Choosing your instruments without ordering: two stage thresholding estimation

Abstract

Donald and Newey (2001) has proposed a data-driven procedure to choose the instruments used in a two stage procedure or in LIML, which heavily assumes that a preference order is available for the instruments. Although such a condition is reasonable in series expansion methods for the higher order member of the basis since the Fourier coefficients of bona fide function go 0 with the order, it is far more questionable for low order ones. When the instruments are not driven by nonparametric expansions but are economic variables as in most applications, this assumption may become inappropriate. Hence Bai and Ng (2009), Caner and Zhang (2010), Carrasco (2008), Kuersteiner and Okui (2009) have proposed various methods to relax the ordered instrument assumption. In this paper we show with a real data example that the order of the instrument can make a strong impact for IV estimation (2SLS, B2SLS or FIML) for the data-driven choice of Donald and Newey (2001). We propose instead a threshold choice of the instruments which does not use any ordering assumption. The proposed estimator is shown to be first order efficient and its second order rate matches Donald and Newey (2001) up to a logarithmic term. A simulation experiment completes our theoretical reults.