1 Introduction

Intellectual capital (IC) is an important topic in management and governance studies. The continuous attention to IC lies in the growing awareness that intangible resources play a central role in the value creation process. The accurate management of IC critically contributes to a firm’s wealth (Zambon et al. 2019). Consequently, measuring and reporting IC constitutes a strategic challenge for firms. Although prior studies identify various models to measure IC (e.g., Stewart 1997; Lev 2001, 2003; Corrado et al. 2004), managerial literature highlights a critical lack of contributions validating or falsifying these models (Pucci et al. 2015). One of the most frequently used measures of IC is Pulic’s (2000) Value Added Intellectual Coefficient (VAIC) (Dumay 2014; Pedro et al. 2018). This paper adds to the debate related to IC measurement by providing a validation of the VAIC. Theoretical and empirical results show that the VAIC depends largely on exogenous technological factors that are not usually associated with IC. The study also provides potential avenues to overcome the limitations of the VAIC and to assist researchers in the more careful use of the VAIC to measure IC. Finally, theoretical and empirical results are discussed in light of the alternative approaches to measuring and reporting IC proposed in recent literature.

IC and intangible assets have been studied in the literature on marketing and management (Bontis 1999; Hilmola et al. 2009), organization (Knott et al. 2003), talent management (Sparrow et al. 2014; McCracken et al. 2018), and finance and accounting (Aboody and Lev 2000; Sullivan and Sullivan 2000; Basu and Waymire 2008). In governance studies, prior literature highlights the importance of corporate governance for managing and developing IC (Zambon et al. 2019). Governance mechanisms should be aligned to IC and human capital in particular to contribute to future value creation (Lajili 2015). Directors’ human capital positively influences firm performance (Volontè and Gantenbein 2016), board turnover after an incident of fraud (D’Onza and Rigolini 2017), and compensation after IPO (Williams et al. 2018). The level of human capital can also positively influence internationalization (Cerrato and Piva 2012). Finally, relational capital represented by heterogeneous relational ties among the board of directors has a strong impact on a firm’s performance (Rossoni et al. 2018).

Among all intangible assets, IC is typically considered strategic because it relates to human resources, customer relationships, customer loyalty, etc. (Lev 2005; Pucci et al. 2015). These assets are fundamental both in the internal managerial focus on value creation processes and the external focus on disclosure and reporting on value creation (Badia et al. 2019; Brosnan et al. 2019). This holds true not only in the private sector but also in the public sector, where some universities adopt performance management systems, including IC management, as a criterion for evaluating their managers (Veltri and Puntillo 2019). Similarly, relational capital fosters collaboration among officers in different ministries as a leading indicator of collaborative governance (Ramadass et al. 2018).

Because IC significantly contributes to value creation, its measurement becomes a primary managerial objective to assess the efficient use and creation of IC (Laing et al. 2010). Badia et al. (2019, p. 299) note that “several attempts have been made to develop measurement and reporting systems for this relevant source of value, but managerial literature has highlighted the limits and difficulties of some of those endeavors”. Accounting research tends to consider IC as a part of intangible assets, thus emphasizing its financial dimension and the need for a reliable measurement and contribution to future economic benefits (Skinner 2008a, b; Guthrie et al. 2012). Conversely, the managerial literature is interested in understanding how IC contributes to value creation (Johanson et al. 2001; Mouritsen et al. 2001). A more recent approach suggests that IC narratives are strongly relevant, in addition to IC numbers. IC numbers, discourse and disclosure, business models, and financial statements represent a corpus that contributes to the dissemination of the firm’s approach to value creation (Mouritsen and Roslender 2009; Nielsen and Roslender 2015). While IC numbers cannot stand alone (Gowthrope 2009), IC measurement remains a fundamental input to internal managerial decision making (Brosnan et al. 2019) and external firm assessment (Badia et al. 2019).

The VAIC model for measuring IC was initially developed by Pulic (2000) and has rapidly become extremely popular in academic research (Dumay 2014; Pedro et al. 2018). Prior literature employing the VAIC focuses on IC performance in the banking sector (Mavridis 2004; Goh 2005; Kamath 2007; Alhassan and Asare 2016), the relationship between IC and market value (Chen et al. 2005), the association between IC and financial performance (Sharabati et al. 2010; Komnenic and Pokrajčić 2012), and the relationship between organizational capital and cost stickiness (Mohammadi and Taherkhani 2017). One reason prompting many researchers to select the VAIC as a proxy for IC is that the VAIC intends to measure the capacity of a firm to transform its stock of IC into value added (Pulic 2008; Iazzolino and Laise 2013). Additionally, the VAIC measures IC by relying on accounting numbers, which provides researchers with an easy and ready-to-use proxy.

