Linganisha mbinu

	VARX ya Paneli	Jopo la Kizingiti VAR	Kigezo Kinachobadilika kwa Wakati cha VAR Iliyoimarishwa na Vipengele
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2013	1996	2005
Mwanzilishi	Canova and Ciccarelli	Bruce Hansen and colleagues	Bernanke, Boivin, and Eliasz
Aina	Multi-equation panel model	Nonlinear panel model	Time-varying system
Chanzo asilia	Canova, F., & Ciccarelli, M. (2013). Panel vector autoregressive models: A survey. Advances in Econometrics, 32, 205-246.	Hansen, B. E. (1996). Inference when a nuisance parameter is not identified under the null hypothesis. Econometric Theory, 12(3), 386-414.	Bernanke, B. S., Boivin, J., & Eliasz, P. S. (2005). Measuring monetary policy. Journal of Political Economy, 113(1), 161-208.
Majina mbadala	Panel VAR-X	Panel-VAR with regime switching	Dynamic factor model with time-varying parameters
Zinazohusiana	3	3	3
Muhtasari	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.	The Threshold Panel VAR extends the standard vector autoregression framework to accommodate regime-switching behavior where relationships change when a threshold variable crosses a critical level. Introduced by Hansen (1996) and applied to panels by Caner and Hansen (2001), it allows different dynamic relationships across regimes (e.g., expansions versus recessions) while exploiting the cross-sectional dimension of panel data. This nonlinear framework captures state-dependent policy effects and economic mechanisms.	TVP-FAVAR is a hybrid framework combining factor-augmented VARs with time-varying parameter estimation via Kalman filtering. Introduced by Bernanke et al. (2005) and refined by Primiceri (2005), it extracts latent economic factors (e.g., a 'common monetary policy shock') from high-dimensional data while allowing VAR coefficients to evolve stochastically over time. This framework captures both reduced-dimensionality patterns and structural instability, making it ideal for studying evolving policy regimes and shock dynamics.