some properties of the liml estimator in a dynamic panel structural equation abstract we investigate the finite sample and asymptotic properties of the within groups wg the random effects quasi maximum likelihood rqml the generalized method of moment gmm and the limited information maximum likelihood liml estimators for a panel autoregressive structural equation model with random effects when both t time dimension and n cross section dimension are large when we use the forward filtering due to alvarez and arellano 2003 the wg the rqml and gmm estimators are significantly biased when both t and n are large while t n is different from zero the liml estimator gives desirable asymptotic properties when t n converges to a constant

testing a linear dynamic panel data model against nonlinear alternatives abstract the most popular econometric models in the panel data literature are the class of linear panel data models with unobserved individual and or time specific effects the consistency of parameter estimators and the validity of their economic interpretations as marginal effects depend crucially on the correct functional form specification of the linear panel data model in this paper a new class of residual based tests is proposed for checking the validity of dynamic panel data models with both large cross sectional units and time series dimensions the individual and time effects can be fixed or random and panel data can be balanced or unbalanced the tests can detect a wide range of model misspecifications in the conditional mean of a dynamic panel data model including functional form and lag misspecification they check a large number of lags so that they can capture misspecification at any lag order asymptotically no common alternative is assumed thus allowing for heterogeneity in the degrees and directions of functional form misspecification across individuals thanks to the use of panel data with large n and t the proposed nonparametric tests have an asymptotic normal distribution under the null hypothesis without requiring the smoothing parameters to grow with the sample sizes this suggests better nonparametric asymptotic approximation for the panel data than for time series or cross sectional data this is confirmed in a simulation study we apply the new tests to test linear specification of cross country growth equations and found significant nonlinearities in mean for oecd countries growth equation for annual and quintannual panel data

the optimal choice of moments in dynamic panel data models this paper derives an approximation of the mean square error mse of the gmm estimator in dynamic panel data models the approximation is based on higher order asymptotic theory under double asymptotics while first order theory under double asymptotics provides information about the bias it does not provide enough information about the variance of the estimator higher order theory enables us to obtain information about the variance from this result a procedure for choosing the number of instruments is proposed the simulations confirm that the proposed procedure improves the precision of the estimator

initial conditions and moment restrictions in dynamic panel data models estimation of the dynamic error components model is considered using two alternative linear estimators that are designed to improve the properties of the standard first differenced gmm estimator both estimators require restrictions on the initial conditions process asymptotic efficiency comparisons and monte carlo simulations for the simple ar 1 model demonstrate the dramatic improvement in performance of the proposed estimators compared to the usual first differenced gmm estimator and compared to non linear gmm the importance of these results is illustrated in an application to the estimation of a labour demand model using company panel data

the effects of dynamic feedbacks on ls and mm estimator accuracy in panel data models the finite sample behavior is analyzed of particular least squares ls and a range of generalized method of moments mm estimators in panel data models with individual effects and both a lagged dependent variable regressor and another explanatory variable the latter may be affected by lagged feedbacks from the dependent variable too asymptotic expansions indicate how the order of magnitude of bias of mm estimators tends to increase with the number of moment conditions exploited they also provide analytic evidence on how the bias of the various estimators depends on the feedbacks and on other model characteristics such as prominence of individual effects and correlation between observed and unobserved heterogeneity simulation results corroborate the theoretical findings and reveal that in small samples of models with dynamic feedbacks none of the techniques examined dominates regarding bias and mean squared error over all parametrizations examined

fixed effects dynamic panel models a factor analytical method we consider the estimation of dynamic panel data models in the presence of incidental parameters in both dimensions individual fixed effects and time fixed effects as well as incidental parameters in the variances we adopt the factor analytical approach by estimating the sample variance of individual effects rather than the effects themselves in the presence of cross sectional heteroskedasticity the factor method estimates the average of the cross sectional variances instead of the individual variances the method thereby eliminates the incidental parameter problem in the means and in the variances over the cross sectional dimension we further show that estimating the time effects and heteroskedasticities in the time dimension does not lead to the incidental parameter bias even when t and n are comparable moreover efficient and robust estimation is obtained by jointly estimating heteroskedasticities

