'FALSE' nad 'yes' after 'no'.

Via the distribution function parameters, binaryChoice supports generic latent linear index binary choice models with additive disturbance terms. It is intended to be called by wrappers like probit. However, it is also visible in the namespace as the user may want to implement her own models using another distribution of the disturbance term.

The model is estimated using Maximum Likelihood and Newton-Raphson optimizer.

probit implements an outlier-robust log-likelihood (Demidenko, 2001). In case of large outliers the analytic Hessian is singular while Fisher scoring approximation (used, for instance, by glm) is invertible. Those values are not reliable in case of outliers.

No attempt is made to establish the existence of the estimator.

Value

An object of class "binaryChoice". It is a list with following components:

Other components are inherited from maxLik.

probit adds class "probit" and following components to the "binaryChoice" object:

Author(s)

Ott Toomet otoomet@ut.ee, Arne Henningsen

References

Demidenko, Eugene (2001) “Computational aspects of probit model”, Mathematical Communications 6, 233-247

See Also

maxLik for ready-packaged likelihood maximisation routines and methods, glm for generalised linear models, including probit, binomial, and probit-methods.

Examples

## A simple MC trial: note probit assumes normal errors
x <- runif(100)
e <- 0.5*rnorm(100)
y <- x + e
summary(probit((y > 0) ~ x))
## female labour force participation probability
data(Mroz87)
Mroz87$kids <- Mroz87$kids5 > 0 | Mroz87$kids618 > 0
Mroz87$age30.39 <- Mroz87$age < 40
Mroz87$age50.60 <- Mroz87$age >= 50
summary(probit(lfp ~ kids + age30.39 + age50.60 + educ + hushrs +
               huseduc + huswage + mtr + motheduc, data=Mroz87))

probit-methods

Description

Methods for probit models

Usage

## S3 method for class 'probit'
fitted(object, ... )

## S3 method for class 'probit'
logLik(object, ... )

## S3 method for class 'probit'
nobs(object, ... )
             
## S3 method for class 'probit'
nObs(x, ... )
             
## S3 method for class 'probit'
print( x, digits = max(3, getOption("digits") - 3), ... )

Arguments

Details

The fitted method returns a vector of fitted values (probabilities). The logLik method returns the log likelihood value of the model. The nobs and nObs methods return the number of observations. The print method prints the call and the estimated coefficients.

Furthermore, some standard methods can be applied to probit models: the coef method returns the vector of the estimated parameters. The df.residual method returns the degrees of freedom of the residuals. The lrtest method can be used to perform likelihood-ratio tests. The stdEr method returns the vector of the standard errors of the estimated parameters. The vcov method returns the variance covariance matrix of the estimated coefficients.

The methods linearPredictors.probit, model.frame.binaryChoice, model.matrix.binaryChoice, residuals.probit, and summary.probit are described at seperate help pages.

Author(s)

Arne Henningsen

See Also

probit, summary.probit, and selection-methods.

RAND Health Insurance Experiment

Description

'The RAND Health Insurance Experiment (RAND HIE) was a comprehensive study of health care cost, utilization and outcome in the United States. It is the only randomized study of health insurance, and the only study which can give definitive evidence as to the causal effects of different health insurance plans. [...] Although the fieldwork of the study was conducted between 1974 and 1982, the results are still highly relevant, since RAND HIE is the only study which can make causal statements.' (Wikipedia, RAND Health Insurance Experiment, https://en.wikipedia.org/w/index.php?title=RAND_Health_Insurance_Experiment&oldid=110166949, accessed April 8, 2007).

Usage

data(RandHIE)

Format

This data frame contains the following columns:

plan

HIE plan number.

site

Participant's place of residence when the participant was initially enrolled.

coins

Coinsurance rate.

tookphys

Took baseline physical.

year

Study year.

zper

Person identifier.

black

1 if race of household head is black.

income

Family income.

xage

Age in years.

female

1 if person is female.

educdec

Education of household head in years.

time

Time eligible during the year.

outpdol

Outpatient expenses: all covered outpatient medical services excluding dental care, outpatient psychotherapy, outpatient drugs or supplies.

drugdol

Drug expenses: all covered outpatient and dental drugs.

suppdol

Supply expenses: all covered outpatient supplies including dental.

