Research Foundations — How Demand Curves Have Been Estimated

This doc summarizes the five method families the simulator is built to replicate and stress-test. Each section ends with “What the simulator borrows.”

1. Uber — Natural experiment + regression discontinuity

Paper: Cohen, Hahn, Hall, Levitt & Metcalfe (2016), Using Big Data to Estimate Consumer Surplus: The Case of Uber, NBER WP 22627.

Setting. ~50M UberX sessions (app opens with a quoted price) across Chicago, LA, NYC, SF in 2015. ~21% of sessions had surge > 1.0x.

Method. The surge algorithm produces a continuous latent multiplier that is rounded to discrete surge levels (1.2x, 1.3x, …). Two sessions with nearly identical latent values can land on opposite sides of a rounding threshold and receive different prices — locally, price assignment is as-good-as-random. A regression discontinuity design compares purchase (ride-request) rates just left and right of each threshold, yielding a local elasticity at each surge level. Stitching local elasticities across the surge distribution traces the demand curve; integrating under it gives consumer surplus (~$2.9B in the four cities; ~$1.60 of surplus per $1 spent).

Data requirements.

Offer-level logs: quoted price + accept/decline for every session, including non-buyers.
The raw (pre-rounding) assignment variable, to define distance-to-threshold.
Enough traffic near each threshold (RD is data-hungry — this is why 50M sessions).

Assumptions.

Continuity: potential outcomes are smooth through the threshold; only price jumps.
No precise manipulation of the running variable by users (riders can’t game rounding).
No sorting: session composition doesn’t change discontinuously at thresholds.

Limitations.

Estimates are LATE — valid at the thresholds, extrapolation between them is assumption-laden.
Short-run elasticity only; ignores intertemporal substitution (users waiting out the surge and re-opening the app later — which also threatens independence across sessions).
Demand found to be surprisingly inelastic; generalizes poorly to markets with closer substitutes.

What the simulator borrows. Phase 3 implements a surge-like pricing rule (latent multiplier + rounding) so RD estimators (rdrobust) can be tested against known truth; session schema stores the latent multiplier in the oracle view.

2. ZipRecruiter — Randomized pricing (the gold standard)

Paper: Dubé & Misra (2023), Personalized Pricing and Consumer Welfare, JPE 131(1). (Earlier version: Scalable Price Targeting, NBER WP 23775.)

Setting. New-customer signups at ZipRecruiter, standard price $99/month.

Method. Stage 1 (Sept 2015): new customers randomly assigned one of ~10 monthly price cells from $19 to $399. Conversion rate per cell is the demand curve — no identification assumptions beyond randomization. Findings: cleanly downward-sloping demand; far less elastic than assumed ($99→$199 cut conversions only ~25%; the firm later moved to $249). Stage 2: demand model with heterogeneous price effects trained on registration covariates (industry, size, location) via regularized ML (lasso-family, weighted-likelihood bootstrap); personalized prices predicted to raise profit 86% vs. status quo and 19% vs. the optimal uniform price. A second experiment validated the counterfactual predictions out of sample — predicted conversion/profit distributions closely matched realized ones.

Data requirements. Ability to randomize price at the unit level; covariates collected pre-assignment; conversion outcome; enough units per cell.

Assumptions. Randomization integrity (no SRM); no interference across units (plausible here — job-posting firms don’t share a capacity pool); stable population during the test.

Limitations.

New customers only; long-run effects (churn, LTV, reputation/fairness blowback) not captured.
One-shot subscription purchase; harder in repeat-purchase retail where reference prices form.
Legal/ethical constraints often cap price randomization ranges in practice.

What the simulator borrows. Phase 1’s default mechanism is exactly this: session- or user-level random price cells. The two-stage pattern (estimate → predict counterfactual → validate against a fresh experiment) is the simulator’s core evaluation loop, since we can always run the “validation experiment” against ground truth.

3. Observational causal ML — Double Machine Learning (DML)

Canon: Chernozhukov et al. (2018), Double/Debiased Machine Learning; software: DoubleML (Python + R), EconML (Python).

Method. Partially linear model log Q = θ·log P + g(X) + u, log P = m(X) + v. Fit flexible ML (boosting/forests) for both nuisance functions with cross-fitting, then regress outcome residuals on treatment residuals — Frisch–Waugh–Lovell with ML. θ is the elasticity; Neyman-orthogonality makes it robust to slow ML convergence. Extends to heterogeneous elasticity θ(X) via CATE learners (causal forests, DR-learner, EconML’s LinearDML).

