Linganisha mbinu

	ARDL za Msalaba-Sehemu	Uchambuzi wa Lag Uliosambazwa kwa Msalaba	NARDL Msalaba-Sehemu	VARX ya Paneli
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model	Regression model
Mwaka wa asili	2006	2001	2014	2013
Mwanzilishi	Pesaran and colleagues	Pesaran, Shin, and Smith	Yongcheol Shin and colleagues	Canova and Ciccarelli
Aina	Dynamic panel model	Distributed lag model	Asymmetric panel model	Multi-equation panel model
Chanzo asilia	Pesaran, M. H., & Smith, R. (2016). Testing weak cross-sectional dependence in large panels. Econometric Reviews, 34(6-10), 1089-1117.	Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships and dynamics. Journal of Applied Econometrics, 16(3), 289-326.	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.	Canova, F., & Ciccarelli, M. (2013). Panel vector autoregressive models: A survey. Advances in Econometrics, 32, 205-246.
Majina mbadala	Panel ARDL with cross-sectional dependence	Panel distributed lag model	NARDL panel	Panel VAR-X
Zinazohusiana	3	3	3	3
Muhtasari	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.	CS-DL (Cross-Sectional Distributed Lag) is a simplified dynamic panel model regressing outcomes on current and lagged explanatory variables without explicit autoregressive terms, while accounting for cross-sectional dependence. Built on Pesaran et al. (2001) and extended by Chudik et al. (2014), it estimates dynamic effects more parsimoniously than ARDL when autocorrelated lags are less critical. This approach is valuable for short-horizon effects and policy impact analysis.	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.	Panel VARX extends vector autoregression to heterogeneous panels with exogenous variables, enabling simultaneous modeling of multiple endogenous variables alongside observed external factors across many units. Introduced by Holtz-Eakin et al. (1988) and advanced by Canova and Ciccarelli (2013), it captures dynamic relationships within units while allowing parameters to vary across units. This framework is essential for macroeconomic panels and understanding cross-unit heterogeneity in responses to common shocks.