We introduce a model of market shares in aggregate markets beginning with the McFadden multiattribute consumer choice theory and extending to allow for lagged individual choice probabilities and unequally spaced historical data. Our market share model admits the use of Bayesian methods (in addition to traditional maximum likelihood methods) to deal with the problem of chronically short historical time series (particularly prices) in many countries for applications such as energy shares. Two applications are presented. In the first (United States electric power fuel shares), fuel shares are modeled as a function of oil, gas, and coal prices and installed generation capacity. We estimate own and cross elasticity parameters and use Bayesian methods both to address short data series and alternative prior beliefs about the parameters. In the second application, we use G8 industrial sector fuel price data to estimate oil, gas, and coal own and cross price parameters in those economies. Both applications employ Bayesian methods to address short historical time series, particularly in the latter application of fuel price data outside the United States.