There is growing awareness within the economics profession of the important role narratives play in the economy. Even though empirical approaches that try to quantify economic narratives are getting increasingly popular, there is no theory or even a universally accepted definition of economic narratives underlying this research. First, we review and categorize the economic literature concerned with narratives and work out the different paradigms that are at play. Only a subset of the literature considers narratives to be active drivers of economic activity. In order to solidify the foundation of narrative economics, we propose a definition of collective economic narratives, isolating five important characteristics. We argue that, for a narrative to be economically relevant, it must be a sense-making story that emerges in a social context and suggests action to a social group. We also systematize how a collective economic narrative differs from a topic and from other kinds of narratives that are likely to have less impact on the economy. With regard to the popular use of topic modeling as an empirical strategy, we suggest that the complementary use of other canonical methods from the natural language processing toolkit and the development of new methods is inevitable to go beyond identifying topics and be able to move towards true empirical narrative economics.