R: Single iteration of estimation procedure from Mogstad,...

ivmteEstimate {ivmte}

R Documentation

Single iteration of estimation procedure from Mogstad, Torgovitsky, Santos (2018)

Description

This function estimates the treatment effect parameters, following the procedure described in Mogstad, Santos and Torgovitsky (2018) (doi: 10.3982/ECTA15463). A detailed description of the module and its features can be found in Shea and Torgovitsky (2021). However, this is not the main function of the module. See ivmte for the main function. For examples of how to use the package, see the vignette, which is available on the module's GitHub page.

Usage

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,
  equal.coef,
  ivlike,
  components,
  subset,
  propensity,
  link = "logit",
  treat,
  solver,
  solver.options,
  solver.presolve,
  solver.options.criterion,
  solver.options.bounds,
  criterion.tol = 0.01,
  initgrid.nx = 20,
  initgrid.nu = 20,
  audit.nx = 2500,
  audit.nu = 25,
  audit.add = 100,
  audit.max = 25,
  audit.tol,
  audit.grid = NULL,
  rescale = TRUE,
  point = FALSE,
  point.eyeweight = FALSE,
  point.center = NULL,
  point.redundant = NULL,
  bootstrap = FALSE,
  count.moments = TRUE,
  orig.sset = NULL,
  orig.criterion = NULL,
  vars_y,
  vars_mtr,
  terms_mtr0,
  terms_mtr1,
  vars_data,
  splinesobj,
  splinesobj.equal,
  noisy = TRUE,
  smallreturnlist = FALSE,
  debug = FALSE,
  environments
)

