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office models of discretionary accruals: Healy (1985); DeAngelo (1986); Jones (1991), a modified version of the Jones model and the Industry Model (formulated by Dechow et al

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themselves). These models are evaluated with reference to Type I and Type II error rates and distribution of residuals.

• A type I error involves incorrectly accepting a research (alternative) hypothesis when the null hypothesis is true. Here, concluding that firms have used earnings management when they have not.

• A type II error involves incorrectly rejecting a research (alternative) hypothesis when the null hypothesis is true. Here, not identifying earnings management when firms have managed earnings.

This study is different from previous studies because they focus on samples of firm-years with extreme financial performance because in this case there are likely to be more motivations for managers to manipulate their earnings.

Dechow, et al (1995) measured potential misspecification by using McNichols and Wilson (1988) analysis as follow:

𝑫𝑫𝑨𝑨𝒕𝒕 = 𝜶𝜶+𝜷𝜷𝑫𝑫𝑨𝑨𝑹𝑹𝑻𝑻𝒕𝒕+∑𝒌𝒌𝒌𝒌=1𝜸𝜸𝒌𝒌𝑿𝑿𝒌𝒌𝒕𝒕+𝜺𝜺𝒕𝒕 ……… (1)

Where; DA is discretionary accruals; PART is the partition dummy for which earnings management prediction; 𝑋𝑋_𝑡𝑡 are variables suggested to influence discretionary accruals; and 𝜀𝜀 is errors.

In most studies, PART is set equal to one for firm-years where the researcher believes earnings management is occurring in response to some stimulus. 𝑿𝑿_𝒕𝒕 cannot usually be observed directly and therefore, is excluded from the model; and discretionary accruals cannot be observed and are measured using a proxy, which Dechow, et al (1995) call DAP and which measures DA with error.

By using this model the researchers cannot arrive at precise results because they cannot categorise relevant variables for discretionary accruals such as, (𝑿𝑿_𝒌𝒌). Therefore, Dechow,

et al (1995) measured the previous model with error:

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Where; 𝐷𝐷𝐴𝐴𝑃𝑃_𝑡𝑡 = Discretionary accruals with error; 𝑏𝑏�= Estimated 𝛽𝛽 with bias and the direction of the bias is the same as the correlation between PART andµ; 𝜇𝜇_𝑡𝑡= Term that capture the omitted 𝑋𝑋_𝑡𝑡 variables and the measurement error in𝐷𝐷𝐴𝐴𝑃𝑃_𝑡𝑡; and 𝜀𝜀_𝑡𝑡= an error term that is independently and identically normally distributed.

The models were run both with and without the variable μ in order to evaluate its effect on the power of this model.

There are three generic statistical problems that occur with the models, and these are: (1) incorrectly attributing earnings management to PART (dummy variable partitioning the data for two groups for earnings management), and this problem lead to increase the probability of Type I error. “This problem will arise when (i) the proxy for discretionary accruals contains measurement error that is correlated with PART and/or (ii) other variables that cause earnings management are correlated with PART and are omitted from the analysis. In this latter case, earnings management is correctly detected by the model, but causality is incorrectly attributed to PART” (page 196).

(2) Unintentionally extracting earnings management caused by PART, which in turn leads to an increase in the probability of Type II error. “This problem will arise when the model used to generate the discretionary accrual proxy unintentionally removes some or all of the discretionary accruals” (page 196). (3) The low power of the available test statistics, leads to increasing the probability of Type II error. This problem will occur when some variables are omitted from discretionary accruals.

Dechow et al (1995) develop the Modified Jones model to address the estimation problems underlying the Jones model (1991). Dechow et al (1995) suggest that the misspecification problems in the Jones model arises due to the omission of a separate variable to reflect managers exercising their discretion over revenues. Therefore, the only difference between the Jones model and the Modified Jones model is the inclusion of the change in credit sales in the model, as a proxy for this. The Dechow et al (1995) model assumes that all the changes in credit sales during the period of study resulted from earnings management, and Jones (1991) includes the credit sales among total revenues.

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𝑻𝑻𝑨𝑨𝒎𝒎,𝒕𝒕 = 𝑰𝑰𝑪𝑪𝑫𝑫𝑰𝑰𝒎𝒎,𝒕𝒕− 𝑪𝑪𝑪𝑪𝑪𝑪𝒎𝒎,𝒕𝒕………...………... (3)

Where; TA is total accruals; NOPI is net operating income; CFO is cash flow from operating activities.

