>How would my keeping my job instead of retiring lower unemployment?
I’m not saying it would lower unemployment, I’m saying it wouldn’t have a positive effect. Look at France. Every means by which the government has intervened into trying to restrict the labor market (shorter work weeks, lower retirement age, etc) has done nothing to help unemployment.
The only means by which a government can affect employment levels (other than direct hiring, and that is recycling other people’s money so it doesn’t work either) is by promoting pro growth policies so companies create wealth and hire people.
The job markets for people at retirement age and for someone out of college are not the same by any means.
But just to directly answer your question, because there is an answer, given the assumption that you are productive in your job, you must produce wealth. That wealth adds to the aggregate wealth of whatever company you work for, and thus enables more profits and the ability to hire more workers.
So yes, you remaining employed at an old age, as long as you are productive, does create more employment. The job market is not a zero sum game. It might seem like it in the small scale, but it really isn’t.