Despite these undeniable advantages, prior studies challenge the validity of the VAIC as a measure of IC. For example, Ståhle et al. (2011) argue that the VAIC strongly depends on labor and physical capital investments and thus constitutes a poor measure of IC. In an attempt to reconcile the debate around the validity of the VAIC, Iazzolino and Laise (2013) suggest that the VAIC is more of a multidimensional measure rather than a direct proxy for IC. While prior literature establishes the limitations of the VAIC as a measure of IC, a systematic theoretical and empirical validation is missing. Consequently, researchers and professionals are left with no guidance regarding the use of the VAIC due to the lack of papers suggesting potential solutions to overcome its inherent limitations. This paper fills this gap in four steps.

First, this study reflects on the critical decomposition of the VAIC provided in Ståhle et al. (2011). By assuming a perfectly competitive setting in which profit is equal to zero, this study theoretically demonstrates that the VAIC is a function of labor share, physical capital share, and interest rate. Moreover, the relationship between the VAIC, the labor share, and the physical capital share is nonlinear. These theoretical results imply that the VAIC is not directly related to IC when markets are perfectly competitive. Consequently, they contribute and advance prior knowledge on the critical decomposition of the VAIC.

Second, this study extends the validity of theoretical findings with a multivariate analysis using archival data. In this setting, the hypothesis of perfect competition is relaxed, and the firm’s profits are allowed to differ from zero. Under this scenario, the VAIC also captures the ability of a firm to generate profits, which may be attributable to multiple factors, including IC. By using a cross-country dataset of 50,310 firms observed over the 2000–2017 period, the multivariate analysis confirms that the VAIC is negatively (positively) associated with the labor (physical capital) share. The model controls for the time-invariant characteristics for any country, industry, and firm by including firm fixed effects and clustering standard errors at the firm level. Despite the absence of perfect competition, these empirical results show that the VAIC still depends largely on exogenous technological factors that are not usually associated with IC. Hence, they inform the empirical IC literature on the need to control for technological factors to avoid endogeneity bias in multivariate analysis.

Third, reflecting on theoretical and empirical findings, this study proposes to control for a firm’s labor share, capital shares, and interest rate to reduce potential measurement biases in empirical research. The present study adopts this solution to investigate the association between IC, proxied by the VAIC, and financial performance. The results show that the VAIC is positively and significantly associated with financial performance when the labor share, capital share, and the interest rate are not included in the model. To ensure that these results are not driven by the technological components of the VAIC and the interest rate, the model is augmented by controlling for these factors. The results from these tests highlight that the association between the VAIC and financial performance is significantly weaker after controlling for its inherent technological components and the interest rate. As a result, this study prompts a careful interpretation of empirical analysis in prior literature when controls for technological factors are missing.

Fourth, the paper discusses the VAIC in light of the theoretical and empirical validation proposed in this study. The VAIC, which claims to represent IC in numbers only, is compared to alternative models of IC reporting by drawing on a multidimensional and performative approach (e.g. Mouritsen 2006; Gowthrope 2009; Melloni 2015; Nielsen and Roslender 2015; Melloni et al. 2016; Bini et al. 2017; Corbella et al. 2019). In empirical research, when properly tuned according to the validation proposed in this paper, the VAIC is capable of serving as a leasing indicator of some potential relation between IC and the main dependent variable of interest. However, the VAIC does not allow a deeper investigation on the dimensions of IC (e.g., relational, structural, or human capital) that influence the variable of interest. Similarly, the VAIC cannot explain how IC contributes to value creation. While not discouraging the use of VAIC, this paper suggests empirical literature to select alternative measures of IC that may be more capable of identifying meaningful associations.

The theoretical and empirical findings from this study are important because the VAIC is extensively used in empirical analyses. Researchers are urged to control for the labor share, capital share, and interest rate and to cautiously interpret the results based on the VAIC as a measure of IC. In fact, empirical studies that do not consider these variables as important determinants of the VAIC may suffer from important endogeneity problems. Additionally, the discussion stemming from the results of this paper leads to a reflection on the use of the VAIC in comparison to alternative models of IC reporting.

