Fine-grained economic study in dynamic settings often requires specifying many state variables, such as when multiple agents are involved or when a rich description is necessary. Yet this brings the curse of dimensionality that has long posed a major estimation challenge in the dynamic modeling literature. To address this issue, I develop a layered-local-iteration (LLI) method that exploits the layered structure of state spaces to perform within-layer parallel computation on GPUs, achieving speedups by orders of magnitude in solving the Bellman equation. By dramatically reducing computation time, LLI substantially expands the class of dynamic models that can be feasibly estimated in empirical work. I apply LLI to study the innovation dynamics of the Chinese electric-vehicle industry. To capture the competitive mechanisms, e.g., knowledge spillovers and infrastructure free-riding, among multiple heterogeneous firms, a high-dimensional state space is necessary. Counterfactual analysis highlights the importance of incorporating firm heterogeneity in innovation policy design: the welfare-maximizing subsidy scheme is a stage-specific mix of R&D subsidies and public-charging subsidies that steers firms toward investments aligned with their comparative advantages, amplifying knowledge spillovers and infrastructure compatibility.

The growing availability of big data enables firms to predict consumer search outcomes and outside options more accurately than consumers themselves. This paper examines how a firm can utilize such superior information to offer personalized buy-now discounts intended to deter consumer search. However, discounts can also serve as signals of attractive outside options, potentially encouraging rather than discouraging consumer search. We show that, despite the firm’s ability to tailor discounts across a continuum of consumer valuations, the firm-optimal equilibrium features a simple two-tier discount scheme, comprising a uniform positive discount when the consumer outside option is intermediate and no discount when the outside option is low or high. Furthermore, compared to a scenario where the firm lacks superior information, we find that the firm earns lower profits, consumers search more while their welfare remains unchanged, and total welfare declines.

To address range anxiety, the main obstacle to electric vehicle (EV) adoption, policymakers and firms have pursued two primary strategies: R&D aimed at driving range extension, and public charging network expansion. Using data from the Chinese automobile market and patent filings, this paper examines how infrastructure expansion stimulates or discourages subsequent innovation. I first identify range-improving patents using a fine-tuned large language model and quantify patents' novelty and impact through text similarity metrics. Next, drawing on the persistent regional sales reliance of Chinese automakers, I construct a sales-weighted index of charging infrastructure exposure. The study provides empirical evidence showing that the interplay of two opposing effects leads to innovation redirection: On one hand, readily available chargers make long driving ranges less critical, potentially crowding out breakthrough innovations aimed at driving-range improvements due to the substitution effect. On the other hand, a more extensive public charging network enlarges the EV market, thereby raising the marginal returns to innovations directed toward other vehicle improvements, creating a synergy effect. Specifically, easier access to public chargers significantly reduces breakthrough driving-range innovations but significantly stimulates non‑driving-range innovations. Overall, it significantly increases the total number of patents in the automotive sector. Furthermore, I estimate a structural choice model of automobiles that captures the substitution between EV driving range and access to public charging network, and simulate automakers’ expected marginal return to quality improvements under a series of counterfactual infrastructure availability. The results show that expanding charging infrastructure may shrink marginal return to driving range extension but always results in higher marginal return to engine power improvement, reinforcing the empirical evidences earlier.