This paper establishes a nonparametric local rank test, a data visualization method, anda reverse modeling strategy to guide model specification for high-dimensional demand systems.The test is applied to the China Living Standards Survey data and indicates local rank up to two.The data visualization method further suggests that the consumers’ preference can be representedby the PIGLOG cost function. The nonparametric budget share Engel curves, however, reject thepopular rank-two AIDS and its preassigned PIGLOG cost function. To obtain a model consistentwith both the data and demand theory, I propose the reverse modeling strategy, which estimatesthe response of budget shares to prices nonparametrically and then recovers the underlyingPIGLOG cost function.