mentdol

Psychotherapy expenses: all covered outpatient psychotherapy services including injections excluding charges for visits in excess of 52 per year, prescription drugs, and inpatient care.

inpdol

Inpatient expenses: all covered inpatient expenses in a hospital, mental hospital, or nursing home, excluding outpatient care and renal dialysis.

meddol

Medical expenses: all covered inpatient and outpatient services, including drugs, supplies, and inpatient costs of newborns excluding dental care and outpatient psychotherapy.

totadm

Hospital admissions: annual number of covered hospitalizations.

inpmis

Incomplete Hospital Records: missing inpatient records.

mentvis

Psychotherapy visits: indicates the annual number of outpatient visits for psychotherapy. It includes billed visits only. The limit was 52 covered visits per person per year. The count includes an initial visit to a psychiatrist or psychologist.

mdvis

Face-to-Face visits to physicians: annual covered outpatient visits with physician providers (excludes dental, psychotherapy, and radiology/anesthesiology/pathology-only visits).

notmdvis

Face-to-Face visits to nonphysicians: annual covered outpatient visits with nonphysician providers such as speech and physical therapists, chiropractors, podiatrists, acupuncturists, Christian Science etc. (excludes dental, healers, psychotherapy, and radiology/anesthesiology/pathology-only visits).

num

Family size.

mhi

Mental health index.

disea

Number of chronic diseases.

physlm

Physical limitations.

ghindx

General health index.

mdeoff

Maximum expenditure offer.

pioff

Participation incentive payment.

child

1 if age is less than 18 years.

fchild

female * child.

lfam

log of num (family size).

lpi

log of pioff (participation incentive payment).

idp

1 if individual deductible plan.

logc

log(coins+1).

fmde

0 if idp=1, ln(max(1,mdeoff/(0.01*coins))) otherwise.

hlthg

1 if self-rated health is good – baseline is excellent self-rated health.

hlthf

1 if self-rated health is fair – baseline is excellent self-rated health.

hlthp

1 if self-rated health is poor – baseline is excellent self-rated health.

xghindx

ghindx (general healt index) with imputations of missing values.

linc

log of income (family income).

lnum

log of num (family size).

lnmeddol

log of meddol (medical expenses).

binexp

1 if meddol > 0.

Source

Data sets of Cameron and Trivedi (2005), http://cameron.econ.ucdavis.edu/mmabook/mmadata.html.

Additional information of variables from Table 20.4 of Cameron and Trivedi (2005) and from Newhouse (1999).

References

Cameron, A. C. and Trivedi, P. K. (2005) Microeconometrics: Methods and Applications, Cambridge University Press.

Newhouse, J. P. (1999) RAND Health Insurance Experiment [in Metropolitan and Non-Metropolitan Areas of the United States], 1974–1982, ICPSR Inter-university Consortium for Political and Social Research, Aggregated Claims Series, Volume 1: Codebook for Fee-for-Service Annual Expenditures and Visit Counts, ICPSR 6439.

Wikipedia, RAND Health Insurance Experiment, https://en.wikipedia.org/wiki/RAND_Health_Insurance_Experiment.

Examples

## Cameron and Trivedi (2005): Section 16.6, page 553ff
data( RandHIE )
subsample <- RandHIE$year == 2 & !is.na( RandHIE$educdec )
selectEq <- binexp ~ logc + idp + lpi + fmde + physlm + disea +
   hlthg + hlthf + hlthp + linc + lfam + educdec + xage + female +
   child + fchild + black
outcomeEq <- lnmeddol ~ logc + idp + lpi + fmde + physlm + disea +
   hlthg + hlthf + hlthp + linc + lfam + educdec + xage + female +
   child + fchild + black
# ML estimation
cameron <- selection( selectEq, outcomeEq, data = RandHIE[ subsample, ] )
summary( cameron )

Residuals of probit models

Description

Calculate residuals of probit models.

