identification and estimation of nonlinear dynamic panel data models with unobserved covariates abstract this paper considers nonparametric identification of nonlinear dynamic models for panel data with unobserved covariates including such unobserved covariates may control for both the individual specific unobserved heterogeneity and the endogeneity of the explanatory variables without specifying the distribution of the initial condition with the unobserved variables we show that the models are nonparametrically identified from two periods of the dependent variable y i t and three periods of the covariate x i t the main identifying assumptions include high level injectivity restrictions and require that the evolution of the observed covariates depends on the unobserved covariates but not on the lagged dependent variable we also propose a sieve maximum likelihood estimator mle and focus on two classes of nonlinear dynamic panel data models i e dynamic discrete choice models and dynamic censored models we present the asymptotic properties of the sieve mle and investigate the finite sample properties of these sieve based estimators through a monte carlo study an intertemporal female labor force participation model is estimated as an empirical illustration using a sample from the panel study of income dynamics psid

theories of learning in games and heterogeneity bias work begins with pooled estimation of the model s under scrutiny i show that in the presence of parameter heterogeneity pooled estimation can produce a severe bias that tends to unduly favor reinforcement learning relative to belief learning this occurs when comparisons are based on goodness of fit and when comparisons are based on the relative importance of the two kinds of learning in hybrid structural models even misspecified random parameter estimators can greatly reduce the bias relative to pooled estimation

longitudinal models for analysis of respiratory function we compare the results of fitting three longitudinal models two autoregressive models the serial correlation model and a damped autoregressive model and a compound symmetry model to data on a cohort of 1154 adult men in boston the serial correlation model assumes that the error terms are autocorrelated with correlation of the form t for visits t years apart while the damped autoregressive assumes that the correlation between error terms of observations t years apart is of the form t the compound symmetry model assumes that the errors are correlated with the same correlation regardless of how far apart observations are in time these three models are all related in that the serial correlation and compound symmetry models are particular cases of the damped autoregressive models that is 1 corresponds to the serial correlation model and 0 corresponds to the compound symmetry model for current smokers the damped autoregressive model provided a significantly better fit than either of the other two models p 0 001 for never smokers the damped autoregressive and compound symmetry models were almost identical with both providing a significantly better fit than the serial correlation model p 0 001

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

are points in tennis independent and identically distributed evidence from a dynamic binary panel data model this article tests whether points in tennis are independent and identically distributed iid we model the probability of winning a point on service and show that points are neither independent nor identically distributed winning the previous point has a positive effect on winning the current point and at important points it is more difficult for the server to win the point than at less important points furthermore the weaker a player the stronger are these effects deviations from iid are small however and hence the iid hypothesis will still provide a good approximation in many cases the results are based on a large panel of matches played at wimbledon 1992 1995 in total almost 90 000 points our panel data model takes into account the binary character of the dependent variable uses random effects to capture the unobserved part of a player s quality and includes dynamic explanatory variables

orthogonality conditions for tobit models with fixed effects and lagged dependent variables abstract this paper presents orthogonality conditions for censored regression models with fixed effects and lagged dependent variables the orthogonality conditions can be used to construct method of moments estimators of the parameters of the model nonlinear fixed effects models are usually estimated by maximum likelihood with the fixed effects treated as parameters to be estimated monte carlo results indicate that in a tobit model with fixed effects and lagged dependent variables the maximum likelihood estimator of the effect of the lagged dependent variable performs poorly the method of moments estimator based on the orthogonality conditions presented here however performs quite well

poncelet s theorem paraorthogonal polynomials and the numerical range of compressed multiplication operators abstract there has been considerable recent literature connecting poncelet s theorem to ellipses blaschke products and numerical ranges summarized for example in the recent book 16 we show how those results can be understood using ideas from the theory of orthogonal polynomials on the unit circle opuc and in turn can provide new insights to the theory of opuc

on new relations between spectral properties of jacobi matrices and their coefficients we study the spectral properties of jacobi matrices by using higher order trace formulae we obtain a result relating the properties of the elements of jacobi matrices and the corresponding spectral measures complicated expressions for traces of some operators can be magically simplified allowing us to apply induction arguments our theorems are generalizations of a recent result of r killip and b simon 17

parameters of interest nuisance parameters and orthogonality conditions an application to autoregressive error component models abstract in general when one considers a set of orthogonality conditions the parameters can be divided into parameters of interest that the econometrician wants to estimate the coefficient of the lagged endogenous variable in the case of an autoregressive error component arec model for instance and nuisance parameters most of the second order terms in an arec model we demonstrate that the elimination of such nuisance parameters using their empirical counterpart does not entail an efficiency loss when only the parameters of interest are estimated applications of our results to both autoregressive error component models and time varying individual fixed effects models are discussed at length they show the nature of the efficiency losses when some orthogonality conditions are left aside

