Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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An Alternative Parametric Estimation of Sample Selection Model: An Application to Car Ownership and Car Expense

비정규분포를 이용한 표본선택 모형 추정: 자동차 보유와 유지비용에 관한 실증분석

  • Received : 2011.10.06
  • Accepted : 2012.03.19
  • Published : 2012.05.31
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Abstract

In a parametric sample selection model, the distribution assumption is critical to obtain consistent estimates. Conventionally, the normality assumption has been adopted for both error terms in selection and main equations of the model. The normality assumption, however, may excessively restrict the true underlying distribution of the model. This study introduces the $S_U$-normal distribution into the error distribution of a sample selection model. The $S_U$-normal distribution can accommodate a wide range of skewness and kurtosis compared to the normal distribution. It also includes the normal distribution as a limiting distribution. Moreover, the $S_U$-normal distribution can be easily extended to multivariate dimensions. We provide the log-likelihood function and expected value formula based on a bivariate $S_U$-normal distribution in a sample selection model. The results of simulations indicate the $S_U$-normal model outperforms the normal model for the consistency of estimators. As an empirical application, we provide the sample selection model for car ownership and a car expense relationship.

표본선택 모형을 최우추정법으로 추정할 때 오차항의 분포를 제대로 가정하는 것이 매우 중요하다. 표본선택 모형의 선택 방정식과 본 방정식의 오차항 분포를 일반적으로 이변량 정규분포로 가정하지만, 이 가정이 오차항의 실제 분포를 과도하게 제약할 가능성이 있다. 본 연구는 표본선택 모형의 오차항 분포로 $S_U$-정규분포를 도입한다. $S_U$-정규분포는 분포의 비대칭성과 초과첨도를 허용한다는 측면에서 정규분포보다 훨씬 유연하면서, 동시에 정규분포를 극한분포의 형태로 포함하고 있다. 또한 정규분포처럼 다변량 분포함수가 존재하기 때문에 표본선택 모형과 같은 다변량 모형에서도 활용할 수 있다. 본 논문은 $S_U$-정규분포를 이용한 표본선택 모형에서 로그우도 함수와 조건부 기댓값을 도출하고, 시뮬레이션을 통해 정규분포 모형과 추정성과를 비교한다. 또한 자동차 보유 가구들의 자동차 유지비에 관한 실제 데이터를 이용하여 $S_U$-정규분포 표본선택 모형의 추정결과를 제시한다.

Keywords

References

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