This is a very interesting question, since innovation is the driving force for any company which struggle for a competitive advantage. However, the answer to your question might depend on the clarification if you think about an innovation culture at the governmental level (i.e. country level), or at an organizational level (i.e. organizational culture). I shall consider in my answer the organizational culture. The most important factors are the following:

1. The leadership vision. Without a well-defined vision it is not possible to develop a sustainable innovation culture.

2. A well-defined set of values stressing the importance of innovation.

3. Human capital. The organization should hire talented and creative people who have the competence of creating new ideas, processes, products and services.

4. A well-defined rewarding system. Innovation is a result of the integration of rational knowledge with emotional knowledge and spiritual knowledge. Innovation means always an extra-effort made by people which cannot be measured in terms of time or money. Thus, people who innovate must feel that the organization has the means of rewarding their efforts.

5. A culture of trust which allows fruitful cooperation between people.

6. A flexible working program since innovation cannot be constrained.

7. A good evaluation system of final results, in order to make adequate correlations between efforts and results.

Each of these factors can be decomposed and detailed in concordance with the purpose of research.

Good luck!

I have two papers on innovation which answer your question fairly and squarely. They are uploaded on Research Gate so you can download them. One is at the firm level and the other is at the industry level.

The essential characteristics of innovation systems are that they recruit and retain highly skilled and motivated people, give them access to knowledge, and then enable them to think and act innovatively. There is no simple universal formula but, specifically, (the demanding) components of an effective innovation system, some of which were identified earlier by @Bratianu, include:

• Clarity in mission statements and goals, which invariably feature a commitment from senior managers to assume responsibility for the risk of failure.
• An organizational culture that values innovation, where there is encouragement for personnel to think differently, take calculated risks, and challenge the status quo. Major forces such as leadership, attitudes to risk, budgeting, audit, performance measurement, recruitment, and open innovation are aligned in support.
• A systems approach to management that understands innovation as one part of a wider context, appreciates interconnections, and can conduct systematic analyses of how a problem interacts with other problems, parts of the organization, projects, etc. Management fosters coordination across these interconnections and stresses integration rather than compartmentalization.
• The adequate resourcing of innovation in line with strategy.
• The placing of responsibility for innovation on all staff.
• Understanding that creativity is desirable but insufficient. Innovation ambassadors must still take responsibility for follow-through.
• An enriched physical workplace that enhances creativity by providing accessible, casual meeting spots; physical stimuli; space for quiet reflection; a variety of communication tools, e.g., white boards, bulletin boards; contact space for clients, audiences, and partners; and room for individual expression, among others.
• Human resource systems that ensure staff have diverse thinking (or learning) styles, giving them a variety of perspectives on single problems.
• Team setups that avoid groupthink and balance the beginner’s mind with experience, freedom with discipline, play with professionalism, and improvisation with planning. Teams embody divergent and convergent thinking, diverse thinking styles, and diversity of skills; and handle conflict.
• High levels of decentralization and functional differentiation and a range of specialized areas within the organization.
• Honed knowledge management systems and processes that constantly bring new ideas, concepts, data, information, and knowledge into the organization.
• Numerous and empowered members of relevant communities and networks of practice.
• Processes and methodologies that identify and share good practice.
• A performance measurement system that measures the innovative pulse of the organization; ensures monitoring and evaluation of inputs, activities, outputs, outcomes, and impacts; and feeds lessons back to the system.
• The instigation of incentives and rewards for innovative individuals and teams.
• Plentiful space for creative thinking and reflective practice, e.g., away-days, brainstorming sessions, peer assists, after-action reviews and retrospects, problem-solving groups, discussion groups and forums.
• Linkages with the marketing function, in ways that involve stakeholders and seek regular feedback.
• Effective dissemination systems.
• Dedication information systems that ensure positive coverage and publicize success.
• Structured intellectual property management systems that identify, protect, value, manage, and audit the organization’s intellectual property.

