On the testing of heterogeneity effects in dynamic unbalanced panel data models (original) (raw)
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ESTIMATING THE HETEROGENEITY EFFECTS IN A PANEL DATA REGRESSION MODEL
Violation of homoscedasticity assumption in a Panel Data Regression Model (PDRM) implies unequal variability of error terms, and this creates heterogeneity problem in estimation. This research thus attempts to investigate the presence and effect of heteroscedasticity in panel data through the estimation of a specified audit fees PDRM using Pooled ordinary least square (POLS, Least square dummy variable (LSDV) technique where all coefficients vary across individual and Random Effect estimator (REM). A conditional Lagrange multiplier test was developed via a two-way error components model, to examine the presence of heteroscedasticity in the fitted POLS model while Hausman test was used to ascertain the suitability of the LSDV Model over Random effect model and vice-versa. The conditional LM test gave a value of 7.1462 with P-value of 0.000000000000446 which shows that there is presence of unequal variance of MA(1) errors among the residuals of the fitted Pooled OLS model, thereby rendered the estimator inconsistent. Both LSDV and RE models were fitted to take care of the challenges posed by the presence of heteroscedasticity and both models captured the goodness of fit better when compared to the Pooled OLS model. However, the Hausman test revealed that random effect model will not be preferable since p-value of the former is less than 0.05.
The correlation between lagged endogenous regressor and the error term, in case of dynamic panel data models, causes the least squares dummy variable (LSDV) estimator to be biased and inconsistent. This problem persists even in case of heteroscedastic errors. In 2006, Bun and Carree, firstly addressed this situation and proposed a bias-corrected LSDV estimator. Earlier other authors have considered the case of simple (static) panel data models allowing heteroscedasticity, and have proposed several versions of estimated generalized least squares (EGLS) estimators using different ways, through which the variance components are estimated. In this study, we have customized them for the dynamic panel data models with cross-sectional heteroscedastic remainder errors and have analyzed their performance as compared to the bias-corrected LSDV estimator using Monte Carlo experiments. The experimental evidences showed that the proposed estimators, particularly extended Heteroscedastic Consistent Covariance Matrix (HCCM)-based EGLS estimators HGLS1s, are attractive choices in the sense of bias and mean squared error (MSE).
A proposed method to estimate dynamic panel models when either N or T or both are not large
2017
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.
Biases in GLS Estimators for Dynamic Panel Data Models allowing Cross- Sectional Heteroscedasticity
The inclusion of lagged dependent variable in the list of explanatory variables introduces the specific estimation problems even the generalized least squares estimator for the dynamic panel data models allowing cross sectional heteroscedasticity becomes biased and inconsistent. In this study, the analytical expressions for the inconsistency have been derived in the first order autoregressive case. A comparison between asymptotic bias and small sample simulated bias has also been carried out. The analytical biases emerged coincident with or a little above the small sample simulated biases. The closeness of the two types of biases mainly depends on coefficient of lagged dependent variable (Gamma) and the number of cross sectional units N.
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).
Inference and Estimation in Small Sample Dynamic Panel Data Models
2002
We study the finite sample properties of the most important methods of estimation of dynamic panel data models in a special class of small samples: a two-sided small sample (i.e., a sample in which the time dimension is not that short but the cross-section dimension is not that large). This case is encountered increasingly in applied work. Our main results are the following: the estimator proposed by Kiviet (1995) outperforms all other estimators considered in the literature. However, standard statistical inference is not valid for any of them. Thus, to assess the true sample variability of the parameter estimates, bootstrap standard errors have to be computed. We find that standard bootstrapping techniques work well except when the autoregressive parameter is close to one. In this last case, the best available solution is to estimate standard errors by means of the Grid-t bootstrap estimator due to Hansen (1999).
Unobserved heterogeneity in panel time series models
Computational Statistics & Data Analysis, 2006
Recently, the large T panel literature has emphasized unobserved, time-varying heterogeneity that may stem from omitted common variables or global shocks that a¤ect each individual unit di¤erently. These latent common factors induce cross-section dependence and may lead to inconsistent regression coe¢ cient estimates if they are correlated with the explanatory variables. Moreover, if the process underlying these factors is nonstationary, the individual regressions will be spurious but pooling or averaging across individual estimates still permits consistent estimation of a long-run coe¢ cient. The need to tackle both error cross-section dependence and persistent autocorrelation is motivated by the evidence of their pervasiveness found in three well-known, international …nance and macroeconomic examples. A range of estimators is surveyed and their …nite-sample properties are examined by means of Monte Carlo experiments. These reveal that a mean group version of the common-correlated-e¤ects estimator stands out as the most robust since it is the preferred choice in rather general (non) stationary settings where regressors and errors share common factors and their factor loadings are possibly dependent. Other approaches which perform reasonably well include the two-way …xed e¤ects, demeaned mean group and between estimators but they are less e¢ cient than the common-correlated-e¤ects estimator.
Journal of Applied Econometrics, 2002
I study a simple, widely applicable approach to handling the initial conditions problem in dynamic, nonlinear unobserved effects models. Rather than attempting to obtain the joint distribution of all outcomes of the endogenous variables, I propose finding the distribution conditional on the initial value (and the observed history of strictly exogenous explanatory variables). The approach is flexible, and results in simple estimation strategies for at least three leading dynamic, nonlinear models: probit, Tobit and Poisson regression. I treat the general problem of estimating average partial effects, and show that simple estimators exist for important special cases.
A New Estimator for Dynamic Panel Data Model with Cross-section Heteroscedasticity
Dynamic panel data models (DPDMs) are getting attraction after the diversifying uses of regular panel data models in many practical data. The available estimation techniques address the problem of biased estimation while handling such DPDMs. In present paper, we extend the estimation technique as proposed by Aslam (2006) for panel data models with unit-specific heteroscedasticity to the DPDMs with the same type of heteroscedasticity, with the hope to reduce estimation bias. Bun and Carree (2005b) has also presented a bias corrected estimator for dynamic panel data models with both time-series and cross-section heteroscedasticity and the present paper also gives a comparison between the two estimation techniques, using Monte Carlo simulations.