---
title: "Testing for Contemporaneous Exogeneity in Linear Time-Series Models"
authors: "Prosper Dovonon; Nikolay Gospodinov"
source: "Federal Reserve Bank of Atlanta (Working Paper 2026-14)"
source_url: "https://www.atlantafed.org/research-and-data/publications/working-papers/2026/09/23/14-testing-for-contemporaneous-exogeneity-in-linear-time-series-models"
paper_id: "Atlanta Fed WP 2026-14"
harvested: 2026-09-28
year: 2026
keywords: [contemporaneous exogeneity, specification test, linear time series, Phillips curve, labor tightness, economic slack, moment conditions, lead-lag validity]
pdf_url: "https://www.atlantafed.org/-/media/Project/Atlanta/FRBA/Documents/research-and-data/publications/working-papers/2026/09/23/14-testing-for-contemporaneous-exogeneity-in-linear-time-series-models.pdf"
---
## 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. DOI: 10.29338/wp2026-14

## Why it's in the StratMac library

- **A falsifiable test for the assumption SM's lead-lag work rests on.** The recession pipeline aligns regressors strictly past-known (t−L, never t+L) and reports lead correlations; that design excludes *look-ahead* but does not establish *contemporaneous exogeneity* of the regressors. This paper supplies a test for exactly that misspecification — and, importantly, one that needs no external instruments, so it is applicable to a FRED-only series panel.
- **Applied to the same objects SM models.** The empirical application is to measures of labor tightness and economic slack in two Phillips-curve versions — the labour-market and inflation relationships behind the `labor` and `money` sections.
- **Directly usable implementation, not theory only.** The test reduces to a standard-normal statistic, so it can be run as a diagnostic panel on candidate regressors before they enter a composite — a concrete robustness annex for the forward-horizon paper's methodology section.
- Companion to the existing macro-signal-detection literature in this library (filter horse races, dimensionality, real-time revision stability).