Housing in developing countries is often inadequate due to overcrowding, lack of suitable shelter, lack of sanitation and exposure to natural hazards. The United Nations classifies these conditions into two types of deficit: quantitative and qualitative. Strategies for eliminating housing deficits need to consider the dynamics of the total dwelling stock in order to balance this objective with other goals, such as employment in the construction sector, costs, and environmental impacts. Existing dwelling stock models were developed mainly for developed countries and are not suitable to address housing deficits. Here we use a case study for Colombia’s housing stock to propose a dynamic stock model that incorporates deficit. We analyze the evolution of the stock under twelve scenarios combining three projections for household growth and four trajectories for eliminating deficit. The model is calibrated using census data, UN population projections, and own appraisals of household size, based on historical trends. Our results show that closing all deficits by 2030 would require upgrading 2.8 to 3.3 million existing dwellings and building 3.6 to 6.3 million new dwellings, depending on demographics. This represents an increase of 97–155% in construction activity. Conversely, if deficit stays at the current 31% level, 5.1 to 7.9 million households would be in deficit by 2030.