A weak instrument F -test in linear IV models with multiple endogenous variables

We consider testing for weak instruments in a model with multiple endogenous variables. Unlike Stock and Yogo (2005), who considered a weak instruments problem where the rank of the matrix of reduced form parameters is near zero, here we consider a weak instruments problem of a near rank reduction of one in the matrix of reduced form parameters. For example, in a two-variable model, we consider weak instrument asymptotics of the form [Formula: see text] where [Formula: see text] and [Formula: see text] are the parameters in the two reduced-form equations, [Formula: see text] is a vector of constants and [Formula: see text] is the sample size. We investigate the use of a conditional first-stage [Formula: see…

• MR
  Medical Research Council

  Awards: MC_UU_12013, MC_UU_12013/9
• EA
  Economic and Social Research Council

  Awards: ES/H005331/1, RES-343-28-0001