P180 Captain reports baggage door warning passing FL255 in climb. Left engine is shut down in accordance with procedures and flight continues to destination.

Narrative

During climb; the Baggage Door Warning light illuminated. The aircraft was at approximately FL255 climbing to FL340. The pilot flying (pilot in command) called for the checklist and the pilot not flying (Second in Command) executed our P180 Emergency checklist. The Pilot flying immediately notified ATC that the aircraft needed to stop climbing at FL280 and was going to troubleshoot a malfunction. The Baggage Door Annunciator checklist called for 'securing of the left engine' which the pilot flying and pilot not flying performed. Pilot flying and pilot not flying determined that aircraft performance and weather conditions would be optimal at FL260; and pilot flying requested FL260 and advised ATC that they had secured the left engine and may be requesting assistance and would desire direct to destination. Pilot flying and pilot not flying reviewed aircraft performance/fuel burn/reserves/landing distances/single engine performance (including single engine approach and landing and single engine go-around) and alternates if a diversion was required. It was determined that the destination field was the most appropriate given pilot familiarity/runway length/ approaches and emergency services available. Pilot flying and pilot not flying requested/declared an emergency with ATC and were assisted by ATC with vectors for destination and emergency crews standing by. Pilot not flying secured cabin and briefed passengers on emergency procedures. Pilot Flying executed the ILS in VMC and performed the single engine landing without incident. Pilot Flying maintained control of the aircraft and taxied to the ramp. Aircraft was determined; upon shutdown; to have a closed baggage door (indicating an errant annunciator indication) and thus no other damage was sustained. Pilot flying and pilot not flying briefed Airport Operations who were waiting on the ramp. The Director of Operations from the plane's management company called the FAA to report the incident as was appropriate.