Power DGP Assumptions

GeoSC estimates its power data-generating process (DGP) from the pre-period outcome matrix.

Each unit is demeaned. Singular value decomposition produces factor loadings and factor scores. When rank is automatic, GeoSC chooses the first rank reaching about 80% cumulative singular-value variance, bounded by power_dgp_max_rank and a short-panel VAR feasibility cap. It then estimates a VAR(1) intercept, transition matrix, and Gaussian innovation covariance on the factor series.

Simulation draws the initial factor state from the estimated marginal normal distribution; it is not conditioned on the final observed factor state. Later states follow the fitted VAR(1). Outcomes combine fixed unit loadings, simulated factors, stored unit means, and independent Gaussian idiosyncratic noise with one pooled residual standard deviation.

Consequences:

• cross-unit dependence is represented through common factors;
• lag-one factor dependence is represented;
• calendar seasonality is not modelled explicitly;
• the fitted VAR transition is not constrained to be dynamically stable;
• idiosyncratic variance is homoskedastic across units and periods;
• non-Gaussian tails, structural breaks, intermittent zeros, and conditional start-state dynamics may be poorly represented;
• rank selection is a heuristic, not cross-validated DGP truth.

Validate simulated moments and time-series behaviour against the use case. Run sensitivity to history, rank, effect pattern, and eligible controls. If design decisions change materially, report DGP dependence rather than one definitive MDE.