Bounding Endogenous Parameters with Generalized Instrumental Moment Inequalities
نویسنده
چکیده
The main approach to handle endogeneity in econometrics has been instrumental variable estimator (IVE). An instrument m requires E(mu) = 0 where u is an error term, and if E(mu) 6= 0 is likely, then m gets discarded. But when E(mu) 6= 0, fairly often one has a good idea on the sign of E(mu), and it will be a waste to toss out the sign information. This paper shows how to make use of the information E(mu) < 0 to obtain an one-sided bound, say (−∞, αL), on the parameter α of interest, calling the variable m a ‘generalized instrumental variable (GIV)’. If the bound excludes 0, then H0 : α ≥ 0 gets rejected. If there are two GIV’s m1 and m2 with E(m1u) < 0 and E(m2u) ≶ 0, then a two-sided bound such as (αL, αU ) or a better one-sided bound {−∞,min(αL1, αL2)} can be obtained. The improvement can result not only from the collection of two “marginal” bounds, but also from the “joint” relations between m1 and m2. The main attraction of our approach lies in its simplicity: whereas most studies in the ‘parameter-bounding’ econometric literature require nonparametric methods, our proposal needs only LSE and a bootstrap. A real data application is done to Korean household data with at least two children. With E(mju) 6= 0 allowed for a GIV mj , so long as mj affects the endogenous regressor of interest (‘inclusion restriction’), mj can be used fruitfully so that literally “nothing gets wasted”.
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