Data requirements. Observational panel with rich confounders X (seasonality, promo, product attributes, competitor context); price variation not fully explained by X.

Assumptions.

Unconfoundedness: all common causes of price and quantity are in X. If price responds to unobserved demand shocks (the normal case for a profit-maximizing pricer), DML alone is biased — you need instruments (DML-IV) or the experiment. See docs/05_endogenous_pricing.md.
Overlap: prices vary within every X stratum.
Cross-fitting to kill regularization/overfitting bias.

Limitations. Zero-sales censoring (sales-only logs can’t show what happened on no-sale days); functional-form choice for the target (log-log imposes constant elasticity); inference on CATEs is delicate.

What the simulator borrows. The oracle lets us generate data where unconfoundedness holds (Phase 2) or fails (Phase 4 endogenous pricing) and measure exactly how wrong DML gets — the kind of estimator due-diligence you can never do on real data.

4. Traditional structural models — BLP / random-coefficients logit & conjoint

Canon: Berry (1994); Berry, Levinsohn & Pakes (1995); Nevo (2000, 2001); software: PyBLP.

Method. Consumers have random utility u_ij = x_j β_i − α_i p_j + ξ_j + ε_ij with random coefficients (β_i, α_i vary across consumers) — heterogeneity is the point. Market shares are the integral of logit choice probabilities over the coefficient distribution. Estimation inverts observed aggregate shares to recover mean utilities, then uses GMM with price instruments to deal with the correlation between price and the unobserved product quality ξ_j (the structural version of endogeneity). Output: full demand system with own- and cross-price elasticities, welfare, merger/counterfactual simulation.

Data requirements. Aggregate market shares by product × market, prices, product characteristics, and instruments (cost shifters, BLP instruments = rivals’ characteristics, Hausman instruments = same product’s price in other markets).

Assumptions. Correct utility specification; instrument validity; equilibrium pricing conduct (often Bertrand-Nash) if supply side is used.

Limitations. Heavy machinery; identification leans on functional form + instruments; computationally finicky (though PyBLP largely tamed this). Conjoint analysis is the stated-preference cousin — cheap, runs in surveys, estimated with mixed logit (mlogit/R, xlogit/Python) — but measures stated, not revealed, WTP.

What the simulator borrows. The generative model. Our population IS a random-coefficients discrete-choice model (finite mixture instead of continuous mixing). This means structural estimators are, by construction, correctly specified in the base case — and we can break them deliberately (misspecified mixing distribution, missing substitutes).

5. What Amazon is going after — forecasting at catalog scale

Sources: Amazon Science, “The history of Amazon’s forecasting algorithm”; MQTransformer (2020); Chronos / Chronos-2; the job posting itself.

Trajectory. Sparse local models → global deep models. DeepAR (2017-era): one RNN trained across all series, probabilistic outputs (quantiles, not point forecasts) — the key insight that cross-learning fixes cold-start and sparse series. MQ-CNN → MQTransformer: multi-horizon quantile forecasts with attention, plus specialized components for seasonality and price-elasticity-driven demand spikes. Chronos-2: a time-series foundation model — zero-shot forecasting with support for known-future covariates (scheduled promotions, holiday calendars, prices) and categorical covariates. The job posting adds the frontier: foundation models that forecast products with no sales history, plus synthetic data generation to augment training corpora.

Data requirements (i.e., what our “ideal dataset” must contain).

Long panel of many related series (cross-learning is the whole trick).
Known-future covariates: price, promo schedule + depth, holiday calendar.
Static metadata: category, attributes (drives cold-start generalization).
Honest demand signal or at least stock status — sales censored by OOS poison training (see docs/02_censored_demand.md).
Probabilistic evaluation targets: quantile loss / CRPS, not just MAPE.

Limitations of the paradigm. Forecasters model conditional correlation, not causation: a price coefficient learned from endogenous historical pricing does not answer “what if we cut price 10%?” That question needs the experimental/causal half of this project — which is exactly why a simulator that produces both (a forecastable panel AND a causally interpretable experiment log) is more than the sum of its parts.

The unifying table

Family	Identification	Unit	Recovers	Fails when
Uber RD	algorithm discontinuity	session	local elasticities	far from thresholds; manipulation
ZipRecruiter RCT	randomization	user/session	whole curve on tested range	interference; range too narrow
DML	unconfoundedness	panel obs	θ, θ(X)	unobserved demand shocks drive price
BLP	instruments + structure	market shares	full demand system	bad instruments; wrong structure
Deep forecasting	none (predictive)	series	conditional forecasts	asked causal questions

demand estimation causal inference forecasting