二分因變數之會計學研究應採用Probit或OLS模型之探討

Abstract

國內二分因變數的會計研究大部份屬於小樣本的情況，因而Probit模型之估計值不一定會較OLS (ordinary least square)更有效率。本研究嘗試由實證的角度，用模擬的方式，希望能知道那種模型較適合國內二分因變數的會計研究?吾人首先由顯著水準及檢定力兩方面著手，比較此二模型在台灣證券市場之實際資料下，何者表現較佳。此外，本研究並分析此二方法在預測能力上之優劣。期望透過這三種比較方式，推論出何種模型較適合國內的會計資料，以期使研究者在面對模型選擇時，能有所依據。本研究利用民國76年至80年的資料做模擬測試，結果顯示：當虛無假設為真時，OLS檢定的統計量之真實顯著水準與理論顯著水準的差距比Probit小;而當虛無假，設不正確時，OLS的檢定力也比Probit為高。另外，在預測能力的比較分析上， 也發現OLS表現比Probit為佳。所以整體而言， 在本研究的樣本量和方法下，OLS 模型比Probit模型更適合國內二分因變數的會計研究。亦即當我們面臨這類會計研究之模型選擇時，簡單的線性迴歸似乎比複雜的Probit模型更為合適。

Noreen (1988) compared the relative performance of Probit and OLS regression significance tests. He concluded that for the kind of data and sample sizes commonly found in accounting classificatory studies, OLS regression performs at least as well as Probit. In this paper, we compared the two models in two respects, significance tests and prediction accuracy. Using empirical data from firms listed on Taiwan Stock Exchange, our simulation indicates the following results: (I) the empirical distributions of the OLS regression conform closer to the theoretical distributions, when the null hypothesis is true, (II) OLS regression is more powerful, when the alternative hypothesis is true, and (III) the correct prediction ratio of OLS regression is higher than that of Probit model. Based on the empirical results, we suggest the use of OLS regression in accounting classificatory studies for the sample sizes similar to our Monte Carlo experiments.