Atl Econ J (2013) 41:193–195 DOI 10.1007/s11293-012-9362-y ANTHOLOGY
Accruals, Errors-in-variables, and Tobin’s q Christian Calmès & Denis Cormier & François-Éric Racicot & Raymond Théoret
Published online: 24 January 2013 # International Atlantic Economic Society 2013
Accrual models are very useful in accounting and finance. They allow the tracking of earnings (Hirshleifer et al. 2004; Roychowdhury 2006; Ronen and Yaari 2008) and are also used to forecast stock market returns (e.g., Fama and French 2007). However, these models tend to be ad hoc ones in which accruals are related to their economic determinants, like property, plant, and equipment (PP&E) and sales (Jones 1991). More recently, cash-flows were added to these models as a forecasting variable for earnings (DeChow 1994), but this method
C. Calmès Université du Québec (Outaouais), 101 St. Jean Bosco, Gatineau, Québec, Canada J8X 3X7 e-mail:
[email protected] D. Cormier Université du Québec (Montréal), 315 Ste. Catherine est, Montréal, Québec, Canada H2X 3X2 e-mail:
[email protected] F.-É. Racicot (*) Telfer School of Management, CGA-Canada Accounting and Governance Research Centre, University of Ottawa, 55 Laurier Avenue East, Ottawa, ON, Canada K1N 6 N5 e-mail:
[email protected] R. Théoret Université du Québec (Montréal), 315 Ste. Catherine est, Montréal, Québec, Canada H2X 3X2 e-mail:
[email protected] C. Calmès : D. Cormier : R. Théoret Chaire d’information financière et organisationnelle, École des sciences de la gestion (UQAM), Montréal, Canada C. Calmès Laboratory for Research in Statistics and Probability, Carleton University, Ottawa, Canada F.-É. Racicot Chaire d’information financière et organisationnelle, ESG-UQAM, Montréal, Canada
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is somewhat arbitrary because it uses leads and lags of cash-flows, which create additional econometric problems. The accrual empirical model we propose retains the general structure of previous models but is more rigorous since it casts accruals in the neo-classical theory of investment. Indeed, accruals are a kind of investment since they include both a firm’s short-term investment (working capital) and long-term investment (PP&E). In the neo-classical model of investment, under the assumption of perfect markets, Tobin’s q, a proxy for the expected net return on investment, is the only variable impacting investment. This variable accounts for the expectations of the firm about its performance. Under the assumption of markets imperfection, control variables must be added to account for the firm’s financial constraints. These variables are: cash-flows, sales, and other variables borrowed from the previous accrual models. Our empirical version of the accruals model obtains: AIitit ¼ a0 þ a1 qit þ Xt θ , where Xt is a vector of control variables and θ is the corresponding vector of parameters. The explanatory variables of our model are contaminated by errors-in-variables. It is especially the case for Tobin’s q. To account for these errors, we rely on a new procedure based on the Hausman artificial regression (Calmès et al. 2013). This procedure, named the Haus-C procedure, is in fact a TSLS regression embedding directly an errors-in-variables test. This test leads to the inclusion of w artificial variables in the regression, one for each endogenous variable. These artificial variables are computed by regressing each endogenous variable on cumulative instruments, which account for non-linearity in the data generating process (DGP). The estimated coefficients of these variables measure the extent of positive bias in the estimation of an endogenous variable if the coefficient is positive and vice-versa if it is negative. The final formulation of our new empirical model is thus: 5 X TAit 1 PPEit SALESit CFit b jt ¼ b1 þ b3 þ b 4 qit þ b 5 þ ϕw þ b2 Ai;t1 Ai;t1 Ai;t1 Ai;t1 Ai;t1 j¼1 j þ "it
ð1Þ
b j , the with TAi, total accruals; Ai, total assets; CFi, cash flows; i, a firm; and w estimated artificial variable for the endogenous j variable. Equation (1) is estimated using our Haus-C procedure. To run the regression, we made a distinction between total accruals, which include depreciation, and current accruals, which exclude them, and are thus more related to short-term investment. Regarding current accruals, our results indicate that, in a first run Eq. (1) using OLS, Tobin’s q and cash-flows are very significant variables. However, we find that the impact of Tobin’s q is strengthened when accounting for endogeneity with Haus-C, with a corresponding decrease in the role played by cashflows. This indicates that cash-flows account for firms’ expectations, a role transferred to Tobin’s q after correcting for errors-in-variables. This is in line with the neoclassical theory of investment which assumes that expectations are incorporated in Tobin’s q. Sales is also a redundant variable when using OLS but becomes significant when accounting for errors-in-variables, suggesting another bias due to endogeneity.
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We obtain similar results when using total accruals instead of current ones as dependent variables. However, the results are less significant, which supports our short-term approach to accruals. Finally, after correcting for errors-in-variables, the distribution of errors is centered around zero, which is not the case with OLS, and is more asymmetrical. Our Haus-C procedure thus seems to reduce the bias in the estimation process, which give rises to non-zero residuals using OLS. Moreover, our finding related to the positive asymmetry of the residuals indicates that firms seem to manage their earnings. Note that the residuals associated with the accrual model, named discretionary accruals, are used to forecast stock returns. Therefore, our residuals seem more relevant for forecasting purposes than those associated with OLS. Acknowledgments We would like to thank the Chaire d’information financière et organisationnelle (ESG-UQAM) for its financial support, and Cheng Few Lee, Steven J. Kachelmeier, Mark A. Trombley and Stephen Young for their valuable comments.
References Calmès, C., Cormier, D., Racicot, F.E., Théoret, R. (2013). Firms’ accruals and Tobin’s q, Aestimatio: The IEB International Journal of Finance, forthcoming. Dechow, P. (1994). Accounting earnings and cash-flows as measures of firm performance. Journal of Accounting and Economics, 18, 3–42. Fama, E. F., & French, K. R. (2007). Dissecting anomalies. Journal of Finance, 63, 1653–1678. Hirshleifer, D., Hou, K., Teoh, S. H., & Zhang, Y. (2004). Do investors overvalue firms with bloated balance sheets? Journal of Accounting and Economics, 38, 297–331. Jones, J. J. (1991). Earnings management during import relief investigations. Journal of Accounting Research, 29, 193–228. Ronen, J., Yaari, V. (2008). Earnings Management: Emerging Insights in Theory, Practice and Research. Springer. Roychowdhury, S. (2006). Earnings management through real activities manipulation. Journal of Accounting and Economics, 42, 335–370.
