Parking is a significant facet of the urban transportation system, with a collective revenue of nearly $30 billion in the United States by the end of 2018. Motivated by the inter-temporal demand and supply imbalance as well as the sub-optimal parking resources utilization in practice, we investigate the structural estimation of the price-occupancy relationship in an urban parking system.In this study, a series of statistical models and variable selection techniques are proposed or implemented which consist of various spatiotemporal variables using the open data set from SFpark as well as API from our industry partner. The parking prices have been updated in response to the change in parking occupancies across a duration of 18 months, which serves as a natural experiment for price-occupancy estimation. A two-step spatiotemporal estimation procedure is adopted to capture the cross-price effects (incentive externalities) and the time effects, wherein variable selection techniques are employed to regulate over-fitting at each estimation step.Our study sheds interesting light on the parking price-occupancy relationship. Firstly, we find that the cross-price elasticity of the streets within a neighborhood can form a significant incentive gradient to induce flexible parking behaviors. Secondly, our results show that the spatial variables play an important role in determining the street occupancy (demand). Also, the drivers tend to avoid the streets with the highest parking rate by considering the neighboring cheaper alternatives. The converse is true sometimes at night or on weekends, as the drivers are relatively insensitive to the upper parking prices therein. Our research is a first step to understand the incentive-driven parking behaviors, which provides the empirical evidence to support parking pricing, operations and eventually infrastructure planning decisions to the policy-makers.