Linganisha mbinu

	ARDL ya Kiasi	NARDL Msalaba-Sehemu	Njia ya Wakati wa Regression ya Kiasi
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2006	2014	2004
Mwanzilishi	Roger Koenker and Zhijie Xiao	Yongcheol Shin and colleagues	Roger Koenker and colleagues
Aina	Conditional distribution model	Asymmetric panel model	Distribution regression
Chanzo asilia	Koenker, R., & Xiao, Z. (2006). Quantile autoregression. Journal of the American Statistical Association, 101(475), 980-990.	Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a system of nonlinear autoregressive distributed lag equations. Econometric Reviews, 33(1), 56-87.	Koenker, R. (2004). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1), 74-89.
Majina mbadala	Quantile ARDL	NARDL panel	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-NARDL extends the nonlinear autoregressive distributed lag (NARDL) model to panel data, capturing asymmetric long-run and short-run relationships where positive and negative changes in explanatory variables have differential effects. Introduced by Shin et al. (2014) and adapted to panels, it allows studying how cross-sectional units respond differently to positive versus negative shocks while maintaining cointegrating relationships. This approach is essential for understanding economic asymmetries in commodity markets, monetary transmission, and labor markets.	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.