Title: Testing Inequalities Linear in Nuisance Parameters (with Gregory Cox and Yuya Shimizu) at the econometrics seminar.

 Abstract- This paper proposes a new test for inequalities that are linear in possibly partially

identified nuisance parameters, called the generalized conditional chi-squared (GCC)

test. It extends the subvector conditional chi-squared (sCC) test in Cox and Shi (2023,

CS23) to a setting where the nuisance parameter is pre-multiplied by an unknown

and estimable matrix of coefficients. Properly accounting for the estimation noise in

this matrix while maintaining the simplicity of the sCC test is the main innovation

of this paper. [How? New variance formula? Rank condition?] As such, the paper

provides a simple solution to a broad set of problems including subvector inference for

models represented by linear programs, nonparametric instrumental variable models

with discrete regressor and instruments, and linear unconditional moment inequality

models. We also derive a simplified formula for computing the critical value that makes

the computation of the GCC test elementary.