Data governance is a decision-making process focused on authority building to specify decision rights and accountability that encourage desired behaviors regarding data use, security, integrity, and availability. The emergence of big data technologies to design public policy and deliver public services requires governments to design data policy and governance. This paper analyzes the dynamics of data governance design in the Brazilian Federal Government, based on institutional analysis and policy development. The paper reports a series of interviews with Brazilian Federal Government policymakers to frame the data policy design dynamics. The paper concludes that the policy design dynamics to data governance are path dependent and shape actions situations that reinforces previous institutions. In the case of the Brazilian Federal Government, the institutional framework is ambiguous, creating situations of conflict and ineffectiveness in the design of the data policy.