Estimating Average Causal Effects from a Fitted MTE Model.

Description

ace estimates Average Causal Effects (ACE) from a fitted MTE model. The estimand can be average treatment effect (ATE), average treatment effect on the treated (ATT), average treatment effect on the untreated (ATU), or the Marginal Policy Relevant Treatment Effect (MPRTE) defined in Zhou and Xie (2019).

Usage

ace(model, estimand = c("ate", "att", "atu", "mprte"), policy = 1)

Arguments

Value

Estimate of ATE, ATT, ATU, or MPRTE

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.

Zhou, Xiang and Yu Xie. 2019. "Marginal Treatment Effects from A Propensity Score Perspective." Journal of Political Economy, 127(6): 3070-3084.

Zhou, Xiang and Yu Xie. 2020. "Heterogeneous Treatment Effects in the Presence of Self-selection: a Propensity Score Perspective." Sociological Methodology.

Examples

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

ate <- ace(mod, "ate")
att <- ace(mod, "att")
atu <- ace(mod, "atu")
mprte1 <- ace(mod, "mprte")
mprte2 <- ace(mod, "mprte", policy = p)
mprte3 <- ace(mod, "mprte", policy = 1-p)
mprte4 <- ace(mod, "mprte", policy = I(p<0.25))
c(ate, att, atu, mprte1, mprte2, mprte3, mprte4)

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

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.

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)
}

Evaluate Marginal Treatment Effects from a Fitted MTE Model.

Description

mte_at evaluates marginal treatment effects at different values of the latent resistance u with a given X=x.

Usage

mte_at(x = NULL, u, model)

Arguments

Value

mte_at returns a data frame.

Examples

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

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)
}

Evaluate Marginal Treatment Effects Projected onto the Propensity Score

Description

mte_tilde_at evaluates marginal treatment effects projected onto the estimated propensity score. The projection is done via the function gam.

Usage

mte_tilde_at(p, u, model, ...)

Arguments

Value

mte_tilde_at returns a list of two elements:

References

Zhou, Xiang and Yu Xie. 2019. "Marginal Treatment Effects from A Propensity Score Perspective." Journal of Political Economy, 127(6): 3070-3084.

Zhou, Xiang and Yu Xie. 2020. "Heterogeneous Treatment Effects in the Presence of Self-selection: a Propensity Score Perspective." Sociological Methodology.

Examples

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

u <- p <- seq(0.05, 0.95, 0.1)
mte_tilde <- mte_tilde_at(p, u, model = mod)

# heatmap showing MTE_tilde(p, u)
if(require("ggplot2")){
ggplot(mte_tilde$df, aes(x = u, y = p, fill = value)) +
  geom_tile() +
  scale_fill_gradient(name = expression(widetilde(MTE)(p, u)), low = "yellow", high = "blue") +
  xlab("Latent Resistance U") +
  ylab("Propensity Score p(Z)") +
  theme_minimal(base_size = 14)
}

mprte_tilde_df <- subset(mte_tilde$df, p == u)

# heatmap showing MPRTE_tilde(p)
if(require("ggplot2")){
ggplot(mprte_tilde_df, aes(x = u, y = p, fill = value)) +
  geom_tile() +
  scale_fill_gradient(name = expression(widetilde(MPRTE)(p)), low = "yellow", high = "blue") +
  xlab("Latent Resistance U") +
  ylab("Propensity Score p(Z)") +
  theme_minimal(base_size = 14)
}

# MPRTE_tilde(p) decomposed into the p-component and the u-component
if(require(tidyr) && require(dplyr) && require(ggplot2)){
mprte_tilde_df %>%
  pivot_longer(cols = c(u_comp, p_comp, value)) %>%
  mutate(name = recode_factor(name,
         `value` = "MPRTE(p)",
         `p_comp` = "p(Z) component",
         `u_comp` = "U component")) %>%
  ggplot(aes(x = p, y = value)) +
  geom_line(aes(linetype = name), size = 1) +
  scale_linetype(name = "") +
  xlab("Propensity Score p(Z)") +
  ylab("Treatment Effect") +
  theme_minimal(base_size = 14) +
  theme(legend.position = "bottom")
}

A Hypothetical Dataset for Illustrative Purpose

Description

A dataset containing 4 columns: y for a continuous outcome, d for a binary treatment, x for a pretreatment covariate, and z for an excluded instrument.

Usage

toydata

Format

An object of class data.frame with 10000 rows and 4 columns.