Relationship, requires input

Food system requires input Crop production

The stored status is what a reviewer approved. The level below it is what the overlapping data support; the two are shown side by side and only a human moves the status.

Stored statusEstablished relationEvidence level (latest analysis)Level 5: Established relation

Mechanism, evidence, reviewer judgements

The edge as stored

Food system requires input Crop production3 evidenceEstablished relation

Food system depends on Crop production.

Mechanism

Cereals, oilseeds, fruit and vegetables come from crop production directly and, through animal feed, indirectly.

Evidence

documentFAO, FAOSTATfao.orgCrop production, food balances and fertilizer use by country.checked 2026-09-07
sourceFAOSTAT (seeded source)checked 2026-09-07
metriccereal-yield

Status: established_identity_or_engineering_relation
Reviewer confidence: 0.99
Stated strength: 1.00
Lag: not stated
Version: curated_seed_v1
Reviewed: 2026-09-07

Confidence and strength are curated judgements recorded with the edge, not measured quantities.

Entity pages: Food system, Crop production. Part of the mechanism Natural gas prices pass through ammonia into nitrogen fertilizer cost, crop yields and food supply.

Level 5 evidence, computed 2026-09-07 22:15 UTC

Correlation

DerivedLevel 5: Established relation

World population against Cereal yield, geography WLD, 64 overlapping years (1961 to 2024). Primary statistics on diff (first differences, because at least one series has a unit root; levels are shown for comparison).

Pearson r (diff)

-0.005

p 0.9698

Spearman rho (diff)

-0.032

p 0.8004

Pearson r (levels)

0.992

two trending series correlate in levels by construction

Rolling r

0.075

min -0.320, max 0.458, 14 sign changes

stored status is an established engineering or identity relation; statistics do not move it

Cross-correlation scan and Granger-style tests

Lead and lag

Direction	Tested	lag 1 p	lag 2 p	lag 3 p	lag 4 p	lag 5 p	min p	Reading
World population helps predict Cereal yield	yes	0.856	0.788	0.875	0.197	0.089	0.0889	no predictive information beyond own past
Cereal yield helps predict World population	yes	0.514	0.597	0.570	0.777	0.897	0.5143	no predictive information beyond own past

Granger-style F-tests on the primary transform: whether lagged values of one series improve a regression of the other on its own lags. Predictive information is not causation; a common driver that moves one series earlier produces the same pattern.

Reading: neither series adds predictive information about the other beyond its own past.

Cointegration: no (p 0.069)
Changepoints: World population: 1, Cereal yield: 1
ADF p (levels): 0.930, 0.761
Service: causal-service/0.1.0

Computed 2026-09-07 22:15 UTC

Causal estimate

ModeledLevel 5: Established relation

Treatment Cereal yield (crop-production), outcome World population (food-system), controls none (no shared upstream node with a series). Method backdoor.linear_regression on diff, n 64.

Estimate (outcome units per treatment unit)

-423.8019

95 percent CI

-22745.7503 to 21898.1465

includes zero

Refutations

2 of 3 passed

Refutation	Effect after	p	Result	Expectation
placebo treatment	620.4592	0.471	failed	placebo treatment (permuted) should produce an effect near zero
random common cause	-198.8721	0.414	passed	estimate should not move materially (p is the probability the change is noise)
data subset	234.8743	0.437	passed	estimate should not move materially (p is the probability the change is noise)

Assumptions

Backdoor adjustment: conditioning on no controls closes every non-causal path between cereal-yield and world-population. Unmeasured common causes would bias the estimate.
Linear, additive effect of the treatment on the outcome across the overlapping periods; no heterogeneous or threshold effects.
Series are first-differenced (a unit-root test rejected stationarity for at least one series); the estimate is a same-period association after adjustment, not a dynamic response.
The direction of the arrow (treatment to outcome) comes from the stored relationship and its mechanism, not from the data.
No reverse causation and no selection into the sample of periods.

Alternative explanations

Reverse causation: the outcome may drive the treatment.
An omitted common cause not in the controls moves both series.
Shared trend or regime: both series respond to the same global shock.
Aggregation: world-level annual data hides country-level variation and timing.
Measurement and revision: both series are estimates that are revised over time.

Identified estimand (DoWhy)

Estimand type: nonparametric-ate

### Estimand : 1
Estimand name: backdoor
Estimand expression:
       d                            
───────────────(E[world-population])
d[cereal-yield]                     
Estimand assumption 1, Unconfoundedness: If U→{cereal-yield} and U→world-population then P(world-population|cereal-yield,,U) = P(world-population|cereal-yield,)

### Estimand : 2
Estimand name: iv
No such variable(s) found!

### Estimand : 3
Estimand name: frontdoor
No such variable(s) found!

stored status is an established engineering or identity relation; statistics do not move it

Alternative explanations for the association

What else could explain it

Both series trend with world development; the primary statistics use first differences to limit that, not remove it.
A common driver (income, urbanisation, technology) can move both series with different lags and produce a lead/lag pattern without any direct effect.
World aggregates hide country composition: a change in which countries report can move a world series.
Reverse direction: Crop production may act on Food system.
Both series are revised by their source; the analysis uses the current vintage, not the vintage available at the time.

What each rung means

Levels

Level 0: No association found
the overlapping data show no significant association.
Level 1: Correlation only
statistically associated in the overlapping periods; no direction, no mechanism.
Level 2: Predictive lead/lag
one series historically contains predictive information about the other.
Level 3: Mechanism supported
a documented physical, economic or institutional mechanism with cited evidence.
Level 4: Causally supported
a backdoor-adjusted estimate that survived refutation, on stated assumptions.
Level 5: Established relation
follows from engineering, accounting or scientific structure.

Every stored run, newest first

Analysis history

2026-09-07 22:15 causal level 5 n 64 causal-service/0.1.0
2026-09-07 22:15 correlate level 5 n 64 causal-service/0.1.0