Testing for Contemporaneous Exogeneity in Linear Time-Series Models
September 23, 2026
Summary
Proposing a new test for contemporaneous exogeneity of regressors in linear time-series models, the authors apply this exogeneity test to measures of labor tightness or economic slack in two versions of the Phillips curve.
View PaperWorking Paper 2026-14
Abstract: We propose a test for contemporaneous exogeneity of regressors in linear time-series models. The test takes the form of a specification test with an expanding number of moment conditions. The test does not require external instruments and is based only on information contained in the regressors. Under the null of exogeneity, the test is characterized by a standard normal limit when the moment conditions are expanding at a particular rate relative to the sample size. We establish the consistency of the test under the alternative hypothesis when testing for exogeneity of the full set as well as a subset of regressors. We apply the proposed exogeneity test to measures of labor tightness or economic slack in two versions of the Phillips curve.
JEL classification: C12, C22, C26, E24, E31
Key words: contemporaneous exogeneity, conditional restrictions, expanding number of moment conditions, specification test, linear time series models, Phillips curve
https://doi.org/10.29338/wp2026-14
The authors thank Marine Carrasco, James MacKinnon, Ulrich Müller, Benoit Perron and participants at the 2025 meeting of the Canadian Econometric Study Group (Ottawa), the 2025 RESA meeting of ENSEA (Abidjan, Côte d'Ivoire), and the 2026 annual conference of the International Association for Applied Econometrics (Carcavelos, Portugal) for very helpful comments and suggestions. The first author acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC). The views expressed here are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.
Prosper Dovonon (corresponding author) is in the Economics Department, Concordia University, 1455 de Maisonneuve Blvd. West, H 1155, Montreal, Quebec, Canada, H3G 1M8. Nikolay Gospodinov is in the Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street NE, Atlanta, GA 30309-4470.
Federal Reserve Bank of Atlanta working papers, including revised versions, are available on the Atlanta Fed's website at www.atlantafed.org. Click "Publications" and then "Working Papers." To receive e-mail notifications about new papers, go to subscribe.