Usage

   ## S3 method for class 'probit'
residuals( object, type = "deviance", ... )

Arguments

Details

The residuals are calculated with following formulas:

Response residuals: r_i = y_i - \hat{y}_i

Pearson residuals: r_i = ( y_i - \hat{y}_i ) / \sqrt{ \hat{y}_i ( 1 - \hat{y}_i ) }

Deviance residuals: r_i = \sqrt{ -2 \log( \hat{y}_i ) } if y_i = 1, r_i = - \sqrt{ -2 \log( 1 - \hat{y}_i ) } if y_i = 0

Here, r_i is the ith residual, y_i is the ith response, \hat{y}_i = \Phi( x_i' \hat{\beta} ) is the estimated probability that y_i is one, \Phi is the cumulative distribution function of the standard normal distribution, x_i is the vector of regressors of the ith observation, and \hat{\beta} is the vector of estimated coefficients.

More details are available in Davison & Snell (1991).

Value

A numeric vector of the residuals.

Author(s)

Arne Henningsen

References

Davison, A. C. and Snell, E. J. (1991) Residuals and diagnostics. In: Statistical Theory and Modelling. In Honour of Sir David Cox, edited by Hinkley, D. V., Reid, N. and Snell, E. J., Chapman & Hall, London.

See Also

probit, residuals, residuals.glm, and probit-methods.

Residuals of Selection Models

Description

Calculate residuals of sample selection models

Usage

## S3 method for class 'selection'
residuals(object, part = "outcome",
   type = "deviance", ... )

Arguments

Details

The calculation of the fitted values that are used to calculate the residuals is described in the details section of the documentation of fitted.selection.

Argument type is only used for binary dependent variables, i.e. if argument part is equal "selection" or the dependent variable of the outcome model is binary. Hence, argument type is ignored if argument part is equal "outcome" and the dependent variable of the outcome model is numeric.

Value

A numeric vector of the residuals.

Author(s)

Arne Henningsen

See Also

residuals, selection, fitted.selection, residuals.probit, and selection-methods.

Internal sampleSelection Functions

Description

Internal sampleSelection Functions

Details

Currently, there are no internal functions in the sampleSelection package.

Heckman-style selection and treatment effect models

Description

This is the frontend for estimating Heckman-style selection models either with one or two outcomes (also known as generalized tobit models). It supports binary outcomes and interval outcomes in the single-outcome case. It also supports normal-distribution based treatment effect models.

For model specification and more details, see Toomet and Henningsen (2008) and the included vignettes “Sample Selection Models”, “Interval Regression with Sample Selection”, and “All-Normal Treatment Effects”.

Usage

selection(selection, outcome, data = sys.frame(sys.parent()),
   weights = NULL, subset, method = "ml",
   type = NULL,
   start = NULL,
   boundaries = NULL,
   ys = FALSE, xs = FALSE, yo = FALSE, xo = FALSE,
   mfs = FALSE, mfo = FALSE,
   printLevel = print.level, print.level=0,
   ...)

heckit( selection, outcome, data = sys.frame(sys.parent()),
   method = "2step", ... )

treatReg(selection, outcome,
   data=sys.frame(sys.parent()),
   mfs=TRUE, mfo=TRUE,
   ...)

Arguments

Details

The dependent variable of of the selection equation (specified by argument selection) must have exactly two levels (e.g., 'FALSE' and 'TRUE', or '0' and '1'). By default the levels are sorted in increasing order ('FALSE' is before 'TRUE', and '0' is before '1'). If the dependent variable of the outcome equation (specified by argument outcome) has exactly two levels, this variable is modelled as a binary variable. If argument boundaries is specified, the outcome equation is estimated as interval regression model and the dependent variable of the outcome equation must be a categorical (factor) variable or a variable of strictly positive integer values, whereas the vector specified by argument boundaries must have one more element than the number of levels or the largest integer, respectively. In all other cases, it is assumed that the dependent variable of the outcome equation is continuous and an ordinary sample selection model is estimated.

For tobit-2 (sample selection) models, only those observations are included in the second step estimation (argument 'outcome'), where the dependent variable variable of the selection equation equals the second element of its levels (e.g., 'TRUE' or '1').

For tobit-5 (switching regression) models, in the second step the first outcome equation (first element of argument 'outcome') is estimated only for those observations, where the dependent variable of the selection equation equals the first element of its levels (e.g., 'FALSE' or '0'). The second outcome equation is estimated only for those observations, where this variable equals the second element of its levels (e.g., 'TRUE' or '1').