The remainder of the paper proceeds as follows. Section 2 describes the VAIC model, its underlying assumptions, and results from prior literature adopting this model. Section 3 proposes a decomposition of the VAIC in a perfectly competitive market and theoretically demonstrates that the VAIC is a function of exogenous technological factors that are not usually associated with IC. Section 4 illustrates the methodology and the results of a multivariate analysis that extends the theoretical findings to a non-perfectly competitive setting. In the spirit of assisting researchers in overcoming the VAIC limitations, Sect. 5 proposes and applies a potential solution for tuning the VAIC to more carefully measure IC. Section 6 offers a discussion of the main findings, outlines the limitations of this study, and provides avenues for future research.

2 Review of the literature on the VAIC model

2.1 The VAIC model

The VAIC model intends to offer a methodology to measure intellectual work efficiency and, therefore, IC efficiency (Pulic 2008; Iazzolino and Laise 2013). The formula of the VAIC is obtained through the following line of reasoning (Pulic 2005; Ståhle et al. 2011). First, value added (VA) is a function of the structural capital (SC) and the human capital (HC) employed; VA is defined as follows:

$$VA = OP + D + A + C ,$$
(1)

where OP is the operating profit, D is depreciation, A is amortization, and C is all employee-related costs. According to Eq. (1), C identifies the HC, while (OP + D + A) measures SC. Thus, Eq. (2) can also be expressed as follows:

$$VA = SC + HC .$$
(2)

The second step to derive the VAIC formula defines human capital efficiency (HCE), structural capital efficiency (SCE), and capital employed efficiency (CEE) as follows:

$$HCE = VA/HC,$$
(3)
$$SCE = SC/VA,$$
(4)
$$CEE = VA/CE,$$
(5)

where CE represents the physical capital employed. It is worth noting that HCE focuses on the contribution of human resources to VA creation, while SCE measures the efficiency of all other components in creating VA (Dženopoljac et al. 2016).

Finally, VAIC is the sum of these three efficiency measures:

$$VAIC = HCE + SCE + CEE .$$
(6)

Thus, in its aggregated form, the VAIC emphasizes a firm’s total efficiency, decomposed into IC efficiency (ICE = HCE + SCE) and financial efficiency (CEE).

2.2 Empirical literature using the VAIC model

Pedro et al. (2018) document that the VAIC was used in 11% of their reviewed papers, resulting in the most popular proxy for IC.Footnote 1 Prior literature initially concentrated on understanding the determinants of VAIC, its variation over time and across countries. Goh (2005) finds that commercial banks in Malaysia show higher human capital efficiency than structural and capital efficiencies. Additionally, they document that domestic banks were generally less efficient than foreign banks and that public banks improve their IC efficiency during the 3 years covered in their study. These results are confirmed for Indian firms operating in the banking and pharmaceutical industry (Kamath 2007, 2008), Japanese banks (Mavridis 2004), and ASEAN countries (i.e., Indonesia, Malaysia, Philippines, Singapore, and Thailand) (Nimtrakoon 2015). However, firms operating in different segments show significant differences in their VAIC (Mavridis 2004; Kamath 2007). Similarly, firms operating in different countries tend to differently emphasize the components of the VAIC (Nimtrakoon 2015). Finally, El-Bannany (2008) documents that profitability and risk are the main determinants of the VAIC for a sample of UK firms during the 1999–2005 period.

Another strand of research concentrates on analyzing the relationship between the VAIC and firm performance. The results from these empirical studies are mixed. Chen et al. (2005) document a positive impact of the VAIC on the market value and financial performance of Taiwanese listed firms. They also highlight that the VAIC is a leading indicator of future financial performance. These results are confirmed for financial firms in different countries (Ting and Lean 2009) and non-financial firms worldwide (Díez et al. 2010; Vishnu and Gupta 2014; Nimtrakoon 2015). Additionally, some studies suggest that a specific component of the VAIC has a stronger correlation with financial performance than other components (Chu et al. 2011; Clarke et al. 2011).

