Linganisha mbinu

	ARDL ya Kiasi	ARDL za Msalaba-Sehemu	Njia ya Wakati wa Regression ya Kiasi
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2006	2006	2004
Mwanzilishi	Roger Koenker and Zhijie Xiao	Pesaran and colleagues	Roger Koenker and colleagues
Aina	Conditional distribution model	Dynamic panel model	Distribution regression
Chanzo asilia	Koenker, R., & Xiao, Z. (2006). Quantile autoregression. Journal of the American Statistical Association, 101(475), 980-990.	Pesaran, M. H., & Smith, R. (2016). Testing weak cross-sectional dependence in large panels. Econometric Reviews, 34(6-10), 1089-1117.	Koenker, R. (2004). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1), 74-89.
Majina mbadala	Quantile ARDL	Panel ARDL with cross-sectional dependence	GMM quantile regression
Zinazohusiana	3	3	3
Muhtasari	QARDL (Quantile Autoregressive Distributed Lag) combines quantile regression with ARDL modeling to estimate conditional relationships at different points of the distribution, revealing heterogeneous short-run and long-run effects. Introduced by Koenker and Xiao (2006) and refined by Cho et al. (2015), it captures how the effect of explanatory variables on outcomes varies across quantiles, essential for understanding tail behavior and distributional impacts rather than just mean effects.	CS-ARDL (Cross-Sectional ARDL) applies the ARDL framework to panel data while explicitly accounting for cross-sectional dependence—correlation of shocks and relationships across units (countries, firms, regions). Introduced by Pesaran and colleagues (2016), it extends panel ARDL methods to handle common factors or global shocks affecting all units simultaneously. This is crucial for realistic modeling of internationally integrated economies and firm networks.	Method of Moments Quantile Regression combines moment-based estimation (GMM) with quantile regression to estimate distribution parameters while handling endogeneity, panel structure, and dynamic relationships. Introduced by Koenker (2004) and developed by Machado and Mata (2005), it enables distributional analysis (not just mean regression) in complex settings like dynamic panels and instrumental-variable contexts. This approach is powerful for understanding heterogeneity in treatment effects and policy impacts.