Econometric recovery canonical · 200 simulated markets × 2 arms × 20 assignment replications

Would an empiricist find this?

Simulation gives ground truth. We generate the observational data a researcher would actually see — markets that adopt personalized pricing where it pays — and ask which standard estimators recover the true effect on consumer surplus.

How biased is each estimator, and does selection on unobservables make it worse?

Bias as % of the estimand (ATT for observational designs, LATE for IV, ATE for the RCT), by strength of selection on the unobserved sophistication of consumers. Error bars are Monte Carlo sd across replications.

What do the estimates look like across replications?

Every replication's estimate (points) against the truth (line), strongest selection.

Why staggered-adoption fixed effects are attenuated

Average consumer-surplus change after adoption relative to the pre-adoption steady state, by periods since adoption. Sellers learn; the effect is dynamic.

Where is the true effect large, and who adopts?

Each simulated market: true effect of adoption on consumer surplus per capita against valuation dispersion; colour = share of strategic consumers (unobserved by the econometrician).

Recovery table

The data-generating process, precisely

Market m has dispersion σ_m ~ U(0.3, 0.8) (observed only through a noisy proxy), median valuation μ_m ~ U(2, 3) (observed), strategic share s_m ~ U(0, 0.4) (unobserved) and a data-broker coverage indicator Z_m ~ Bernoulli(0.5) that lowers adoption cost and enters nothing else. Adoption: D_m = 1[−0.3 + 1·(σ_m−0.55)/0.15 − g·(s_m−0.2)/0.12 + 1.5·Z_m + logistic error > 0], with g the selection-on-unobservables strength (0, 1, 2). Outcomes Y_m(0), Y_m(1) are the steady-state consumer surplus per capita under uniform and individualized-regression pricing, simulated with the same population seed. The panel has 24 periods; adopters switch at a random period in the middle third and their post-adoption series includes the seller's learning phase. Estimators: naive OLS; OLS with the observed controls (σ proxy, μ); 2SLS with Z; a randomized re-assignment; two-way fixed effects on the staggered panel; a clean-control DiD (adopters' last six periods vs pre, minus never-adopters).

What this does not show. The IV is valid by construction — exclusion is imposed, not argued. In the field, "data availability" instruments would rarely satisfy it. The value of the exercise is the size and direction of the biases under selection that mimics the economics of adoption, and the attenuation of TWFE under dynamic effects.