Causal Inference Without Trusting the Predictor: Target-Preserving Calibration Under Population Shift

Under population shift, averaging machine-learned counterfactual predictions over a large target sample can become nearly deterministic while retaining causal bias. We study target-population average treatment effects when outcomes appear only in a labeled source sample and the target population contributes covariates alone. We introduce transport-calibrated causal prediction-powered inference (TC-CPI). With correct fixed propensity and transport weights, its mixing weight reallocates two unbiased estimates of the same prediction mean, one averaged in the target sample and the other transported from the source, while labeled residual correction preserves the causal estimand for every fixed predictor and weight. The exactly quadratic conditional variance yields a closed-form oracle weight; independent calibration attains asymptotic variance no larger than either endpoint. Population shift also creates two limits: learned density ratios give generic interior weights a first-order imbalance term that cross-fitting does not remove, while the efficiency bound weights source-outcome noise by $r^2$, so unlimited target covariates cannot compensate for poor source coverage. These limits yield conditional-shift sensitivity intervals and optimal prospective label and treatment allocation. Known design weights and bounds give finite-sample concentration intervals; with learned nuisances, cross-fitted asymptotic inference is valid under an explicit drift condition. Simulations, a 500,000-row randomized advertising study, and Project STAR test the variance geometry and transport penalty.