This paper presents a framework for estimating non-Walrasian models with many markets based on the virtual price approach in Lee (1986). The paper discusses an open economy multi-market non-Walrasian model with many agents and government production. The modeling of the labor markets is built on the assumption that each combination of worker and firm is a separate micro labor market. The econometric specifcation in the paper assumes log-linear virtual prices. Despite the use of such a simple specification it is apparent that when there are a large number of markets, the computational burden of estimation becomes heavy due to the large number of possible rationing regimes. The model presented in the paper can be viewed as a basis for either doing econometric work within a multi-market representative agent framework or for developing methods for aggregating across micro markets.