Simulated participation of SYNTHETIC agents. "Participation" is the simulated seasonal decision to maintain inter-row ground cover; it is not observed adoption.
No parameter is empirically calibrated. Intervals are 95% percentile-bootstrap intervals over 20 Monte Carlo repetitions: they describe simulation noise, not confidence about real programmes.
Budget: uncapped (expenditure = sum of entitlements).
Primary comparison · equal actual expenditure C1 protocol
Each mechanism's outcome is interpolated linearly along its own cost–participation frontier (reward-scale grid λ) at the same actual expenditure per farmer, within each repetition (common random numbers), without extrapolation. Primary target: 200 MU per farmer over 12 seasons (pre-specified).
Δ horizon-mean participation (P1) at matched expenditure
Primary endpoint P1, paired difference to S0
View data table
Δ sustained participation (P2) at matched expenditure
Primary endpoint P2 (≥ 4 consecutive seasons)
View data table
Cost–participation frontiers
P1 against actual expenditure; points = reward scales λ (λ = 0 is the control)
Bands: 95% bootstrap intervals of P1 at each λ.
View data table
Cost–sustained-participation frontiers
P2 against actual expenditure
View data table
Matched-expenditure estimates (all targets)
Difference to the control at equal expenditure · [95% interval] · repetitions in which the target lies within the observed spending range.
| Target (MU / farmer) | Mechanism | P1 at target | Δ P1 vs S0 | Δ P2 vs S0 | Net additional seasons / farmer | Availability |
|---|---|---|---|---|---|---|
| 100 | S1 Fixed | 31.2% [30.0%, 32.5%] |
+7.5 pp [+7.0 pp, +8.0 pp] |
+9.6 pp [+8.5 pp, +10.8 pp] |
0.902 | Available (20/20) |
| 100 | S2 Performance-based | 31.0% [29.7%, 32.3%] |
+7.3 pp [+6.8 pp, +7.9 pp] |
+10.0 pp [+8.9 pp, +11.3 pp] |
0.877 | Available (20/20) |
| 100 | S3 Tiered | 30.8% [29.3%, 32.2%] |
+7.0 pp [+6.6 pp, +7.5 pp] |
+9.8 pp [+8.7 pp, +10.9 pp] |
0.846 | Available (20/20) |
| 100 | S3R Tiered, relative | 30.9% [29.5%, 32.2%] |
+7.1 pp [+6.7 pp, +7.6 pp] |
+9.9 pp [+8.8 pp, +11.1 pp] |
0.858 | Available (20/20) |
| 200 · primary | S1 Fixed | 37.0% [35.9%, 38.0%] |
+13.3 pp [+12.5 pp, +14.0 pp] |
+17.0 pp [+14.8 pp, +19.1 pp] |
1.594 | Available (20/20) |
| 200 · primary | S2 Performance-based | 36.2% [35.0%, 37.4%] |
+12.5 pp [+11.7 pp, +13.1 pp] |
+16.7 pp [+15.0 pp, +18.4 pp] |
1.496 | Available (20/20) |
| 200 · primary | S3 Tiered | 35.7% [34.2%, 37.1%] |
+12.0 pp [+11.3 pp, +12.6 pp] |
+16.1 pp [+14.4 pp, +17.6 pp] |
1.436 | Available (20/20) |
| 200 · primary | S3R Tiered, relative | 36.2% [34.8%, 37.5%] |
+12.4 pp [+11.7 pp, +13.1 pp] |
+16.5 pp [+14.8 pp, +18.0 pp] |
1.492 | Available (20/20) |
| 300 | S1 Fixed | 41.8% [40.8%, 42.9%] |
+18.1 pp [+17.1 pp, +19.0 pp] |
+22.9 pp [+20.1 pp, +25.5 pp] |
2.170 | Available (20/20) |
| 300 | S2 Performance-based | 40.7% [39.4%, 41.9%] |
+16.9 pp [+16.0 pp, +17.9 pp] |