This is my contribution for the longevity of an innovation culture

Knowledge

Knowledge is undoubtedly the most important factor of innovation. Not so much the academic knowledge, or the one obtained by the recruitment of talents or consultants, but the one the company itself can generate. This knowledge is produced, initially, through the socialization of employees, consultants, customers and suppliers, who build the tacit knowledge. This is a type of knowledge that is not visible to others except those involved, as it happens with the knowledge necessary to play music, or speak a language, which complement themselves well beyond the strictly musical or linguistic skills, respectively. In a second stage, the explicit knowledge, which can be verbally reproduced and translated into projects, publications, communications. In turn, this explicit knowledge gives rise to new tacit knowledge, in a continuous spiral of knowledge production that is difficult to transfer outside established networks.

Projects

The execution of big projects allows the company to mobilize the knowledge and positive emotions of employees in a single goal. Without disregarding the attainment of sectorial objectives, set by management, the company must develop projects involving the largest possible number of areas, geographic locations and employees, also providing the interconnection between the various hierarchical levels and the triangle suppliers - production / research - customers.

Disciplinary differentiation is necessary for the production of knowledge, which lies usually in the areas / departments / services of the company. However, it is by conducting interdisciplinary projects that opportunities are created for the transfer of the knowledge needed to integrate the areas and for the creation of new knowledge. Projects must be generated from objectives defined by management, which give rise to a selection of problems suggested by the project teams, also responsible for the proposed solutions for each problem, i.e., the projects and the respective action plans.

It is the balance between disciplinary differentiation of the segments of the organizational system, and their integration into projects, in order to ensure unity in the company's efforts, that the optimization of results for innovation can best be achieved.

Top management and strategic innovation

Nothing really important and innovative can happen in the company if management is not fully involved. Management’s role is not to innovate but rather to provide the conditions for this to happen, making the fundamental strategic decisions. And more important than knowing if managers have the personality characteristics and leadership styles best suited to innovation, is whether managers are effective in producing satisfaction, cohesion and results, i.e., a resonant leadership, harmonizing the consideration for employees with the necessary structuring of tasks and objectives.

To achieve this, management has to be close to the collaborators, wanting to know their desires, interests and limitations, and developing initiatives that will increase satisfaction and company commitment because, in order to innovate, people need to work harder and better.

Instead of making efforts on how to find managers with favorable styles for innovation, we should understand the conditions that the company requires, in terms of the dynamics of technology and capital, which "does not allow" managers to be of less quality, "forcing" everyone to submit themselves to that dynamic. Thus, the management of a company with a dynamic of continuous innovation, rather than create barriers to innovation proposals, encourages the production of ideas and considers this attitude part of the routine work. In addition, if management requires that ideas are presented almost in the form of a pre-prototype, with feasibility issues and results for the company properly studied, this is not resistance to change, but good management.

Innovation at the operational level

Another decisive factor in the innovation process is the participation of middle management and the "shop floor" in its fundamental function of "taking bottlenecks away" from the functioning of the company's operating processes, including those caused by innovations. What happens is that each innovation project is always experimental at the beginning and, therefore, incomplete. To become fully functional, it needs a number of complementary operations for replacing the lost balance, particularly those that have to do with the internal efficiency in areas such as management control, communication, motivation, supervision and customer relations. This is the work of the operational levels, almost "invisible", but no less important for the implementation of a given innovation. Thus, the innovations introduced, according to the perspective of those who have the task of implementing them, can cause reactions intended to provide some internal stability, which is fundamental to make the necessary changes (the so called "bottlenecks"). This should not be seen as resistance to change but rather as an integral part of the innovation process.

Vindication processes also provided strong reasons for workers to fight for the company's success, if they know they are included in its direct benefits. The existence of representative bodies such as the workers' councils, who negotiate directly with management, helps to create goals for the organizational base, which increase their willingness to work harder and better - the "secret" of innovation. The mix of high quality top management and board of the workers’ council can operate miracles.