indirect inference for dynamic panel models maximum likelihood ml estimation of the autoregressive parameter of a dynamic panel data model with fixed effects is inconsistent under fixed time series sample size and large cross section sample size asymptotics this paper proposes a general computationally inexpensive method of bias reduction that is based on indirect inference shows unbiasedness and analyzes efficiency monte carlo studies show that our procedure achieves substantial bias reductions with only mild increases in variance thereby substantially reducing root mean square errors the method is compared with certain consistent estimators and is shown to have superior finite sample properties to the generalized method of moment gmm and the bias corrected ml estimator

alternative approximations to the distributions of instrumental variable estimators the paper considers the ols the iv and two method of moments estimators mm and mmk of the coefficients of a single equation where the explanatory variables are correlated with the disturbance term the mm and mmk estimators are generalizations of the liml and limlk estimators respectively multivariate first order approximations to the distributions are derived under normality using a parameter sequence where the number of instruments increases as the number of observations increases numerical results show these approximations are more accurate compared to large sample approximations even if the number of instruments is small the moments of the multivariate limit distributions of the mm and mmk estimators can be consistently estimated under a variety of parameter sequences including the large sample sequence the new approximate confidence regions perform well in terms of exact levels compared to traditional ones the iv estimator of the coefficient of a single explanatory endogenous variable is interpreted as a shrinkage estimator which is dominated in practical cases by the mm and mmk estimators in terms of nearness to the true value in the sense of pitman

asymptotic inference for dynamic panel estimators of infinite order autoregressive processes abstract in this paper we consider the estimation of a dynamic panel autoregressive ar process of possibly infinite order in the presence of individual effects we employ double asymptotics under which both the cross sectional sample size and the length of time series tend to infinity and utilize the sieve ar approximation with its lag order increasing with the sample size we establish the consistency and asymptotic normality of the fixed effects estimator and propose a bias corrected fixed effects estimator based on a theoretical asymptotic bias term monte carlo simulations demonstrate the usefulness of bias correction as an illustration the proposed methods are applied to dynamic panel estimation of the law of one price deviations among us cities

asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and t are large we consider a dynamic panel ar 1 model with fixed effects when both n and t are large under the t fixed n large asymptotic approximation the ordinary least squares ols or gaussian maximum likelihood estimator mle is known to be inconsistent due to the well known incidental parameter problem we consider an alternative asymptotic approximation where n and t grow at the same rate it is shown that although ols or the mle is asymptotically biased a relatively simple fix to ols or the mle results in an asymptotically unbiased estimator under the assumption of gaussian innovations the bias corrected mle is shown to be asymptotically efficient by a hajek type convolution theorem

estimating dynamic panel data discrete choice models with fixed effects abstract this paper considers the estimation of dynamic binary choice panel data models with fixed effects it is shown that the modified maximum likelihood estimator mmle used in this paper reduces the order of the bias in the maximum likelihood estimator from o t 1 to o t 2 without increasing the asymptotic variance no orthogonal reparametrization is needed monte carlo simulations are used to evaluate its performance in finite samples where t is not large in probit and logit models containing lags of the endogenous variable and exogenous variables the estimator is found to have a small bias in a panel with eight periods a distinctive advantage of the mmle is its general applicability estimation and relevance of different policy parameters of interest in this kind of models are also addressed

on the effect of mean nonstationarity in dynamic panel data models abstract in this paper we investigate the effect of mean nonstationarity on the first difference generalized method of moments fd gmm estimator in dynamic panel data models we find that when data is mean nonstationary and the variance of individual effects is significantly larger than that of disturbances the fd gmm estimator performs quite well we demonstrate that this is because the correlation between the lagged dependent variable and instruments gets larger owing to the unremoved individual effects i e instruments become strong this implies that under mean nonstationarity the fd gmm estimator does not always suffer from the weak instruments problem even when data is persistent