Although the above-reported studies point towards a positive relationship between VAIC and financial performance, other studies document inconsistent and, sometimes, opposite results. Some studies support a positive relationship between the VAIC and financial performance for specific industries only (Zeghal and Maaloul 2010; Pucar 2012), for human capital only (Maditinos et al. 2011; Komnenic and Pokrajčić 2012; Joshi et al. 2013), or for capital-employed efficiency only (Dženopoljac et al. 2016). Other studies show mixed associations between the components of the VAIC and financial performance (Firer and Williams 2003; Kamath 2008; Ghosh and Mondal 2009; Mehralian et al. 2012). Sardo and Serrasquiero (2017) highlight that these mixed results for the components of the VAIC depend on their ability to impact financial performance in the short or long run. Bayraktaroglu et al. (2019) identify moderating variables in the relationship between the VAIC and financial performance. Moreover, in their study on Brazilian real estate companies, Britto et al. (2014) show a negative relationship between VAIC and both market value and return on invested capital. Similar findings are documented in different countries (Dženopoljac et al. 2017) and in the public sector (Morariu 2014).

Finally, other studies concentrate on the potential use of the VAIC as a management tool. In their study on the Australian hotel industry, Laing et al. (2010) find that managers can use the VAIC model as a robust tool for assessing the efficient use of IC in their organizations. Additionally, Mohammadi and Taherkhani (2017) document no relation between the VAIC and cost stickiness.

3 Theoretical decomposition of the VAIC in a perfectly competitive setting

Despite the widespread use of the VAIC, prior studies challenge its validity as a measure of IC by critically analyzing its constructs. In particular Ståhle et al. (2011), suggest that the VAIC depends on labor and physical capital investments. This study elaborates on this intuition and provides a theoretical decomposition of VAIC in a perfectly competitive market.

Because the VAIC computation is based on the relationships between VA and its components, this study first recalls some results related to these relationships in perfectly competitive markets with a standard specification of the production function. In particular, it is assumed that the final output results from three different inputs (human capital, physical capital, and an intermediate good) and a traditional Cobb–Douglas production function, as follows:

$$Y = F\left( {H,K,I} \right) = AH^{\alpha } K^{\beta } I^{\gamma } ,\quad with \;\alpha , \beta , \gamma > 0,$$
(7)

where Y is the total output, A is the state of technology, H is the stock of human capital, K is the stock of physical capital, I is the flow of the intermediate good, and α, β, and γ are the elasticity coefficients of human capital, physical capital, and an intermediate good, respectively. In general, an elasticity coefficient indicates the percentage change in the production level when the corresponding input changes by one percentage point. Given Eq. (7), the profit (\(\varPi\)) function is:

$$\varPi = pY - wH - rK - p_{I} I,$$
(8)

where p is the price level of the final output, w is the nominal wage level, r is the interest rate, and pI is the price of the intermediate input. Because markets are perfectly competitive, the firm is a price-taker in all markets. From Eq. (8), the amount of VA the firm generates can also be derived:

$${\text{VA}} \equiv pY - p_{I} I = \varPi + wH + rK.$$
(9)

Equation (10) provides the extended expression of the VAIC:

(10)

Using Eq. (9) yields:

$${\text{VAIC}} = \frac{\varPi + wH + rK}{wH} + 1 - \frac{wH}{\varPi + wH + rK} + \frac{\varPi + wH + rK}{K}.$$
(11)

In the long run, the assumption of a perfectly competitive market for the final good implies no profits (i.e., Π = 0). Therefore, Eq. (11) becomes:

$${\text{VAIC}} = 1 + \frac{rK}{wH} + 1 - \frac{wH}{wH + rK} + \frac{wH}{K} + r.$$
(12)

Because firms want to maximize their profits, the first-order conditions (FOCs) of Eq. (8) must be computed. In particular, the FOCs for H and K lead to the following redistributive results: wH = αpY and rK = βpY. This result also implies that α = wH/pY and β = rK/pY, which means that human and physical capital elasticities (α and β) are equal to the labor and capital share, respectively (wH/pY and rK/pY). Moreover, the relation (wH)/(rK) = α/β can be written. By inserting these basic results into the operative definition of VAIC, the following equation can be obtained:

(13)

When markets are perfectly competitive and in long-run equilibrium, Eq. (13) demonstrates that the VAIC is a function of the elasticity coefficient of human capital (α), the elasticity coefficient of physical capital (β), and the interest rate (r). In particular, both the HCE and the SCE components negatively depend on α and positively depend on β, while the opposite is true for the CEE component. Thus, while the relationship between the VAIC and r is certainly positive, the relationship between the VAIC and the elasticity coefficients is ambiguous.

