Hidden behind that appearance of objectivity, though, is a Pentagon information apparatus that has used those analysts in a campaign to generate favorable news coverage of the administration’s wartime performance, an examination by The New York Times has found. The effort, which began with the buildup to the Iraq war and continues to this day, has sought to exploit ideological and military allegiances, and also a powerful financial dynamic: Most of the analysts have ties to military contractors vested in the very war policies they are asked to assess on air.