Linganisha mbinu

	Nafasi ya Fama-MacBeth	Makadirio ya Kienyeji	VARX ya Paneli	Kigezo Kinachobadilika kwa Wakati cha VAR Iliyoimarishwa na Vipengele
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model	Regression model
Mwaka wa asili	1973	2005	2013	2005
Mwanzilishi	Eugene Fama and James MacBeth	Oscar Jorda	Canova and Ciccarelli	Bernanke, Boivin, and Eliasz
Aina	Cross-sectional regression	Multi-horizon regression	Multi-equation panel model	Time-varying system
Chanzo asilia	Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81(3), 607-636.	Jorda, O. (2005). Estimation and inference of impulse responses by local projections. American Economic Review, 95(1), 161-182.	Canova, F., & Ciccarelli, M. (2013). Panel vector autoregressive models: A survey. Advances in Econometrics, 32, 205-246.	Bernanke, B. S., Boivin, J., & Eliasz, P. S. (2005). Measuring monetary policy. Journal of Political Economy, 113(1), 161-208.
Majina mbadala	Two-step cross-sectional regression	LP-IR, Multi-horizon regression	Panel VAR-X	Dynamic factor model with time-varying parameters
Zinazohusiana	3	3	3	3
Muhtasari	The Fama-MacBeth procedure is a two-step regression methodology for analyzing cross-sectional relationships while controlling for time-series structure. Introduced by Fama and MacBeth (1973), it first estimates time-series parameters for each cross-sectional unit, then regresses outcomes on those parameters across the cross-section, averaging results over time. This approach elegantly separates within-unit dynamics from cross-sectional heterogeneity and provides standard errors robust to panel structure.	Local Projections (LP) is a semi-parametric method for estimating impulse responses directly via multi-horizon regressions, bypassing VAR-model specification. Introduced by Jorda (2005), it projects outcomes h periods ahead onto current shocks and lags, producing impulse-response functions without assuming a particular lag structure or VAR order. This flexibility has made it the dominant approach in applied macroeconomics for measuring policy effects and shock transmission.	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.	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.