A Note on Bias in First-Differenced AR(1) Models

In this note, we derive the finite sample bias of the modified ordinary least squares (MOLS) estimator, which was suggested by Wansbeek and Knaap (1999) and reconsidered by Hayakawa (2006a,b). From the formula for the finite sample bias, we find that the bias of the MOLS estimator becomes small as $\rho$, the autoregressive parameter, approaches unity. Simulation results indicate that the MOLS estimator has very small bias and that its empirical size is close to the nominal one.

First Difference or Forward Orthogonal Deviation- Which Transformation Should be Used in Dynamic Panel Data Models?: A Simulation Study

This paper compares the performances of the generalized method of moments (GMM) estimator of dynamic panel data model wherein unobserved individual effects are removed by the forward orthogonal deviation or the first difference. The simulation results show that the GMM estimator of the model transformed by the forward orthogonal deviation tends to work better than that transformed by the first difference.dynamic panel data model, first difference, forward orthogonal deviation, GMM

On the Effect of Nonstationary Initial Conditions in Dynamic Panel Data Models

In this paper, we consider dynamic panel data models with possibly nonstationary initial conditions. We derive the asymptotic properties of the GMM estimators with various kinds of instruments when both N and T are large, where N and T denote the dimensions of the cross section and time series. We find that when initial conditions are nonstationary and the degree of heterogeneity, which is measured by the variance ratio of individual effects to the disturbances, is large, the biases and variances of the GMM estimators become small. We demonstrate that this is because the correlation between the lagged dependent variable and instruments gets larger due to the unremoved individual effects. This implies that the instruments become strong when initial conditions are nonstationary and the degree of heterogeneity is large. For the purpose of comparison, we also derive the asymptotic properties of the within groups and the LIML estimators. Numerical studies are conducted to assess the properties of these estimators.Dynamic panel data models, many instruments, generalized method of moments estimator, nonstationary initial conditions, degree of heterogeneity.

Dynamic Panel Data Models with Cross Section Dependence and Heteroscedasticity

In this paper, we show that the bias-corrected first-difference (BCFD) estimator suggested by Chowdhury (1987) can be applied to the case where the error terms are cross-sectionally dependent and heteroscedastic. By deriving the finite sample bias of the BCFD estimator, we find that the BCFD estimator has small bias when T, the dimension of the time series, is not very large and ƒÏ, the autoregressive parameter, is close to one. Simulation results show that the BCFD estimator performs better than existing estimators, especially when T is not very large.

A Simple Efficient Instrumental Variable Estimator in Panel AR(p) Models

In this paper, we show that for panel AR(p) models with iid errors, an instrumental variable (IV) estimator with instruments in the backward orthogonal deviation has the same asymptotic distribution as the infeasible optimal IV estimator when both N and T, the dimensions of the cross section and the time series, are large. If we assume that the errors are normally distributed, the asymptotic variance of the proposed IV estimator is shown to attain the lower bound when both N and T are large. A simulation study is conducted to assess the estimator.panel AR(p) models, the optimal instruments, the backward orthogonal deviation

The Asymptotic Properties of the System GMM Estimator in Dynamic Panel Data Models When Both N and T are Large

This paper complements Alvarez and Arellano (2003) by showing the asymptotic properties of the system GMM estimator for AR(1) panel data models when both N and T tend to infinity. We show that the system GMM estimator with the instruments which Blundell and Bond (1998) used will be inconsistent when both N and T are large. We also show that the system GMM estimator with all available instruments, including redundant ones, will be consistent if ƒÐ ƒÅ 2/ƒÐ v2 = 1-ƒ¿ holds.

