Lane changes can induce natural large perturbations in traffic flow and are known to impact traffic throughput and energy consumption. Their precise effects are understudied. The primary aim of this article is to present a model for lane changing that is tractable for system-level analysis and yet captures qualities of microscopic vehicle dynamics. We present a stochastic lane changing model, which permits a two-stage reduction: 1) of the (microscopic) multi-lane problem into a stochastic single-lane problem, and 2) of the stochastic single-lane model into a Markov chain macroscopic model which captures system-level lane-changing characteristics. The first reduction contributes the first model of lane changing as a single-lane process, which permits the simplification of theoretical analysis. The Markov chain macroscopic model permits the computation of statistics on the traffic parameters, such as expected velocity and headway, thus permitting the quantification of the effect of lane changes on traffic flow. We validate the proposed model on NGSIM and confirm the accuracy of the Markov chain for computing headway statistics. Finally, counter to a common view of lane changes as perturbations which contribute to shockwave formation, we observe that lane changes reduce the variance of the velocity by 10% on a 230-meter ring road benchmark, which suggests that discretionary lane changes may serve to reduce stop and go waves rather than increase them.