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

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.