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

root n consistent semiparametric estimators of a dynamic panel sample selection model abstract this paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule when the latent equations contain possibly predetermined variables lags of the dependent variables and unobserved individual effects the selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations we derive a set of conditional moment restrictions that are then exploited to construct a three step sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample selection term in the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of berkson s minimum chi square sieve method and a first step kernel estimator for the selection probability this second step estimator is of interest in its own right it can be used to semiparametrically estimate a panel data binary response model with a nonparametric individual specific effect without making any other distributional assumptions we show that both estimators second and third stage are n consistent and asymptotically normal

cmv the unitary analogue of jacobi matrices we discuss a number of properties of cmv matrices by which we mean the class of unitary matrices studied recently by cantero moral and velazquez we argue that they play an equivalent role among unitary matrices to that of jacobi matrices among all hermitian matrices in particular we describe the analogues of well known properties of jacobi matrices foliation by co adjoint orbits a natural symplectic structure algorithmic reduction to this shape lax representation for an integrable lattice system ablowitz ladik and the relation to orthogonal polynomials as offshoots of our analysis we will construct action angle variables for the finite ablowitz ladik hierarchy and describe the long time behavior of this system 2006 wiley periodicals inc

monte carlo evidence on panel data regressions with ar 1 disturbances and an arbitrary variance on the initial observations abstract for the ar 1 model one implicitly assumes a specific variance on the initial observation or that the process started a long time ago to insure homoscedasticity this paper investigates anderson and hsiao s 1982 suggestion of an arbitrary variance on the initial observation of the autoregressive process this is done in a panel data framework regardless of when the ar 1 process started one can translate this starting date into an effective initial variance assumption this effective initial variance can be estimated with panel data and tested for departures from homoscedasticity the consequences of this departure on various estimators is studied via monte carlo experiments the following estimators are compared ols iterative cochrane orcutt ico and two maximum likelihood mle estimators one corresponding to the usual stationary assumption denoted by bm beach and mackinnon 1978 and another mle corresponding to the arbitrary variance assumption on the initial observations both mle s can be achieved as iterative gls the former using a prais winsten pw transformation and the latter using a generalized pw transformation gpw some of the major findings are the following bm performs poorly for large departures of the variance of the initial observations from the usual homoscedastic assumption whereas the mle corresponding to the gpw transformation is robust to various assumptions on the variance of the initial observations ico continues to perform poorly relative to estimators that use all time series observations even though the co estimator of performs well compared to that of gpw the t statistic which tests the true value of the parameter may be misleading for ols and bm depending upon the departure of the initial variance from the homoscedastic assumption however this t statistic performs well for the gpw estimator finally the likelihood ratio test which tests the usual homoscedastic assumption on the initial disturbances and a pre test estimator based on this test perform well in monte carlo experiments and are recommended

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

sum rules via large deviations in this paper a sum rule means a relationship between a functional defined on a subset of all probability measures on r involving the reverse kullback leibler divergence with respect to a particular distribution and recursion coefficients related to the orthogonal polynomial construction the first sum rule is the szeg o verblunsky theorem see simon 2011 theorem 1 8 6 p 29 and concerns the case of trigonometrical polynomials on the torus more recently killip and simon killip and simon 2003 have given a revival interest to this subject by showing a quite surprising sum rule for measures dominating the semicircular distribution indeed this sum rule includes a contribution of the atomic part of the measure away from the support of the circular law in this paper we recover this sum rules by using only large deviations tools on random matrices furthermore we obtain new up to our knowledge magic sum rules for the reverse kullback leibler divergence with respect to the pastur marchenko or kesten mckay distributions as in the semicircular case these formulas generally include a contribution of the atomic part appearing away from the support of the reference measure from the point of view of large deviations we obtain these formulas by showing a large deviation principle for the point mass measure concentrated on random eigenvalues of classical ensembles and combine it with a large deviation principle due to gamboa and rouault 2011 for the recursion coefficients

asymptotic distributions of impulse response functions in short panel vector autoregressions this paper establishes the asymptotic distributions of the impulse response functions in panel vector autoregressions with a fixed time dimension it also proves the asymptotic validity of a bootstrap approximation to their sampling distributions the autoregressive parameters are estimated using the gmm estimators based on the first differenced equations and the error variance is estimated using an extended analysis of variance type estimator contrary to the time series setting we find that the gmm estimator of the autoregressive coefficients is not asymptotically independent of the error variance estimator the asymptotic dependence calls for variance correction for the orthogonalized impulse response functions simulation results show that the variance correction improves the coverage accuracy of both the asymptotic confidence band and the studentized bootstrap confidence band for the orthogonalized impulse response functions

gmm redundancy results for general missing data problems we consider questions of efficiency and redundancy in the gmm estimation problem in which we have two sets of moment conditions where two sets of parameters enter into one set of moment conditions while only one set of parameters enters into the other we then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest and the second set of moment conditions is for the selection process we use these results to explain the counterintuitive result in the literature that under an ignorability assumption that justifies gmm with weighted moment conditions weighting using estimated probabilities of selection is better than weighting using the true probabilities we also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid and we show that when weighting is not needed for consistency it is also not useful for efficiency

tests for the error component model in the presence of local misspecification it is well known that most of the standard specification tests are not valid when the alternative hypothesis is misspecified this is particularly true in the error component model when one tests for either random effects or serial correlation without taking account of the presence of the other effect in this paper we study the size and power of the standard rao s score tests analytically and by simulation when the data are contaminated by local misspecification these tests are adversely affected under misspecification we suggest simple procedures to test for random effects or serial correlation in the presence of local serial correlation or random effects and these tests require ordinary least squares residuals only our monte carlo results demonstrate that the suggested tests have good finite sample properties for local misspecification and in some cases even for far distant misspecification our tests are also capable of detecting the right direction of the departure from the null hypothesis we also provide some empirical illustrations to highlight the usefulness of our tests

