mte {localIV}

Fitting a Marginal Treatment Effects (MTE) Model.

Description

mte fits a MTE model using either the semiparametric local instrumental variables (local IV) method or the normal selection model (Heckman, Urzua, Vytlacil 2006). The user supplies a formula for the treatment selection equation, a formula for the outcome equations, and a data frame containing all variables. The function returns an object of class mte. Observations that contain NA (either in selection or in outcome) are removed.

Usage

mte(
  selection,
  outcome,
  data = NULL,
  method = c("localIV", "normal"),
  bw = NULL
)

mte_localIV(mf_s, mf_o, bw = NULL)

mte_normal(mf_s, mf_o)

Arguments

selection

A formula representing the treatment selection equation.

outcome

A formula representing the outcome equations where the left hand side is the observed outcome and the right hand side includes predictors of both potential outcomes.

data

A data frame, list, or environment containing the variables in the model.

method

How to estimate the model: either "localIV" for the semiparametric local IV method or "normal" for the normal selection model.

bw

Bandwidth used for the local polynomial regression in the local IV approach. Default is 0.25.

mf_s

A model frame for the treatment selection equations returned by model.frame

mf_o

A model frame for the outcome equations returned by model.frame

Details

mte_localIV estimates \textup{MTE}(x, u) using the semiparametric local IV method, and mte_normal estimates \textup{MTE}(x, u) using the normal selection model.

Value

An object of class mte.

coefs

A list of coefficient estimates: gamma for the treatment selection equation, beta10 (intercept) and beta1 (slopes) for the baseline outcome equation, beta20 (intercept) and beta2 (slopes) for the treated outcome equation, and theta1 and theta2 for the error covariances when method = "normal".

ufun

A function representing the unobserved component of \textup{MTE}(x, u).

ps

Estimated propensity scores.

ps_model

The propensity score model, an object of class glm if method = "localIV", or an object of class selection if method = "normal".

mf_s

The model frame for the treatment selection equation.

mf_o

The model frame for the outcome equations.

complete_row

A logical vector indicating whether a row is complete (no missing variables) in the original data

call

The matched call.

References

Heckman, James J., Sergio Urzua, and Edward Vytlacil. 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity." The Review of Economics and Statistics 88:389-432.

See Also

mte_at for evaluating MTE at different values of the latent resistance u; mte_tilde_at for evaluating MTE projected onto the propensity score; ace for estimating average causal effects from a fitted mte object.

Examples

mod <- mte(selection = d ~ x + z, outcome = y ~ x, data = toydata, bw = 0.25)

summary(mod$ps_model)
hist(mod$ps)

mte_vals <- mte_at(u = seq(0.05, 0.95, 0.1), model = mod)
if(require("ggplot2")){
  ggplot(mte_vals, aes(x = u, y = value)) +
  geom_line(size = 1) +
  xlab("Latent Resistance U") +
  ylab("Estimates of MTE at Mean Values of X") +
  theme_minimal(base_size = 14)
}