Linganisha mbinu

	Njia ya Wastani wa Kikundi (PMG)	Kipimo cha Vikomo vya ARDL (Kipimo cha Vikomo cha Pesaran)	Kielelezo cha Athari Zilizowekwa za Data ya Paneli
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1999	2001	2014
Mwanzilishi	Pesaran, Shin & Smith	Pesaran, Shin & Smith	Hsiao (textbook treatment); within transformation of panel data
Aina	Panel cointegration estimator	Cointegration test / Autoregressive distributed lag model	Panel data regression
Chanzo asilia	Pesaran, M. H., Shin, Y., & Smith, R. P. (1999). Pooled mean group estimation of dynamic heterogeneous panels. Journal of the American Statistical Association, 94(446), 621–634.	Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds Testing Approaches to the Analysis of Level Relationships. Journal of Applied Econometrics, 16(3), 289–326.	Hsiao, C. (2014). Analysis of Panel Data (3rd ed.). Cambridge University Press.
Majina mbadala	PMG Estimator, Pooled Mean Group, PMG Panel Estimator, Havuzlanmış Ortalama Grup Tahmincisi	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	fixed effects model, within estimator, panel fixed-effects regression, Panel Veri — Sabit Etkiler Modeli
Zinazohusiana	2	4	5
Muhtasari	The Pooled Mean Group (PMG) estimator, introduced by Pesaran, Shin, and Smith (1999), is a panel data technique designed for dynamic heterogeneous panels where the long-run equilibrium relationship is common across groups but short-run dynamics and error variances are allowed to differ. It is particularly suited for macro-panels with moderate N and T, such as cross-country growth, energy consumption, and financial development studies.	The ARDL bounds test is an autoregressive distributed lag method that tests for a cointegrating (long-run level) relationship between time series, introduced by Pesaran, Shin and Smith in 2001. Unlike the Johansen procedure, it remains valid whether the variables are I(0), I(1) or a mix of the two, and it is more reliable than Johansen in small samples of roughly 30 to 80 observations.	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).