विधियों की तुलना करें

	पूर्णतः संशोधित ओएलएस (एफएमओएलएस) अनुमानक	साधारण न्यूनतम वर्ग (OLS) समाश्रयण	पैनल कोइंटीग्रेशन परीक्षण (पेड्रोनी, काओ, वेस्टरलुंड)	पैनल डेटा फिक्स्ड इफेक्ट्स मॉडल
क्षेत्र	अर्थमिति	अर्थमिति	अर्थमिति	अर्थमिति
परिवार	Regression model	Regression model	Regression model	Regression model
उद्भव वर्ष	1990	2019	2004	2014
प्रवर्तक	Phillips & Hansen (time series); Pedroni (heterogeneous panels)	Wooldridge (textbook treatment); classical least squares	Pedroni; Kao; Westerlund	Hsiao (textbook treatment); within transformation of panel data
प्रकार	Cointegrating regression estimator	Linear regression	Panel cointegration test	Panel data regression
मौलिक स्रोत	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.
उपनाम	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
संबंधित	5	5	3	5
सारांश	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).