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This study provides an econometric methodology to test a linear structural relationship among economic variables. We propose the so-called distance-difference (DD) test and show that it has omnibus power against arbitrary nonlinear structural relationships. If the DD-test rejects the linear model hypothesis, a sequential testing procedure assisted by the DD-test can consistently estimate the degree of a polynomial function that arbitrarily approximates the nonlinear structural equation. Using extensive Monte Carlo simulations, we confirm the DD-test's finite sample properties and compare its performance with the sequential testing procedure assisted by the J-test and moment selection criteria. Finally, through investigation, we empirically illustrate the relationship between the value-added and its production factors using firm-level data from the United States. We demonstrate that the production function has exhibited a factor-biased technological change instead of Hicks-neutral technology presumed by the Cobb-Douglas production function.

Original languageEnglish
JournalEconometric Theory
Publication statusAccepted/In press - 2022

Bibliographical note

Funding Information:
The Editor (Peter Phillips), the Co-Editor (Patrik Guggenberger), and two anonymous referees provided very helpful comments for which we are most grateful. The authors are also benefited from discussions with Juwon Seo. Cho further acknowledges with gratitude the research grant provided by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2018S1A5A2A01035256).

Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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