Asymptotic inference for non–shift-share recentered instruments

Develop general asymptotic inference results for recentered formula instruments that are not linear shift-share combinations of shocks, applicable both to linear instrumental variables models and to the nonlinear generalized method-of-moments estimation of mixed logit demand using recentered instruments; in addition, adapt existing sufficient conditions for consistency for such instruments to the nonlinear mixed logit demand setting.

Background

The paper develops recentered formula instruments that combine exogenous cost shocks with potentially endogenous product characteristics to estimate demand models. For shift-share versions of these instruments, the authors provide asymptotic results using a many-shocks framework and relate identification and inference to existing shift-share IV theory.

However, for recentered instruments that are not linear shift-share aggregates of shocks, existing theory is limited. Prior work provides sufficient conditions for consistency in linear IV settings, but general asymptotic inference results—covering both linear IV and the nonlinear GMM demand estimation considered here—are not currently available. The authors explicitly note this gap and defer adaptation of linear results to their nonlinear setting to future work.