This paper considers an empirical semiparametric model for two-sided markets. Contrary to existing empirical literature on two-sided markets, we specify network effects and probability distribution functions of net benefits of the two sides nonparametrically. We then estimate the model by nonparametric instrumental variables regression for local daily newspapers from the USA. We show that semiparametric specification is supported by the data and the network effects are neither linear nor monotonic. With a numerical illustration we demonstrate that the mark-up of the newspaper on each side changes drastically with the nonlinearly specified network effects from the case with linear network effects.