the time series and cross section asymptotics of dynamic panel data estimators 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

another look at the instrumental variable estimation of error components models this article develops a framework for efficient iv estimators of random effects models with information in levels which can accommodate predetermined variables our formulation clarifies the relationship between the existing estimators and the role of transformations in panel data models we characterize the valid transformations for relevant models and show that optimal estimators are invariant to the transformation used to remove individual effects we present an alternative transformation for models with predetermined instruments which preserves the orthogonality among the errors finally we consider models with predetermined variables that have constant correlation with the effects and illustrate their importance with simulations

individual and time effects in nonlinear panel models with large n t fixed eects estimators of nonlinear panel data models can be severely biased because of the well known incidental parameter problem we develop analytical and jackknife bias corrections for nonlinear models with both individual and time eects under asymptotic sequences where the time dimension t grows with the cross sectional dimension n the time eects introduce additional incidental parameter bias as the existing bias corrections apply to models with only individual eects we derive the appropriate corrections the basis for the corrections are general asymptotic expansions of xed eects estimators with incidental parameters in multiple dimensions we apply the expansions to m estimators with concave objective functions in parameters for panel models with additive individual and time eects these estimators cover xed eects estimators of the most popular limited dependent variable models such as logit probit ordered probit tobit and poisson models our analysis therefore extends the use of large t bias adjustments to an important class of models we also develop bias corrections for functions of the data parameters and individual and time eects including average partial eects in this case the incidental parameter bias is asymptotically of second order in general but the corrections improve nite sample properties

on the unbiased asymptotic normality of quantile regression with fixed effects abstract nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data in a large class of such models including probit proportional hazard and quantile regression to name just a few it is impossible to difference out the individual effects and inference is usually justified in a large n large t asymptotic framework however there is a considerable gap in the type of assumptions that are currently imposed in models with smooth score functions such as probit and proportional hazard and quantile regression in the present paper we show that this gap can be bridged and establish unbiased asymptotic normality for fixed effects quantile regression panels under conditions on n t that are very close to what is typically assumed in standard nonlinear panels our results considerably improve upon existing theory and show that quantile regression is applicable to the same type of panel data in terms of n t as other commonly used nonlinear panel data models thorough numerical experiments confirm our theoretical findings

efficient gmm estimation of spatial dynamic panel data models with fixed effects abstract in this paper we derive the asymptotic properties of gmm estimators for the spatial dynamic panel data model with fixed effects when n is large and t can be large but small relative to n the gmm estimation methods are designed with the fixed individual and time effects eliminated from the model and are computationally tractable even under circumstances where the ml approach would be either infeasible or computationally complicated the ml approach would be infeasible if the spatial weights matrix is not row normalized while the time effects are eliminated and would be computationally intractable if there are multiple spatial weights matrices in the model also consistency of the mle would require t to be large and not small relative to n if the fixed effects are jointly estimated with other parameters of interest the gmm approach can overcome all these difficulties we use exogenous and predetermined variables as instruments for linear moments along with several levels of their neighboring variables and additional quadratic moments we stack up the data and construct the best linear and quadratic moment conditions an alternative approach is to use separate moment conditions for each period which gives rise to many moments estimation we show that these gmm estimators are n t consistent asymptotically normal and can be relatively efficient we compare these approaches on their finite sample performance by monte carlo

stability of essential spectra of self adjoint subspaces under compact perturbations abstract this paper studies stability of essential spectra of self adjoint subspaces i e self adjoint linear relations under finite rank and compact perturbations in hilbert spaces relationships between compact perturbation of closed subspaces and relatively compact perturbation of their operator parts are first established this gives a characterization of compact perturbation in terms of difference between the operator parts of perturbed and unperturbed subspaces it is shown that a self adjoint subspace is still self adjoint under either relatively bounded perturbation with relative bound less than one or relatively compact perturbation or compact perturbation with a certain additional condition by using these results invariance of essential spectra of self adjoint subspaces is proved under relatively compact and compact perturbations separately as a special case finite rank perturbation is discussed the results obtained in this paper generalize the corresponding results for self adjoint operators to self adjoint subspaces