Treatment effect models are a version of tobit-5 models where the two outcomes are “participation” and “non-participation”. treatReg takes an equal set of explanatory variables for both of these choices and assumes that the corresponding parameters are equal. In typical treatment effect model the selection outcome variable (participation decision) is included as an explanatory variable for the outcome. If this is not done, treatReg amounts to estimating two equations with correlated error structure.

NA-s are allowed in the data. These are ignored if the corresponding outcome is unobserved, otherwise observations which contain NA (either in selection or outcome) are removed.

These selection models assume a known (multivariate normal) distribution of error terms. Because of this, the instruments (exclusion restrictions) are not necessary. However, if no instruments are supplied, the results are based solely on the assumption on multivariate normality. This may or may not be an appropriate assumption for a particular problem. Note also that standard errors tend to be large without a strong exclusion restriction.

If argument method is equal to "ml" (the default), the estimation is done by the maximum likelihood method, where the Newton-Raphson algorithm is used by default. Argument maxMethod (see tobit2fit) can be used to chose other algorithms for the maximisation of the (log) likelihood function.

If argument method is equal to "ml" (the default) and argument start is NULL (the default), the starting values for the maximum-likelihood (ML) estimation of a tobit-2 or tobit-5 model are obtained by an initial two-step estimation of this model.

The two-step estimation of interval-regression models with sample-selection has not yet been implemented. If no starting values for a maximum-likelihood (ML) estimation of an interval-regression model with sample-selection are specified (i.e., argument start is NULL, the default), starting values are obtained by an initial estimation of a tobit-2 model, where the dependent variable of the outcome equation is set to the mid points of the boudaries of the intervals. By default, the starting values are obtained by a maximum-likelihood (ML) estimation of the tobit-2 model, whereas the starting values for the maximum-likelihood (ML) estimation of the tobit-2 model are obtained by a 2-step estimation of the tobit-2 model. If argument start is set to "2step", the starting values for the maximum-likelihood (ML) estimation of an interval-regression model with sample-selection are directly obtained by a 2-step estimation of the tobit-2 model (i.e., without a subsequent ML estimation of the tobit-2 model).

Methods that can be applied to objects returned by selection() are described on the help page selection-methods.

Value

'selection' returns an object of class "selection". If the model estimated by Maximum Likelihood (argument method = "ml"), this object is a list, which has all the components of a 'maxLik' object, and in addition the elements 'twoStep', 'start, 'param', 'termS', 'termO', 'outcomeVar', and if requested 'ys', 'xs', 'yo', 'xo', 'mfs', and 'mfo'. If a tobit-2 (sample selection) model is estimated by the two-step method (argument method = "2step"), the returned object is a list with components 'probit', 'coefficients', 'param', 'vcov', 'lm', 'sigma', 'rho', 'invMillsRatio', and 'imrDelta'. If a tobit-5 (switching regression) model is estimated by the two-step method (argument method = "2step"), the returned object is a list with components 'coefficients', 'vcov', 'probit', 'lm1', 'lm2', 'rho1', 'rho2', 'sigma1', 'sigma2', 'termsS', 'termsO', 'param', and if requested 'ys', 'xs', 'yo', 'xo', 'mfs', and 'mfo'.

Note

The 2-step estimate of 'rho' may be outside of the [-1,1] interval. In that case the standard errors of invMillsRatio may be meaningless.

Author(s)

Arne Henningsen, Ott Toomet otoomet@ut.ee

References

Cameron, A. C. and Trivedi, P. K. (2005) Microeconometrics: Methods and Applications, Cambridge University Press.

Greene, W. H. (2003) Econometric Analysis, Fifth Edition, Prentice Hall.

Heckman, J. (1976) The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models, Annals of Economic and Social Measurement, 5(4), p. 475-492.

Johnston, J. and J. DiNardo (1997) Econometric Methods, Fourth Edition, McGraw-Hill.

Lee, L., G. Maddala and R. Trost (1980) Asymetric covariance matrices of two-stage probit and two-stage tobit methods for simultaneous equations models with selectivity. Econometrica, 48, p. 491-503.

Petersen, S., G. Henningsen and A. Henningsen (2017) Which Households Invest in Energy-Saving Home Improvements? Evidence From a Danish Policy Intervention. Unpublished Manuscript. Department of Management Engineering, Technical University of Denmark.

