Do elections motivate incumbent politicians to serve their voters? In this paper, we use millions of service requests placed by residents in US cities to measure constituency responsiveness. We then test whether an unusual policy change in New York City, which enabled city councilors to run for three rather than two terms in office, improved constituency responsiveness in previously term-limited councilors' districts. Using difference-in-differences, we find robust evidence for this. Taking advantage of differential timing of local election races in New York City and San Francisco, we also find late-term improvements to responsiveness in districts represented by reelection-seeking incumbents. Elections improve municipal services, but also create cycles in constituency responsiveness. These findings have implications for theories of representative democracy.