To further investigate the relationship between the VAIC, the elasticity coefficient of human capital (α), and the elasticity coefficient of physical capital (β), this study numerically simulates Eq. (13) by assuming reasonable values for the study parameters (i.e., α and β range between 0 and 1). Figures 1, 2, 3 and 4 report different VAIC functions for different interest rate levels (1%, 5%, 10% and 20%). According to Figs. 1 and 2, the relationship between the VAIC and the elasticity coefficients is increasing in β but decreasing in α. In contrast, a nonlinear relationship between the VAIC and coefficients appears when the interest rate increases (Figs. 3 and 4). In particular, Fig. 4 shows that the VAIC first decreases with small elasticity coefficient values and then increases.

Fig. 1
figure 1

VAIC function (r = 1%)

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Fig. 2
figure 2

VAIC function (r = 5%)

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Fig. 3
figure 3

VAIC function (r = 10%)

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Fig. 4
figure 4

VAIC function (r = 20%)

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To conclude, this analysis shows that the VAIC may have ambiguous behavior when the elasticity coefficients (especially the elasticity coefficient of human capital) are relatively low. Ceteris paribus, efficient firms adopting human capital-intensive technologies could show lower VAIC levels only as a result of their higher HCE. In contrast, the VAIC tends to be higher if a firm pays higher interest rates on physical capital. These relations imply that two firms with the same stock of IC and managerial capabilities may show different VAIC levels due to their technological constraints.

4 Empirical analysis of the decomposition of VAIC

The decomposition of the VAIC in Eq. (13) assumes a perfectly competitive market, which in the long run is inherently characterized by the absence of supernormal profits (i.e., the excess profit above the minimum return necessary to keep an organization in business). Under this assumption, the value added is completely exhausted by the factors of production, meaning that the VAIC captures only technological parameters and the cost of physical capital. However, real markets may violate perfect competition, with firms exhibiting non-zero supernormal profits. In this scenario, the VAIC also captures the ability of a firm to generate profits due to multiple factors, including IC. This section extends the validity of theoretical findings with a multivariate analysis employing archival data. In the empirical analysis, we test the association between the VAIC and firm performance while controlling for the capital share, labor share, and cost of capital.

4.1 Empirical model

This study draws upon previous literature (Goebel 2015) and regresses the VAIC performance on the interest rate, human and physical capital elasticity.Footnote 2 The following regression model is estimated (firm subscripts are suppressed):

$$\begin{aligned} VAIC_{t} & = \, \theta_{0} \, + \;\theta_{1} LABOR_{t} + \, \theta_{2} CAPITAL_{t} + \, \theta_{3} R_{t} \\ & \quad + \, \theta_{4} INTANGIBLES_{t} + \, \theta_{5} R\& D_{t} + \, \theta_{6} LEV_{t} + \, \theta_{7} PAYMENT_{t} \\ & \quad + \, \theta_{8} SIZE_{t} + {\text{Firm FE }} + {\text{ Year FE}} + \, \varepsilon_{t} \\ \end{aligned}$$
(14)

Consistent with prior literature (e.g., Nimtrakoon 2015; Dženopoljac et al. 2016; Mohammadi and Taherkhani 2017), the study measures the dependent variable VAIC (i.e., Pulic 1998, 2000) as the sum of HCE, SCE, and CEE. Further details on the calculation of these variables are provided in Sect. 2 and in Appendix. With respect to the main variables of interest, LABOR and CAPITAL represent measures of labor and capital elasticity, respectively, and are proxied by staff expenses (LABOR) and capital expenditures (CAPITAL) divided by total sales.Footnote 3 Similarly, R represents the interest rate proxied by the cost of debt capital. To further investigate the relationship between LABOR, CAPITAL, R and VAIC, Eq. (14) is also estimated by replacing VAIC with its components (HCE, SCE, and CEE). The study expects to find a negative association between both HCE and SCE and LABOR and a positive association with CAPITAL, while the opposite will be true for the CEE component.

Following previous literature, the study also includes some additional firm-level controls that can influence the VAIC (Goebel 2015). Accordingly, this study controls for the level of intangible assets (INTANGIBLES), the level of research and development expenses (R&D), the leverage ratio (LEV), the mean industry-year level of staff expenses (PAYMENT), and the natural logarithm of total sales (SIZE). Finally, the study also considers country, industry, and firm time-invariant characteristics and cross-sectional variation by adding firm and year fixed effects and clustering standard errors at the firm level. Continuous variables are winsorized at the 1% and 99% levels, except SIZE, which is expressed as a natural logarithm. Appendix provides additional information about variable definitions and their sources.

