방법 비교

	Hausman 명세 검정 (고정 효과 vs. 임의 효과)	FMOLS (Fully Modified OLS) 추정량	패널 공적분 검정 (페드로니, 카오, 웨스터룬드)
분야	계량경제학	계량경제학	계량경제학
계열	Regression model	Regression model	Regression model
기원 연도	1978	1990	2004
창시자	Jerry A. Hausman	Phillips & Hansen (time series); Pedroni (heterogeneous panels)	Pedroni; Kao; Westerlund
유형	Specification test for panel data models	Cointegrating regression estimator	Panel cointegration test
원전	Hausman, J. A. (1978). Specification Tests in Econometrics. Econometrica, 46(6), 1251–1271.	Phillips, P. C. B. & Hansen, B. E. (1990). Statistical Inference in Instrumental Variables Regression with I(1) Processes. Review of Economic Studies, 57(1), 99–125.	Pedroni, P. (2004). Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis. Econometric Theory, 20(3), 597–625.
별칭	Hausman specification test, FE vs RE test, Durbin-Wu-Hausman test, Hausman Spesifikasyon Testi (FE vs RE)	fully modified OLS, Phillips-Hansen FMOLS, Tam Düzeltilmiş OLS (FMOLS)	Pedroni cointegration test, Kao cointegration test, Westerlund cointegration test, panel long-run equilibrium tests
관련	5	5	3
요약	The Hausman test is a specification test, introduced by Jerry A. Hausman in 1978, that decides between the fixed-effects (FE) and random-effects (RE) estimators in panel data models. The null hypothesis is that the random-effects estimator is consistent and efficient and should be preferred; the alternative is that random effects is inconsistent and fixed effects is required because the unit-specific effects are correlated with the explanatory variables.	Fully Modified OLS, introduced by Phillips and Hansen (1990), estimates the long-run coefficients of a cointegrating relationship among I(1) variables. It applies a semi-parametric correction to ordinary least squares to remove the bias that endogeneity and serial correlation otherwise induce in cointegrated time series or panel data.	Panel cointegration tests check whether a set of integrated variables share a stable long-run equilibrium relationship across a panel of cross-sectional units. Pedroni (1999, 2004) provides heterogeneous-panel tests with seven statistics, Kao (1999) gives an ADF-based homogeneous-panel test, and Westerlund (2007) adds error-correction-based tests robust to structural breaks and cross-sectional dependence.