Social media are used as main discussion channels by millions of individuals every day. The content individuals produce in daily social-media-based micro-communications, and the emotions therein expressed, may impact the emotional states of others. A recent experiment performed on Facebook hypothesized that emotions spread online, even in absence of non-verbal cues typical of in-person interactions, and that individuals are more likely to adopt positive or negative emotions if these are over-expressed in their social network. Experiments of this type, however, raise ethical concerns, as they require massive-scale content manipulation with unknown consequences for the individuals therein involved. Here, we study the dynamics of emotional contagion using a random sample of Twitter users, whose activity (and the stimuli they were exposed to) was observed during a week of September 2014. Rather than manipulating content, we devise a null model that discounts some confounding factors (including the effect of emotional contagion). We measure the emotional valence of content the users are exposed to before posting their own tweets. We determine that on average a negative post follows an over-exposure to 4.34% more negative content than baseline, while positive posts occur after an average over-exposure to 4.50% more positive contents. We highlight the presence of a linear relationship between the average emotional valence of the stimuli users are exposed to, and that of the responses they produce. We also identify two different classes of individuals: highly and scarcely susceptible to emotional contagion. Highly susceptible users are significantly less inclined to adopt negative emotions than the scarcely susceptible ones, but equally likely to adopt positive emotions. In general, the likelihood of adopting positive emotions is much greater than that of negative emotions.