Designing Independent Variation: A Guided Iteration Methodology for Price Experiments in Short, Correlated Panels

Pedro Cadahia

Papers from arXiv.org

Abstract: Estimation error in short, correlated pricing panels is dominated by trajectory dispersion rather than sampling noise, creating an identification shortfall that only independently assigned variation can resolve. We propose a guided iteration methodology to decide how much variation to generate, where, and for how long: a cyclic price-perturbation scheme under a revenue-at-risk budget, framed as variance minimization over design-specific error covariances, analogous to portfolio selection. We establish four key results: (1) a closed-form minimum-variance combination rule; (2) proof that a convex cost of intensity yields an interior, spread-out allocation, whereas under a concave tolerable-volume-loss cost, concentrating intensity into fewer perturbations pays off only with heterogeneous candidates, priced-in fixed costs, or perturbations beyond the cost curve's inflection point; (3) a discounted recursion yielding a data-dependent exit timeline from the experimentation zone; and (4) an application to Dominick's retail data, in which about five designed independent units match the precision of approximately 700 passive equivalents in the anchor category, while a fast proxy across ten categories achieves a median 97% variance reduction relative to passive panels. Sixteen comparisons (eleven pre-specified) support the theory: greedy selection achieves 90-93% of the global optimum across more than fifty exhaustively verifiable instances, and the recursion reaches its predicted 90%-of-steady-state benchmark two cycles early, though a parametric bootstrap indicates that its delta-method interval understates the right-tail risk. Boundary conditions show that regularized covariance estimators extend plug-in noise tolerance from 29% to beyond 50%, submodularity holds up to a clear curvature threshold, and a shared shock imposes a fundamental precision floor.

Date: 2026-10
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