Control functions in nonseparable simultaneous equations models

Published on 5 July 2014

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has thus far been unknown. In this paper, we define a new property of functions called control function separability and show it provides a complete characterization of the structural systems of simultaneous equations in which the control function procedure is valid.

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has thus far been unknown. In this paper, we define a new property of functions called control function separability and show it provides a complete characterization of the structural systems of simultaneous equations in which the control function procedure is valid.

    Authors

    Richard Blundell
    Richard Blundell

    CPP Co-Director

    Richard is Co-Director of the Centre for the Microeconomic Analysis of Public Policy (CPP) and Senior Research Fellow at IFS.

    Resource details

    DOI
    10.3982/QE281
    Publisher
    Wiley

    Suggested citation

    Blundell, R and Matzkin, R. (2014). Control functions in nonseparable simultaneous equations models. London: Wiley.

    More from IFS

    Understand this issue

    State Pension claim form

    Where next for the state pension?

    presentation
    IFS researchers presented findings from a major new report on the future of the state pension in the UK, published as part of the Pensions Review.

    13 December 2023

    Nice houses with city in the background

    Social mobility and wealth

    presentation

    IFS researchers shared findings from ESRC-funded research on social mobility and its drivers.

    12 December 2023

    Policy analysis

    Academic research

    Working paper cover

    Firm quality and health maintenance

    working paper

    We estimate the impact of firm quality – primarily measured by firm productivity – on the health maintenance of employees.

    18 December 2024