+22.5 pp [+20.3 pp, +24.6 pp] |
2.034 | Available (20/20) |
| 300 | S3 Tiered | 39.5% [38.2%, 40.7%] |
+15.8 pp [+15.0 pp, +16.6 pp] |
+20.9 pp [+18.8 pp, +22.6 pp] |
1.892 | Available (20/20) |
| 300 | S3R Tiered, relative | 40.1% [39.0%, 41.3%] |
+16.4 pp [+15.6 pp, +17.2 pp] |
+21.7 pp [+19.7 pp, +23.5 pp] |
1.971 | Available (20/20) |
| 400 | S1 Fixed | 46.0% [45.0%, 47.0%] |
+22.3 pp [+21.2 pp, +23.4 pp] |
+28.1 pp [+25.2 pp, +30.9 pp] |
2.680 | Available (20/20) |
| 400 | S2 Performance-based | 44.3% [43.2%, 45.4%] |
+20.6 pp [+19.5 pp, +21.7 pp] |
+27.0 pp [+24.8 pp, +29.3 pp] |
2.475 | Available (20/20) |
| 400 | S3 Tiered | 42.9% [41.6%, 44.2%] |
+19.2 pp [+18.3 pp, +20.2 pp] |
+25.1 pp [+23.0 pp, +27.1 pp] |
2.308 | Available (20/20) |
| 400 | S3R Tiered, relative | 43.6% [42.5%, 44.9%] |
+19.9 pp [+19.0 pp, +20.9 pp] |
+26.3 pp [+24.3 pp, +28.4 pp] |
2.390 | Available (20/20) |
Pairwise differences at the primary target (200 MU)
Effect sizes with 95% Monte Carlo intervals; "share A > B" is the fraction of repetitions in which A exceeds B. These describe the model, not statistical superiority of real programmes.
| A − B | Δ P1 | share A > B | Δ P2 | share A > B |
|---|---|---|---|---|
| S1 Fixed − S2 Performance-based | +0.8 pp [+0.5 pp, +1.1 pp] |
95 % | +0.2 pp [-0.7 pp, +1.2 pp] |
40 % |
| S1 Fixed − S3 Tiered | +1.3 pp [+0.8 pp, +1.8 pp] |
95 % | +0.9 pp [-0.5 pp, +2.2 pp] |
65 % |
| S1 Fixed − S3R Tiered, relative | +0.8 pp [+0.5 pp, +1.2 pp] |
85 % | +0.4 pp [-0.4 pp, +1.3 pp] |
45 % |
| S2 Performance-based − S3 Tiered | +0.5 pp [+0.1 pp, +0.9 pp] |
65 % | +0.6 pp [-0.1 pp, +1.4 pp] |
50 % |
| S2 Performance-based − S3R Tiered, relative | +0.0 pp [-0.2 pp, +0.3 pp] |
45 % | +0.2 pp [-0.2 pp, +0.6 pp] |
45 % |
| S3 Tiered − S3R Tiered, relative | -0.5 pp [-0.8 pp, -0.1 pp] |
30 % | -0.4 pp [-1.3 pp, +0.5 pp] |
40 % |
Outcomes at reward scale λ = 1 · not expenditure-matched
At a common λ, mechanisms spend different amounts (see actual expenditure). Differences here confound mechanism design with spending level; use the matched comparison above for mechanism contrasts.
Horizon-mean participation (P1)
Primary endpoint
View data table
Sustained participation (P2)
≥ 4 consecutive seasons
View data table
Actual expenditure per farmer
MU over the horizon (after any rationing)
View data table
Participation over seasons
Per-season participation share
View data table
Continuation probability
P(participate in t | participated in t−1)
View data table
Dis-adoption by season
Share of farmers stopping in each season
View data table
Deadweight share of payments
Payments in farmer-seasons that also participate in the paired control (synthetic counterfactual)
View data table
Cost-effectiveness at λ = 1
Primary estimator: pooled ratio Σ expenditure / Σ net additional participant-seasons across repetitions, with 95% bootstrap interval. The per-run mean of ratios is secondary (metric table below).
