@TechReport{iza:izadps:dp13803,
            	author={Baltagi, Badi H. and Pirotte, Alain and Yang, Zhenlin},
            	title={Diagnostic Tests for Homoskedasticity in Spatial Cross-Sectional or Panel Models},
            	year={2020},
	month={Oct},
            	institution={Institute of Labor Economics (IZA)},
            	address={Bonn},
            	type={IZA Discussion Paper},
            	number={13803},
            	url={https://www.iza.org/publications/dp13803},
	abstract={We propose an Adjusted Quasi-Score (AQS) method for constructing tests for homoskedasticity in spatial econometric models. We first obtain an AQS function by adjusting the score-type function from the given model to achieve unbiasedness, and then develop an Outer-Product-of-Martingale-Difference (OPMD) estimate of its variance. In standard problems where a genuine (quasi) score vector is available, the AQS-OPMD method leads to finite sample improved tests over the usual methods. More importantly in non-standard problems where a genuine (quasi) score is not available and the usual methods fail, the proposed AQS-OPMD method provides feasible solutions. The AQS tests are formally derived and asymptotic properties examined for three representative models: spatial cross-sectional, static or dynamic panel models. Monte Carlo results show that the proposed AQS tests have good finite sample properties.},
	keywords={non-normality;martingale difference;incidental parameters;heteroskedasticity;fixed effects;adjusted quasi-scores;short dynamic panels;spatial effects},
            }