Most leaders would say they influence their culture by participating in the formulation of the culture program in a workshop, and promoting the output to their team, conducting appraisals that have values in the content and giving out annual awards for people who are ambassadors of the values. When recruiting they wheel out the culture and values statements to ensure fit and support an annual engagement survey and action plans. These actions however are not the actions that shape a culture.
What your people are actually being influenced by and judging you by is your decision making, how you treat every team member not just managers, the energy you create in the company and how open, authentic and trustworthy you are.
Decision Making: EVERY decision you make is being judged for consistency, fairness and business impact. Do you provide a rationale for your decision making or is it because I said so? Are you more worried about politics and your own career survival? Your true intentions and motivation behind your decisions are more transparent than you think.
How You Treat Every Team Member: Do you manage up well but not have the time of day for the individual? Are you approachable and authentic? Do you manage your emotions effectively and show respect and value all team members?
The Energy You Create: Do you inspire and therefore create an inspirational work environment? Do you encourage risk taking and allow mistakes or do you tightly control? Do you encourage solution and innovation thinking? Do you give recognition and encouragement? Do you mentor and coach? Are you accessible? How do you walk around the office, do you smile?
How Open, Authentic and Trustworthy You Are: Your people have a very attuned meter to gauge your authenticity and how believable you are. Leaders that are authentic and trustworthy people will willingly follow them through change even when making difficult decisions. Are you human or a corporate cut out?
When you don't focus on these areas the impact on culture destroys any "culture and values program" you are implementing. When every member of the executive team focuses on these areas the positive impact on culture can be monumental!