incidental parameters initial conditions and sample size in statistical inference for dynamic panel data models abstract we use a quasi likelihood function approach to clarify the role of initial values and the relative sample size of the cross section dimension n and the time series dimension t on the asymptotic properties of estimators for dynamic panel data models with the presence of individual specific effects we show that a properly specified quasi likelihood estimator qmle that uses the mundlak chamberlain approach to condition the unobserved effects and initial values on the observed strictly exogenous covariates is asymptotically unbiased if n goes to infinity whether t is fixed or goes to infinity monte carlo studies are conducted to demonstrate the importance of properly treating initial values in getting valid statistical inference the simulation results also suggest that to deal with the incidental parameters issues arising from the presence of individual specific effects or initial values following the mundlak s 1978 suggestion to condition on the time series average of individual s observed regressors performs better than conditioning on each observed variable at all different time periods

bootstrap inference for linear dynamic panel data models with individual fixed effects abstract this paper s main contribution is to propose and theoretically justify the application of bootstrap methods for inference in autoregressive panel data models with fixed effects whereas the focus of the existing literature has been on bias correcting the standard fixed effects ols estimator due to the well known incidental parameter bias our focus here is on improving the quality of inference by relying on the bootstrap instead of the standard normal distribution when computing critical values for test statistics in particular we show by simulation that confidence intervals based on the normal distribution can be very distorted in finite samples instead a bootstrap that resamples the residuals and generates the bootstrap observations recursively using the estimated autoregressive panel data model greatly reduces these distortions we show that this recursive design residual based bootstrap fixed effects ols estimator contains a built in bias correction term that mimics the incidental parameter bias thus this method can be used to approximate the bias as well as the entire distribution of the biased fixed effects ols estimator this is in contrast with two other methods we consider a fixed design residual based bootstrap and a pairs bootstrap whose distributions are incorrectly centered at zero as it turns out both the recursive design and the pairs bootstrap are asymptotically valid when applied to the bias corrected estimator but the fixed design bootstrap is not in the simulations the recursive design bootstrap is the method that does best overall

a maximum likelihood method for the incidental parameter problem this paper uses the invariance principle to solve the incidental parameter problem of 35 we seek group actions that pre serve the structural parameter and yield a maximal invariant in the parameter space with flxed dimension m estimation from the likeli hood of the maximal invariant statistic yields the maximum invariant likelihood estimator mile consistency of mile for cases in which the likelihood of the maximal invariant is the product of marginal likelihoods is straightforward we illustrate this result with a sta tionary autoregressive model with flxed efiects and an agent speciflc monotonic transformation model asymptotic properties of mile when the likelihood of the maxi mal invariant does not factorize remain an open question we are able to provide consistency asymptotic normality and e ciency results of mile when invariance yields wishart distributions two examples are an instrumental variable iv model and a dynamic panel data model with flxed efiects

periodic solutions of a quartic nonautonomous equation on considere des equations de la forme z z 4 t z 3 t z 2 t z on donne un ensemble qui a au moins huit solutions periodiques les coefficients sont des polynomes quadratiques en cost et sint

gmm estimation of social interaction models with centrality this paper considers the specification and estimation of social interaction models with network structures and the presence of endogenous contextual correlated and group fixed effects when the network structure in a group is captured by a graph in which the degrees of nodes are not all equal the different positions of group members as measured by the bonacich 1987 centrality provide additional information for identification and estimation in this case the bonacich centrality measure for each group can be used as an instrument for the endogenous social effect but the number of such instruments grows with the number of groups we consider the 2sls and gmm estimation for the model the proposed estimators are asymptotically efficient respectively within the class of iv estimators and the class of gmm estimators based on linear and quadratic moments when the sample size grows fast enough relative to the number of instruments

