The Information Loss of the Binary Logit in the Study of Financial Statements: A Comparison of Three Probability Models

以二元邏輯斯模型研究財務報表之資訊損失：比較三個機率模型

Ou 與Penman (1989a； 1989b)及Holthausen 與Larcker (1992)等人使用了二元機率預測模型Pr 用來探討財務報表資訊對非常報酬的預測能力，這個機率模型提供了一個研究財務報表資訊的方法，這些研究的共同特性就是將連續的因變數如未來一期的累積異常報酬(CAR)或盈餘變動數轉換成不連續的二元的反應變數(正或負)，Ou (1990)認為將連續變數轉換成不連續的二元變數可以降低盈餘變數衡量上極端值在估計模型時所造成的影響。而在另一方面Penman (1992)則認為將一連續變數轉換成二元變數形同將有用的資訊拋棄不用，因此這些研究所使用的機率估計模型應有改進的空間，針對此一問題，本研究以財務報表資訊對預測未來一年CAR 的能力，分別比較三個機率模型，詳言之，除了將連續的CAR 轉換成二元的反應變數套入二元邏輯斯機率模型外，本研究並將CAR 按其大小分成十等級，轉換成一個多元有序的反應變數(ordered response variable)，以有序邏輯斯作為機率估計模型，以及將連續的CAR 以普通最小平方法為基楚的機率估計模型，此外並以主要成份析降低財務比率間的共線問題。

In the study of financial statement information, it is argued that the binary logit loses information. To investigate this issue, this study compares the relative performance of three probability models (the binary logit, the ordered logit, and an OLS-based probability model) in predicting one-year-ahead cumulative abnormal returns (CAR). Compared with the other two models, the binary logit appears to lose some information in CAR, leading to a more than 2.1% loss in average annual hedging profits for the 1982-1991 period in the study sample. However, no consistent, significant differences are observed between the OLS-based probability model and the ordered logit. The result is interpreted as the existence of noise contained in the magnitude of CAR.