Toomet, O. and A. Henningsen, (2008) Sample Selection Models in R: Package sampleSelection. Journal of Statistical Software 27(7), https://www.jstatsoft.org/v27/i07/

Wooldridge, J. M. (2003) Introductory Econometrics: A Modern Approach, 2e, Thomson South-Western.

See Also

summary.selection, selection-methods, probit, lm, and Mroz87 and RandHIE for further examples.

Examples

## Greene( 2003 ): example 22.8, page 786
data( Mroz87 )
Mroz87$kids  <- ( Mroz87$kids5 + Mroz87$kids618 > 0 )
# Two-step estimation
summary( heckit( lfp ~ age + I( age^2 ) + faminc + kids + educ,
   wage ~ exper + I( exper^2 ) + educ + city, Mroz87 ) )
# ML estimation
summary( selection( lfp ~ age + I( age^2 ) + faminc + kids + educ,
   wage ~ exper + I( exper^2 ) + educ + city, Mroz87 ) )

## Example using binary outcome for selection model.
## We estimate the probability of womens' education on their
## chances to get high wage (> $5/hr in 1975 USD), using PSID data
## We use education as explanatory variable
## and add age, kids, and non-work income as exclusion restrictions.
data(Mroz87)
m <- selection(lfp ~ educ + age + kids5 + kids618 + nwifeinc,
   wage >= 5 ~ educ, data = Mroz87 )
summary(m)


## example using random numbers
library( "mvtnorm" )
nObs <- 1000
sigma <- matrix( c( 1, -0.7, -0.7, 1 ), ncol = 2 )
errorTerms <- rmvnorm( nObs, c( 0, 0 ), sigma )
myData <- data.frame( no = c( 1:nObs ), x1 = rnorm( nObs ), x2 = rnorm( nObs ),
   u1 = errorTerms[ , 1 ], u2 =  errorTerms[ , 2 ] )
myData$y <- 2 + myData$x1 + myData$u1
myData$s <- ( 2 * myData$x1 + myData$x2 + myData$u2 - 0.2 ) > 0
myData$y[ !myData$s ] <- NA
myOls <- lm( y ~ x1, data = myData)
summary( myOls )
myHeckit <- heckit( s ~ x1 + x2, y ~ x1, myData, print.level = 1 )
summary( myHeckit )

## example using random numbers with IV/2SLS estimation
library( "mvtnorm" )
nObs <- 1000
sigma <- matrix( c( 1, 0.5, 0.1, 0.5, 1, -0.3, 0.1, -0.3, 1 ), ncol = 3 )
errorTerms <- rmvnorm( nObs, c( 0, 0, 0 ), sigma )
myData <- data.frame( no = c( 1:nObs ), x1 = rnorm( nObs ), x2 = rnorm( nObs ),
   u1 = errorTerms[ , 1 ], u2 = errorTerms[ , 2 ], u3 = errorTerms[ , 3 ] )
myData$w <- 1 + myData$x1 + myData$u1
myData$y <- 2 + myData$w + myData$u2
myData$s <- ( 2 * myData$x1 + myData$x2 + myData$u3 - 0.2 ) > 0
myData$y[ !myData$s ] <- NA
myHeckit <- heckit( s ~ x1 + x2, y ~ w, data = myData )
summary( myHeckit )  # biased!
myHeckitIv <- heckit( s ~ x1 + x2, y ~ w, data = myData, inst = ~ x1 )
summary( myHeckitIv ) # unbiased

## tobit-5 example
N <- 500
   library(mvtnorm)
   vc <- diag(3)
   vc[lower.tri(vc)] <- c(0.9, 0.5, 0.6)
   vc[upper.tri(vc)] <- vc[lower.tri(vc)]
   eps <- rmvnorm(N, rep(0, 3), vc)
   xs <- runif(N)
   ys <- xs + eps[,1] > 0
   xo1 <- runif(N)
   yo1 <- xo1 + eps[,2]
   xo2 <- runif(N)
   yo2 <- xo2 + eps[,3]
   a <- selection(ys~xs, list(yo1 ~ xo1, yo2 ~ xo2))
   summary(a)

## tobit2 example
   vc <- diag(2)
   vc[2,1] <- vc[1,2] <- -0.7
   eps <- rmvnorm(N, rep(0, 2), vc)
   xs <- runif(N)
   ys <- xs + eps[,1] > 0
   xo <- runif(N)
   yo <- (xo + eps[,2])*(ys > 0)
   a <- selection(ys~xs, yo ~xo)
   summary(a)

