Robust Standard Errors in Transformed Likelihood Estimation of Dynamic Panel Data Models

Hayakawa, Kazuhiko; Pesaran, M. Hashem

doi:10.2139/ssrn.2047069

Cited by 10 publications

(31 citation statements)

References 51 publications

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“…In particular, for the heteroscedastic case we redefine quantities in Proposition in the following way:

{italicσ}_{0}^{2} \equiv \underset{N \to \infty}{falselim} \frac{1}{N} \sum_{i = 1}^{N} {italicσ}_{0, i}^{2}, {italicα}_{0} \equiv \frac{1 - {italicϕ}_{0}^{2}}{σ_{0}^{2}} \underset{N \to \infty}{falselim} \frac{1}{N} \sum_{i = 1}^{N} var (y_{i, 0} - \frac{{italicη}_{i}}{false(1 - ϕ_{0} false)}) .

As a result, the two key parameters α 0 and ϕ 0 that determine the shape of the log‐likelihood function are the same, but slightly redefined. In this way this paper also completes the analysis of Hayakawa and Pesaran (), who do not fully investigate the shape of the TML likelihood function in such a setting.…”

Section: Multiple Solutions and Bounded Estimationsupporting

confidence: 52%

“…The likelihood function in is defined for all values of

ϕ \in R

, hence from a theoretical and computational point of view there are no reasons to consider a restricted parameter space for estimation. Nevertheless, some studies (Hsiao et al ., , p. 135 and Hayakawa and Pesaran, , p. 123, footnote 14) restrict ϕ ∈ (−1;1). This may have consequences for the finite sample properties of the resulting estimators, as we shall see below.…”

Section: Estimation For the Panel Ar(1) Modelmentioning

confidence: 99%

“…Monte Carlo evidence in Hsiao et al . (), Alvarez and Arellano () and Hayakawa and Pesaran (), suggest that these likelihood‐based approaches can serve as viable alternatives to the usual GMM estimators. Just like for GMM, however, the application of ML estimators is not without its own problems.…”

Section: Introductionmentioning

confidence: 99%

“… The estimators considered in this paper remain consistent even if in the population some variance components are heteroscedastic over i . In this case both estimators presented should be treated as pseudo maximum likelihood estimators, see also Hayakawa and Pesaran (). …”

mentioning

confidence: 99%

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On Maximum Likelihood Estimation of Dynamic Panel Data Models

2017

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We analyse the finite sample properties of maximum likelihood estimators for dynamic panel data models. In particular, we consider transformed maximum likelihood (TML) and random effects maximum likelihood (RML) estimation. We show that TML and RML estimators are solutions to a cubic first‐order condition in the autoregressive parameter. Furthermore, in finite samples both likelihood estimators might lead to a negative estimate of the variance of the individual‐specific effects. We consider different approaches taking into account the non‐negativity restriction for the variance. We show that these approaches may lead to a solution different from the unique global unconstrained maximum. In an extensive Monte Carlo study we find that this issue is non‐negligible for small values of T and that different approaches might lead to different finite sample properties. Furthermore, we find that the Likelihood Ratio statistic provides size control in small samples, albeit with low power due to the flatness of the log‐likelihood function. We illustrate these issues modelling US state level unemployment dynamics.

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“…In particular, for the heteroscedastic case we redefine quantities in Proposition in the following way:

{italicσ}_{0}^{2} \equiv \underset{N \to \infty}{falselim} \frac{1}{N} \sum_{i = 1}^{N} {italicσ}_{0, i}^{2}, {italicα}_{0} \equiv \frac{1 - {italicϕ}_{0}^{2}}{σ_{0}^{2}} \underset{N \to \infty}{falselim} \frac{1}{N} \sum_{i = 1}^{N} var (y_{i, 0} - \frac{{italicη}_{i}}{false(1 - ϕ_{0} false)}) .

Section: Multiple Solutions and Bounded Estimationsupporting

confidence: 52%

“…The likelihood function in is defined for all values of

ϕ \in R

Section: Estimation For the Panel Ar(1) Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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On Maximum Likelihood Estimation of Dynamic Panel Data Models

2017

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“…A number of well-known GMM estimation methods have been proposed, including Hsiao (1981 and1982), Arellano and Bond (1991), Ahn and Schmidt (1995), Arellano and Bover (1995), Blundell and Bond (1998), and Hayakawa (2012), among others. Unlike the likelihood-based methods in the literature (Hsiao et al, 2002, andPesaran, 2015), the GMM methods apply to autoregressive (AR) panels as well as to AR panels augmented with strictly or weakly exogenous regressors. However, the GMM approach is subject to a number of drawbacks.…”

Section: Introductionmentioning

confidence: 99%

A Bias-Corrected Method of Moments Approach to Estimation of Dynamic Short-T Panels

Chudík

Pesaran

2017

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. This paper contributes to the GMM literature by introducing the idea of self-instrumenting target variables instead of searching for instruments that are uncorrelated with the errors, in cases where the correlation between the target variables and the errors can be derived. The advantage of the proposed approach lies in the fact that, by construction, the instruments have maximum correlation with the target variables and the problem of weak instrument is thus avoided. The proposed approach can be applied to estimation of a variety of models such as spatial and dynamic panel data models. In this paper we focus on the latter and consider both univariate and multivariate panel data models with short time dimension. Simple Bias-corrected Methods of Moments (BMM) estimators are proposed and shown to be consistent and asymptotically normal, under very general conditions on the initialization of the processes, individual-speci.c e¤ects, and error variances allowing for heteroscedasticity over time as well as cross-sectionally. Monte Carlo evidence document BMM.s good small sample performance across di¤erent experimental designs and sample sizes, including in the case of experiments where the system GMM estimators are inconsistent. We also .nd that the proposed estimator does not su¤er size distortions and has satisfactory power performance as compared to other estimators. Terms of use: Documents inJEL-Codes: C120, C130, C230.

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