# Harmonising effect sizes — F4-conf-03

# Question

Re-express five printed treatment effects (data/effects.json, E1–E5), reported as a semi-elasticity (log points), a percentage-point effect, an elasticity and a linear-probability coefficient, on the target definition stated for each item. We may use only quantities printed in the cited extract and an explicitly stated transformation. Where the target cannot be reached, we say so and name the missing quantity.

# Data and exclusions

The inputs are the four source extracts under data/sources/ plus data/effects.json and data/README.md. Line counts are in n_input_rows. All extract SHA-256 hashes match the README (out/state/data_audit.md). No item was excluded (out/exclusions.csv: 5 − 0 = 5), so n_analysed = 5. Problems found in the inputs are listed in data_issues. The ones that matter:

• The DCR abstract says fatal hospitalisations "fall by 35%". Table 7 (5 km) prints −0.354 log points, which is ≈ −29.8%, in line with Section 6.1 ("approximately 30%").
• The DCR paper prints the same ATT with SE 0.210 (Table 6) and 0.218 (Table A19), and gives 608 vs 640 control regions.
• The minimum-wage Table 2 prints a 0.047 MW change, but its note says "about 4%".
• In the Benin Table 3, the "% Change" cell (−0.3685) differs in the 4th decimal from −0.0962/0.261.
• RESEA: the abstract's 1.5 pp is a rounding of the table's 1.47 pp.

# Method

Each transformation follows the TASK.md conventions (formula and printed inputs are in harmonised.<id>.transformation; source cells are in harmonised.<id>.locator):

• E1: 100·(exp(b) − 1), with b = −0.431 (Table 6, ATT, 5 km).
• E2: 100·Δ/p, with Δ = 1.47 pp (Table 2, Reemployment, ATE) and p = 75.0% (Table 2, Control mean).
• E3: 100·η·g, with η = −0.388 (Table 2, employment elasticity w.r.t. MW) and g = 0.047 (Table 2, "% MW changes"). The target definition says to use the size of the increase as printed in the table.
• E4: absolute change = R0·(exp(b) − 1), with b = −0.354 (Table 7, Drug-related (fatal), 5 km). This needs the counterfactual level R0 of the fatal rate per 100,000.
• E5: 100·β, with β = −0.0962 (Table 3, Treatment, column (4)).

As a P2 baseline, the printed numbers read at face value are stored under baseline_naive. out/analysis.py locates each table row by pattern, prints the source lines it uses, and writes out/results.json deterministically. No randomness is involved (random_seed = null).

# Results

• E1: the DCR opening implies a −35.0141% change in the drug-related hospitalisation rate, 5 km buffer (harmonised.E1.value). This matches the printed "% change" of −35.0%. The naive log-point reading would give −43.1 (baseline_naive.E1_logpoints_times_100_pct).
• E2: RESEA selection raises reemployment by 1.96% of the control mean (harmonised.E2.value).
• E3: the 2023 minimum-wage rise (0.047) implies a −1.8236% change in employment (harmonised.E3.value).
• E4: not harmonisable (harmonised.E4.harmonisable = false, harmonised.E4.value = null). The extract prints no baseline or counterfactual level of the fatal drug-related hospitalisation rate per 100,000 in the treated regions. That quantity is named in harmonised.E4.missing_quantity. Only the relative change (≈ −29.8%) can be computed, and it is not the requested target.
• E5: free cesarean access lowers the probability of infant death or stillbirth by −9.62 percentage points (harmonised.E5.value).
• Overall: 4 items harmonised (n_harmonised) and 1 not harmonisable (n_not_harmonisable). Every item has either a value or a justified statement of impossibility, so feasibility = "complete" (feasibility_reason = null).

# Uncertainty

No standard errors or confidence intervals were propagated; the task asks only for point estimates.

• E5 is exact: it is a pure change of units.
• E2 is exact given the printed inputs. However, it divides a block-adjusted ATE by the raw control-group mean, and the inputs themselves are rounded (1.47, 75.0).
• E1 is exact under the stated convention. As a reading of the true change in the rate level it is approximate: exp(ATT) − 1 is a change in the geometric mean, and Jensen's inequality applies. The input b is also rounded to 3 decimals.
• E3 is a linear approximation (η·g). It also depends on which MW change is used: with the note's "about 4%" the result would be −1.5520% instead of −1.8236% (data_issues).

# Limitations and open issues

• E4 cannot be computed from the admissible evidence. No outside or remembered baseline rate was used.
• E3 depends on which printed size of the minimum-wage change is used. We follow the target definition and use the table value, 0.047.
• The source inconsistencies listed in data_issues were recorded but not resolved. None of them changes the cells used for E1–E3 and E5.
• Values are kept to 4 decimals of the computed transformation. Printed inputs are used exactly as printed.