LEXINGTON — Kentucky is still not building nearly enough homes across all incomes, but especially for lower-income people, to bridge the state’s large housing supply gap that’s burdening some Kentuckians with severe housing costs, according to a state housing executive. A chart presented by Wendy Smith with the Kentucky Housing Corporation shows the number of buildings permits in Kentucky for housing. The Kentucky Housing Corporation is a quasi-governmental agency that manages federal and state housing funding. Wendy Smith, the deputy director of housing programs at the Kentucky Housing Corporation, argued state and federal policymakers are not doing nearly enough to address the state’s housing supply gap. Affordable housing advocates and nonprofit builders have previously called for hundreds of millions of dollars to go into the Affordable Housing Trust Fund managed by the housing corporation to help subsidize housing construction.