Career
He was chairman of the Self-Government Party (Sjálvstýrisflokkurin) until April 2015 and is a former President of the West Nordic Council (2008-2009). He was leader of his party′s parliamentary group 2001-2011 as well as party chairman 2003-2010 and again 2011-2015. In November 2011 Højgaard became Minister of Internal Affairs, in the centre-right ABDH government.
The plan with the private company was skipped, instead the plan is that the tunnel shall be made by and owned by the government.