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The Effects of Scale Differences on Inferences in Accounting Research: Coefficient Estimates, Tests of Incremental Association, and Relative Value Relevance

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  • Lo, Kin

Abstract

Firms' financial data vary considerably with the size of their operations. Such scale differences potentially confound several types of inferences, of which this paper analyzes three. This paper evaluates two potential solutions to these inference problems suggested by theory: (i) deflating the data by a proxy for scale; and (ii) including a scale proxy as an independent variable. First, simulations show that deflating the data more effectively mitigates coefficient bias than including that proxy as an independent variable. Reconciling this result with the opposing conclusion of Barth and Kallapur (1996, Contemporary Accounting Research) reveals that the prior results depend on assumptions that are economically and statistically unreasonable. Second, the deflation approach results in more accurate tests of incremental association in terms of mean squared error. Third, deflating by a scale proxy results in well-specified tests of relative association using Vuong's (1989) Z-statistic for non-nested models whereas including the scale proxy as an independent variable results in overstated significance. Given the additional advantages of deflation with respect to heteroscedasticity and the coefficient of determination (R2) demonstrated in prior studies, researchers should generally deflate their models when scale differences exist in the data.

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  • Lo, Kin, 2004. "The Effects of Scale Differences on Inferences in Accounting Research: Coefficient Estimates, Tests of Incremental Association, and Relative Value Relevance," Working papers 555684, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    • Handle: RePEc:mit:sloanp:5420
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    File URL: http://hdl.handle.net/1721.1/5420
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    1. Joy Begley & Gerald A. Feltham, 2002. "The Relation between Market Values, Earnings Forecasts, and Reported Earnings," Contemporary Accounting Research, John Wiley & Sons, vol. 19(1), pages 1-48, March.
    2. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    3. Christie, Andrew A., 1987. "On cross-sectional analysis in accounting research," Journal of Accounting and Economics, Elsevier, vol. 9(3), pages 231-258, December.
    4. Peter D. Easton & Gregory A. Sommers, 2003. "Scale and the Scale Effect in Market-based Accounting Research," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(1-2), pages 25-56.
    5. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    6. Easton, PD, 1998. "Discussion of revalued financial, tangible, and intangible assets: Association with share prices and non-market-based value estimates," Journal of Accounting Research, Wiley Blackwell, vol. 36, pages 235-247.
    7. Mary E. Barth & Sanjay Kallapur, 1996. "The Effects of Cross†Sectional Scale Differences on Regression Results in Empirical Accounting Research," Contemporary Accounting Research, John Wiley & Sons, vol. 13(2), pages 527-567, September.
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    Cited by:

    1. Elnathan, Dan & Gavious, Ilanit & Hauser, Shmuel, 2010. "An analysis of private versus public firm valuations and the contribution of financial experts," The International Journal of Accounting, Elsevier, vol. 45(4), pages 387-412, December.
    2. Misund, Bård, 2015. "Vertical Integration and Value Relevance: Empirical Evidence from Oil and Gas Producers," UiS Working Papers in Economics and Finance 2015/14, University of Stavanger.
    3. Aharon, David Y. & Gavious, Ilanit & Yosef, Rami, 2010. "Stock market bubble effects on mergers and acquisitions," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(4), pages 456-470, November.
    4. Misund, Bård & Asche, Frank & Osmundsen, Petter, 2008. "Industry upheaval and valuation: Empirical evidence from the international oil and gas industry," The International Journal of Accounting, Elsevier, vol. 43(4), pages 398-424, December.
    5. Shu, Yan & Broadstock, David C. & Xu, Bing, 2013. "The heterogeneous impact of macroeconomic information on firms' earnings forecasts," The British Accounting Review, Elsevier, vol. 45(4), pages 311-325.
    6. Jihene Chedlia Soussi, 2012. "Impact of Voluntary Disclosure on the Relevance of Accounting Information," Journal of Education and Vocational Research, AMH International, vol. 3(5), pages 138-153.

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