Addressing unobserved endogeneity bias in accounting studies: control and sensitivity methods by variable type

Together with their associated statistical routines, this paper describes the control and sensitivity methods that can be employed by accounting researchers to address the important issue of unobserved (omitted) variable bias in regression and matching models according to the types of variables employed. As with other social science disciplines, an important and pervasive issue in observational (non-experimental) accounting research is omitted variable bias (endogeneity). Causal inferences for endogenous explanatory variables are biased. This occurs in regression models where an unobserved (confounding) variable is correlated with both the dependent (outcome) variable in a regression model and the causal explanatory (often a selection) variable of interest. The Heckman treatment effect model has been widely employed to control for hidden bias for continuous outcomes and endogenous binary selection variables. However, in accounting studies, limited (categorical) dependent variables are a common feature and endogenous explanatory variables may be other than binary in nature. The purpose of this paper is to provide an overview of contemporary control methods, together with the statistical routines to implement them, which extend the Heckman approach to binary, multinomial, ordinal, count and percentile outcomes and to where endogenous variables take various forms. These contemporary methods aim to improve causal estimates by controlling for hidden bias, though at the price of increased complexity. A simpler approach is to conduct sensitivity analysis. This paper also presents a synopsis of a number of sensitivity techniques and their associated statistical routines which accounting researchers can employ routinely to appraise the vulnerability of causal effects to potential (simulated) unobserved bias when estimated with conventional regression and propensity score matching estimators.     

Panel Cointegration Analysis of Audit Pricing Model

This paper addresses two issues that arise from testing and estimating cointegration in accounting research. The first issue is the failure to use more powerful cointegration tests by earlier researchers. This has led to the problem of low test power in the cointegration procedures employed in the earlier accounting literature. Another issue that has not received much attention in earlier studies of audit pricing is the endogeneity bias that arises from the endogenous nature of the regressors. Commonly used regressors such as auditee size and auditee complexity are endogenous and are often related to audit fees through a system of simultaneous equations. Endogeneity bias suggests that the conventional OLS estimators are biased.Using more powerful panel sample estimation procedures, we find that elasticities of total assets are in general under-estimated in the earlier studies when the conventional OLS method was used. We also find that the earlier studies tend to under-state the effects of the foreign subsidiary ratio and over-state the effect of the ratio of account receivables to total assets on audit fees.JEL Classification: C33, M41     

Quantile regression estimates and the analysis of structural breaks

The paper considers a test for structural breaks based on quantile regressions instead of OLS estimates. Besides granting robustness, this allows us to verify the impact of a break in more than one point of the conditional distribution. The quantile regression test is then repeatedly implemented as a diagnostic tool to uncover partial or spurious breaks. The test is also implemented to measure the contribution of each explanatory variable to the instability of the regression coefficients, thus finding which one of the different possible sources of breaks linked to the nature of the explanatory variables is the most effective. A real data example of exchange rates shows the presence of a time-driven break, but only at the lower quartile, while the analysis of the explanatory variable excludes its involvement in the break. Since the asymptotic distribution of the OLS test for structural change depends on i.i.d. normal errors and on the exogeneity of the explanatory variables, a Monte Carlo study analyses the behavior of OLS and quantile regression tests for structural changes with lagged endogenous variables, non-normal errors, spurious or partial breaks, and misspecification.     

Estimating firm-level and country-level effects in cross-sectional analyses: An application of hierarchical modeling in corporate disclosure studies

Researchers in the field of international accounting are often confronted with observations of firms clustered into higher-level units such as countries. Using data from a corporate disclosure study including 797 firm observations from 34 countries, we demonstrate that the inferences obtained from the most commonly used Ordinary Least Square (OLS) test, which pools the firm and country data either under the disaggregation or aggregation approach, are problematic and misleading. To overcome the methodological limitation, we subsequently employ hierarchical modeling to simultaneously estimate both firm-level (within-country) and country-level (cross-country) disclosure determinants. We find that the clustering effects are significant in almost all firm-level variables. Once such effects are adjusted, only three firm-specific variables are significantly associated with corporate disclosure. Evidence provided by this study has important implications for most international accounting studies conducted in cross-level contexts.     

