A simultaneous equation model for uneven data: theory and application

We introduce a new modified nonlinear simultaneous equation model to handle uneven data and proves the large-sample properties (the consistency and the asymptotic normality) of the maximum likelihood estimators (MLE) in this modified model. These results make it possible to simulate the market interactions and equilibrium outcomes based on uneven data. The large-sample properties ensure the reasonable of the results of simulation theoretically. When the framework is applied to the U.S. automobile market in which most data are uneven data, the demand and price parameters for models are obtained. Then the model can simulate the market share distribution and evolution of price when a decision is applied and help the manufacturers find the best decision.