many ivs estimation of dynamic panel regression models with measurement error abstract in this paper we investigate a dynamic linear panel regression model with measurement error we consider the panel data estimation whose time dimension t is not small and comparable to the cross sectional dimension n first we show that the 2sls estimator suffers from the bias problem due to many instrumental variables using the alternative asymptotics where t 3 n goes to a constant as n t we characterize its asymptotic bias due to many ivs as a bias reduction method we investigate the jive and derive its limiting distribution under the alternative asymptotics

panel models with interactive effects abstract the multiplication of individual specific effects and time specific effects provides a more general formulation than the traditionally used additive form to capture the unobserved heterogeneity in panel data modeling it is also a useful approach for dimension reduction for modeling cross section dependence however and are unobservable we explore the implications for econometric modeling under various formulations of the interactive effects models and suggest a quasi likelihood approach as a common framework to study issues of estimation and statistical inference when regressors are either strictly exogenous or predetermined and under different combinations of the data size of cross sectional dimension n and time series dimensions t we also suggest some computationally simpler estimation methods in light of the quasi likelihood approach monte carlo studies are conducted to highlight the issues involved

quasi ml estimation of the panel ar 1 model with arbitrary initial conditions abstract in this paper we show that the quasi ml estimation method yields consistent random and fixed effects estimators for the autoregression parameter in the panel ar 1 model with arbitrary initial conditions and possibly time series heteroskedasticity even when the error components are drawn from heterogeneous distributions we investigate both analytically and by means of monte carlo simulations the properties of the qml estimators for the re q mle for is asymptotically at least as robust to individual heterogeneity and when the data are i i d and normal at least as efficient as the fe q mle for furthermore the qml estimators for only suffer from a weak moment conditions problem when is close to one if the cross sectional average of the variances of the errors is almost constant over time e g under time series homoskedasticity however in this case the qml estimators for are still consistent when is local to or equal to one although they converge to a non normal possibly asymmetric distribution at a rate that is lower than n 1 2 but at least n 1 4 finally we study the finite sample properties of two types of estimators for the standard errors of the qml estimators for and the bounds of qml based confidence intervals for

estimation of dynamic models with error components abstract observations on n cross section units at t time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit different assumptions about the initial conditions are a initial state fixed b initial state random c the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed and d the unobserved individual effect independent of the unobserved dynamic process with initial value random asymptotic properties of the maximum likelihood and covariance estimators are obtained when t and when n the relationship between the pseudo and conditional maximum likelihood estimators is clarified a simple consistent estimator that is independent of the initial conditions and the way in which t or n is also suggested

panel data models with interactive fixed effects this paper considers large n and large t panel data models with unobservable multiple interactive eects these models are useful for both micro and macro econometric modelings in earnings studies for example workers motivation persistence and diligence combined to influence the earnings in addition to the usual argument of innate ability in macroeconomics the interactive eects represent unobservable common shocks and their heterogeneous responses over cross sections since the interactive eects are allowed to be correlated with the regressors they are treated as fixed eects parameters to be estimated along with the common slope coecients the model is estimated by the least squares method which provides the interactive eect s counterpart of the within estimator we first consider model identification and then derive the rate of convergence and the limiting distribution of the interactive eect s estimator of the common slope coecients the estimator is shown to be p nt consistent this rate is valid even in the presence of correlations and heteroskedasticities in both dimensions a striking contrast with fixed t framework in which serial correlation and heteroskedasticity imply unidentification the asymptotic distribution is not necessarily centered at zero biased corrected estimators are derived we also derive the constrained estimator and its limiting distribution imposing additivity coupled with interactive eects the problem of testing additive versus interactive eects is also studied we also derive identification conditions for models with grand mean time invariant regressors and common regressors it is shown that there exists a set of necessary and sucient identification conditions for those models given identification the rate of convergence and limiting results continue to hold

