Inference and Estimation in Small Sample Dynamic Panel Data Models (original) (raw)
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The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators
Econometrica, 2003
In this paper we derive the asymptotic properties of within groups (WG), GMM, and LIML estimators for an autoregressive model with random effects when both T and N tend to infinity. GMM and LIML are consistent and asymptotically equivalent to the WG estimator. When T /N → 0 the fixed T results for GMM and LIML remain valid, but WG, although consistent, has an asymptotic bias in its asymptotic distribution. When T /N tends to a positive constant, the WG, GMM, and LIML estimators exhibit negative asymptotic biases of order 1/T , 1/N , and 1/ 2N − T , respectively. In addition, the crude GMM estimator that neglects the autocorrelation in first differenced errors is inconsistent as T /N → c > 0, despite being consistent for fixed T. Finally, we discuss the properties of a random effects pseudo MLE with unrestricted initial conditions when both T and N tend to infinity.
A proposed method to estimate dynamic panel models when either N or T or both are not large
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Traditionally the bias of an estimator has been reduced asymptotically to zero by enlarging data panel dimensions N or T or both. This research proposes a novel econometric modelling method to separate and measure the bias of an estimator without altering data panel dimensions. This is done by recursively decomposing its bias in systematic and nonsystematic parts. This novel method addresses the bias of an estimator as a type of asymptotic serial correlation problem. Once this method disentangles bias components it could provide consistent estimators and adequate statistic inference. This recursive bias approach is missed from the current bias literature. This novel method results do not cast doubt about the asymptotic bias approach conclusions, but made them incomplete. Monte Carlo simulations find consistent sample estimators asymptotic convergence with population estimators by enlarging the sample size. In these simulations the population estimator value is provided beforehand the simulation begins. The mean advantage of the alternative recursive estimator bias approach is that the sample estimator recursively converges with population estimators without enlarging sample size. Importantly this novel method avoids researcher bias criteria, which consist on an arbitrary a priori population estimator value selection.
Finite-sample comparison of alternative methods for estimating dynamic panel data models
Journal of Applied Econometrics, 2012
The Wooldridge method is based on a simple and novel strategy to deal with the initial values problem in nonlinear dynamic random-effects panel data models. The characteristic of the method makes it very attractive in empirical applications. However, its finite sample performance and robustness are not fully known as of yet. In this paper we investigate the performance and robustness of this method in comparison with an ideal case in which the initial values are known constants; the worst scenario is based on an exogenous initial values assumption, and the Heckman's reduced-form approximation method, which is widely used in the literature. The dynamic random-effects probit and Tobit (type I) models are used as working examples. Various designs of the Monte Carlo experiments and two further empirical illustrations are provided. The results suggest that the Wooldridge method works very well only for the panels of moderately long duration (longer than 5-8 periods). Heckman's reduced-form approximation is suggested for short panels (shorter than 5 periods). It is also found that all the methods tend to perform equally well for panels of long duration (longer than 15-20 periods).
A Comparative Analysis of Different IV and GMM Estimators of Dynamic Panel Data Models
International Statistical Review, 2007
It is well known that the usual procedures for estimating panel data models are inconsistent in the dynamic setting. A large number of consistent estimators however, have been proposed in the literature. This paper provides a survey of the majority of mainstream estimators, which tend to consist of IV and GMM ones. It also considers a newly proposed extension to the promising Wansbeek-Bekker estimator (Harris & Mátyás, 2000). To provide guidance to the applied researcher working on micro-datasets, the small sample performance of these estimators is evaluated using a set of Monte Carlo experiments.
Efficient estimation of dynamic panel data models: Alternative assumptions and simplified estimation
Journal of Econometrics, 1997
This paper considers the estimation of dynamic models for panel data. It shows how to count and express the moment conditions implied by a variety of covariance restrictions. These conditions can be imposed in a GMM framework. Many of the moment conditions are nonlinear in the parameters. We derive a simple linearized estimator that is asymptotically as efficient as the nonlinear GMM estimator, and convenient tests of the validity of the nonlinear restrictions.
