| Title: | Local Average Response Functions for Instrumental Variable Estimation of Treatment Effects |
|---|---|
| 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. |
| Authors: | Weihua An and Xuefu Wang, Indiana University Bloomington |
| Maintainer: | Weihua An <[email protected]> |
| License: | GPL-3 |
| Version: | 1.4 |
| Built: | 2024-08-26 06:21:42 UTC |
| Source: | CRAN |
Cross-sectional data with 9,275 observations including 11 variables on eligibility for and participation in 401(k) along with income and demographic information.
data(c401k)data(c401k)
piraparticipation in IRA, participation = 1
nettfanet family financial assets in $1000
p401kparticipation in 401(k), participation = 1
e401keligibility for 401(k), eligible = 1
incincome
incsqincome square
marrmarital status, married = 1
malesex, male = 1
ageage
agesqage square
fsizefamily size
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.
The Wooldridge Data Sets (Wooldridge 2010), originally entitled "401ksubs.dta" in Stata format, available at http://www.stata.com/texts/eacsap/.
Wooldridge, Jeffrey M. 2010. Econometric Analysis of Cross Section and Panel Data. 2nd Edition. MIT Press.
data(c401k)data(c401k)
Provides cross-validation of a linear regression model
cvlm(form.lm, data, m=10, seed = NULL)cvlm(form.lm, data, m=10, seed = NULL)
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. |
This function finds the optimal order of the covariates power series through cross-validation.
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. |
In making the code, we adopted part of the CVlm in DAAG (Maindonald and Braun, 2015).
https://cran.r-project.org/package=DAAG
Weihua An, Departments of Sociology and Statistics, Indiana University Bloomington, [email protected].
Xuefu Wang, Department of Statistics, Indiana University Bloomington, [email protected].
Internal function used by npse to generate covariates power series.
Generate.Powers(X, lambda)Generate.Powers(X, lambda)
X |
covariates. |
lambda |
the maximal order of power series. |
Weihua An, Departments of Statistics and Sociology, Indiana University Bloomington, [email protected].
Xuefu Wang, Department of Statistics, Indiana University Bloomington, [email protected].
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.
larf(formula, treatment, instrument, data, method = "LS", AME = FALSE, optimizer = "Nelder-Mead", zProb = NULL)larf(formula, treatment, instrument, data, method = "LS", AME = FALSE, optimizer = "Nelder-Mead", zProb = NULL)
formula |
specification of the outcome model in the form like either |
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 |
zProb |
a vector containing the probability of receiving the treatment inducement (i.e., instrument = 1) that have been estimated by semiparametrical methods. |
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.
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. |
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.
Weihua An, Departments of Sociology and Statistics, Indiana University Bloomington, [email protected].
Xuefu Wang, Department of Statistics, Indiana University Bloomington, [email protected].
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/.
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)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)
It is the work-horse function for its high-level interface larf.
larf.fit(Y, X, D, Z, method, AME, optimizer, zProb)larf.fit(Y, X, D, Z, method, AME, optimizer, zProb)
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 |
zProb |
a vector containing the probability of receiving the treatment inducement (i.e., instrument = 1) that have been estimated by semiparametrical methods. |
Weihua An and Xuefu Wang, Departments of Sociology and Statistics, Indiana University Bloomington
Use the optimal order of power series of covariates to predict outcome. The optimal order of power series is determined by cross-validation.
npse(formula, order = 3, m = 10, seed = NULL)npse(formula, order = 3, m = 10, seed = NULL)
formula |
specification of the outcome model in the form like either |
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. |
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.
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 |
CV.Res |
The residual sum of squares of the cross-validations. |
seed |
The random seed. |
Weihua An, Departments of Sociology and Statistics, Indiana University Bloomington, [email protected].
Xuefu Wang, Department of Statistics, Indiana University Bloomington, [email protected].
Abadie, Alberto. 2003. "Semiparametric Instrumental Variable Estimation of Treatment Response Models." Journal of Econometrics 113: 231-263.
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$fitted) ## End(Not run)data(c401k) attach(c401k) ## Not run: # binary outcome Z <- c401k$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)
Predict new outcomes based on the model fitted by larf.
## S3 method for class 'larf' predict(object, newCov, newTreatment, ...)## S3 method for class 'larf' predict(object, newCov, newTreatment, ...)
object |
an object of class |
newCov |
A matrix containing the new covariates. |
newTreatment |
A vector containing the new binary treatment. |
... |
currently not used. |
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.
predicted.values |
The function returns a vector of the predicted outcomes. |
Weihua An and Xuefu Wang, Departments of Statistics and Sociology, Indiana University Bloomington
Methods to display brief results of a larf object.
## S3 method for class 'larf' print(x, digits = 4, ...)## S3 method for class 'larf' print(x, digits = 4, ...)
x |
an object of class |
digits |
The number of significant digits to be printed in the reports of the results. |
... |
currently not used. |
Weihua An and Xuefu Wang, Departments of Statistics and Sociology, Indiana University Bloomington
Summary of an object in the larf class.
## S3 method for class 'larf' summary(object, ...)## S3 method for class 'larf' summary(object, ...)
object |
an object of class |
... |
currently not used. |
Weihua An and Xuefu Wang, Departments of Statistics and Sociology, Indiana University Bloomington
Methods to display the variance covariance matrix of the model parameters estimated by larf.
## S3 method for class 'larf' vcov(object, ...)## S3 method for class 'larf' vcov(object, ...)
object |
an object of class |
... |
currently not used. |
Weihua An and Xuefu Wang, Departments of Statistics and Sociology, Indiana University Bloomington