Supplement to “improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients

IN THIS SECTION, we discuss the implementation details for MPEC and NFP applied to the BLP demand estimation problem. For a gradient-based solver to perform effectively, researchers need to provide the first-order and secondorder closed-form derivatives along with their respective sparsity patterns. Without this additional information, both MPEC and NFP may fail to converge or may require considerably more iterations (and hence more computation time) to find a solution to the optimization problem. We provide derivatives and sparsity patterns in our publicly available MATLAB code. Below, we provide formulas for the derivatives and sparsity patterns. We also use specific numerical examples to explore the implications of derivatives and sparsity patterns for the performance of the optimization algorithms.