Prop 40, JR analysis: checks against the paper’s variations

The net present value under every other set of assumptions the authors print

JR analysis of California Proposition 40: Overview · Open Output: Explorer · Open Analysis: Report and Slides · Open Materials (guide)

Also in this project: Comparison overview · BSZ analysis overview

suppressPackageStartupMessages(library(knitr))
for (f in list.files("../R", pattern = "\\.R$", full.names = TRUE)) source(f)
# The explorer's own data file, read as the explorer reads it (R/site.R)
G <- read_site_grid_js("explorer/grid.js")
hl <- read.csv("data/headlines.csv")
printed <- read.csv("data/printed-tables.csv")
h <- function(v, q, col = "reproduced") hl[[col]][hl$version == v & hl$quantity == q]
ss <- formals(compute_npv_mc_ssrn)
num <- function(x, d = 1, plus = FALSE) {
  s <- formatC(abs(x), format = "f", digits = d, big.mark = ",")
  ifelse(x < 0, paste0("−", s), if (plus) paste0("+", s) else s)
}
words <- function(n) c("one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten")[n]
dollars <- function(x) gsub("$", "\\$", x, fixed = TRUE)   # a literal $ in a markdown table cell
md_table <- function(d) {
  d[] <- lapply(d, dollars)
  cat("\n\n::: {.table-scroll}\n\n", paste(kable(d, format = "pipe", align = "l"), collapse = "\n"),
      "\n\n:::\n\n", sep = "")
}
main <- site_grid_js_cell(G, from = "nber")[["mean_npv"]]
seeded <- h("nber", "mc_mean_npv")
# the first version's Monte Carlo: the explorer's "ssrn" setting
first <- site_grid_js_cell(G, from = "ssrn")[["mean_npv"]]
# the first version's Table 9, recomputed (the explorer cannot fix the revenue at one value)
t9 <- compute_npv_table9()
p9 <- printed[printed$table == "table9" & printed$column == "npv", ]
t9$printed <- p9$printed[match(paste0(t9$scenario, "@", t9$r), p9$row)]
# the repository's 2% case (NPV_plots/npv_decomposition_2pct.pdf prints -67.2): no OPA setting;
# hand-built inputs so that f = 1 - WT/baseline equals the script's 0.554 (as in
# feedback/scenario-tests-2026-10-15/jr-sensitivity.R, case 5)
base2 <- 0.02 * ss$baseline_revenue / 0.05
two_pct <- compute_npv_table9(baseline = base2,
  scenarios = list(two_pct = list(label = "2%", WT = (1 - 0.554) * base2, C = 4.55)), r_values = 0.03)$npv
match_word <- function(printed, ...) if (any(round(c(...), 1) == printed)) "Match" else "No match"
nine <- list(six_confirmed = "Six departures", central = "Central", lit_calibrated = "Literature calibrated")
rows9 <- lapply(names(nine), function(s) {
  x <- t9[t9$scenario == s, ]
  x <- x[order(x$r), ]
  data.frame(
    Variation = sprintf("%s: revenue $%sB, income tax $%sB a year, share lost %s%%", nine[[s]],
                        sub("0$", "", formatC(x$WT[1], format = "f", digits = 2)),
                        sub("0$", "", formatC(x$C[1], format = "f", digits = 2)), num(100 * x$f[1], 1)),
    Source = "SSRN, Table 9",
    Printed = paste(num(x$printed, 1, plus = TRUE), collapse = " / "),
    `This OPA` = paste(num(x$npv, 2, plus = TRUE), collapse = " / "),
    Result = if (all(round(x$npv, 1) == x$printed)) "Match" else "No match",
    `How to set it` = "R code", check.names = FALSE)
})
dl <- function(k, i) G$dials[[which(vapply(G$dials, `[[`, "", "key") == k)]]$labels[[i + 1L]]
sl <- unlist(G$named$ssrn); names(sl) <- vapply(G$dials, `[[`, "", "key")
results <- rbind(
  data.frame(Variation = "Main assumptions, for reference", Source = "NBER, p.35",
             Printed = num(h("nber", "mc_mean_npv", "printed"), 1),
             `This OPA` = sprintf("%s (seeded run %s)", num(main, 2), num(seeded, 2)),
             Result = match_word(h("nber", "mc_mean_npv", "printed"), main, seeded),
             `How to set it` = "Explorer, as it opens", check.names = FALSE),
  data.frame(Variation = sprintf("Revenue drawn from $%sB to $%sB, and the share lost tied to the revenue (f = 1 − revenue / %s)",
                                 dl("wt_lo", sl[["wt_lo"]]), dl("wt_hi", sl[["wt_hi"]]), ss$baseline_revenue),
             Source = "SSRN, p.20", Printed = num(h("ssrn", "mc_mean_npv", "printed"), 1),
             `This OPA` = num(first, 2), Result = match_word(h("ssrn", "mc_mean_npv", "printed"), first),
             `How to set it` = sprintf("Explorer: from the main setting, set the lowest revenue to %s, the highest to %s and the share lost to \"%s\"",
                                       dl("wt_lo", sl[["wt_lo"]]), dl("wt_hi", sl[["wt_hi"]]), dl("f", sl[["f"]])),
             check.names = FALSE),
  do.call(rbind, rows9),
  data.frame(Variation = "Tax rate 2% instead of 5%, central inputs, r − g of 3%",
             Source = "Authors' repository, a plot", Printed = num(-67.2, 1), `This OPA` = "none",
             Result = "Cannot be set", `How to set it` = "None", check.names = FALSE))
n_printed <- nrow(results) - 2                  # the variations the papers print
n_match <- sum(results$Result[2:(n_printed + 1)] == "Match")
settings <- site_checks_table(G)