| Mechanism | Pooled cost per additional participant-season | 95% interval | Actual expenditure / farmer | Budget utilisation |
|---|---|---|---|---|
| S1 Fixed | 173.9 MU | [167.7 MU, 180.8 MU] | 669.9 MU | n/a (uncapped) |
| S2 Performance-based | 166.0 MU | [157.3 MU, 175.6 MU] | 429.6 MU | n/a (uncapped) |
| S3 Tiered | 196.0 MU | [187.7 MU, 204.6 MU] | 570.5 MU | n/a (uncapped) |
| S3R Tiered, relative | 185.4 MU | [176.9 MU, 194.9 MU] | 536.1 MU | n/a (uncapped) |
Distribution, equity and additionality
Payments by baseline ground-cover tercile
Share of all payments received by each tercile of q0
Under absolute thresholds (S3) high-baseline farmers can be paid without improving.
View data table
Reward parity profile
Mean entitlement after k consecutive seasons (reference population, λ = 1)
Analytic diagnostic, not a simulation outcome: S1 pays its full reward from season 1, accumulation-based mechanisms only later.
View data table
Subgroup outcomes at λ = 1
Terciles of baseline ground cover q0 and of adoption cost C (within each repetition). Net position = payments − practice costs incurred (MU per farmer over the horizon; non-monetary benefits excluded).
| Subgroup | S0 No incentive | S1 Fixed | S2 Performance-based | S3 Tiered | S3R Tiered, relative |
|---|---|---|---|---|---|
| Baseline cover · low participation · payment share · net position |
22.8%
no payments · -194.5 MU
|
55.3%
32.8% · 162.3 MU
|
43.6%
31.0% · 15.0 MU
|
32.2%
10.5% · -97.8 MU
|
45.6%
30.8% · 90.7 MU
|
| Baseline cover · middle participation · payment share · net position |
23.5%
no payments · -209.1 MU
|
56.8%
33.6% · 150.7 MU
|
47.4%
35.8% · 28.1 MU
|
50.6%
34.3% · 124.0 MU
|
50.6%
36.3% · 117.7 MU
|
| Baseline cover · high participation · payment share · net position |
24.8%
no payments · -213.3 MU
|
55.3%
33.6% · 169.8 MU
|
45.0%
33.2% · 27.1 MU
|
60.7%
55.2% · 379.1 MU
|
47.2%
33.0% · 104.5 MU
|
| Adoption cost · low participation · payment share · net position |
31.7%
no payments · -193.3 MU
|
64.4%
38.1% · 372.8 MU
|
54.5%
40.0% · 184.1 MU
|
57.0%
39.0% · 321.3 MU
|
56.3%
38.6% · 278.9 MU
|
| Adoption cost · middle participation · payment share · net position |
23.4%
no payments · -221.0 MU
|
56.3%
33.3% · 143.2 MU
|
46.1%
33.7% · 3.4 MU
|
48.2%
32.5% · 109.3 MU
|
49.2%
33.9% · 87.9 MU
|
| Adoption cost · high participation · payment share · net position |
16.3%
no payments · -202.9 MU
|
47.0%
28.6% · -27.3 MU
|
35.5%
26.3% · -113.2 MU
|
39.0%
28.6% · -13.4 MU
|
38.2%
27.5% · -49.4 MU
|
All metrics at λ = 1 — mean [95% bootstrap interval]
Primary endpoints are marked. n/a = undefined in every repetition; "undef." counts excluded repetitions.
