Using partial least squares in archival accounting research: an application to earnings quality measuring

ABSTRACT

Despite the advantages of Structural Equation Modelling (SEM) over regression models that have contributed to its popularisation in several fields of research in social sciences, it has not been broadly applied in archival accounting research. In this paper, we present a guidance for the application of SEM – and, particularly, the Partial Least Squares (PLS) method – to the (arguably) most recurrent topic on empirical archival accounting research: earnings quality. We highlight several problems that arise in earnings quality measuring, indicating how PLS can help to overcome them. We also run a simulation process whose results show that PLS method outperforms the other approaches even in situations of limited information.

RESUMEN

A pesar de las ventajas de los Modelos de Ecuaciones Estructurales (SEM) respecto a los modelos de regresión que han contribuido a su popularización en diversos campos de invenstigación en Ciencias Sociales, no ha sido ampliamente aplicada en la investigación contable de archivo. En este estudio, presentamos una guía para la aplicación del SEM - y, en particular, el método de Mínimos Cuadrados Parciales (PLS) - al tema (posiblemente) más recurrente en investigación empírica contable de archivo: la calidad del resultado. Destacamos diversos problemas que surgen en la medición de la calidad del resultado, indicando cómo PLS puede ayudar a solventarlos. Asimismo desarrollamos un proceso de simulación cuyos resultados muestran cómo el método PLS supera a otros métodos incluso en situaciones de información limitada.

KEYWORDS:

• Structural equation models (SEM)
• partial least squares (PLS)
• earnings dimensions
• earnings quality concept
• earnings quality construct
• earnings quality measuring

PALABRAS CLAVE:

• Modelos de Ecuaciones Estructurales (SEM)
• Mínimos Cuadrados Parciales (PLS)
• dimensiones de la calidad del resultado
• concepto de calidad del resultado
• constructo de calidad del resultado
• medición de la calidad del resultado

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. In this paper, we will use the terms ‘latent variables’ and ‘constructs’ indistinctly.

2. Some examples of these measures are (the absence of) abnormal accruals, the absence of discontinuities in the cross-sectional distribution of earnings, the predictability or the smoothness of reported earnings, the value relevance of earnings or book values, the degree of accounting conservatism, investors’ reactions to reported earnings, or the opinion of external parties.

3. We define conceptual variables as the representation of ideas or abstract concepts that researchers establish to design the models (Sarstedt et al., 2016).

4. For simplicity, we focus on the specific conceptualisation of earnings quality, not discussing the conceptualisation of the dependent variable.

5. Licerán-Gutiérrez and Cano Rodríguez (2018) document that more than 90% of empirical papers on earnings quality used a measure based on a single proxy (70.8% used just one proxy, 22.7% used several proxies in separate models).

6. The fewer indicators included in the model, however, the lower the reliability of the set of indicators.

7. Given that all the formative indicators influence the same construct, it can be expected some correlation among them, but the model does not assume nor require it (Jarvis et al., 2003).

8. The typical proxies for investor responsiveness are the earnings response coefficient (ERC) and the R² from the earnings-return model (Dechow et al., 2010). Other proxies that could be classified in this category are the value relevance of earnings or book value (Barth et al., 2008; Francis et al., 2004).

9. For instance, Gaio and Raposo (Gaio & Raposo, 2011) used an index that included both accounting-based earnings attributes (formatively related to earnings quality according to our analysis) and market-based earnings attributes (reflectively related to earnings quality according to our analysis).

10. This lack of discussion keeps being present even in those papers that try to measure earnings quality using SEM. For instance, Hinson and Utke (Hinson & Utke, 2018) use a reflective relationship between the earnings quality construct and its empirical measures (earnings volatility, the absolute value of abnormal accruals based on balance, and the absolute value of abnormal accruals based on cash-flow statement) in their SEM model, but without justifying the reasons for expecting such reflective relationship.

11. Dichev and Tang (2009) show that earnings predictability increases with earnings persistence and decreases with earnings variability, and that low-volatility earnings show greater persistence than high-volatility earnings. Additionally, by smoothing earnings, managers make earnings more predictable and with a lower variability (Chaney et al., 2008; Dechow et al., 2010).

12. This criterion states that any latent construct shares more variance with its assigned indicators than with any other latent variable in the structural model (Hair et al., 2011, 2016; Henseler et al., 2015). The measure is indicative of appropriate discriminant validity whenever the AVE of each construct is greater than its highest squared correlation with any other construct (Hair et al., 2011, 2016; Henseler et al., 2015, 2009; Roldán & Sánchez-Franco, 2012).

13. The HTMT ratio is an estimate of what would be the true correlation between two constructs if they were perfectly measured (Hair et al., 2016), and it is considered a more reliable criterion to assess discriminant validity (Nitzl, 2016) than the Fornell-Larcker criterion. The threshold for this criterion depends on whether latent variables are conceptually very similar (values above 0.90 indicate lack of discriminant validity) or, on the contrary, more distinct (values above 0.85 are unacceptable) (Hair et al., 2016; Henseler et al., 2015).

14. It is considered that the indicator represents accurately the construct when its loading exceeds 0.7 (Carmines & Zeller, 1979), although some authors consider that values between 0.40 and 0.70 are acceptable (Chin, 1998; Hair et al., 2011, 2016; Roldán & Sánchez-Franco, 2012). Values below 0.40 show that the indicator is not representing appropriately the latent variable (Hair et al., 2011; Henseler et al., 2009; Roldán & Sánchez-Franco, 2012).

15. It is considered that a given set of indicators show an acceptable degree of internal consistency when this measure exceeds values of 0.60–0.70 in exploratory research, or 0.70–0.90 in more advanced stages of research (Hair et al., 2011, 2016; Henseler et al., 2009; Numally & Bernstein, 1994; Roldán & Sánchez-Franco, 2012). Values below 0.60 indicate that the set of indicators are not representing the same construct (Hair et al., 2016; Henseler et al., 2009).

16. An AVE value higher than 0.5 is considered as acceptable, as the construct would be explaining more than the half of the variance of its indicators (Hair et al., 2011, 2016; Henseler et al., 2009; Roldán & Sánchez-Franco, 2012).

17. These values are consistent with the empirical correlations observed by Dechow et al. (2010) among the different earnings properties.

18. We repeated the simulation process with different values for parameter a (specifically, 1, 0.25 and 0.1). The results (untabulated) were not qualitatively different from those reported.

19. The estimation errors of the factor analysis index, however, get slightly reduced when the number of indicators is reduced.

Additional information

Funding

This work is funded by FPI Acción 16 UJA and the research project UJA/2015/06/04.