My engine light has been on for months. I have taken the car in several times.
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did not use to have them. I know it is for pollution control. But does it have any effect on the car its self?
The short answer is "no" - your car will do just fine without the catalytic converter working at peak efficiency. In fact, the emissions are probably not much greater than they were before the light came on.
The long answer involves knowing what "codes" are being seen by the shop when they read them. Although the codes are specific, they aren't always clear and don't often point right to the specific problem... that's why the shop has danced around things like this. In fact, replacing the catalytic converter may not be the solution, and that's a good reason for them to evade it for so long. If you can find out what the codes are (they will be in the form of a "P" followed by 4 digits, like "P0452") and relate them here, we can confuse you more <8^P
There are two downsides I can think of in having the light on, other than the distraction. There is a small risk that another problem that would normally turn on the light will now be missed, and I don't believe you can legally sell a car in the US with the "check engine" light on (not sure about that.)
Mike