مقایسهٔ روش‌ها

	تخمین‌گر OLS کاملاً تعدیل‌شده (FMOLS)	رگرسیون حداقل مربعات معمولی (OLS)	آزمون‌های هم‌انباشتگی پانل (پدرونی، کائو، وسترلوند)	مدل اثرات ثابت داده‌های پانل
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	1990	2019	2004	2014
پدیدآور	Phillips & Hansen (time series); Pedroni (heterogeneous panels)	Wooldridge (textbook treatment); classical least squares	Pedroni; Kao; Westerlund	Hsiao (textbook treatment); within transformation of panel data
نوع	Cointegrating regression estimator	Linear regression	Panel cointegration test	Panel data regression
منبع بنیادین	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.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	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.	Hsiao, C. (2014). Analysis of Panel Data (3rd ed.). Cambridge University Press.
نام‌های دیگر	fully modified OLS, Phillips-Hansen FMOLS, Tam Düzeltilmiş OLS (FMOLS)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	Pedroni cointegration test, Kao cointegration test, Westerlund cointegration test, panel long-run equilibrium tests	fixed effects model, within estimator, panel fixed-effects regression, Panel Veri — Sabit Etkiler Modeli
مرتبط	5	5	3	5
خلاصه	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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	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.	The Panel Data Fixed Effects model estimates relationships from panel data (the same units observed over several time periods) while controlling for unit- and/or time-specific effects, supporting causal inference. It is developed as the within estimator in standard treatments such as Hsiao's Analysis of Panel Data (2014).