Catalytic converters are part of a car's exhaust system that reduce the amount of nitrous oxide produced by burning fuel. When working properly the converter should not affect fuel economy, but it can if it becomes clogged or damaged.
If your car's catalytic converter becomes plugged or clogged, it restricts the airflow of exhaust from the engine. This causes more and more exhaust to build up in the engine which reduces the amount of new, combustible oxygen the engine pulls in. A common cause of a clogged catalytic converter is overheating due to a misfiring spark plug.
When it is receiving less oxygen, the engine must work harder to achieve speed. This increased work lowers fuel economy, reduces power when driving at high speeds and can cause overheating and stalling. If your car runs normally for a few minutes after starting, but then begins to cough or sputter, your converter may be clogged. Especially if you have noticed other symptoms, have your mechanic check the car's exhaust backpressure.
If your catalytic converter is clogged or damaged, it will need to be replaced. Make sure to investigate the reason that the first converter was ruined so the replacement does not suffer the same fate.