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Published online by Cambridge University Press:  19 September 2022

Jaedo Choi
University of Michigan
Hyungsik Roger Moon
University of Southern California and Yonsei University
Jin Seo Cho*
Yonsei University
Address correspondence to Jin Seo Cho, School of Economics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea; e-mail:


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.

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

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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).



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