| Metric | S0 No incentive | S1 Fixed | S2 Performance-based | S3 Tiered | S3R Tiered, relative |
|---|---|---|---|---|---|
| Participation | |||||
| Horizon-mean participation (P1) primary share of farmers (0–1) |
23.7%
[22.1%, 25.3%]
|
55.8%
[54.4%, 57.3%]
|
45.3%
[43.3%, 47.1%]
|
48.0%
[46.1%, 49.7%]
|
47.8%
[45.9%, 49.7%]
|
| Δ horizon-mean participation vs control primary percentage points |
n/a | +32.1 pp
[+30.9 pp, +33.3 pp]
|
+21.6 pp
[+20.4 pp, +22.8 pp]
|
+24.3 pp
[+23.1 pp, +25.4 pp]
|
+24.1 pp
[+22.7 pp, +25.5 pp]
|
| Initial participation (season 1) share of farmers (0–1) |
17.3%
[15.6%, 18.8%]
|
39.3%
[37.3%, 41.3%]
|
28.2%
[26.1%, 30.4%]
|
30.7%
[28.5%, 32.8%]
|
29.3%
[27.4%, 31.3%]
|
| Final-season participation share of farmers (0–1) |
24.6%
[22.0%, 27.4%]
|
58.0%
[55.5%, 60.7%]
|
48.7%
[46.0%, 51.7%]
|
51.8%
[49.0%, 54.5%]
|
51.9%
[49.6%, 54.1%]
|
| Ever participated share of farmers (0–1) |
68.1%
[65.9%, 70.2%]
|
91.4%
[90.5%, 92.3%]
|
81.9%
[79.9%, 83.8%]
|
81.9%
[80.2%, 83.5%]
|
81.2%
[79.4%, 83.0%]
|
| Sustained participation | |||||
| Sustained participation (P2) primary share of farmers (0–1) |
23.7%
[20.9%, 26.0%]
|
63.8%
[61.6%, 65.8%]
|
51.6%
[49.3%, 54.0%]
|
54.2%
[51.6%, 56.7%]
|
55.1%
[52.6%, 57.8%]
|
| Δ sustained participation vs control primary percentage points |
n/a | +40.2 pp
[+37.7 pp, +42.5 pp]
|
+27.9 pp
[+25.3 pp, +30.2 pp]
|
+30.6 pp
[+28.3 pp, +32.5 pp]
|
+31.4 pp
[+29.1 pp, +33.9 pp]
|
| Continuation probability probability (0–1) |
68.3%
[66.1%, 70.5%]
|
84.9%
[84.0%, 85.7%]
|
84.3%
[83.0%, 85.4%]
|
86.6%
[85.5%, 87.6%]
|
86.5%
[85.5%, 87.5%]
|
| Dis-adoption rate probability (0–1) |
31.7%
[29.7%, 33.8%]
|
15.1%
[14.3%, 16.0%]
|
15.7%
[14.7%, 16.9%]
|
13.4%
[12.4%, 14.6%]
|
13.5%
[12.6%, 14.5%]
|
| Mean consecutive participation duration seasons |
2.7
[2.6, 2.8]
|
4.5
[4.3, 4.6]
|
4.3
[4.2, 4.5]
|
4.8
[4.6, 4.9]
|
4.7
[4.5, 4.9]
|
| Participated in every season share of farmers (0–1) |
1.7%
[1.1%, 2.3%]
|
13.3%
[11.4%, 15.2%]
|
9.8%
[8.2%, 11.4%]
|
12.9%
[10.8%, 15.2%]
|
11.6%
[9.7%, 13.3%]
|
| Re-adopters share of farmers (0–1) |
29.3%
[27.5%, 31.1%]
|
45.9%
[44.1%, 47.7%]
|
35.7%
[34.0%, 37.3%]
|
33.0%
[31.2%, 34.6%]
|
33.5%
[32.0%, 35.1%]
|
| Re-adoption frequency events per farmer |
0.4
[0.4, 0.4]
|
0.6
[0.6, 0.6]
|
0.4
[0.4, 0.5]
|
0.4
[0.4, 0.4]
|
0.4
[0.4, 0.4]
|
| Spending & cost-effectiveness | |||||
| Actual expenditure per farmer MU per farmer over the horizon |
0.0 MU
[0.0 MU, 0.0 MU]
|
669.9 MU
[652.0 MU, 686.5 MU]
|
429.6 MU
[409.2 MU, 450.3 MU]
|
570.5 MU
[541.7 MU, 598.8 MU]
|
536.1 MU
[512.4 MU, 560.2 MU]
|
| Total expenditure MU |
