The housing_adjustment project implements my 2013 paper The Effects of Housing Adjustment Costs on Consumption Dynamics. That working paper is available on the Office of Financial Research's Staff Discussion Paper website (link).
The code is all in Matlab . The basic approach is value function iteration. Due to non-linearity in the optimal policy function and the desire for a precisely estimated solution, a value function iteration would be too slow. I make use of three enhancements to improve performance. First, I designed to run in parallel and scale well to a large number of nodes. Second, it makes use of dynamic grid points and Howard's improvement algorithm which are value function iteration specific performance enhancement techniques . Third, I replaced Matlab code with C code in the most performance intensive part of the code. Enhancements two and three improve performance 20-50 times and enhancement one scales roughly linearly in the number of nodes.