The purpose of this paper is the explanation of the dynamics of innovation activity in Russia (on the example of the level of innovation activity of organizations) and identification of the problems for innovative development, based on the methodology of narrative institutional analysis. Research methods are narrative and content analysis, a graphical method for displaying statistical data. The study formulates the differences in the interpretation and methods of analysis of narratives between the narrative economy (in the tradition of R. Schiller) and the narrative analysis in other social sciences. The application of the approach of narrative economics to the study of the Russian innovation system provides a study of narratives that combines the qualitative and quantitative research methods. Narratives in R. Schiller’s approach are interpreted as stories or expressed explanations of events, discussed in conversations, news, and social media to stimulate interest or demonstrate emotions. The problem of interrelation between the narratives about the innovation activity and the indicators of the innovation activity is considered. The distinction between the direct and indirect influence of narratives on indicators of innovative activity is proposed. The direct influence of narratives on the indicators of innovation activity may include modifying the methods for calculating indicators. The indirect influence of narratives on the indicators of innovation activity may include modifying the motivation and level of activity of the actors of the national innovation system. The observed dynamics of indicators of innovative activity indicate its stagnation, at the same time, the volume of discussion in the media about innovations is increasing. The paper discusses possible reasons that impede the strengthening of innovative development. The main focus is on assessing the importance of the problem of business demand for innovations and commercialization of innovations. The paper formulates a theoretical framework that summarizes the types of problems that may arise during the implementation of innovative activities. There are five types of problems that may arise during the implementation of innovative activities. The first type of the problems is caused by government compulsion, institutional constraints and intervention in economic activity. The second type of problem is caused by the opportunism of individuals who are selfish at any cost and are capable for violating rules and agreements. The third type of problem is associated with the difficulty of coordination and adapting the plans of free individuals, each of whom has only a part of the common knowledge that should be used in economic activity. The fourth type of problems is the lack of resources and knowledge for innovation; it is well studied by economic science. The fifth type of problems is the inability of individuals to make the optimal choice; in relation to the Russian innovation system, this is only a hypothesis and has not yet been studied. The first three «ideal types» of problems are incorporated in the narrative of the low demand for innovation from the business side.