응용통계연구 (The Korean Journal of Applied Statistics)

  • 제31권6호
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  • Pages.677-692
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  • 2018
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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모수, 비모수, 베이지안 출산율 모형을 활용한 합계출산율 예측과 비교

A comparison and prediction of total fertility rate using parametric, non-parametric, and Bayesian model

  • Oh, Jinho (Statistical Research Institute, Statistics Korea)
  • 투고 : 2018.06.28
  • 심사 : 2018.10.24
  • 발행 : 2018.12.31
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초록

최근 2017년 우리나라 합계출산율은 1.05명로 2005년 1.08명 수준으로 회귀하는 현상을 보이고 있다. 1.05명은 인구대체선(2.1명), 안전선(1.5명)과도 거리가 먼 초저출산 수준이고 마치 초저출산 덫에 빠질 우려가 있다. 이에 합계출산율의 합리적인 예측과 이를 통한 출산정책에 유용한 자료를 제공하는 것은 그 어느 때 보다도 중요하다. 그 동안 다양한 통계적 방법으로 합계출산율 추이를 예측하였는데, 데이터 완비성이 높고 품질이 좋은 경우 모형 접근인 모수적 방법, 데이터 추이가 단절되거나 변동이 심한 경우 평활과 가중치를 적용한 비모수적 방법, 데이터 부족과 품질 등으로 선진국의 출산율 3단계 전이현상을 참고하여 이들의 사전분포를 활용하는 베이지안 방법 등이 적용되어 왔다. 본 연구는 최근 변동이 심한 우리나라 출산율에 모수, 비모수, 그리고 베이지안 방법을 적용하여 추정과 예측을 실시하고 도출된 결과 비교를 통해 적합성과 타당성 측면에서 어떤 방법이 합리적인지 모색하고자 한다. 분석결과 합계출산율 예측값 순위는 통계청 합계출산율이 가장 높고, 베이지안, 모수, 비모수 순으로 나타났다. 2017년 TFR 1.05명 수준을 감안할 때 모수, 비모수모형으로 도출된 합계출산율 예측값이 합리적이다. 또한 출산율 자료완비성이 높고 품질이 우수할 경우 계산 효율성과 적합도 관점에서 모수적 추정과 예측 접근 방법이 타 방법보다 우수한 것으로 도출되었다.

The total fertility rate of Korea was 1.05 in 2017, showing a return to the 1.08 level in the year 2005. 1.05 is a very low fertility level that is far from replacement level fertility or safety zone 1.5. The number may indicate a low fertility trap. It is therefore important to predict fertility than at any other time. In the meantime, we have predicted the age-specific fertility rate and total fertility rate by various statistical methods. When the data trend is disconnected or fluctuating, it applied a nonparametric method applying the smoothness and weight. In addition, the Bayesian method of using the pre-distribution of fertility rates in advanced countries with reference to the three-stage transition phenomenon have been applied. This paper examines which method is reasonable in terms of precision and feasibility by applying estimation, forecasting, and comparing the results of the recent variability of the Korean fertility rate with parametric, non-parametric and Bayesian methods. The results of the analysis showed that the total fertility rate was in the order of KOSTAT's total fertility rate, Bayesian, parametric and non-parametric method outcomes. Given the level of TFR 1.05 in 2017, the predicted total fertility rate derived from the parametric and nonparametric models is most reasonable. In addition, if a fertility rate data is highly complete and a quality is good, the parametric model approach is superior to other methods in terms of parameter estimation, calculation efficiency and goodness-of-fit.

키워드

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Figure 2.1. Trend of TFR and ASFR for 1970–2017. TFR = total fertility rate; ASFR = age-specific fertility rate.

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Figure 2.2. Trend of childbearing population and total parity.

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Figure 2.3. The three phases for TFR and trajectory on decline function.

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Figure 3.1. Parameter estimate of GLG. GLG = generalized log gamma.

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Figure 3.2. Prediction for birth-order and TFR by GLG. TFR = total fertility rate; GLG = generalized log gamma.

GCGHDE_2018_v31n6_677_f0006.png 이미지

Figure 3.3. Estimation and prediction for TFR by FDM. TFR = total fertility rate; FDM = functional data model.

GCGHDE_2018_v31n6_677_f0007.png 이미지

Figure 3.4. Prediction by Bayesian and pattern on declined function for Korea. TFR = total fertility rate.

Table 3.1. TFR for Korea of WPP 2017

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Table 3.2. Results on prediction of scenarios for bayesTFR

GCGHDE_2018_v31n6_677_t0002.png 이미지

Table 3.3. A comparison of TFR on various fertility models

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Table 3.4. The results of various fertility models

GCGHDE_2018_v31n6_677_t0004.png 이미지

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