There have been relatively few attempts to construct local housing market models in the United Kingdom - particularly models with an explicit treatment of land supply. In this paper we report the results of a pilot study designed to test the practicability of estimating a system of equations which describe housing market dynamics at the local level. Former district council areas in Central Scotland are used as a proxy for local housing markets within a region, thereby providing a panel dataset. A simple supply-demand system with separate equations for inward and outward household migration is modelled using two-stage least squares. The empirical results are varied, with some equations and coefficients performing more closely in line with prior expectations than others. House price levels are explained largely with reference to household income, socioeconomic status, and past levels of house price growth. Higher price levels and higher deprivation diminish inward migration. There are also suggestions in the results that higher rates of new-build supply partly cause higher inward migration. The rate of outward migration increases with ethnicity and wealth and decreases with deprivation. The empirical performance of the new-build supply equation is poor although the results do yield some interesting insights. House building output generally decreases as the proportion of 'small' sites in the land supply increases. There is also evidence that house building output decreases as land supply in neighbouring areas increases. We conclude the paper by outlining further directions for modelling prices, supply, and migration at local housing market level. In particular, the case is made for further work involving the collection of wider and longer panel datasets and for extending the pilot study work beyond Scotland.