In his paper titled The Detection of Earnings Manipulation (1999), Professor Beneish determined a model to predict earnings manipulation in companies. In table 5 of this paper, he determines probability cutoffs that minimize the expected cost of misclassification. In the notes to this table, he provides a formula that computes the expected costs of misclassification which is easy to follow. However, what I am not following is how he determined the specific cutoff points that minimize the expected costs of misclassification.
I have seen a PhD titled An Investigation of Earnings Management and Earnings Manipulation in the UK by Dr P Marinakis which does the same thing in Chapter 8 section 5.4, but he too does not explain how he determined the cutoff points to minimize the expected cost of misclassification.
Maybe I am missing something simple, please assist.
@Professor Onipe Adabenege Yahaya. Thank you for your response. Yes, he derives three cut-off points of -1.89, -1.78 and -1.49 representing the different error cost ratios of 10:1, 20:1 and 40:1 respectively. He derives these scores by using the cut-off probabilities and the normal probability table.
He explains that the cut-off probabilities are computed to minimise the expected cost of misclassification. He provides a formula for the expected cost of misclassification (ECM) as ECM = P(M)PICI + [1 - P(M)]PIICII but does not explain how this ECM was minimised when determining the cut-offs or how the cut-offs were even determined.
There are three cut-off points (-1.89, -1.78 and -1.49) derived for the 'assumed' different error cost ratio levels of 10:1, 20:1 and 40:1 respectively, derived by using the cut-off probabilities along with the normal probability table.
So, to minimize the the expected cost of wrong (mis) classification, the cut-off probabilities are determined using the formula:
ECM = P(M)PICI + [1 - P(M)]PIICII,
where;
ECM = Expected Cost of miscalculation, P(M) = the prior probability of encountering earnings manipulators, PI = the conditional probability of a Type I error occurring; PII = the conditional probability of Type II error; CI = Cost of Type I error and CII = Cost of Type II error.
However, it remains hazy how this ECM was minimized in the determination of the cut-offs or how the cut-offs were even derived except as indicated above. Therefore, for now, any score above the cut off implies likelihood of manipulation, while a 'less than' M-score signals a low probability that the company's earnings have been manipulated.
Thank you Professor Bassey Ina Ibor
What I ended up doing was calculating the M-score for each observation and ranking them from highest to lowest. I then calculated the type I and type II errors had that observation's M-score been the cut-off point. I then used the error cost ratio as the cost of type I and type II errors (for example, when using the level of 10:1, I substituted 10 for the cost of type I and 1 for the cost of type II - I had previously used this to successfully replicate Beneish's calculation for the "cost of model errors relative to naive strategy").
I was then able to use these values to calculate the ECM as per the formula provided. After this, I could graph the ECM curve (or sort the ECMs) to determine the lowest point.
Based on the lowest ECM, I could then determine the relevant M-score and the associated cutoff probability.
This method seemed to work but it also seemed to be backward as I expected that I should first determine the cutoff probability and then derive the M-score rather than first determining the M-score and then deriving the associated cut-off probability.
I love the novelty here, which will surely enthuse more conversations on the definitive approach. Thumbs up Alastair!
- Badges
- Science topic
- Similar topics
- Philosophy
- Esthetics
- Interpretation