사건연구방법론에서 소표본 문제와 모형의 검정력

본 연구는 사건연구방법론에 있어서 소표본 문제가 모형의 검정력에 어떠한 영향을 미치는가를 시뮬레이션 분석을 통해 살펴본다. 또한, 유의성 검정방법의 선택 및 시장지수의 선택 등이 소표본 문제로 인한 검정력 감소 현상을 해결하는 데 어느 정도 기여할 수 있는지에 대해서도 함께 고찰한다.<BR> 시뮬레이션 결과에 의하면 표본의 크기가 작아짐에 따라 소표본 그룹의 제1종 오류의 확률은 유의수준 범위를 벗어나지 않는 적정 수준을 유지하고 있으나, 제2종 오류의 확률은 큰 폭으로 증가하는 경향을 보이고 있다. 이로 인해 소표본 그룹에 있어서 모형의 검정력은 대표본에 비해 현저히 낮았다. 그리고, 귀무가설의 유의성을 검정하는 검정방법의 선택은 소표본 문제로 인한 검정력 감소 현상을 해결하는 데 상당한 도움을 줄 수 있으나, 시장지수의 선택은 그렇지 못한 것으로 나타났다. 특히, 표본의 크기가 20개인 소표본 그룹에서는 검정통계량의 분포가 근사적으로 정규 분포에 따르고 있어 설정의 오류 가능성이 매우 낮으며, 유의성 검정 시에 개별주식 시계열 검정법을 사용할 경우 모형의 검정력도 크게 향상시킬 수 있다.

This paper investigates the effect of small sample size problems on the power of the test in the event study methodologies by using the simulation technique. This paper also examines to what extent the significance test and market index abate the statistical errors resulting from small sample problems and increase the power of the test for the following three models of estimating abnormal performance: (a) mean adjusted returns model, (b) market adjusted returns model, and (c) market model.<BR> In order to assess the impact of small sample size problems by the simulation method, this paper employs four different sample size groups which consist of two hundred and fifty samples of 50, 20, 10 and 5 securities, respectively. For each sample in each sample size group, the securities are selected from the pool of 789 securities for which daily return data of at least 3 years are available on the Stock DB of Korea Securities Research Institute (KRSI). For each security, a hypothetical event date is randomly selected with replacement using a uniform probability distribution from October 31, 1980 through December 22, 2003.<BR> This paper uses 250 daily return observations for the period around the hypothetical event day `0` of each firm, starting at day -244 and ending at day +5 relative to the event date. The first 239 days are defined as the estimation period. Parameters for each of the three performance models are estimated using the daily return data of the estimation period. The following 11 days from -5 day through +5 days are defined as the event period.<BR> A particular level of excess return is artificially introduced into a given sample by transforming its actual return data. For example, to simulate 1% abnormal performance for each security of a given sample, 0.01 is added to the actual daily return of the hypothetical event date for each sample security. In the event study methodologies, there are two types of statistical errors in the significance test of null hypothesis: Type Ⅰ and Type Ⅱ errors. While Type Ⅰ error is to reject the null hypothesis of no excess returns when it is true, Type Ⅱ error is to fail to reject the null hypothesis of no excess returns when it is false. Therefore, the power of a test is calculated as [1 - the probability of Type Ⅱ errors].<BR> The results of this paper can be summarized as follows:<BR> (1) For the sample size groups of 50 and 20 securities, the empirical distributions of mean excess returns seem close to normal and those of the test statistics are close to unit normal across all the three performance models. On the contrary, for small sample groups of 10 and 5 securities, both the mean excess returns and the test statistics are highly non-normal.<BR> (2) For a given level of excess return, larger samples more accurately detect the presence of abnormal performance across all the three performance models. It means that when there exist the small sample problems, the probability of Type Ⅱ er