# Journal of the Royal Statistical Society: Series A (Statistics in Society)

© Royal Statistical Society

Edited By: H. Goldstein and L. Sharples

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ISI Journal Citation Reports © Ranking: 2015: 13/49 (Social Sciences Mathematical Methods); 24/123 (Statistics & Probability)

Online ISSN: 1467-985X

Associated Title(s): Journal of the Royal Statistical Society: Series B (Statistical Methodology), Journal of the Royal Statistical Society: Series C (Applied Statistics), Significance

#### 176:3

**Measures of the economic value of probabilities of bankruptcy****, by D J Johnstone et al., Journal of the Royal Statistical Society, Series A, Statistics in Society, Volume 176, part 3 (2013), pages 635 - 653**

The spreadsheet is largely self explanatory.

Column A Date of observation

Column B 1=failed 0=not failed (this shows the state of the firm at the observation date)

Column C-G Probabilities of failure estimated using 5 different models (C Hillegeist model; D Ohlson model re-estimated; E Ohlson model with Ohlson’s own parameter values; F simple average of models C,D and E; F simple average of models C and D)

Columns M-Q Log scores (of all five models respectively)

Columns R-V Quadratic scores

Columns W-AA Exponential scores

Columns AC-AG Reciprocal scores

Columns AI-AM Square root scores

The average scores are at the foot of each column.

The spreasdsheet starts with the actual outcome (Failed firms=1, Not Failed=0) and 5 separate columns of probabilities. These 5 probabilities are each labelled at the top of the column. The first three columns are logit probabilities found by estimating Ohlson's model.

Model (i) called "Old" has the original Ohlson paramter estimates. Model (ii) called "Hillegeist" has the Hillegeist estimates. Model (iii) called "New" has our estimates. Model (iv) is the average of (i)-(iii). Model (v) is the average of (ii) and (iii).

The 5 distinctly coloured and labelled sets of 5 columns calculate the 5 di¤erent probability score functions (beta = ??1; 0; 0:5; 1; 2) for each model. Their averages reported in the paper are at the bottom of each column. There are n = 11973 rows of probabilities for all models.

Table 4. Average Utility Gain Over n = 11973 Trials

beta | Model(i) | Model (ii) | Model (iii) | Model (iv) | Model (v) |

-1 | -1069.15 | -8-51 | -197.45 | 0.03 | 0.11 |

0 | -2.44 | -0.11 | -0.37 | 0.02 | 0.03 |

1/2 | -0.24 | -0.04 | -0.01 | 0.01 | 0.03 |

1 | -0.14 | -0.02 | 0.05 | 0.01 | 0.05 |

2 | -1.13 | -0.01 | 0.27 | 0.07 | 0.19 |

David Johnstone

University of Sydney Business School

University of Sydney

Sydney

NSW 2006

Australia

E-mail: David.johnstone@sydney.edu.au