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

62 Pages Posted: 26 Feb 2019

See all articles by Arun G. Chandrasekhar

Arun G. Chandrasekhar

Stanford University - Department of Economics

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics; New Economic School

Francesca Molinari

Cornell University - Department of Economics

Paul Schrimpf

University of British Columbia (UBC) - Vancouver School of Economics

Date Written: February 2019

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.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Suggested Citation

Chandrasekhar, Arun G. and Chernozhukov, Victor and Molinari, Francesca and Schrimpf, Paul, Best Linear Approximations to Set Identified Functions: With an Application to the Gender Wage Gap (February 2019). NBER Working Paper No. w25593. Available at SSRN: https://ssrn.com/abstract=3341253

Arun G. Chandrasekhar (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-262f
Cambridge, MA 02142
United States
617-253-4767 (Phone)
617-253-1330 (Fax)

HOME PAGE: http://www.mit.edu/~vchern/

New Economic School

100A Novaya Street
Moscow, Skolkovo 143026
Russia

Francesca Molinari

Cornell University - Department of Economics ( email )

414 Uris Hall
Ithaca, NY 14853-7601
United States
607-255-6367 (Phone)
607-255-2818 (Fax)

HOME PAGE: http://www.arts.cornell.edu/econ/fmolinari/

Paul Schrimpf

University of British Columbia (UBC) - Vancouver School of Economics ( email )

997-1873 East Mall
Vancouver, British Columbia V6T 1Z1
Canada

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
1
Abstract Views
81
PlumX Metrics