Small Sample Bias Propreties of the System GMM Estimator in Dynamic Panel Data Models

This paper examines analytically and experimentally why the system GMM estimator in dynamic panel data models is less biased than the first differencing or the level estimators even though the former uses more instruments. We find that the bias of the system GMM estimator is a weighted sum of the biases in opposite directions of the first differencing and the level estimator. We also find that an important condition for the system GMM estimator to have small bias is that the variances of the individual effects and the disturbances are almost of the same magnitude. If the variance of individual effects is much larger than that of disturbances, then all GMM estimators are heavily biased. To reduce such biases, we propose bias-corrected GMM estimators. On the other hand, if the variance of individual effects is smaller than that of disturbances, the system estimator has a more severe downward bias than the level estimator.

Efficient GMM Estimation of Dynamic Panel Data Models Where Large Heterogeneity May Be Present

This paper addresses the many instruments problem, i.e. (1) the trade-off between the bias and the efficiency of the GMM estimator, and (2) inaccuracy of inference, in dynamic panel data models where unobservable heterogeneity may be large. We find that if we use all the instruments in levels, although the GMM estimator is robust to large heterogeneity, inference is inaccurate. In contrast, if we use the minimum number of instruments in levels in the sense that we use only one instrument for each period, the performance of the GMM estimator is heavily affected by the degree of heterogeneity, that is, both the asymptotic bias and the variance are proportional to the magnitude of heterogeneity. To address this problem, we propose a new form of instruments that are obtained from the so-called backward orthogonal deviation transformation. The asymptotic analysis shows that the GMM estimator with the minimum number of new instruments has smaller asymptotic bias than the estimators typically used such as the GMM estimator with all instruments in levels, the LIML estimators and the within-groups estimators, while the asymptotic variance of the proposed estimator is equal to the lower bound. Thus both the asymptotic bias and the variance of the proposed estimators become small simultaneously. Simulation results show that our new GMM estimator outperforms the conventional GMM estimator with all instruments in levels in term of the RMSE and in terms of accuracy of inference. An empirical application with Spanish firm data is also provided.Dynamic panel data, many instruments, generalized method of moments estimator, unobservable large heterogeneity

Asymptotic Properties of the Efficient Estimators for Cointegrating Regression Models with Serially Dependent Errors

In this paper, we analytically investigate three efficient estimators for cointegrating regression models: Phillips and Hansen's (1990) fully modified OLS estimator, Park's (1992) canonical cointegrating regression estimator, and Saikkonen's (1991) dynamic OLS estimator. First, by the Monte Carlo simulations, we demonstrate that these efficient methods do not work well when the regression errors are strongly serially correlated. In order to explain this result, we assume that the regression errors are generated from a nearly integrated autoregressive (AR) process with the AR coefficient approaching 1 at a rate of 1/T , where T is the sample size. We derive the limiting distributions of the three efficient estimators as well as the OLS estimator and show that they have the same limiting distribution under this assumption. This implies that the three efficient methods no longer work well when the regression errors are strongly serially correlated. Further, we consider the case where the AR coefficient in the regression errors approaches 1 at a rate slower than 1/T . In this case, the limiting distributions of the efficient estimators depend on the approaching rate. If the rate is slow enough, the efficiency is established for the three estimators; however, if the approaching rate is relatively fast, they have the same limiting distribution as the OLS estimator. This result explains why the effect of the efficient methods diminishes as the serial correlation in the regression errors gets stronger.Cointegration, second-order bias, fully modified regressions, canonical cointegrating regressions, dynamic ordinary least squares regressions

The Role of "Leads" in the Dynamic OLS Estimation of Cointegrating Regression Models

In this paper, we consider the role of "leads" of the first difference of integrated variables in the dynamic OLS estimation of cointegrating regression models. We demonstrate that the role of leads is related to the concept of Granger causality and that in some cases leads are unnecessary in the dynamic OLS estimation of cointegrating regression models. Based on a Monte Carlo simulation, we find that the dynamic OLS estimator without leads substantially outperforms that with leads and lags; we therefore recommend testing for Granger noncausality before estimating models.Cointegration, dynamic ordinary least squares estimator, Granger causality