Estimation and Inference for a Partially Identified: Dependence Operator

How much of an economy's hidden web of influence can data pin down, and how much stays uncertain? This paper treats the economy as a source whose stationary, differenced series reveal a directed dependence network only in part: its spectrum and dominant comovement are firmly fixed, a propagation multiplier only once a damping constant is chosen, and any single link's direction not at all. It supplies estimators with error bars for what is firmly fixed, a factor-corrected rule for how many patterns a panel resolves and how sharply, coverage-valid ranges for what is only partly fixed, and a calibrated test for directed flow. It draws a line: forecastability is capped by the source's novelty, so structure can be recovered sharply yet not forecast, and no estimate is a forecast.