Non-discretionary accruals (NDAC) are modeled by:

𝑻𝑻𝑨𝑨𝒎𝒎,𝒕𝒕 𝑨𝑨𝒎𝒎,𝒕𝒕−1= 𝒎𝒎1 ( 1 𝑨𝑨𝒎𝒎,𝒕𝒕−1) +𝒎𝒎2( ∆𝑹𝑹𝑬𝑬𝑰𝑰𝒎𝒎,𝒕𝒕−∆𝑹𝑹𝑬𝑬𝑪𝑪𝒎𝒎,𝒕𝒕 𝑨𝑨𝒎𝒎,𝒕𝒕−1 ) + 𝒎𝒎3 ( 𝑫𝑫𝑫𝑫𝑬𝑬𝒎𝒎,𝒕𝒕 𝑨𝑨𝒎𝒎,𝒕𝒕−1) + 𝜺𝜺𝒎𝒎,𝒕𝒕……….... (4)

Where; TAi,t is the total accruals for the company (i) during period (t); ∆REVi, t is the

changes in the revenue (from credit sales) for company (i) during period (t); ∆RECi, t is

the changes in account receivable for company (i) during period (t); PPEi, t is Property,

Plant and Equipment; Ai, t-1 is the total assets for company (i) for end of period (t-1); and 𝜀𝜀𝑖𝑖,𝑡𝑡 is random error.

Discretionary accruals are defined as follows:

𝐃𝐃𝐃𝐃𝐖𝐖𝐢𝐢,𝐭𝐭 = 𝐏𝐏𝐃𝐃𝐢𝐢,𝐭𝐭 - 𝐍𝐍𝐃𝐃𝐃𝐃𝐖𝐖𝐢𝐢,𝐭𝐭 ………. (6)

Ultimately, if the null hypothesis stated that discretionary accruals are less than or equal zero is rejected, then the alternative hypothesis stated that accruals are managed upwards will be accepted (Healy, 1985).

The Modified Jones model is one of the most powerful earnings management models for two reasons:

• Since it is the first paper that used time series data to conduct the research.

• The standard errors resulting from the Jones model are lower than for other models which imply that it is a more powerful to detect earnings management.

The fifth model, Dechow et al (1991) test the Industry Model, which they devised themselves. This model is similar to the Jones model, except that it assumes that “nondiscretionary accruals are fixed all the times” and also that the difference in the components of nondiscretionary accruals is common across all firms in a given industry. Nondiscretionary accruals are defined, in this case, as below:

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• Where; 𝑇𝑇𝐴𝐴_𝑡𝑡 is the median value of total accruals; and 𝛾𝛾_1,2 are the firm specific parameters.

Dechow et al (1995) use four samples to test the various earnings management models, and these are:

• The first sample is compiled from 1000 firm-years are selected from 168771 US firm-years from 1950 to 1991, to test the problem of incorrectly attributing earnings management to PART, particularly to measure the error of discretionary accruals (µ).

• The second sample is compiled from a pool of firms with distinctively different financial performance and where, as mentioned previously, is assumed to give greater incentives for earnings management.

• The third sample is compiled from the firm-years into which the researchers have artificially inserted synthetic accruals manipulations. These accruals include (1) expense manipulation over two periods (deferred expenses which reverse the following period). (2) Revenue manipulation: achieved by increasing accruals, revenue and accounts receivable (assuming that all costs are fixed). (3) Margin manipulation: premature recognition of revenue assuming all costs are variable. • The last sample consists of 56 firm-years from firms subject to the securities

exchange commission (SEC) enforcement actions for allegedly overstating annual earnings. This sample is established to test the earnings management in firms that violated the generally accepted accounting principles.

Dechow et al (1995) draw the following conclusions: the low explanatory power of discretionary accruals models, the problem of finding suitable proxies, the problem of confounding variables, measurement error and the low power of statistical tests suggest that the Type II errors are generally much more of a problem for discretionary accruals than Type I errors.

The models appear well specified, particularly when applied to firms with distinctively different financial performances (and these are arguably the most likely to employ earnings management). However, based on the assumption that economically plausible magnitudes of earnings management would be around 1% to 5% of total assets, the models have low power for detecting effects of this size. The modified version of the Jones model has the highest power and, in particular, is the model that produces the lowest incidence of Type II errors.

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The researchers suggest that given the low power of the models, a sample of several hundred firms would be needed in order to provide a reasonable chance of detecting earnings management of the order of 1% of total assets. Researchers also need to be aware of the characteristics of their sample in order to avoid using a model of non- discretionary accruals that unintentionally removes some of the discretionary accruals (e.g. using the industrial model when discretionary accruals are correlated across the industry or the DeAngelo (1986) model when firms are in financial distress).