4.2 Sample description

The sample includes all firm-year observations available in COMPUSTAT GlobalFootnote 4 for the 2000–2017 period. The study drops firm-year observations with missing accounting information required to estimate Eq. (14). Singleton groups (i.e., groups with only one observation) are removed, as prior literature demonstrates that including these observations can inflate the statistical significance (Correia 2015). In addition, observations with a negative book value of equity and a negative VAIC are removed, as a negative value of “value-added” does not generate a meaningful analysis (see Firer and Williams 2003; Shiu 2006; Chan 2009; Chu et al. 2011; Pal and Soriya 2012). Consequently, the final sample consists of 50,310 firm-year observations (i.e., 8401 firms across 81 countries).

Panel A of Table 1 reports the sample distribution by industry-year. Most observations are clustered in the information technology (11,041), industrials (11,120), materials (7624), consumer discretionary (7755), and healthcare (5454) industry sectors. Panel B of Table 1 reveals that most observations are from India (8815), Taiwan (4767), the UK (4519), China (3253), and Germany (2994).

Table 1 Sample distribution
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4.3 Descriptive statistics and univariate analysis

Table 2 reports the descriptive statistics for the dependent and independent variables entering the multivariate analysis. The mean (median) VAIC measure is 7.52 (2.7), while the mean (median) values of HCE, SCE, and CEE are 6.43 (1.81), 0.55 (0.47), and 0.33 (0.26), respectively. Focusing on the main variables of interest, the mean (median) LABOR, CAPITAL and R values are 0.21 (0.15), 0.09 (0.04), and 0.10 (0.06), respectively. On average (median), intangible assets represent 12% (3.4%) of total assets (INTANGIBLES). Related to intangibles, research and development expenditures (R&D) are approximately 2.9% (1%). Finally, the leverage ratio (LEV) is on average (median) 1.74 (1.1), while only 6.2% of firms in the study’s sample have a level of staff compensation higher than the mean value by sector-year (PAYMENT).

Table 2 Descriptive statistics
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Table 3 presents the Pearson correlation coefficients for all variables in the multivariate analysis. Consistent with Eq. (13), it is observed that LABOR is negatively (positively) and significantly correlated with HCE (CEE) (p < 0.01). Notice that, contrary to theoretical predictions, the association between LABOR and SCE is positive and statistically significant (p < 0.01). However, this coefficient may be misleading because it is based on simple, univariate correlations. This fact leads to a negative and significant association between LABOR and VAIC (p < 0.01). Fully consistent with the prediction from Eq. (13), CAPITAL is negatively correlated with CEE (p < 0.01) and positively correlated with HCE (p < 0.01) and SCE (p < 0.01), resulting in a positive and significant association between CAPITAL and VAIC (p < 0.01).

Table 3 Pearson correlation coefficients
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4.4 Multivariate analysis

Table 4 reports the results for the tests regarding the influence of interest rate, labor and capital shares on the VAIC. Column (1) shows the baseline model that includes labor share (LABOR), capital share (CAPITAL), and the interest rate (R) without including firm and year fixed effects. Columns (2) and (3) progressively augment the baseline model with the controls from Eq. (14). The results confirm that the theoretical model based on perfectly competitive markets also remains valid in a non-perfectly competitive setting. In fact, Table 4 shows that the labor share (LABOR) has a negative and statistically significant association with VAIC (p < 0.01), while the capital share (CAPITAL) has a positive and statistically significant association with VAIC (p < 0.01). However, the relation between the interest rate (R) and VAIC is not statistically significant. As shown in the theoretical derivation, this result occurs because the interest rate enters only the CEE component of VAIC. All other controls are in line with prior literature (e.g., Goebel 2015). The multivariate analysis confirms that, despite not being directly related to a firm’s IC, labor and capital shares are two fundamental drivers of VAIC.

