Joint tests for dynamic and spatial effects in short panels with fixed effects and heteroskedasticity
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Joint tests for dynamic and spatial effects in short panels with fixed effects and heteroskedasticity Zhenlin Yang1 Received: 3 February 2020 / Accepted: 2 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Simple and reliable tests are proposed for testing the existence of dynamic and/or spatial effects in fixed-effects panel data models with small T and possibly heteroskedastic errors. The tests are constructed based on the adjusted quasi scores (AQS), which correct the conditional quasi scores given the initial differences to account for the effect of initial values. To improve the finite sample performance, standardized AQS tests are also derived, which are shown to have much improved finite sample properties. All the proposed tests are robust against nonnormality, but some are not robust against cross-sectional heteroskedasticity (CH). A different type of adjustments is made on the AQS functions, leading to a set of tests that are fully robust against unknown CH. Monte Carlo results show excellent finite sample performance of the standardized versions of the AQS tests. Keywords Adjusted quasi scores · Dynamic effect · Fixed effects · Heteroskedasticity · Initial conditions · Nonnormality · Short panels · Tests · Spatial effects JEL Classification C12 · C18 · C21 · C23
An early version was circulated under the title: Joint Tests for Dynamic and Spatial Effects in Short Panels with Fixed Effects. I would like to thank Peter Robinson, Fei Jin, Lung-Fei Lee, James LeSage, the participants of the 15th International Workshop on Spatial Econometrics and Statistics, Orleans, 27–28 May 2016 and the 2nd Econometrics Workshop at the Chinese University of Hong Kong, 29 April 2017, Guest Editors Qi Li and Vasilis Sarafidis, and two anonymous referees, for their helpful comments. I am grateful to Singapore Management University for financial support under Grant C244/MSS14E002.
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Zhenlin Yang [email protected] School of Economics, Singapore Management University, 90 Stamford Road, Singapore 178903, Singapore
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Z. Yang
1 Introduction Panel data (PD) model has been an important tool for applied economics researchers over the past few decades. However, there have been growing concerns on whether the panel models are dynamic in nature due to the impacts from the past to the current and future ‘economic’ performance, and whether the models contain spatial dependence caused by the interactions among economic agents or social actors (e.g., neighborhood effects, copy-catting, social network, and peer group effects). In other words, there have been growing concerns from applied researchers on whether a spatial dynamic panel data model (SDPD) is more appropriate than a regular PD model, or a regular dynamic panel data (DPD) model, or a static spatial panel data (SPD) model. Thus, it is highly desirable to device simple and reliable tests helping applied researchers to choose the most appropriate model. The spatial dynamic panel data (SDPD) model that our tests concern takes the form: yt =
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