Beginning in 1986, Shanghai has implemented an interesting car ownership policy, namely an auction of the right to register private cars. In this paper, we propose a structural vector auto-regression (SVAR) approach to characterize the price formation process and to evaluate the performance of the Shanghai auction. We find three key results: (1) the price formation mechanism remained intact when the auction switched from on-site bidding to the two-stage format in 2008; (2) before 2008, short-term price fluctuations could be managed by varying the quota; after 2008, such manipulation ceased to be effective; (3) the number of bidders, or demand, ultimately drove the price in later years, casting doubt on the viability of the new price-controlled procedure that has created more than 250,000 bidders in waiting until April 2016. We also analyze how annual socio-economic variables affect quota, price, and the number of bidders using a simultaneous equations model. Due to data limitations, such an analysis is less conclusive. We argue that the SVAR framework can be improved and applied to other cities in evaluating their car ownership practices.