Arguments

`data`	`data.frame` or `data.table` used to estimate the treatment effects.
`target`	character, target parameter to be estimated. The function allows for ATE (`'ate'`), ATT (`'att'`), ATU (`'atu'`), LATE (`'late'`), and generalized LATE (`'genlate'`).
`late.Z`	vector of variable names used to define the LATE.
`late.from`	baseline set of values of Z used to define the LATE.
`late.to`	comparison set of values of Z used to define the LATE.
`late.X`	vector of variable names of covariates to condition on when defining the LATE.
`eval.X`	numeric vector of the values to condition variables in `late.X` on when estimating the LATE.
`genlate.lb`	lower bound value of unobservable `u` for estimating the generalized LATE.
`genlate.ub`	upper bound value of unobservable `u` for estimating the generalized LATE.
`target.weight0`	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.
`target.weight1`	user-defined weight function for the treated group defining the target parameter. See `target.weight0` for details.
`target.knots0`	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.
`target.knots1`	user-defined set of functions defining the knots associated with spline weights for the treated group. See `target.knots0` for details.
`m0`	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.
`m1`	one-sided formula for the marginal treatment response function for the treated group. See `m0` for details.
`uname`	variable name for the unobservable used in declaring the MTRs. The name can be provided with or without quotation marks.
`m1.ub`	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.
`m0.ub`	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.
`m1.lb`	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.
`m0.lb`	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.
`mte.ub`	numeric value for upper bound on treatment effect parameter of interest.
`mte.lb`	numeric value for lower bound on treatment effect parameter of interest.
`m0.dec`	logical, set to `FALSE` by default. Set equal to `TRUE` if the MTR for the control group should be weakly monotone decreasing.
`m0.inc`	logical, set to `FALSE` by default. Set equal to `TRUE` if the MTR for the control group should be weakly monotone increasing.
`m1.dec`	logical, set to `FALSE` by default. Set equal to `TRUE` if the MTR for the treated group should be weakly monotone decreasing.
`m1.inc`	logical, set to `FALSE` by default. Set equal to `TRUE` if the MTR for the treated group should be weakly monotone increasing.
`mte.dec`	logical, set to `FALSE` by default. Set equal to `TRUE` if the MTE should be weakly monotone decreasing.
`mte.inc`	logical, set to `FALSE` by default. Set equal to `TRUE` if the MTE should be weakly monotone increasing.
`equal.coef`	one-sided formula to indicate which terms in `m0` and `m1` should be constrained to have the same coefficients. These terms therefore have no effect on the MTE.
`ivlike`	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`. If no argument is passed, then a linear regression will be performed to estimate the MTR coefficients.
`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.
`subset`	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`.
`propensity`	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`).
`link`	character, name of link function to estimate propensity score. Can be chosen from `'linear'`, `'probit'`, or `'logit'`. Default is set to `'logit'`. The link should be provided with quoation marks.
`treat`	variable name for treatment indicator. The name can be provided with or without quotation marks.
`solver`	character, name of the programming package in R used to obtain the bounds on the treatment effect. The function supports `'gurobi'`, `'cplexapi'`, `rmosek`, `'lpsolveapi'`. The name of the solver should be provided with quotation marks.
`solver.options`	list, each item of the list should correspond to an option specific to the solver selected.
`solver.presolve`	boolean, default set to `TRUE`. Set this parameter to `FALSE` if presolve should be turned off for the LP/QCQP problems.
`solver.options.criterion`	list, each item of the list should correspond to an option specific to the solver selected. These options are specific for finding the minimum criterion.
`solver.options.bounds`	list, each item of the list should correspond to an option specific to the solver selected. These options are specific for finding the bounds.
`criterion.tol`	tolerance for the criterion function, and is set to 1e-4 by default. The criterion measures how well the IV-like moments/conditional means are matched using the l1-norm. Statistical noise may prohibit the theoretical LP/QCQP problem from being feasible. That is, there may not exist a set of MTR coefficients that are able to match all the specified moments. The function thus first estimates the minimum criterion, which is reported in the output under the name 'minimum criterion', with a criterion of 0 meaning that all moments were able to be matched. The function then relaxes the constraints by tolerating a criterion up to `minimum criterion * (1 + criterion.tol)`. Set `criterion.tol` to a value greater than 0 to allow for more conservative bounds.
`initgrid.nx`	integer determining the number of points of the covariates used to form the initial constraint grid for imposing shape restrictions on the MTRs.
`initgrid.nu`	integer determining the number of points in the open interval (0, 1) drawn from a Halton sequence. The end points 0 and 1 are additionally included. These points are always a subset of the points defining the audit grid (see `audit.nu`). These points are used to form the initial constraint grid for imposing shape restrictions on the `u` components of the MTRs.
`audit.nx`	integer determining the number of points on the covariates space to audit in each iteration of the audit procedure.
`audit.nu`	integer determining the number of points in the open interval (0, 1) drawn from a Halton sequence. The end points 0 and 1 are additionally included. These points are used to audit whether the shape restrictions on the `u` components of the MTRs are satisfied. The initial grid used to impose the shape constraints in the LP/QCQP problem are constructed from a subset of these points.
`audit.add`	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.
`audit.max`	maximum number of iterations in the audit procedure.
`audit.tol`	feasibility tolerance when performing the audit. By default to set to be 1e-06, which is equal to the default feasibility tolerances of Gurobi (`solver = "gurobi"`), CPLEX (`solver = "cplexapi"`), and Rmosek (`solver = "rmosek"`). This parameter should only be changed if the feasibility tolerance of the solver is changed, or if numerical issues result in discrepancies between the solver's feasibility check and the audit.
`audit.grid`	list, contains the `A` matrix used in the audit for the original sample, as well as the RHS vector used in the audit from the original sample.
`rescale`	boolean, set to `TRUE` by default. This rescalels the MTR components to improve stability in the LP/QCQP optimization.
`point`	boolean. Set to `TRUE` if it is believed that the treatment effects are point identified. If set to `TRUE` and IV-like formulas are passed, then a two-step GMM procedure is implemented to estimate the treatment effects. Shape constraints on the MTRs will be ignored under point identification. If set to `TRUE` and the regression-based criteria is used instead, then OLS will be used to estimate the MTR coefficients used to estimate the treatment effect. If not declared, then the function will determine whether or not the target parameter is point identified.
`point.eyeweight`	boolean, default set to `FALSE`. Set to `TRUE` if the GMM point estimate should use the identity weighting matrix (i.e. one-step GMM).
`point.center`	numeric, a vector of GMM moment conditions 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.
`point.redundant`	vector of integers indicating which components in the S-set are redundant.
`bootstrap`	boolean, indicates whether the estimate is for the bootstrap.
`count.moments`	boolean, indicate if number of linearly independent moments should be counted.
`orig.sset`	list, only used for bootstraps. The list contains the gamma moments for each element in the S-set, as well as the IV-like coefficients.
`orig.criterion`	numeric, only used for bootstraps. The scalar corresponds to the minimum observational equivalence criterion from the original sample.
`vars_y`	character, variable name of observed outcome variable.
`vars_mtr`	character, vector of variables entering into `m0` and `m1`.
`terms_mtr0`	character, vector of terms entering into `m0`.
`terms_mtr1`	character, vector of terms entering into `m1`.
`vars_data`	character, vector of variables that can be found in the data.
`splinesobj`	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 naming each basis spline.
`splinesobj.equal`	list of spline components in the MTRs for treated and control groups. The structure of `splinesobj.equal` is the same as `splinesobj`, except the splines are restricted to those whose MTR cofficients should be constrained to be equal across treatment groups.
`noisy`	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.
`smallreturnlist`	boolean, default set to `FALSE`. Set to `TRUE` to exclude large intermediary components (i.e. propensity score model, LP/QCQP model, bootstrap iterations) from being included in the return list.
`debug`	boolean, indicates whether or not the function should provide output when obtaining bounds. The option is only applied when `solver = 'gurobi'` or `solver = 'rmosek'`. The output provided is the same as what the Gurobi API would send to the console.
`environments`	a list containing the environments of the MTR formulas, the IV-like formulas, and the propensity score formulas. If a formula is not provided, and thus no environment can be found, then the parent.frame() is assigned by default.

Details

The treatment effects parameters the user can choose from are 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.

There are two approaches to estimating the treatment effect parameters. The first approach restricts the set of MTR coefficients on each term of the MTRs to be consistent with the regression estimates from the specifications passed through ivlike. The bounds on the treatment effect parameter correspond to finding coefficients on the MTRs that maximize their average difference. If the model is point identified, then GMM is used for estimation. Otherwise, the function solves an LP problem. The second approach restricts the set of MTR coefficients to fit the conditional mean of the outcome variable. If the model is point identified, then constrained least squares is used for estimation. Otherwise, the function solves a QCQP.

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. Specifically, bounds and monotonicity restrictions are permitted. These constraints are first enforced over a subset of points in the data. An iterative audit procedure is then performed to ensure the constraints hold more generally.

Value

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/QCQP problem.

[Package ivmte version 1.4.0 Index]