In this contribution, variance properties of L2 model reduction are studied. That is, given an estimated model of high order we study the resulting variance of an L2 reduced approximation. The main result of the paper is showing that estimating a low-order output error (OE) model via L2 model reduction of a high-order model gives a smaller variance compared to estimating a low-order model directly from data in case of undermodeling. This has previously been shown to hold for Finite Impulse Response models, but is in this paper extended to general linear OE models.