This function estimates bounds on treatment effect parameters, following the procedure described in Mogstad, Torgovitsky (2017). Of the target parameters, the user can choose from the ATE, ATT, ATU, LATE, and generalized LATE. The user is required to provide a polynomial expression for the marginal treatment responses (MTR), as well as a set of regressions. By restricting the set of coefficients on each term of the MTRs to be consistent with the regression estimates, the function is able to restrict itself to a set of MTRs. The bounds on the treatment effect parameter correspond to finding coefficients on the MTRs that maximize their average difference.
ivmteEstimate(data, target, late.Z, late.from, late.to, late.X, eval.X,
genlate.lb, genlate.ub, target.weight0, target.weight1,
target.knots0 = NULL, target.knots1 = NULL, m0, m1, uname = u,
m1.ub, m0.ub, m1.lb, m0.lb, mte.ub, mte.lb, m0.dec, m0.inc, m1.dec,
m1.inc, mte.dec, mte.inc, ivlike, components, subset, propensity,
link = "logit", treat, lpsolver, criterion.tol = 0,
initgrid.nx = 20, initgrid.nu = 20, audit.nx = 2500,
audit.nu = 25, audit.add = 100, audit.max = 25,
audit.grid = NULL, save.grid = FALSE, point = FALSE,
point.eyeweight = FALSE, point.center = NULL,
point.redundant = NULL, count.moments = TRUE, orig.sset = NULL,
orig.criterion = NULL, vars_y, vars_mtr, terms_mtr0, terms_mtr1,
vars_data, splinesobj, noisy = TRUE, smallreturnlist = FALSE,
seed = 12345, debug = FALSE, environments)data.frame or data.table used to estimate
the treatment effects.
character, target parameter to be
estimated. Currently function allows for ATE ('ate'),
ATT ('att'), ATU ('atu'), LATE ('late'),
and generalized LATE ('genlate').
vector of variable names used to define the LATE.
baseline set of values of Z used to define the LATE.
comparison set of values of Z used to define the LATE.
vector of variable names of covariates which we condition on when defining the LATE.
numeric vector of the values at which we condition
variables in late.X on when estimating the LATE.
lower bound value of unobservable u for
estimating the generalized LATE.
upper bound value of unobservable u for
estimating the generalized LATE.
user-defined weight function for the control
group defining the target parameter. A list of functions can be
submitted if the weighting function is in fact a spline. The
arguments of the function should be variable names in
data. If the weight is constant across all observations,
then the user can instead submit the value of the weight
instead of a function.
user-defined weight function for the treated
group defining the target parameter. See target.weight0
for details.
user-defined set of functions defining the
knots associated with spline weights for the control group. The
arguments of the function should consist only of variable names
in data. If the knots are constant across all
observations, then the user can instead submit the vector of
knots instead of a function.
user-defined set of functions defining the
knots associated with spline weights for the treated group. See
target.knots0 for details.
one-sided formula for the marginal treatment response
function for the control group. Splines may also be
incorporated using the expression uSpline, e.g.
uSpline(degree = 2, knots = c(0.4, 0.8), intercept =
TRUE). The intercept argument may be omitted, and is
set to TRUE by default.
one-sided formula for marginal treatment response
function for treated group. Splines can also be incorporated
using the expression "uSplines(degree, knots, intercept)". The
intercept argument may be omitted, and is set to
TRUE by default.
variable name for the unobservable used in declaring the MTRs. The name can be provided with or without quotation marks.
numeric value for upper bound on MTR for the treated group. By default, this will be set to the largest value of the observed outcome in the estimation sample.
numeric value for upper bound on MTR for the control group. By default, this will be set to the largest value of the observed outcome in the estimation sample.
numeric value for lower bound on MTR for the treated group. By default, this will be set to the smallest value of the observed outcome in the estimation sample.
numeric value for lower bound on MTR for the control group. By default, this will be set to the smallest value of the observed outcome in the estimation sample.
numeric value for upper bound on treatment effect parameter of interest.
numeric value for lower bound on treatment effect parameter of interest.
logical, set to FALSE by default. Set equal to
TRUE if the MTR for the control group should be weakly
monotone decreasing.
logical, set to FALSE by default. Set equal to
TRUE if the MTR for the control group should be weakly
monotone increasing.
logical, set to FALSE by default. Set equal to
TRUE if the MTR for the treated group should be weakly
monotone decreasing.
logical, set to FALSE by default. Set equal to
TRUE if the MTR for the treated group should be weakly
monotone increasing.
logical, set to FALSE by default. Set equal
to TRUE if the MTE should be weakly monotone decreasing.
logical, set to FALSE by default. Set equal
to TRUE if the MTE should be weakly monotone increasing.
formula or vector of formulas specifying the
regressions for the IV-like estimands. Which coefficients to
use to define the constraints determining the treatment effect
bounds (alternatively, the moments determining the treatment
effect point estimate) can be selected in the argument
components.
a list of vectors of the terms in the regression
specifications to include in the set of IV-like estimands. No
terms should be in quotes. To select the intercept term,
include the name intercept. If the factorized
counterpart of a variable is included in the IV-like
specifications, e.g. factor(x) where x = 1, 2, 3,
the user can select the coefficients for specific factors by
declaring the components factor(x)-1, factor(x)-2,
factor(x)-3. See l on how to input the
argument. If no components for a IV specification are given,
then all coefficients from that IV specification will be used
to define constraints in the partially identified case, or to
define moments in the point identified case.
