CV

As electricity grids decarbonize, fossil-fuelled generators that supply stability as a by-product of energy are pushed out of merit, forcing operators to source it from costly network equipment or by running those generators out of merit anyway. While there is substantial financial outlay to acquire stability from alternative sources in grids across the world, there is little understanding of the economic trade-off of these alternatives. I study South Australia, among the world’s fastest-decarbonizing grids. Estimating gas-generator costs from a dynamic entry game from Ciliberto, et al (2021), I re-solve the market with and without the need for stability. The economic cost of stability is A$19.2 million per year, approximately 1.7% of energy revenues. The state’s A$180 million synchronous condensers saved at most A$3.0 million per year, breaking even only at a negative discount rate. These results provide insight on a cost-effective way to support the decarbonization of electricity grids.

Maximum likelihood estimation of dynamic discrete choice models in the tradition of Rust (1987) requires solving a nonconvex program, and consistency and asymptotic normality hold only at the global maximizer, which no existing method guarantees. For models with linear-in-parameters payoffs and fixed shock-distribution parameters, we modify the MPEC of Su et al (2012) by relaxing the equality that defines the ex-ante value function and penalizing the slack. The modified program is globally convex for logit and binary probit, the most common distributions in the literature. With probability approaching one the relaxation is exact, so every maximizer is a global maximizer of the original MPEC and converges to the unique population maximum. A simple sufficient condition, positive Lagrange multipliers on the relaxed constraint, certifies exactness ex post at any candidate solution for any estimation method. We show that the relaxed program can be expressed as a convex conic program when the shock distribution is T1EV. We extend the relaxed model to incorporate k-step updating for efficiency, and to discrete unobserved heterogeneity. In Monte Carlo experiments we certify global optimality in over 99.5% of samples at the largest sample sizes.