SSRN Electronic Journal
We use a quasi-likelihood function approach to clarify the role of initial values and the relative size of the cross-section dimension N and the time series dimension T in the asymptotic distribution of dynamic panel data models with the presence of individual-speci…c e¤ects. We show that the quasi-maximum likelihood estimator (QMLE) treating initial values as …xed constants is asymptotically biased of order q N T 3 as T goes to in…nity for a time series models and asymptotically biased of order q N T for a model that also contains other covariates that are correlated with the individual-speci…c e¤ects. Using Mundlak-Chamberlain approach to condition the e¤ects on the covariates can reduce the asymptotic bias to the order of q N T 3 , provided the data generating processes for the covariates are homogeneous across cross-sectional units. On the other hand, the QMLE combining the Mundlak-Chamberlain approach with the proper treatment of initial value distribution is asymptotically unbiased if N goes to in…nity whether T is …xed or goes to in…nity. Monte Carlo studies are conducted to demonstrate the importance of properly treating initial values in getting valid statistical inference. The results also suggest that when using the conditional approach to get around the issue of incidental parameters, in …nite sample it is perhaps better to follow Mundlak's (1978) suggestion to simply condition the individual This paper was stimulated by the private communication with Jushan Bai. We would like to thank him for pointing out the terms that cancel the impact of individual-speci…c e¤ects and the impact of correlation between the errors of the equation and the lagged dependent variables. We would also like to thank the editor Oliver Linton, an associate editor, two anonymous referees and Elie Tamer for helpful comments. Partial research support by China NSF #71103004 and #71631004 to the …rst author is also gratefully acknowledged.
Estimation of dynamic panel data models with a lot of heterogeneity
Econometric Reviews, 2021
The commonly used 1-step and 2-step System GMM estimators for the panel AR(1) model are inconsistent under mean stationarity when the ratio of the variance of the individual e¤ects to the variance of the idiosyncratic errors is unbounded when N ! 1. The reason for their inconsistency is that their weight matrices select moment conditions that do not identify the autoregressive parameter. This paper proposes a new 2-step System estimator that is still consistent in this case provided that T > 3: Unlike the commonly used 2-step System estimator, the new estimator uses an estimator of the optimal weight matrix that remains consistent in this case. We also show that the commonly used 1-step and 2-step Arellano-Bond GMM estimators and the Random E¤ects Quasi MLE remain consistent under the same conditions. To illustrate the usefulness of our new System estimator we revisit the growth study of Levine et al. (2000).
Initial-Condition Free Estimation of Fixed Effects Dynamic Panel Data Models
It is well known that (quasi) MLE of dynamic panel data (DPD) models with short panels depends on the assumptions on the initial values; ignoring them or a wrong treatment of them will result in inconsistency or serious bias. This paper introduces a initial-condition free method for estimating the fixed-effects DPD models, through a simple modification of the quasi-score. An outer-product-of-gradients (OPG) method is also proposed for robust inference. The MLE of Hsiao, Pesaran and Tahmiscioglu (2002, Journal of Econometrics), where the initial observations are modeled, is extended to quasi MLE and an OPG method is proposed for robust inference. Consistency and asymptotic normality for both estimation strategies are established, and the two methods are compared through Monte Carlo simulations. The proposed method performs well in general, whether the panel is short or not. The quasi MLE performs comparably, except when model does not contain time-varying regressor, or the panel is not short and the dynamic parameter is small. The proposed method is much simpler and easier to apply.
The Robustness of Estimators for Dynamic Panel Data Models to Misspecification
The Singapore Economic Review, 2009
Transition from economic theory to a testable form of model invariably involves the use of certain "simplifying assumptions." If, however, these are not valid, misspecified models result. This article considers estimation of the dynamic linear panel data model, which often forms the basis of testable economic hypotheses. The estimators of such a model are frequently similarly based on certain assumptions which appear to be often untenable in practice. Here, the performance of these estimators is analyzed in scenarios where the theoretically required conditions are not met. Specifically, we consider three such instances of serial correlation of the idiosyncratic disturbance terms; correlation of the idiosyncratic disturbance terms and explanatory variables; and, finally, cross-sectional dependence (as a robustness check to these findings, we also consider correlations between observed and unobserved heterogeneity terms). The major findings are that the limited tests readily...
A Comparative Analysis of Different Estimators for Dynamic Panel Data Models
2017
It has become increasingly obvious that the estimation of dynamic panel data models has become one of the major issues in recent econometric research as evidenced by the plethora of papers on the subject. It is well known that the usual techniques for estimating panel data models are inconsistent in the dynamic setting. However, numerous consistent estimators have been proposed in the literature. In this paper, two new estimators are offered (one each for the fixed and random effects specifications), and their small sample performance compared with that of all of the existing estimators. It is hoped that the results of these experiments will provide invaluable guidance to applied researchers as to which is the preferred estimator(s). Finally, the divergences in point estimates of all of these estimators is illustrated with an application to a consumer demand schedule of laundry detergent in the metropolitan district of Melbourne, Australia. JEL Classification: C13, C15 and C23. May-96 * Research assistance by Ritchard Longmire and L&sz\6 Konya is kindly acknowledged. We are also grateful to Merran Evans for helpful suggestions. Any remaining errors are our own. ' This is not strictly true as the simulated (absolute) biases were estimated as: 0.022,0.008,0.014 and 0.0038 (Tables A4 to A7). The exact asymptotic biases can be calculated using Nickell's (1981) equation (25). These were respectively calculated as: 0.023, 0.007, 0.010 and 0.0025.