Bounds testing approaches to the analysis of level relationships
Abstract
Abstract This paper develops a new approach to the problem of testing the existence of a level relationship between a dependent variable and a set of regressors, when it is not known with certainty whether the underlying regressors are trend‐ or first‐difference stationary. The proposed tests are based on standard F ‐ and t ‐statistics used to test the significance of the lagged levels of the variables in a univariate equilibrium correction mechanism. The asymptotic distributions of these statistics are non‐standard under the null hypothesis that there exists no level relationship, irrespective of whether the regressors are I (0) or I (1). Two sets of asymptotic critical values are provided: one when all regressors are purely I (1) and the other if they are all purely I (0). These two sets of critical values provide a band covering all possible classifications of the regressors into purely I (0), purely I (1) or mutually cointegrated. Accordingly, various bounds testing procedures are proposed. It is shown that the proposed tests are consistent, and their asymptotic distribution under the null and suitably defined local alternatives are derived. The empirical relevance of the bounds procedures is demonstrated by a re‐examination of the earnings equation included in the UK Treasury macroeconometric model. Copyright © 2001 John Wiley & Sons, Ltd.
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The ARDL model is particularly suitable when variables are a mix of I(0) and I(1) but none are I(2), ensuring robustness and consistency of long-run and short-run estimations in small samples.
“As noted by Pesaran et al. (2001), the ARDL model is particularly suitable when variables are a mix of I(0) and I(1) but none are I(2), ensuring the robustness and consistency of long-run and short-run estimations in small samples.”
From The Impact of the Fed’s Monetary Policy on Cryptocurrencies: Novel Policy Implications for Central Banks (2025) · cites this paper as Pesaran et al. (2001)
Pretesting variables for unit roots before ARDL estimation is essential.
“Pretesting variables before proceeding with ARDL estimation is essential.”
From Public debt and inflation nexus in Nigeria: An ARDL bounds test approach (2021) · cites this paper as Pesaran et al. (2001)
The presence of an I(2) variable would render the use of an ARDL technique inappropriate because the critical values of the F-statistics computed by Pesaran et al. (2001) are based on the assumption that the variables are either I(0) or I(1).
“The presence of an I(2) variable would render the use of an ARDL technique inappropriate because the critical values of the F-statistics computed by Pesaran et al. (2001) are based on the assumption that the variables are either I(0) or I(1) (see also Odhiambo, 2009).”
From Public debt and inflation nexus in Nigeria: An ARDL bounds test approach (2021) · cites this paper as Pesaran et al. (2001)
A bounds test for cointegration was used to verify the presence of a long-run equilibrium relationship between GDP and airline demand variables.
“Following the lag selection, a bounds test for cointegration was used to verify the presence of a longrun equilibrium relationship between GDP and airline demand variables, accounting for both the I(0) and I(1) variables (Pesaran et al., 2001).”
From Passenger and Freight Demand under Macroeconomic Volatility: Evidence from South Korea and The United States (2026) · cites this paper as Pesaran et al., 2001
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- Authors
- Pesaran, M. H., Shin, Y., & Smith, R. J.
- Affiliations
- University of Cambridge (GB)
- University of Edinburgh (GB)
- University of Bristol (GB)
- Corresponding author
- Pesaran, M. Hashem
- Venue
- Journal of Applied Econometrics
- Publisher
- Wiley
- Published
- 2001-05
- Volume
- 16
- Issue
- 3
- Pages
- 289-326
- ISSN
- 0883-7252 (ISSN-L)
- 1099-1255
- OpenAlex
- W1966910378
- Cited by
- 20,385
- References
- 44
- Citations by year
- 2026: 1722 · 2025: 1743 · 2024: 1890 · 2023: 2335 · 2022: 2077 · 2021: 1924 · 2020: 1602 · 2019: 1183 · 2018: 882 · 2017: 796 · 2016: 634 · 2015: 601 · 2014: 564 · 2013: 484 · 2012: 391
- FWCI
- 84.06
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Applied Econometrics (publishedVersion)
- Topics
- Social Sciences › Economics, Econometrics and Finance › General Economics, Econometrics and Finance › Monetary Policy and Economic Impact
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Diverse Scientific and Economic Studies
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Keywords
- bounds testing, cointegration, asymptotic critical values, local alternatives, earnings equations
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