Inference for best linear approximations to set identified functions

Arun Chandrasekhar, Victor Chernozhukov, Francesca Molinari and Paul Schrimpf ()
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Paul Schrimpf: Institute for Fiscal Studies and The University of British Columbia

No CWP43/12, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any functions, including ones carrying an index, which can be estimated parametrically or non-parametrically. The identification region of the parameters of the best linear approximation is characterised via its support function, and limit theory is developed for the latter. We prove that the support function approximately converges to a Gaussian process, and validity of the Bayesian bootstrap is established. The paper nests as special cases the canonical examples in the literature: mean regression with interval valued outcome data and interval valued regressor data. Because the bounds may carry an index, the paper covers problems beyond mean regression; the framework is extremely versatile. Applications include quantile and distribution regression with interval valued data, sample selection problems, as well as mean, quantile and distribution treatment effects. Moreover, the framework can account for the availability of instruments. An application is carried out, studying female labor force participation along the lines of Mulligan and Rubinstein (2008).

Keywords: Set identified function; best linear approximation; partial identification; support function; bayesian bootstrap; convex set (search for similar items in EconPapers)
JEL-codes: C13 C31 (search for similar items in EconPapers)
Date: 2012-12-17
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (26)

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Working Paper: Inference for best linear approximations to set identified functions (2012)
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