0.0 MU
[0.0 MU, 0.0 MU]
|
66,985.0 MU
[65,304.5 MU, 68,775.1 MU]
|
42,957.1 MU
[40,691.2 MU, 45,158.3 MU]
|
57,050.0 MU
[54,192.3 MU, 59,806.6 MU]
|
53,612.5 MU
[51,210.0 MU, 56,055.4 MU]
|
| Budget utilisation share of nominal budget (0–1) |
n/a | n/a | n/a | n/a | n/a |
| Cost per additional participant-season (per-run ratio) MU per participant-season |
n/a | 174.9 MU
[168.2 MU, 181.8 MU]
|
167.7 MU
[157.0 MU, 178.3 MU]
|
197.0 MU
[187.7 MU, 206.7 MU]
|
187.4 MU
[177.6 MU, 197.9 MU]
|
| Additionality (synthetic counterfactual) | |||||
| Net additional participant-seasons farmer-seasons |
n/a | 385.3
[369.7, 399.1]
|
258.9
[244.4, 273.6]
|
291.0
[276.8, 305.5]
|
289.1
[273.3, 307.1]
|
| Gross additional participant-seasons farmer-seasons |
n/a | 385.3
[370.2, 399.9]
|
258.9
[243.3, 273.5]
|
291.0
[277.5, 304.1]
|
289.1
[272.0, 306.9]
|
| Displaced participant-seasons farmer-seasons |
n/a | 0.0
[0.0, 0.0]
|
0.0
[0.0, 0.0]
|
0.0
[0.0, 0.0]
|
0.0
[0.0, 0.0]
|
| Deadweight share of payments share of expenditure (0–1) |
n/a | 42.4%
[40.2%, 44.7%]
|
49.6%
[46.8%, 52.0%]
|
41.8%
[39.1%, 44.4%]
|
45.2%
[42.5%, 48.0%]
|
| Deadweight payments MU |
n/a | 28,460.0 MU
[26,634.6 MU, 30,275.6 MU]
|
21,383.0 MU
[19,637.9 MU, 22,972.8 MU]
|
24,032.5 MU
[21,713.6 MU, 26,499.1 MU]
|
24,332.5 MU
[22,315.0 MU, 26,258.2 MU]
|
| Distribution & equity | |||||
| Payment Gini (all farmers) index (0–1) |
n/a | 0.337
[0.325, 0.350]
|
0.549
[0.533, 0.565]
|
0.576
[0.559, 0.595]
|
0.553
[0.536, 0.569]
|
| Payment Gini (recipients) index (0–1) |
n/a | 0.275
[0.263, 0.286]
|
0.449
[0.434, 0.463]
|
0.383
[0.367, 0.398]
|
0.400
[0.386, 0.415]
|
| Share of farmers paid share of farmers (0–1) |
0.0%
[0.0%, 0.0%]
|
91.4%
[90.5%, 92.3%]
|
81.9%
[80.0%, 83.8%]
|
68.6%
[66.8%, 70.4%]
|
74.5%
[72.5%, 76.5%]
|
| Net financial position of participants MU per farmer over the horizon |
-301.6 MU
[-316.3 MU, -287.0 MU]
|
176.5 MU
[161.7 MU, 192.3 MU]
|
28.6 MU
[12.7 MU, 44.0 MU]
|
168.4 MU
[145.7 MU, 192.9 MU]
|
128.3 MU
[108.8 MU, 145.6 MU]
|
| Participants with non-negative net financial position share of participants (0–1) |
0.0%
[0.0%, 0.0%]
|
80.5%
[78.7%, 82.3%]
|
39.1%
[36.2%, 41.8%]
|
53.6%
[51.4%, 56.2%]
|
51.4%
[48.9%, 53.8%]
|
| Payments to farmers already above the lowest S3 threshold at baseline share of expenditure (0–1) |
n/a | 14.9%
[12.8%, 17.0%]
|
14.6%
[12.3%, 17.0%]
|
28.5%
[25.4%, 31.8%]
|
14.6%
[12.0%, 17.1%]
|
| Ground cover | |||||
| Mean ground-cover gain ground-cover fraction |
0.084
[0.078, 0.089]
|
0.185
[0.178, 0.191]
|
0.163
[0.156, 0.170]
|
0.172
[0.164, 0.178]
|
0.175
[0.169, 0.183]
|