Table 4 Association between labor share (LABOR), capital share (CAPITAL), interest rate (R), and VAIC
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Table 5 reports the results for the investigation into the influence of LABOR, CAPITAL, and R on the VAIC components. Accordingly, VAIC is replaced with HCE, SCE, and CEE, and the model is estimated in Eq. (14). The results show that CAPITAL is positively correlated with HCE and SCE, negatively correlated with CEE, and statistically significant at a conventional level (p < 0.01). Table 5 also shows that LABOR is negatively correlated with HCE (p < 0.01) and positively correlated CEE (p < 0.05). Finally, LABOR is not linearly correlated with SCE. This lack of correlation may be caused by the linearization of a nonlinear expression. Additionally, R is positively correlated with SCE and CEE. These findings are in line with our theoretical results and confirm that LABOR, CAPITAL and R are important drivers of VAIC and its components (HCE, SCE, and CEE) in a non-perfectly competitive setting.

Table 5 Association between labor share (LABOR), capital share (CAPITAL), interest rate (R), and the components of VAIC
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5 Tuning the VAIC

The preceding two sections demonstrate that the VAIC is largely influenced by exogenous technological factors that are unrelated to IC. While this result constitutes a criticism of the use of the VAIC as a measure of IC, in a non-perfect competitive setting, the VAIC also captures the ability of a firm to generate profits. This ability may be attributable to numerous circumstances, including IC. In the spirit of assisting empirical researchers, this section shows a potential solution for tuning the VAIC to more carefully measure IC.

Stemming from prior section’s results, this paper argues that controlling for the interest rate, labor and capital share in an empirical analysis is fundamental to avoiding potential biases. Not including LABOR, CAPITAL, and R as additional controls may lead to serious omitted variable concerns and biased estimations. By contrast, including LABOR, CAPITAL, and R helps in ensuring that VAIC does not proxy for exogenous technological factors and the interest rate. Far from perfectly proxying for IC, VAIC will then capture the ability of a firm to generate profits and, therefore, time-varying heterogeneity across firms.

To test the potential solution identified above, this study investigates the association between VAIC and financial performance. Drawing upon previous literature (Pal and Soriya 2012; Sardo and Serrasqueiro 2017; Dženopoljac et al. 2019), the following regression model is estimated (firm subscripts are suppressed):

$$\begin{aligned} PERFORMANCE_{t} & = \, \theta_{0} + \, \theta_{1} VAIC_{t} + \, \theta_{2} LABOR_{t} + \, \theta_{3} CAPITAL_{t} + \, \theta_{4} R_{t} \\ & \quad + \, \theta_{5} INTANGIBLES_{t} + \, \theta_{6} R\& D_{t} + \, \theta_{7} LEV_{t} + \, \theta_{8} PAYMENT_{t} \\ & \quad + \, \theta_{9} SIZE_{t} + {\text{Firm FE }} + {\text{ Year FE}} + \, \varepsilon_{t} \\ \end{aligned}$$
(15)

where PERFORMANCE is return on assets (ROA), return on equity (ROE), and return on investments (ROI), alternatively, and all other variables are as defined earlier. Equation (15) is estimated excluding LABOR, CAPITAL, and R, then excluding VAIC and, finally, including all these variables. If not controlling for LABOR, CAPITAL, and R generates biased estimations, the coefficient of VAIC obtained when non-controlling for these variables should be significantly different than that when controlling for these factors.

Table 6 reports the results of the estimation of Eq. (15) with alternative measures of financial performance. The results show that the VAIC is significantly associated with financial performance (0.018, Column (1); 0.051, Column (4); 0.079, Column (7); p < 0.01). Similarly, LABOR, CAPITAL, and R are also associated with financial performance [− 6.178, 1.749, and 1.175 Column (2); (− 13.597, 5.427, and 2.027, Column (5); (− 30.592, 8.743, and 3.884, Column (8)]. Finally, when VAIC, LABOR, CAPITAL, and R are included in the estimation of Eq. (15), the results show that all these variables are significantly related to financial performance. However, when controlling for LABOR, CAPITAL, and R, the coefficient of VAIC is significantly different than when not controlling for these factors.Footnote 5 Thus, the estimations produced, including LABOR, CAPITAL, and R, are more careful and ensure that the association between the VAIC and financial performance is not overestimated. When controlling for technological factors, explanatory power varies from 45.7% when using ROE as a measure of financial performance to 66.5% when employing ROI (adjusted r-squared in columns (6) and (9), respectively). This difference can be attributed to the underlying difference in calculating ROE, ROA, and ROI. In fact, ROE and ROA include non-operating items that are not considered when calculating ROI. As VAIC refers to a firm’s operations, the explanatory power is higher when using ROI to proxy financial performance than when using ROA and ROE.