An Empirical Investigation of the Arbitrage Pricing Theory

Empirical tests are reported for Ross' [48] arbitrage theory of asset pricing. Using data for individual equities during the 1962–72 period, at least three and probably four priced factors are found in the generating process of returns. The theory is supported in that estimated expected returns depend on estimated factor loadings, and variables such as the own standard deviation, though highly correlated (simply) with estimated expected returns, do not add any further explanatory power to that of the factor loadings.     

Stock Market Efficiency and the Federal Budget Deficit: Another Anomaly?

This paper investigates the efficiency of the U.S. stock market as it pertains to a number of major macrofinance variables that theory and empirical evidence suggest are important in rational stock pricing decisions. A multivariate vector autoregressive analysis is used to draw efficiency inferences. The estimated factor pricings are consistent with theory and previous empirical research. In addition, these results indicate that the stock market may be inefficient with respect to the federal budget deficit variable. Similar apparent inefficiency evidence is obtained for the term structure and risk premium variables. The authors cannot reject the efficiency hypothesis for industrial production, inflation, and base money. Using indirect causality tests, the authors find plausible intermediate information linkages connecting variables in the system. The term structure and risk premia variables consistently appear important as intermediate conduits through which information about other factors impact stock returns.     

Financial statement recasting and credit risk assessment

This article examines the importance of adjustments to corporate financial statements for credit risk assessment. Prior research has tended to examine individual adjustments one at a time. As correlations among adjustments and control variables may bias inferences when researchers examine a single adjustment and ignore other adjustments, our results provide important new information about previous research by documenting whether or not such bias exists. We find that financial statement recasting adjustments – which aim to better reflect firms' indebtedness, financing costs and recurring earnings than reported financial numbers – are reflected in bond yield spreads and have an economically significant impact on credit pricing and loss forecasting. Among individual adjustment categories, we find that those for off‐balance‐sheet leases, defined benefit pensions and securitized debt have an economically significant impact on credit pricing and loss forecasting.     

Taming the Factor Zoo: A Test of New Factors

We propose a model selection method to systematically evaluate the contribution to asset pricing of any new factor, above and beyond what a high-dimensional set of existing factors explains. Our methodology accounts for model selection mistakes that produce a bias due to omitted variables, unlike standard approaches that assume perfect variable selection. We apply our procedure to a set of factors recently discovered in the literature. While most of these new factors are shown to be redundant relative to the existing factors, a few have statistically significant explanatory power beyond the hundreds of factors proposed in the past.     

Consistent estimation of cross-sectional models in event studies

Event studies often include cross-sectional regressions of announcementeffects on exogenous variables. If the event is voluntary andinvestors are rational, then standard OLS and GLS estimatorsare inconsistent. Consistent ML estimators are constructed fora cross-sectional model of horizontal mergers relating announcementeffects to exogenous characteristics of firms and industries.The OLS and ML estimates differ dramatically for bidders butnot for targets. The evidence suggests that manager of bidders,but not targets, have valuable private information about thepotential synergies from proposed mergers.     

Asymmetry in earnings timeliness and persistence: a simultaneous equations approach

This study addresses simultaneity bias in piecewise linear forms of the earnings-return relation. We specify an overidentified system of simultaneous equations that incorporates both asymmetric earnings timeliness and asymmetric earnings persistence specifications and implement two-stage least squares for this piecewise linear system. Estimation of a system that is piecewise linear in endogenous variables presents several issues that are unprecedented in the accounting literature. Findings provide evidence that the asymmetric timeliness specification is particularly affected by simultaneity and that failing to correct for simultaneity results in coefficient estimates that potentially understate the degree of asymmetric earnings timeliness. Moreover, inferences regarding how conditional conservatism has evolved over time are sensitive to whether OLS or 2SLS coefficients are used as the basis of comparison.     

Brand Values and Capital Market Valuation

Brand value estimates are significantly positively related to prices and returns, incremental to accounting variables. Questionable brand value estimate reliability underlies lack of financial statement recognition for brands. Findings suggest estimates are relevant and sufficiently reliable to be reflected in share prices. Simultaneous equations estimation reveals inferences are unaffected by potential bias resulting from simultaneity between brand value estimates and equity market value. Brand value estimates are positively associated with advertising expense, operating margin, and market share. Yet, brand value estimates provide significant explanatory power for prices incremental to these variables, and to recognized brand assets and analysts earnings forecasts.     

