Consumers interact with firms across multiple devices, browsers, and machines
these interactions are often recorded with different identifiers for the same consumer. The failure to correctly match different identities leads to a fragmented view of exposures and behaviors. This paper studies the identity fragmentation bias, referring to the estimation bias resulted from using fragmented data. Using a formal framework, we decompose the contributing factors of the estimation bias caused by data fragmentation and discuss the direction of bias. Contrary to conventional wisdom, this bias cannot be signed or bounded under standard assumptions. Instead, upward biases and sign reversals can occur even in experimental settings. We then compare several corrective measures, and discuss their respective advantages and caveats.