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Empirical Economics

Erschienen in:

23.09.2020

Joint tests for dynamic and spatial effects in short panels with fixed effects and heteroskedasticity

verfasst von: Zhenlin Yang

Erschienen in: Empirical Economics | Ausgabe 1/2021

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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.

Vorheriger Artikel General diagnostic tests for cross-sectional dependence in panels

Nächster Artikel A homogeneous approach to testing for Granger non-causality in heterogeneous panels

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Other works on short SDPD models include Elhorst (2010), Su and Yang (2015), Qu et al. (2016), and Kuersteiner and Prucha (2018). However, most of the research on SDPD models focuses on long panels (with large n and large T), see, e.g., Yang et al. (2006), Mutl (2006), Yu et al. (2008), Yu and Lee (2010), Lee and Yu (2010b, (2012, (2014); Bai and Li (2015), and Shi and Lee (2017).

Interestingly, this method finds root in Neyman and Scott (1948) on modified likelihood equations. Chudik and Pesaran (2017) use similar ideas to give a bias-corrected method of moments estimation.

This typically occurs to the estimator of the spatial error parameter; see Lee (2004), Liu and Yang (2015), Su and Yang (2015), and Yang (2018a). However, this feature is not explicitly reflected in the subsequent developments as the implementations of the tests do not require \(\iota \).

The concentrated AQS function for \(\rho \) contained in (2.16) clearly shows that the M-estimator is not only consistent when T is fixed but also eliminates the bias of order \(O(T^{-1})\). In contrast, the estimator based on the unadjusted score is inconsistent when T is fixed and has a bias of order \(O(T^{-1})\) when T grows with n. See Hahn and Kuersteiner (2002), and Yang (2018a, (2018b) for more discussions.

As \({{\mathbf {M}}}^{*}=\Omega ^{-1}-\Omega ^{-1}\Delta X(\Delta X^{\prime }\Omega ^{-1}\Delta X)^{-1}\Delta X^{\prime }\Omega ^{-1}\), calculations of \(\Omega ^{\frac{1}{2}}\) and \(\Omega ^{-\frac{1}{2}}\) are avoided.

The Rook and Queen schemes are standard. For Group-I, we first generate \(k=\sqrt{n}\) groups of sizes \(n_g \sim U(.5{\bar{n}}, 1.5{\bar{n}})\), \(g=1, \cdots , k\) and \({\bar{n}}=n/k\), and then adjust \(n_g\) so that \(\sum _{g=1}^k n_g = n\). For Group-II, we first generate 6 groups of fixed sizes (3, 5, 7, 9, 11, 15), and replicate these groups r times to give \(n=r\times 50\). See Lin and Lee (2010) and Yang (2018a) for details in generating these spatial layouts.

In both (ii) and (iii), the generated errors are standardized to have mean zero and variance \(\sigma _v^2\).

See Lee and Yu (2016) for a detailed discussion on parameter identification of the SDPD model.

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Titel: Joint tests for dynamic and spatial effects in short panels with fixed effects and heteroskedasticity
verfasst von: Zhenlin Yang
Publikationsdatum: 23.09.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 1/2021
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-020-01935-y

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