Type: Package
Title: Local Average Response Functions for Instrumental Variable Estimation of Treatment Effects
Version: 1.4
Date: 2016-07-25
Author: Weihua An and Xuefu Wang, Indiana University Bloomington
Maintainer: Weihua An <weihuaan@indiana.edu>
Description: Provides instrumental variable estimation of treatment effects when both the endogenous treatment and its instrument are binary. Applicable to both binary and continuous outcomes.
Imports: Formula
License: GPL-3
Packaged: 2016-07-26 01:01:20 UTC; weihuaan
NeedsCompilation: no
Repository: CRAN
Date/Publication: 2016-07-26 12:04:14

Generating Powers Series of Variables

Description

Internal function used by npse to generate covariates power series.

Usage

Generate.Powers(X, lambda)

Arguments

X

covariates.

lambda

the maximal order of power series.

Author(s)

Weihua An, Departments of Statistics and Sociology, Indiana University Bloomington, weihuaan@indiana.edu.
Xuefu Wang, Department of Statistics, Indiana University Bloomington, wangxuef@umail.iu.edu.

See Also

larf, npse

c401k

Description

Cross-sectional data with 9,275 observations including 11 variables on eligibility for and participation in 401(k) along with income and demographic information.

Usage

data(c401k)

Format

pira

participation in IRA, participation = 1

nettfa

net family financial assets in $1000

p401k

participation in 401(k), participation = 1

e401k

eligibility for 401(k), eligible = 1

inc

income

incsq

income square

marr

marital status, married = 1

male

sex, male = 1

age

age

agesq

age square

fsize

family size

Details

An exemplary data to illustrate the usage of larf. The data includes both a binary outcome (pira) and a continuous outcome (nettfa). The treatment is participation in 401k, p401k. Eligibility for 401(k), e401k, is used as an instrument for p401k.

Source

The Wooldridge Data Sets (Wooldridge 2010), originally entitled "401ksubs.dta" in Stata format, available at http://www.stata.com/texts/eacsap/.

References

Wooldridge, Jeffrey M. 2010. Econometric Analysis of Cross Section and Panel Data. 2nd Edition. MIT Press.

See Also

larf, larf.fit

Examples

data(c401k)

Cross-validation of a Linear Regression Model

Description

Provides cross-validation of a linear regression model

Usage

cvlm(form.lm, data, m=10, seed = NULL)

Arguments

form.lm

formula of the regression model.

data

data including outcome and covaraites.

m

the number of folds to be used in cross-validation.

seed

random starting number used to replicate cross-validation.

Details

This function finds the optimal order of the covariates power series through cross-validation.

Value

sumres

Sum of residual squares divided by degree of freedom.

df

Degree of freedom which equals to the number of valid predictions minus the number of parameters.

m

the number of folds to be used in cross-validation.

seed

The random seed.

Note

In making the code, we adopted part of the CVlm in DAAG (Maindonald and Braun, 2015).
https://cran.r-project.org/package=DAAG

Author(s)

Weihua An, Departments of Sociology and Statistics, Indiana University Bloomington, weihuaan@indiana.edu.
Xuefu Wang, Department of Statistics, Indiana University Bloomington, wangxuef@umail.iu.edu.

See Also

larf, npse

Local Average Response Functions for Instrumental Variable Estimation of Treatment Effects

Description

The function provides instrumental variable estimation of treatment effects when both the endogenous treatment and its instrument are binary. Applicable to both binary and continuous outcomes.

Usage

larf(formula, treatment, instrument, data, method = "LS",  
     AME = FALSE, optimizer = "Nelder-Mead", zProb = NULL)

Arguments

formula

specification of the outcome model in the form like either y ~ x1 + x2 or y ~ X where X is a matrix containing all the covariates excluding the treatment. Also support multi-part formulas (Zeileis and Croissant, 2010). For example, y + d ~ x1 + x2 | z, where d represents the treatment and z the instrument.

treatment

A vector containing the binary treatment.

instrument

A vector containing the binary instrument for the endogenous treatment.

data

an optional data frame. If unspecified, the data will be taken from the working environment.

method

the estimation method to be used. The default is “LS", standing for least squares. “ML", standing for maximum likelihood, is an alternative.

