library(here)
library(tidyverse)
library(gt)
source(here("04-topics/rep-chv2011/Rcode/chv2011-gt-quarto.R"))

table_a1a <- tribble(
  ~parameter, ~definition,
  "ATE", "Integral of MTE against weight h_ATE(x, u_S)",
  "TT", "Integral of MTE against weight h_TT(x, u_S) = 1{S=1}",
  "TUT", "Integral of MTE against weight h_TUT(x, u_S) = 1{S=0}",
  "PRTE", "Policy-relevant TE for a discrete policy change",
  "IV", "Weighted average of MTE with instrument-specific weights",
  "OLS", "Weighted average of MTE with OLS selection weights"
)

table_a1b <- tribble(
  ~parameter, ~weight,
  "ATE", "$f_{P|X}(u_S)$",
  "TT", "$1\\{P > u_S\\}$",
  "TUT", "$1\\{P \\leq u_S\\}$",
  "PRTE", "Policy-specific (see Table 1)",
  "IV", "$f_{P|X}(u_S) \\cdot (Z - E[Z|X]) / E[Z|X,P=u_S]$",
  "OLS", "$f_{P|X}(u_S) \\cdot (P - u_S)$"
)

gt_tbl <- bind_rows(
  table_a1a |> mutate(panel = "Table A-1A: Treatment effects as weighted averages of MTE"),
  table_a1b |> mutate(panel = "Table A-1B: Weights for ATE, TT, TUT, PRTE, IV and OLS")
) |>
  select(panel, parameter, definition = definition, weight) |>
  gt(groupname_col = "panel") |>
  tab_header(title = "Table A-1", subtitle = "Weight definitions (Heckman and Vytlacil 2005)")

table_data <- list(a1a = table_a1a, a1b = table_a1b)
save(table_data, gt_tbl, file = here("04-topics/rep-chv2011/Rcode/Table_A1.RData"))