## Example for treatment regressions
## Estimate the effect of treatment on income
## selection outcome: treatment participation, logical (treatment)
## selection explanatory variables: age, education (years)
##   unemployment in 1974, 1975, race
## outcome: log real income 1978
## outcome explanatory variables: treatment, age, education, race.
## unemployment variables are treated as exclusion restriction
data(Treatment, package="Ecdat")
a <- treatReg(treat~poly(age,2) + educ + u74 + u75 + ethn,
              log(re78)~treat + poly(age,2) + educ + ethn,
              data=Treatment)
print(summary(a))

selection-methods

Description

Methods for selection models

Usage

## S3 method for class 'selection'
logLik(object, ... )

## S3 method for class 'selection'
nobs(object, ... )
             
## S3 method for class 'selection'
nObs(x, ... )
             
## S3 method for class 'selection'
print( x, digits = max(3, getOption("digits") - 3), ... )

Arguments

Details

The logLik method returns the log likelihood value of the model. The nobs and nObs methods return the number of observations. The print method prints the call and the estimated coefficients.

Furthermore, some standard methods can be applied to selection models: The lrtest method can be used to perform likelihood-ratio tests. The stdEr method returns the vector of the standard errors of the estimated parameters.

The methods coef.selection, fitted.selection model.frame.selection, model.matrix.selection, residuals.selection, summary.selection, and vcov.selection are described at seperate help pages.

Author(s)

Arne Henningsen

See Also

selection, summary.selection, and probit-methods.

Survey Responses on Smoking Behaviour

Description

'Instructional dataset, N=807, cross-sectional individual data on smoking accompanying Introductory Econometrics: A Modern Approach, Jeffrey M. Wooldridge, South-Western College Publishing, (c) 2000 and Jeffrey M. Wooldridge, Econometric Analysis of Cross Section and Panel Data, MIT Press, (c) 2001.' (https://ideas.repec.org/p/boc/bocins/smoke.html#biblio, accessed February 27, 2017). This dataset is a subset of data used in Mullahy (1997). Data was collected in 1979 and 1980 through the Smoking Supplement to the US National Health Interview Survey.

Usage

data(Smoke)

Format

This data frame contains the following columns:

educ

Years of schooling.

age

Respondents age in years.

cigpric

State cigarette price, cents per pack.

income

Annual income in USD.

restaurn

Dummy variable indicating if state restaurant smoking restrictions are in place.

smoker

Dummy variable indicating if person has smoked at least one cigarette.

cigs_intervals

Number of cigarettes smoked per day, coded in intervals with intervals boundaries: (0,5,10,20,50)

cigs

Number of cigarettes smoked per day.

Source

Wooldridge(2009)'s dataset also available in other formats at https://ideas.repec.org/p/boc/bocins/smoke.html#biblio.

Original data used in Mullahy (1985) and Mullahy (1997).

References

Jeffrey, M. Wooldridge (2009), Introductory Econometrics: A modern approach, Canada: South-Western Cengage Learning.

Mullahy, John (1997), Instrumental-Variable Estimation of Count Data Models: Applications to Models of Cigarette Smoking Behavior, Review of Economics and Statistics 79, 596-593.

Mullahy, John (1985) Cigarette Smoking: Habits, Health Concerns, and Heterogeneous Unobservables in a Microeconometric Analysis of Consumer Demand, Ph.D. dissertation, University of Virginia.

Examples

data( Smoke )
# boundaries of the intervals
bounds <- c(0,5,10,20,50,Inf)
## Not run: 
# estimation with starting values obtained by a ML estimation 
# of a standard tobit-2 model with the dependent variable 
# of the outcome equation equal to the mid-points of the intervals
res <- selection( smoker ~ educ + age, cigs_intervals ~ educ, 
  data = Smoke, boundaries = bounds )
summary( res )

# estimation with starting values obtained by a two-step estimation 
# of a standard tobit-2 model with the dependent variable 
# of the outcome equation equal to the mid-points of the intervals
res2 <- selection( smoker ~ educ + age, cigs_intervals ~ educ, 
  data = Smoke, boundaries = bounds, start = "2step" )
summary( res2 )

## End(Not run)

# estimation with starting values that are very close to the estimates
# (in order to reduce the execution time of running this example) 
resS <- selection( smoker ~ educ + age, cigs_intervals ~ educ, 
  data = Smoke, boundaries = bounds, 
  start = c( 0.527, -0.0482, -0.0057, 4.23, -0.319, 2.97, 2.245 ) )
summary( resS )

Summarizing Probit Estimations

Description

Print or return a summary of a probit estimation.