Impact of an accounting environment on cash flow prediction

This study investigates the impact of an accounting environment on the performance of cash flow prediction models. It is hypothesized that the cash flow model by Barth, Cram, and Nelson [Acc. Rev. 76 (2001) 27] performs well in countries where the accruals are used mainly to correct cash flows to better reflect current profitability of the firm, i.e., in countries with high information content of accruals. The results suggest that the model performs consistently across countries, except in Germany. As hypothesized, the impacts of the explanatory variables are similar in market-oriented countries with separated financial accounting and taxation, with strong shareholder protection and legislation based on common-law origin, i.e., in countries with high quality of accruals. By contrast, the impacts are different in countries with low quality of accruals. The results imply that the cash flow prediction model by Barth et al. [Acc. Rev. 76 (2001) 27] can be used in different kinds of accounting environments. However, the exact parameter values are dependent on the accounting environment.     

Defining management accounting constructs: A methodological note on the risks of conceptual misspecification

This paper stresses the need for a sound conceptual specification of research constructs prior to fitting them to explanatory models. It emphasizes that in addressing the conceptual level of the predictive validity framework [Libby, R., Bloomfield, R., & Nelson, M. (2002). Experimental research in financial accounting. Accounting, Organizations and Society, 27, 775–810], special attention must be paid to two issues: (1) the production of a specific agreed-upon meaning and domain for each construct of interest; and (2) the specification and conceptual justification of the nature and direction of the epistemic relationships between constructs, dimensions and indicators (i.e., reflective vs. formative models; latent vs. emergent models). The paper highlights the importance of both issues especially in the case of practice-defined variables, and it provides guidelines on how to address both aspects of conceptual specification. While the issues raised are pertinent to many research areas, the paper concentrates on the implications for management accounting and control systems (MACS) research, using interactive use of control systems [Simons, R. (1995a). Levers of control. Boston: Harvard Business School Press] to illustrate how researchers should go about specifying meaning and epistemic relationships in MACS research.     

Liquidity biases in asset pricing tests

Microstructure noise in security prices biases the results of empirical asset pricing specifications, particularly when security-level explanatory variables are cross-sectionally correlated with the amount of noise. We focus on tests of whether measures of illiquidity, which are likely to be correlated with the noise, are priced in the cross-section of stock returns, and show a significant upward bias in estimated return premiums for an array of illiquidity measures in Center for Research in Security Prices (CRSP) monthly return data. The upward bias is larger when illiquid securities are included in the sample, but persists even for NYSE/Amex stocks after decimalization. We introduce a methodological correction to eliminate the biases that simply involves weighted least squares (WLS) rather than ordinary least squares (OLS) estimation, and find evidence of smaller, but still significant, return premiums for illiquidity after implementing the correction.     

Functional fixation revisited: the effects of feedback and a repeated measures design on information processing changes in response to an accounting change

This study uses a product pricing laboratory experiment to evaluate the presence of functional fixation and extends prior research, particularly the work of Bloom et al. (1984) and Murray (1991) [Bloom, R., Elgers, P. T., & Murray, D. (1984). Functional fixation in product pricing: A comparison of individuals and groups. Accounting, Organizations and Society, 9(1), 1–11; Murray, D. (1991). Data fixation: Methodological refinements and additional empirical evidence. Behavioral Research in Accounting, 3, 25–38] by incorporating a repeated measures design and a feedback variable. Functional fixation was assessed by the degree of information processing changes in response to an accounting change. The accounting change, in the form of a change in depreciation method (straight line to accelerated or accelerated to straight line, respectively), was varied by the period in which the change occurred and by whether judgment policy feedback was provided. Ten experimental conditions were utilized in the study: two control conditions with no accounting change, four second-period accounting change conditions (two with feedback and two without), and four third-period accounting change conditions (two with feedback and two without). A total of 190 subjects participated in the study and made product pricing decisions for three sets of thirty products each, each constituting a separate period. In four of the 10 conditions, subjects received feedback during the second and third period in the form of cue weights and estimated prices based on the preceding task. Overall, results indicate that functional fixation is present, and that the period of the accounting change and feedback do not significantly influence it. However, feedback was differentially effective depending on the period in which the accounting change occurred, such that although it did not reduce fixation, it resulted in pricing differences obtaining from a revised consideration of the variables underlying the pricing decision model. The results of a second experiment with a larger number of periods were basically similar in demonstrating fixation effects. The results are discussed in terms of their implications for functional fixation as well as directions for future research.     