a single subset condition or list of subset
conditions corresponding to each regression specified in
ivlike. The input must be logical. See l
on how to input the argument. If the user wishes to select
specific rows, construct a binary variable in the data set, and
set the condition to use only those observations for which the
binary variable is 1, e.g. the binary variable is use,
and the subset condition is use == 1.
formula or variable name corresponding to
propensity to take up treatment. If a formula is declared, then
the function estimates the propensity score according to the
formula and link specified in link. If a variable name
is declared, then the corresponding column in the data is taken
as the vector of propensity scores. A variable name can be
passed either as a string (e.g propensity = 'p'). , a
variable (e.g. propensity = p), or a one-sided formula
(e.g. propensity = ~p.
character, name of link function to estimate propensity
score. Can be chosen from 'linear', 'probit', or
'logit'. Default is set to 'logit'.
variable name for treatment indicator. The name can be provided with or without quotation marks.
character, name of the linear programming package
in R used to obtain the bounds on the treatment effect. The
function supports 'gurobi', 'cplexapi',
'lpsolveapi'.
tolerance for violation of observational
equivalence, set to 0 by default. Statistical noise may
prohibit the theoretical LP problem from being feasible. That
is, there may not exist a set of coefficients on the MTR that
are observationally equivalent with regard to the IV-like
regression coefficients. The function therefore first estimates
the minimum violation of observational equivalence. This is
reported in the output under the name 'minimum criterion'. The
constraints in the LP problem pertaining to observational
equivalence are then relaxed by the amount minimum
criterion * (1 + criterion.tol). Set criterion.tol to a
value greater than 0 to allow for more conservative bounds.
integer determining the number of points of the covariates used to form the initial constraint grid for imposing shape restrictions on the MTRs.
integer determining the number of evenly spread
points in the interval [0, 1] of the unobservable u used
to form the initial constraint grid for imposing shape
restrictions on the MTRs.
integer determining the number of points on the covariates space to audit in each iteration of the audit procedure.
integer determining the number of points in the
interval [0, 1], corresponding to space of unobservable
u, to audit in each iteration of the audit procedure.
maximum number of points to add to the initial
constraint grid for imposing each kind of shape constraint. For
example, if there are 5 different kinds of shape constraints,
there can be at most audit.add * 5 additional points
added to the constraint grid.
maximum number of iterations in the audit procedure.
list, contains the A A matrix used in the audit for the original sample, as well as the RHS vector used in the audit from the original sample.
boolean, set to FALSE by default. Set to
true if the fine grid from the audit should be saved. This
option is used for inference procedure under partial
identification, which uses the fine grid from the original
sample in all bootstrap resamples.
boolean, default set to FALSE. Set to
TRUE if it is believed that the treatment effects are
point identified. If set to TRUE, then a two-step GMM
procedure is implemented to estimate the treatment
effects. Shape constraints on the MTRs will be ignored under
point identification.
boolean, default set to FALSE. Set to
TRUE if the GMM point estimate should use the identity
weighting matrix (i.e. one-step GMM).
numeric, a vector of GMM moment conditoins evaluated at a solution. When bootstrapping, the moment conditions from the original sample can be passed through this argument to recenter the bootstrap distribution of the J-statistic.
vector of integers indicating which components in the S-set are redundant.
boolean, indicate if number of linearly independent moments should be counted.
list, only used for bootstraps. The list caontains the gamma moments for each element in the S-set, as well as the IV-like coefficients.
numeric, only used for bootstraps. The scalar corresponds to the minimum observational equivalence criterion from the original sample.
character, variable name of observed outcome variable.
character, vector of variables entering into
m0 and m1.
character, vector of terms entering into
m0.
character, vector of terms entering into
m1.
character, vector of variables that can be found in the data.
list of spline components in the MTRs for treated
and control groups. Spline terms are extracted using
removeSplines. This object is supposed to be a
dictionary of splines, containing the original calls of each
spline in the MTRs, their specifications, and the index used
for renaming each component.
boolean, default set to TRUE. If TRUE,
then messages are provided throughout the estimation
procedure. Set to FALSE to suppress all messages,
e.g. when performing the bootstrap.
boolean, default set to FALSE. Set to
TRUE to exclude large intermediary components
(i.e. propensity score model, LP model, bootstrap iterations)
from being included in the return list.
integer, the seed that determines the random grid in the audit procedure.
boolean, indicates whether or not the function should
provide output when obtaining bounds. The option is only
applied when lpsolver = 'gurobi'. The output provided is
the same as what the Gurobi API would send to the console.
a list containing the environments of the MTR formulas, the IV-like formulas, and the propensity score formulas. If a formulas is not provided, and thus no environment can be found, then the parent.frame() is assigned by default.
Returns a list of results from throughout the estimation procedure. This includes all IV-like estimands; the propensity score model; bounds on the treatment effect; the estimated expectations of each term in the MTRs; the components and results of the LP problem.
The estimation procedure relies on the propensity to take up treatment. The propensity scores can either be estimated as part of the estimation procedure, or the user can specify a variable in the data set already containing the propensity scores.
Constraints on the shape of the MTRs and marginal treatment effects (MTE) can be imposed by the user, also. Specifically, bounds and monotonicity restrictions are permitted. These constraints are only enforced over a subset of the data. However, an audit procedure randomly selects points outside of this subset to determine whether or not the constraints hold. The user can specify how stringent this audit procedure is using the function arguments.