Usage

   ## S3 method for class 'probit'
summary( object, ... )
   ## S3 method for class 'summary.probit'
print( x, ... )

Arguments

Value

The summary method returns an object of class summary.probit; the print method prints summary results and returns the argument invisibly.

Author(s)

Arne Henningsen

See Also

probit and probit-methods.

Summarizing Selection Estimations

Description

Print or return a summary of a selection estimation.

Usage

   ## S3 method for class 'selection'
summary(object, ...)
   ## S3 method for class 'summary.selection'
print(x,
      digits = max(3, getOption("digits") - 3),
      part = "full", ...)

Arguments

Details

The variance-covariance matrix of the two-step estimator is currently implemented only for tobit-2 (sample selection) models, but not for the tobit-5 (switching regression) model.

Value

Summary methods return an object of class summary.selection. Print methods return the argument invisibly.

Author(s)

Arne Henningsen, Ott Toomet otoomet@ut.ee

See Also

summary, selection, and selection-methods.

Examples

## Wooldridge( 2003 ): example 17.5, page 590
data( Mroz87 )
wooldridge <- selection( lfp ~ nwifeinc + educ + exper + I( exper^2 ) +
   age + kids5 + kids618, log( wage ) ~ educ + exper + I( exper^2 ),
   data = Mroz87, method = "2step" )

# summary of the 1st step probit estimation (Example 17.1, p. 562f)
# and the 2nd step OLS regression (example 17.5, page 590)
summary( wooldridge )

# summary of the outcome equation only
print(summary(wooldridge), part="outcome")

Fitting Parametric Sample Selection Models

Description

These functions do the actual fitting of tobit-2 (sample selection) and tobit-5 (switching regression) models by Maximum Likelihood (ML) estimation. The arguments must be given as numeric vectors/matrices, initial value of parameters must be specified. These functions are called by selection and are intended for sampleSelection internal use. The function tobit2Bfit does the actual fitting of tobit-2 (sample selection) models with a binary dependent variable of the outcome model (YO) using a double-probit specification.

Usage

tobit2fit( YS, XS, YO, XO, start, weights = NULL, print.level = 0,
   maxMethod = "Newton-Raphson", ... )

tobit2Bfit( YS, XS, YO, XO, start, weights = NULL, print.level = 0,
   maxMethod = "BHHH", ... )

tobit5fit( YS, XS, YO1, XO1, YO2, XO2, start, print.level = 0,
   maxMethod = "Newton-Raphson", ... ) 

Arguments

Value

Object of class "selection". It inherits from class "maxLik" and includes two additional components: $tobitType, numeric tobit model classifier (see Amemiya, 1985), and $method, either "ml" or "2step", specifying the estimation method.

Author(s)

Ott Toomet otoomet@ut.ee, Arne Henningsen

References

Amemiya, T. (1985) Advanced Econometrics, Harvard University Press

See Also

selection, maxLik

Extract Variance Covariance Matrix

Description

This function extracts the coefficient variance-covariance matrix from sample selection models.

Usage

## S3 method for class 'selection'
vcov(object, part = "full", ...)

Arguments

Details

The variance-covariance matrix of a two-step estimate is currently only partly implemented. The unimplemented part of the matrix is filled with NAs.

Value

the estimated variance covariance matrix of the coefficients.

Author(s)

Arne Henningsen, Ott Toomet otoomet@ut.ee

See Also

vcov, selection, coef.selection, and selection-methods.

Examples

## Estimate a simple female wage model taking into account the labour
## force participation
   data(Mroz87)
   a <- heckit(lfp ~ huswage + kids5 + mtr + fatheduc + educ + city,
               log(wage) ~ educ + city, data=Mroz87)
## extract the full variance-covariance matrix:
vcov( a )
## now extract the variance-covariance matrix of the outcome model only:
vcov( a, part = "outcome" )