ATE with Generalized Empirical Likelihood estimation
Function to estimate the average treatment effect with the sample being balanced by GEL.
ATEgel(g, balm, w=NULL, y=NULL, treat=NULL, tet0=NULL,momType=c("bal","balSample","ATT"),
popMom = NULL, family=c("linear","logit", "probit"),
type = c("EL", "ET", "CUE", "ETEL", "HD", "ETHD", "RCUE"),
tol_lam = 1e-9, tol_obj = 1e-9, tol_mom = 1e-9, maxiterlam = 100,
optfct = c("optim", "nlminb"),
optlam = c("nlminb", "optim", "iter", "Wu"), data=NULL,
Lambdacontrol = list(),
model = TRUE, X = FALSE, Y = FALSE, ...)
checkConv(obj, tolConv=1e-4, verbose=TRUE, ...)g |
A formula as |
obj |
Object of class |
balm |
A formula for the moments to be balanced between the treated and control groups (see details) |
y |
The response variable when |
treat |
The treatment indicator when |
w |
A formula to add covariates to the main regression. When
|
tet0 |
A 3 \times 1 vector of starting values. If not provided, they are obtained using an OLS regression |
momType |
How the moments of the covariates should be balanced. By default, it is simply balanced without restriction. Alternatively, moments can be set equal to the sample moments of the whole sample, or to the sample moments of the treated group. The later will produce the average treatment effect of the treated (ATT) |
popMom |
A vector of population moments to use for balancing. It can be used of those moments are available from a census, for example. When available, it greatly improves efficiency. |
family |
By default, the outcome is linearly related to the treatment indicators. If the outcome is binary, it is possible to use the estimating equations of either the logit or probit model. |
type |
"EL" for empirical likelihood, "ET" for exponential tilting, "CUE" for continuous updated estimator, "ETEL" for exponentially tilted empirical likelihood of Schennach(2007), "HD" for Hellinger Distance of Kitamura-Otsu-Evdokimov (2013), and "ETHD" for the exponentially tilted Hellinger distance of Antoine-Dovonon (2015). "RCUE" is a restricted version of "CUE" in which the probabilities are bounded below by zero. In that case, an analytical Kuhn-Tucker method is used to find the solution. |
tol_lam |
Tolerance for λ between two iterations. The
algorithm stops when \|λ_i -λ_{i-1}\| reaches
|
maxiterlam |
The algorithm to compute λ stops if there
is no convergence after "maxiterlam" iterations (see
|
tol_obj |
Tolerance for the gradiant of the objective function to
compute λ (see |
optfct |
Algorithm used for the parameter estimates |
tol_mom |
It is the tolerance for the moment condition ∑_{t=1}^n p_t g(θ(x_t)=0, where p_t=\frac{1}{n}Dρ(<g_t,λ>) is the implied probability. It adds a penalty if the solution diverges from its goal. |
optlam |
Algorithm used to solve for the lagrange multiplier in
|
data |
A data.frame or a matrix with column names (Optional). |
Lambdacontrol |
Controls for the optimization of the vector of
Lagrange multipliers used by either |
model, X, Y |
logicals. If |
verbose |
If TRUE, a summary of the convergence is printed |
tolConv |
The tolerance for comparing moments between groups |
... |
More options to give to |
We want to estimate the model Y_t = θ_1 + θ_2 treat +
ε_t, where θ_2 is the treatment effect. GEL is
used to balance the sample based on the argument x above.
For example, if we want the sample mean of x1 and x2 to be
balanced between the treated and control, we set x to
~x1+x2. If we want the sample mean of x1, x2,
x1*x2, x1^2 and x2^2, we set x to
~x1*x2 + I(x1^2) + I(x2^2).
'gel' returns an object of 'class' '"ategel"'
The functions 'summary' is used to obtain and print a summary of the results.
The object of class "ategel" is a list containing the same elements
contained in objects of class gel.
Lee, Seojeong (2016), Asymptotic refinements of misspecified-robust bootstrap for GEL estimators, Journal of Econometrics, 192, 86–104.
Schennach, Susanne, M. (2007), Point Estimation with Exponentially Tilted Empirical Likelihood. Econometrica, 35, 634-672.
Wu, C. (2005), Algorithms and R codes for the pseudo empirical likelihood method in survey sampling. Survey Methodology, 31(2), page 239.
Chausse, P. (2010), Computing Generalized Method of Moments and Generalized Empirical Likelihood with R. Journal of Statistical Software, 34(11), 1–35. URL https://www.jstatsoft.org/v34/i11/.
Chausse, P. and Giurcanu, M. and Luta, G. (2021) Estimating the Average Causal Effect using Generalized Empirical Likelihood Methods, Work in progress.
data(nsw) # Scale income nsw$re78 <- nsw$re78/1000 nsw$re75 <- nsw$re75/1000 res <- ATEgel(re78~treat, ~age+ed+black+hisp+married+nodeg+re75, data=nsw,type="ET") summary(res) chk <- checkConv(res) res2 <- ATEgel(re78~treat, ~age+ed+black+hisp+married+nodeg+re75, data=nsw,type="ET", momType="balSample") summary(res2) chk2 <- checkConv(res2)
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