Pearl Layer 1 — Association

Observational AssociationP(Y | X) — what correlates with what, without intervening

How to read this output

The result has two tables (substitution + fringe), each with one row per bin. Read each row as: 'in this bin, the observed quantity behaved like…'

count — sample size — number of simulation years in this bin

e.g. count=11 means 11 of the simulated years fell into this bin

mean_Q_sub / mean_Q_fringe — average substitution-supply or fringe-supply level inside the bin (units: same as Q)

e.g. mean_Q_fringe=4.97 in the Q4 (highest-price) bin → fringe producers entered when price was high

std_Q_sub / std_Q_fringe — within-bin variability of the quantity. If std=0 the quantity was constant in this bin.

spearman_rho_… — rank correlation between the quantity and the binning variable (range −1 to +1)

e.g. ρ=+0.76 means strong positive monotone association (the quantity rises with the binning variable in rank-order)

spearman_pval — p-value under H₀ of zero correlation. Small p → unlikely to be noise.

e.g. p=0.027 → significant at the 5% level (but with this small N treat any p > 0.01 with caution)

null (None) — a None means the statistic is undefined for that bin — usually because there was no variance (e.g. Q_sub = 0 throughout)

Key takeaway: A large |ρ| with small p says 'X and Y co-move'. It does NOT say 'X caused Y'. To distinguish, climb the ladder to L2 (intervention) or L3 (counterfactual).

What L1 (Association) computes

Formal: P(Y | X) — conditional distribution of Y given observed X, no manipulation

Substitution association — Spearman rank correlation

bin = { restricted: years where shock.export_restriction > 0,
        normal:     years where shock.export_restriction = 0 }

ρ_sub  = corr_Spearman( Q_sub_t , shock.export_restriction_t )
         within each bin   (return ρ, p-value, mean & std of Q_sub)

Fringe association — Spearman by price quartile

Q1..Q4 = price quartiles over the simulation horizon

ρ_fringe = corr_Spearman( Q_fringe_t , P_t )
           within each quartile (return ρ, p-value, mean & std of Q_fringe)

Caveat: ρ measures association only. A non-zero ρ does NOT imply 'restriction caused substitution' — a confounder (e.g. policy regime, year fixed effects) could explain both. Use L2 to sever those confounders via graph surgery.

Source: src/minerals/pearl_layers.py — observe_substitution_association(), observe_fringe_association()

No L1 query run yet

Pick a scenario on the left and click Run L1 Association. The result shows observational correlations — the first rung of Pearl's ladder, before any intervention or counterfactual reasoning.