Generalized Nonlinear Difference-in-Difference-in-Differences

25 Pages Posted: 28 Jun 2019

See all articles by Adam Glynn

Adam Glynn

Emory University

Nahomi Ichino

University of Michigan at Ann Arbor

Date Written: June 1, 2019


Difference-in-difference-in-differences (DiDiD) allow for the correction of unmeasured con-founding and function as a robustness check for difference-in-differences (DiD) techniques. However, this technique is not scale invariant and requires that the outcome variable be measured on units for which the treatment could have had no effect in either the pretreatment or post-treatment periods. Athey and Imbens (2006) provides a scale invariant, nonlinear DiD approach known as Changes-in-Changes (CiC). Sofer et al. (2016) extends CiC by showing that pre-treatment outcome measures are a special case of placebo (negative) outcomes and proposes a generalization of CiC called Negative Outcome Control (NOC). We develop a generalized nonlinear DiDiD approach we call NOCNOC that can be used either in the traditional DiDiD setting or when a placebo outcome is available in the pre and post-treatment data. We show that NOCNOC can correct for bias in Di-DiD, CiC, and NOC. We apply this method to a study of whether exposure to candidate debates affected Nepalese citizens' sense of political efficacy.

Suggested Citation

Glynn, Adam and Ichino, Nahomi, Generalized Nonlinear Difference-in-Difference-in-Differences (June 1, 2019). V-Dem Working Paper 2019:90, Available at SSRN: or

Adam Glynn (Contact Author)

Emory University ( email )

201 Dowman Drive
Atlanta, GA 30322
United States

Nahomi Ichino

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics