Best Linear Approximations to Set Identified Functions: With an Application to the Gender Wage Gap

Arun Chandrasekhar, Victor Chernozhukov, Francesca Molinari and Paul Schrimpf

No 25593, NBER Working Papers from National Bureau of Economic Research, Inc

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 carry an index, and to be unknown but parametrically or non-parametrically estimable functions. The identification region of the parameters of the best linear approximation is characterized via its support function, and limit theory is developed for the latter. We prove that the support function can be approximated by a Gaussian process and establish validity of the Bayesian bootstrap for inference. Because the bounds may carry an index, the approach covers many canonical examples in the partial identification literature arising in the presence of interval valued outcome and/or regressor data: not only mean regression, but also quantile and distribution regression, including sample selection problems, as well as mean, quantile, and distribution treatment effects. In addition, the framework can account for the availability of instruments. An application is carried out, studying female labor force participation using data from Mulligan and Rubinstein (2008) and insights from Blundell, Gosling, Ichimura, and Meghir (2007). Our results yield robust evidence of a gender wage gap, both in the 1970s and 1990s, at quantiles of the wage distribution up to the 0.4, while allowing for completely unrestricted selection into the labor force. Under the assumption that the median wage offer of the employed is larger than that of individuals that do not work, the evidence of a gender wage gap extends to quantiles up to the 0.7. When the assumption is further strengthened to require stochastic dominance, the evidence of a gender wage gap extends to all quantiles, and there is some evidence at the 0.8 and higher quantiles that the gender wage gap decreased between the 1970s and 1990s.

JEL-codes: C13 C31 (search for similar items in EconPapers)
Date: 2019-02
New Economics Papers: this item is included in nep-ecm and nep-ore
Note: DEV LS PE TWP
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.nber.org/papers/w25593.pdf (application/pdf)

Related works:
Working Paper: Best linear approximations to set identified functions: with an application to the gender wage gap (2019)
Working Paper: Best linear approximations to set identified functions: with an application to the gender wage gap (2019)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberwo:25593

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/w25593

Access Statistics for this paper

More papers in NBER Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().