statistical inference for panel dynamic simultaneous equations models abstract we study the identification and estimation of panel dynamic simultaneous equations models we show that the presence of time persistent individual specific effects does not lead to changes in the identification conditions of traditional cowles commission dynamic simultaneous equations models however the limiting properties of the estimators depend on the way the cross section dimension n or the time series dimension t goes to infinity we propose three limited information estimator panel simple instrumental variables piv panel generalized two stage least squares pg2sls and panel limited information maximum likelihood estimation pliml we show that they are all asymptotically unbiased independent of the way of how n or t tends to infinity monte carlo studies are conducted to compare the performance of the pliml piv pg2sls the arellano bond type generalized method of moments and the akashi kunitomo least variance ratio estimator we demonstrate that the reliability of statistical inference depends critically on whether an estimator is asymptotically unbiased or not

efficient estimation of models for dynamic panel data abstract in this paper we consider a dynamic model for panel data we show that under standard assumptions there are more moment conditions than are currently exploited in the literature some of these are linear but others are quadratic so that nonlinear gmm is required we also show that exogenous regressors generate a larger number of relevant moment conditions in a dynamic model than they would in a static model

the effects of dynamic feedbacks on ls and mm estimator accuracy in panel data models some additional results in this paper we show that the order of magnitude of the finite sample bias of the gmmld 2 estimator of bun and kiviet 2006 reduces from o t n t o o 1 n if the original level model is transformed by the upper triangular cholesky factorization of the inverse of the pseudo variance matrix of error component ui wherein true values of the variances of individual effects and disturbances may not be used some variants of the system gmm estimator that are associated with the cholesky transformed model are also discussed

estimating long run relationships from dynamic heterogeneous panels in panel data four procedures are widely used pooling aggregating averaging group estimates and cross section regression in the static case if the coefficients differ randomly all four procedures give unbiased estimates of coefficient means in the dynamic case when the coefficients differ across groups pooling and aggregating give inconsistent and potentially highly misleading estimates of the coefficients though the cross section can provide consistent estimates of the long run effects the theoretical results on the properties of the four procedures are illustrated by uk labour demand functions for 38 industries over 30 years

on bias inconsistency and efficiency of various estimators in dynamic panel data models abstract when a model for panel data includes lagged dependent explanatory variables then the habitual estimation procedures are asymptotically valid only when the number of observations in the time dimension t gets large usually however such datasets have substantial sample size in the cross section dimension n whereas t is often a single digit number results on the asymptotic bias n in this situation have been published a decade ago but hence far analytic small sample assessments of the actual bias have not been presented here we derive a formula for the bias of the least squares dummy variable lsdv estimator which has a o n 1 t 3 2 approximation error in a simulation study this is found to be remarkably accurate due to the small variance of the lsdv estimator which is usually much smaller than the variance of consistent generalized method of moments estimators a very efficient procedure results when we remove the bias from the lsdv estimator the simulations contain results for a particular operational corrected lsdv estimation procedure which in many situations proves to be much more efficient than various instrumental variable type estimators

fixed effects estimation of structural parameters and marginal effects in panel probit models fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem in this paper i characterize the leading term of a large t expansion of the bias of the mle and estimators of average marginal effects in parametric fixed effects panel binary choice models for probit index coefficients the former term is proportional to the true value of the coefficients being estimated this result allows me to derive a lower bound for the bias of the mle i then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity i subsequently propose new bias corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors

gmm inference when the number of moment conditions is large abstract asymptotic theory typically presumes that the dimensionality of econometric models is independent of the sample size even though this presumption is often quite unrealistic in gmm estimation whenever optimal instruments are not available it can frequently be shown that adding over identifying restrictions moment conditions will increase asymptotic precision however the conventional asymptotics which underlies this view insists that the number of moment conditions remain finite even though the number of available moment conditions may grow without bound we consider the explicit dependence of the number of moment conditions or instruments q n on the sample size n and establish that under conventional regularity conditions for the estimation of a linear model with general heteroskedasticity q n 3 n 0 is a sufficient condition for the validity of conventional asymptotic inference about the gmm estimator