AME

whether average marginal effects (AME) should be reported. The default is FALSE, in which case marginal effects at the means (MEM) are reported.

optimizer

the optimization algorithm for the ML method. It should be one of “Nelder-Mead", “BFGS", “CG", “L-BFGS-B", “SANN", or “Brent". See optim in R for more detail.

zProb

a vector containing the probability of receiving the treatment inducement (i.e., instrument = 1) that have been estimated by semiparametrical methods.

Details

larf is the high-level interface to the work-horse function larf.fit. A set of standard methods (including print, summary, coef, vcov, fitted, resid, predict) can be used to extract the corresponding information from a larf object.

The function provides instrumental variable estimation of treatment effects when both the endogenous treatment and its instrument (i.e., the treatment inducement) are binary. The method (Abadie, 2003) involves two steps. First, pseudo-weights are constructed from the probability of receiving the treatment inducement. By default the function estimates the probability by a Probit regression. But it also allows users to employ the probability that has been estimated by semiparametric methods. Second, the pseudo-weights are used to estimate the local average response function of the outcome conditional on the treatment and covariates. The function provides both least squares and maximum likelihood estimates of the conditional treatment effects.

Value

coefficients

Estimated coefficients.

SE

Standard errors of the estimated coefficients.

MargEff

Estimated marginal effects, available only for binary outcomes.

MargStdErr

Standard errors of the estimated marginal effects, available only for binary outcomes.

vcov

Variance covariance matrix of the estimated coefficients.

fitted.values

Predicted outcomes based on the estimated model. They are probabilities when the outcome is binary.

Note

We derived part of the code from the Matlab code written by Professor Alberto Abadie, available at http://www.hks.harvard.edu/fs/aabadie/larf.html. We thank Onur Altindag and Behzad Kianian for helpful suggestions on improving the computation.

Author(s)

Weihua An, Departments of Sociology and Statistics, Indiana University Bloomington, weihuaan@indiana.edu.
Xuefu Wang, Department of Statistics, Indiana University Bloomington, wangxuef@umail.iu.edu.

References

Abadie, Alberto. 2003. "Semiparametric Instrumental Variable Estimation of Treatment Response Models." Journal of Econometrics 113: 231-263.
An, Weihua and Xuefu Wang. 2016. "LARF: Instrumental Variable Estimation of Causal Effects through Local Average Response Functions." Journal of Statistical Software 71(1): 1-13.
Zeileis, Achim and Yves Croissant. 2010. "Extended Model Formulas in R: Multiple Parts and Multiple Responses." Journal of Statistical Software 34(1): 1-13. http://www.jstatsoft.org/v34/i01/.

See Also

larf.fit, c401k

Examples

data(c401k)
attach(c401k)

## Not run: 
# Continuous outcome. Treatment effects of participation in 401(k) 
# on net family financial assest
est1 <- larf(nettfa ~ inc + age + agesq + marr + fsize, treatment = p401k, 
instrument = e401k, data = c401k)
summary(est1)

# Nonparametric estimates of the probability of 
# receiving the treatment inducement
library(mgcv)
firstStep <- gam(e401k ~ s(inc) + s(age) + s(agesq) + marr + s(fsize), 
data=c401k, family=binomial(link = "probit"))
zProb <- firstStep$fitted
est2<- larf(nettfa ~ inc + age + agesq + marr + fsize, treatment = p401k, 
instrument = e401k, data = c401k, zProb = zProb)
summary(est2) 

# Binary outcome. Treatment effects of participation in 401(k) 
# on participation in IRA
est3 <- larf(pira ~ inc + age + agesq + marr + fsize, treatment = p401k, 
instrument = e401k, data = c401k)
summary(est3) 

## End(Not run)

Fitting the Local Average Response Function

Description

It is the work-horse function for its high-level interface larf.

Usage

larf.fit(Y, X, D, Z, method, AME, optimizer, zProb)

Arguments

Y

a vector containing the outcome.

X

a matrix containing the covariates excluding the treatment.

D

a vector containing the binary treatment.

Z

a vector containing the binary instrument for the endogenous treatment.

method

the estimation method to be used. The default is “LS", standing for least squares. “ML", standing for maximum likelihood, is an alternative.

