A B737-700 'STAB OUT OF TRIM' light illuminated at cruise. Descending out of RVSM; the main electric trim failed making the stabilizer trim inoperative. An emergency was declared.

Narrative

During cruise phase at FL400 3 hours into flight; the 'Stabilizer Out of Trim' light on the instrument panel came on. We immediately pulled out the QRH checklist and started it. The first step was to hold the control column firmly before disconnecting the autopilot; so we turned the seatbelt sign on and told the Flight Attendants to take their seats. We disconnected the autopilot and the aircraft barely moved indicating that it was still in trim. The electric trim thumb switches did work to electrically trim the aircraft. We then attempted to reconnect the autopilot and still got the 'Stabilizer Out of Trim' light. We decided to keep the autopilot off. We contacted ATC; told them we were 'Unable RVSM due to equipment' and were given a slow descent to FL280. We notified Dispatch via ACARS. We contacted Maintenance Control via ACARS for some troubleshooting help. They suggested cycling the p-18-1 c2 CB and also to try both A and B autopilots. Both suggestions did not fix the problem. On the descent the electric trim switches became inoperative. We then got into the QRH for the Stabilizer Trim Inoperative checklist. We did this because after discussion we didn't trust the electric trim and did not want it to run away. We decided to declare an emergency with ATC; Approach; because it was a flight control malfunction. We also requested the Crash Fire Rescue crew be standing by. We advised the Flight Attendants of the situation and also made a PA announcement to the passengers that they may notice the fire trucks on landing due to a nuisance trim malfunction we were experiencing. I did emphasize that it was a precautionary measure and that the aircraft was fully controllable. We were given a long final for runway and we made an uneventful flaps 15 degree landing.