All four variations the JR papers print reproduce at the paper’s rounding. A fifth, in the authors’ repository, uses a lower tax rate, which cannot be set in this OPA. None of the five changes a single assumption, so the papers give no printed check of the explorer’s named settings.

What was checked

The main estimate of the JR analysis is a mean net present value of −$38.9 billion (NBER chapter, September 2026, p.35). This OPA computes it as −$38.98 billion exactly, and as −$38.89 billion with the authors’ random seed. The September chapter prints no net present value under other assumptions. The first version (SSRN, March 2026) prints four, and the authors’ public repository holds one more. Each check below sets the same assumptions in this OPA and compares the result with the printed figure.

Each of the five changes two or more inputs at once from the main estimate. The first version’s Monte Carlo changes the revenue range and the rule for the share of income tax lost. Each scenario of its Table 9 fixes four inputs at single values.

Results

All figures are net present values in billions of dollars. Table 9 prints three values per scenario, one for each value of r − g (1.5%, 3% and 4.5%). “Match” means this OPA’s value rounds to the printed figure.

md_table(results)

Variation	Source	Printed	This OPA	Result	How to set it
Main assumptions, for reference	NBER, p.35	−38.9	−38.98 (seeded run −38.89)	Match	Explorer, as it opens
Revenue drawn from $35B to $67.51B, and the share lost tied to the revenue (f = 1 − revenue / 94.2)	SSRN, p.20	−24.7	−24.71	Match	Explorer: from the main setting, set the lowest revenue to 35, the highest to 67.51 and the share lost to “tied to revenue”
Six departures: revenue $67.51B, income tax $3.3B a year, share lost 28.3%	SSRN, Table 9	+5.2 / +36.3 / +46.7	+5.18 / +36.34 / +46.73	Match	R code
Central: revenue $42.0B, income tax $4.55B a year, share lost 55.4%	SSRN, Table 9	−126.1 / −42.0 / −14.0	−126.09 / −42.04 / −14.03	Match	R code
Literature calibrated: revenue $35.0B, income tax $5.8B a year, share lost 62.8%	SSRN, Table 9	−208.0 / −86.5 / −46.0	−208.00 / −86.50 / −46.00	Match	R code
Tax rate 2% instead of 5%, central inputs, r − g of 3%	Authors’ repository, a plot	−67.2	none	Cannot be set	None

What could not be checked

The tax rate. This OPA has no setting for a wealth tax rate other than 5%. The repository’s 2% case is reproduced only by building its inputs by hand (−67.22).

The explorer’s named settings. The explorer offers “Rate 1.5%” and “Rate 4.5%”, each of which changes one input from the main estimate, and “Litigation weight q = 0.5”, which changes two (q, and the revenue floor raised to 35 so the risk is not counted twice). The authors print no net present value for any of them.

Who ran these checks

Claude Code agents chose the variations from the papers and ran the checks on 15 October 2026. The scripts were then rerun once, in a separate session, with the same results.