AME

whether average marginal effects (AME) should be reported. The default is FALSE, in which case marginal effects at the means (MEM) are reported.

optimizer

the optimization algorithm for the ML method. It should be one of “Nelder-Mead", “BFGS", “CG", “L-BFGS-B", “SANN", or “Brent". See optim in R for more detail.

zProb

a vector containing the probability of receiving the treatment inducement (i.e., instrument = 1) that have been estimated by semiparametrical methods.

Author(s)

Weihua An and Xuefu Wang, Departments of Sociology and Statistics, Indiana University Bloomington

See Also

larf, c401k

Nonparametric Power Series Estimation

Description

Use the optimal order of power series of covariates to predict outcome. The optimal order of power series is determined by cross-validation.

Usage

npse(formula, order = 3, m = 10, seed = NULL)

Arguments

formula

specification of the outcome model in the form like either z ~ x1 + x2 or z ~ X where X is the covariate matrix.

order

the maximal order of power series to be used.

m

the number of folds to be used in cross-validation.

seed

random starting number used to replicate cross-validation.

Details

This function predicts the outcome based on the optimal order of covariates power series. The optimal order of the power series is determined by cross-validation. For example, it can be used to predict the probabilty of receiving treatment inducment based on covariates.

Value

fitted

Predicted outcomes based on the estimated model. They are probabilities when the outcome is binary.

Lambda

The optimal order of power series determined by cross-validation.

Data.opt

The data including z and the optimal covariates power series.

CV.Res

The residual sum of squares of the cross-validations.

seed

The random seed.

Author(s)

Weihua An, Departments of Sociology and Statistics, Indiana University Bloomington, weihuaan@indiana.edu.
Xuefu Wang, Department of Statistics, Indiana University Bloomington, wangxuef@umail.iu.edu.

References

Abadie, Alberto. 2003. "Semiparametric Instrumental Variable Estimation of Treatment Response Models." Journal of Econometrics 113: 231-263.

See Also

larf, larf.fit

Examples

data(c401k)
attach(c401k)

## Not run: 
# binary outcome
Z <- c401k$e401k

# covariates
X <- as.matrix(c401k[,c("inc", "male", "fsize"  )])

# get nonparametric power series estimation of the regression of Z on X
zp <- npse(Z~X, order = 5, m = 10, seed = 681)

# sum of residual squares of the cross-validations
zp$CV.Res

# the opitimal order of the power series
zp$Lambda

# summary of the predictions based on the optimal power series
summary(zp$fitted)

## End(Not run)

Predictions Based on the Estimated LARF

Description

Predict new outcomes based on the model fitted by larf.

Usage

## S3 method for class 'larf'
predict(object, newCov, newTreatment, ...)

Arguments

object

an object of class larf as fitted by larf.

newCov

A matrix containing the new covariates.

newTreatment

A vector containing the new binary treatment.

...

currently not used.

Details

Predicted outcomes are based on the estimated coefficients and new covariates and/or new treatment. The predicted outcomes are probabilities when the outcome is binary.

Value

predicted.values

The function returns a vector of the predicted outcomes.

Author(s)

Weihua An and Xuefu Wang, Departments of Statistics and Sociology, Indiana University Bloomington

See Also

larf, larf.fit

Print Results of the Estimated LARF

Description

Methods to display brief results of a larf object.

Usage

## S3 method for class 'larf'
print(x, digits = 4, ...)

Arguments

x

an object of class "larf" as fitted by larf.

digits

The number of significant digits to be printed in the reports of the results.

...

currently not used.

Author(s)

Weihua An and Xuefu Wang, Departments of Statistics and Sociology, Indiana University Bloomington

See Also

larf, larf.fit

Summary of the Estimated LARF

Description

Summary of an object in the larf class.

Usage

## S3 method for class 'larf'
summary(object, ...)

Arguments

object

an object of class "larf" as fitted by larf.

...

currently not used.

Author(s)

Weihua An and Xuefu Wang, Departments of Statistics and Sociology, Indiana University Bloomington

See Also

larf, larf.fit

Variance Covariance Matrix of the Parameters in the Estimated LARF

Description

Methods to display the variance covariance matrix of the model parameters estimated by larf.

Usage

## S3 method for class 'larf'
vcov(object, ...)

Arguments

object

an object of class "larf" as fitted by larf.

...

currently not used.

Author(s)

Weihua An and Xuefu Wang, Departments of Statistics and Sociology, Indiana University Bloomington

See Also

larf, larf.fit