Linganisha mbinu

	Njia ya Wakati wa Regression ya Kiasi	Mchanganuo wa Kiasi-Patanishi	NARDL Msalaba-Sehemu
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2004	2012	2014
Mwanzilishi	Roger Koenker and colleagues	Oliver Linton and Yoon-Jin Whang	Yongcheol Shin and colleagues
Aina	Distribution regression	Correlation measure	Asymmetric panel model
Chanzo asilia	Koenker, R. (2004). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1), 74-89.	Linton, O., & Whang, Y. J. (2012). Quantile comparisons of time series data. Journal of Econometrics, 170(2), 242-257.	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.
Majina mbadala	GMM quantile regression	—	NARDL panel
Zinazohusiana	3	3	3
Muhtasari	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.	The cross-quantilogram extends the cross-correlogram concept to quantile pairs of two time series, measuring dependence at different quantile levels. Introduced by Linton and Whang (2012), it captures how shocks at specific quantile levels in one series relate to movements in another, enabling asymmetric dependence analysis. This approach is particularly valuable when downside and upside risk correlations differ materially.	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.