To rerun them from the repository root, with a clone of the authors’ repository:

export RAUH_REPO_DIR=<path to the authors' repository>
Rscript feedback/scenario-tests-2026-10-15/jr-sensitivity.R

The full record, with the source of every figure, is in jr-sensitivity.md. A second record, jr.md, checks ten other combinations the papers print. Nine reproduce. Seven round to the printed digit. The other two reproduce once the paper’s own rounding and seed are allowed for: the September ceiling and semi-elasticity (the chapter rounds the ceiling to 72 before computing 5.73; note 4) and the first version’s Monte Carlo (within Monte Carlo error; note 9).

fin <- extract_nber_final()
dom <- fin[fin$panel == "domestic", ]
# the seven publicly reported moves, Zuckerberg (after the snapshot) and the three reported
# leavers the chapter moves out of the base on PDF p.23
exp_set <- dom$bucket %in% c("removed_departed", "zuckerberg") |
  dom$name %in% c("Jan Koum", "Reed Hastings", "Andy Fang")
stopifnot(sum(exp_set) == 11)
exp_share <- 100 * sum(dom$face_tax_5pct[exp_set]) / sum(dom$face_tax_5pct)

The tenth, the chapter’s “expanded departures” (Table 8, about 42% of the base, semi-elasticity 8.41), is the one of the ten that does not reproduce exactly. The set the chapter describes, the seven moves plus the post-snapshot and reported departures, gives 41.8% of the base in the authors’ person-level file. That rounds to the printed 42%, but its semi-elasticity is 8.35, not 8.41. The shared materials do not say which set gives 8.41. The figure compares the departures with the literature; it is not an input to any estimate.

Settings the papers do not print

This OPA lets a reader change assumptions the papers hold fixed. The table below lists nine such changes, each made from the September chapter’s main assumptions, with the result this OPA gives. Each changes one assumption, except the litigation weight, which the explorer pairs with a higher revenue floor. The papers print no figure for any of them, so they are untested against the authors’ own work.

The author of this OPA has sent this table to the original authors, asking them to test whether they obtain the same results. Their responses will be posted here.

The mean net present value is in billions of dollars. This OPA computes the exact average of the authors’ formula over the same random draws, not a new seeded run. A seeded run of the authors’ script differs from it by sampling error only (at the main setting, −38.89 against −38.98). Each setting can be made in the explorer, and each value below is the one the explorer shows.

md_table(data.frame(
  `Setting changed from the main assumptions` = settings$setting,
  `Mean net present value` = num(settings$mean_npv, 2),
  `Share of runs below zero` = paste0(num(settings$pct_negative, 1), "%"),
  `Authors' result` = c("", rep("Pending", nrow(settings) - 1)),
  check.names = FALSE))

Setting changed from the main assumptions	Mean net present value	Share of runs below zero	Authors’ result
None, the main assumptions, for reference	−38.98	85.3%
r − g, the discount rate net of growth, fixed at 1.5% (instead of drawn from 1.5% to 4.5%)	−100.50	100.0%	Pending
r − g, the discount rate net of growth, fixed at 4.5%	−9.50	63.2%	Pending
Revenue multiplied by a chance of surviving in court of 0.50, with the lowest revenue the draw can pick raised to $35B (instead of $0) so the risk is not counted twice (the explorer’s “Litigation weight q = 0.5”)	−48.23	99.0%	Pending
Yearly income tax fixed at $3.3B (instead of drawn from $3.3B to $5.8B)	−18.38	71.1%	Pending
Yearly income tax fixed at $5.8B	−59.58	94.7%	Pending
Lost income tax grows a further 0.5% a year on top of the authors’ r − g (this OPA’s illustration)	−58.62	90.9%	Pending
Lost income tax grows a further 1% a year on top of the authors’ r − g (this OPA’s illustration)	−96.81	95.1%	Pending
Lowest revenue the draw can pick of $35B (instead of $0)	−21.48	71.8%	Pending
Share of the income tax base that leaves fixed at 0.283 (instead of drawn from 0.30 to 0.60)	−11.21	64.0%	Pending

The litigation row raises the lowest revenue with q, as the explorer’s “Litigation weight q = 0.5” setting does. The draw’s 0 floor already halves the mean revenue (0.5 × 72), so q with that floor would count the risk of the Act being struck down twice.

The share of runs below zero is exact (85.3%). The authors’ seeded run gives 85.17%, printed 85.2%.

The two tables are built when this page is rendered: the settings from the explorer’s data file, site/explorer/grid.js, and the variations from the same pipeline, so they cannot drift from the explorer. tests/testthat/test-site.R checks the rendered page against that file.