Inventory policy, accruals quality and information risk

This paper provides evidence consistent with firms with Last-in-first-out (LIFO) inventory policy being priced by the market as having lower information risk than First-in-first-out (FIFO) firms. Furthermore, the paper shows that this pricing differential is sustained after controlling for accruals quality, suggesting that the inventory policy signals some information risk characteristics that are not captured by accruals quality measure. We investigate the relation between inventory policy and accruals quality and find that accruals quality is systematically worse for FIFO firms than for LIFO firms after controlling for correlated omitted variables and known firm attributes. These findings complement the currently established relationship between the cost of capital, market pricing and accruals quality by focusing on the need for understanding the incremental effects of individual accounting policies.     

Cointegration Analysis of Audit Pricing Model: A Panel Unit Root Test Approach

In this study, we provide evidence on the stationarity of real audit fees and the major explanatory variables frequently used in the audit pricing models from a pooled data set, using panel unit root tests developed by Im et al. (1997). The panel unit root test supports the hypothesis of non‐stationarity of audit fees and their major determinants. We demonstrate that variables in the audit pricing model that were previously found to have impact on audit fees may turn out to be useless when more powerful tests like panel tests are applied to these variables. Our evidence implies that failing to employ appropriate procedure to test cointegration and to specify the appropriate model for audit fees and their determinants would generate results that may have exaggerated the effects of some variables on audit fees.     

Owner liability and financial reporting information as predictors of firm default in bank loans

We examine the effects of owner liability and non-accounting and financial accounting information on the probability of default as defined in Basel II in bank loan contracted by non listed firms. We model default as a function of owner liability and accounting and non-accounting information of non-listed firms, drawing on 43,117 annual accounts of 16,029 firms over a 7-year period. Our estimations based on mixed logistic regressions with random parameters show that the predicted default probability of full-liability firms is 0.72 times that of limited liability firms. The likelihood ratio test for omitted variables confirms the additional predictive ability of liability status over and above other non-accounting and financial accounting information. A Heckman self-selection model does not indicate sampling bias. The particular definition of default used in the study enables the findings to be generalizable across other institutional contexts.     

Return Distributions and Improved Tests of Asset Pricing Models

We compare and contrast some existing ordinary least squares(OLS)- and generalized method of moments (GMM)-based tests ofasset pricing models with a new more general test. This newtest is valid under the assumption that returns are ellipticallydistributed, a necessary and sufficient assumption of the linearcapital asset pricing model (CAPM). This new test fails to rejectthe CAPM on a dataset of stocks sorted by market valuations,whereas similar tests constructed from OLS and GMM estimationmethods reject the linear CAPM. We also find that outliers reducethe OLS-estimated mispricing of the linear CAPM on monthly returnssorted by previous performance, that is, momentum. Monte Carloevidence supports superior size and power properties of thenew test relative to OLS- and GMM-based tests.     

Information Asymmetry and Voluntary SFAS 157 Fair Value Disclosures by Bank Holding Companies During the 2007 Financial Crisis

We hand‐collect SFAS 157 voluntary fair value disclosures of 18 bank holding companies. The SEC's Division of Corporate Finance likely targeted these entities in 2008 through their “Dear CFO” letters in which they requested specific, additional disclosure items. We collect disclosures that match the SEC recommendations and create eight common factor disclosure variables to examine the effect of such disclosures on information asymmetry. We find that disclosure variables about the use of broker quotes or prices from pricing services and the use of market indices and illiquidity adjustments are related to lower information asymmetry. However, disclosure variables about valuation techniques and asset‐backed securities are related to greater information asymmetry. We also document that disclosure complexity, and disclosure tone (uncertainty and litigious) is related to greater information asymmetry. These findings are consistent with criticism that corporate disclosures are voluminous; management may obfuscate unfavorable information which in turn increases market participants’ assessment of uncertainty associated with the fair value measures. We caveat that the setting of the financial crisis and a small sample size may limit the ability to generalize these inferences to other time periods or other financial firms.