Table 6 Association between labor share (LABOR), capital share (CAPITAL), interest rate (R), VAIC and firm performance
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6 Discussion and conclusions

The use of the VAIC as a measure of IC is consistently growing due to its reliance on accounting numbers and its ease of calculation. Motivated by prior critiques of the VAIC’s validity, this study offers a theoretical decomposition of the VAIC in a perfectly competitive setting and demonstrates that the VAIC is a function of the elasticity coefficient of human capital, the elasticity coefficient of physical capital, and the interest rate. The theoretical results are extended to non-perfectly competitive settings through a multivariate analysis of a cross-country panel of 50,310 firm-year observations covering the years 2000–2017. Reflecting on the theoretical and empirical findings, this study proposes guidance for the use of the VAIC to overcome its inherent limitations. More specifically, this study suggests that future empirical literature control for a firm’s interest rate, labor and capital shares to reduce potential measurement biases. In an additional analysis investigating the association between the VAIC and financial performance, the results show that this association is weaker when controlling for the interest rate, labor and capital share, prompting a more careful interpretation of the results.

The results of this study prompt a reflection on the use of the VAIC as a measure of IC and should be interpreted in light of the growing body of literature suggesting a multidimensional and performative approach to IC. This paper suggests that the VAIC construct is unrelated to IC from a theoretical perspective that assumes a perfectly competitive market. Conversely, from an empirical perspective, it shows that when relaxing the perfect competition assumption, the VAIC captures the ability of a firm to generate profits. Hence, the VAIC can be cautiously used as a leading indicator of IC. When properly tuned according to the validation proposed in this paper, academic studies may adopt the VAIC in empirical analyses to identify some potential relation between IC and the main dependent variable of interest. In case they find a significant relation, they are advised to investigate more deeply in order to identify the component of IC and the mechanisms through which IC affects the main dependent variable of interest.

Conversely, the VAIC can provide little or no information on how IC contributes to the value creation process. In fact, the concept of IC has many dark sides, which cannot be easily captured in the VAIC numbers or other models (Gowthrope 2009). As a result, the correlation between IC numbers is sometimes useless (Mouritsen and Roslender 2009). Hence, recent literature clearly outlines that the metrics of IC cannot stand alone but should be read and interpreted in connection to disclosure following a performative approach (Mouritsen 2006).

Although there is no single solution to measuring and reporting IC, prior literature identifies some practice-based patterns. For example, Corbella et al. (2019) demonstrate that some concepts inspired by the International Integrated Reporting Council Framework are considered pivotal in defining categories of IC and identifying its contribution to value creation. Nielsen and Roslender (2015) show how business model discourse and disclosure can contribute to improving the information content of financial statements by also including information on IC and its contribution to value creation. Another strand of research concentrates on the interaction between business models and non-financial key performance indicators to obtain a more integrated framework that can provide more relevant and performative disclosure to users (Bini et al. 2017, 2018). While empirical content analysis demonstrates a tendency toward impression management (Melloni 2015; Melloni et al. 2016), integrated reporting, business models, key performance indicators, and IC definitely show a strong link and influence each other in practice (Zambon et al. 2019).

Compared to the VAIC, these approaches are certainly more exhaustive in explaining the contribution of IC to the value creation process. Despite its inherent limitations, the VAIC offers a ready-to-use measure based on accounting numbers. Conversely, collecting and analyzing information conveyed through integrated reporting, business models, and key performance indicators is certainly more complicated and costlier. In the end, the two approaches serve two different purposes. The VAIC provides a superficial tool for measuring IC that can be used to identify some potential relation to value creation while being incapable of any deeper investigation. Conversely, integrated reporting, business models, and key performance indicators allow a granular—albeit time and resource consuming—understanding of the contribution of IC to the value creation process.

Despite its contributions, this study is subject to some potential limitations that generate avenues for future research. First, this study limits its theoretical decomposition of the VAIC to a perfectly competitive setting. Future studies may question the decomposition of VAIC in different settings, such as monopolies, oligopolies, and other market forms. Second, the study empirically validates its theoretical model with a linear regression model. Future contributions could investigate the existence of a nonlinear relationship between the VAIC, labor share, and capital share. Finally, future research could use nonmonetary measures of market competition, such as the Herfindahl–Hirschman index or other concentration indices, to test whether these measures moderate the role of VAIC in explaining firms’ performance.