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

on brownian motion simple paths and loops we provide a decomposition of the trace of the brownian motion into a simple path and an independent brownian soup of loops that intersect the simple path more precisely we prove that any subsequential scaling limit of the loop erased random walk is a simple path a new result in three dimensions which can be taken as the simple path of the decomposition in three dimensions we also prove that the hausdorff dimension of any such subsequential scaling limit lies in 1 frac 5 3 we conjecture that our decomposition characterizes uniquely the law of the simple path if so our results would give a new strategy to the existence of the scaling limit of the loop erased random walk and its rotational invariance

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

random walk loop soup the brownian loop soup introduced by lawler and werner 2004 is a poissonian realization from a finite measure on unrooted loops this measure satisfies both conformal invariance and a restriction property in this paper we define a random walk loop soup and show that it converges to the brownian loop soup in fact we give a strong approximation result making use of the strong approximation result of komlos major and tusnady to make the paper self contained we include a proof of the approximation result that we need

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

the use of an autoregressive model for the analysis of longitudinal data in epidemiologic studies korn and whittemore1 2 have presented methods for analyzing longitudinal data where the number of observations per individual is large relative to the number of variables considered for each subject however this is often not the case in epidemiologic studies since one usually collects data at relatively few time points and the quantity of data collected for each individual at each time point is typically extensive we present here an autoregressive model for analyzing longitudinal data of this type for the case of a continuous outcome variable some of the important features of this model are that one can 1 in the same analysis consider both independent variables that are time dependent and those that are fixed over time 2 partially use data for an individual where some examinations are missing 3 assess relationships between changes in outcome and exposure over short periods of time 4 use ordinary multiple regression methods anderson3 has considered this type of model but to our knowledge the model has never been applied to biostatistical problems we illustrate these methods with data from a longitudinal study that seeks to identify the role of personal cigarette smoking on changes in pulmonary function in children

long difference instrumental variables estimation for dynamic panel models with fixed effects this paper proposes a new instrumental variables estimator for a dynamic panel model with fixed effects with good bias and mean squared error properties even when identification of the model becomes weak near the unit circle we adopt a weak instrument asymptotic approximation to study the behavior of various estimators near the unit circle we show that an estimator based on long differencing the model is much less biased than conventional implementations of the gmm estimator for the dynamic panel model we also show that under the weak instrument approximation conventional gmm estimators are dominated in terms of mean squared error by an estimator with far less moment conditions the long difference ld estimator mimics the infeasible optimal procedure through its reliance on a small set of moment conditions

smoothed quantile regression for panel data abstract this paper studies fixed effects estimation of quantile regression models for panel data under an asymptotic framework where both the numbers of individuals and time periods grow at the same rate we show that the fixed effects estimator for the smoothed objective function has a limiting normal distribution with a bias in the mean and provide the analytic form of the asymptotic bias we propose a one step bias correction estimator based on the analytic bias formula obtained from the asymptotic analysis importantly our results cover the case that observations are dependent over time we illustrate the effects of the bias correction through simulations

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

formulation and estimation of dynamic models using panel data abstract this paper presents a statistical analysis of time series regression models for longitudinal data with and without lagged dependent variables under a variety of assumptions about the initial conditions of the processes being analyzed the analysis demonstrates how the asymptotic properties of estimators of longitudinal models are critically dependent on the manner in which samples become large by expanding the number of observations per person holding the number of people fixed or by expanding the number of persons holding the number of observations per person fixed the paper demonstrates which parameters can and cannot be identified from data produced by different sampling plans

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

critical exponent for the loop erased self avoiding walk by monte carlo methods a monte carlo simulation was performed for loop erased self avoiding walks lesaw to ascertain the exponentv for the z2 and z3 lattices the estimated values were 2v 1 600 0 006 in two dimensions and 2v 1 232 0 008 in three dimensions leading to the conjecturev 4 5 for the two dimensional lesaw these results add to existing evidence that the loop erased self avoiding walks are not in the same universality class as self avoiding walks

pooled mean group estimation of dynamic heterogeneous panels abstract it is now quite common to have panels in which both t the number of time series observations and n the number of groups are quite large and of the same order of magnitude the usual practice is either to estimate n separate regressions and calculate the coefficient means which we call the mean group mg estimator or to pool the data and assume that the slope coefficients and error variances are identical in this article we propose an intermediate procedure the pooled mean group pmg estimator which constrains long run coefficients to be identical but allows short run coefficients and error variances to differ across groups we consider both the case where the regressors are stationary and the case where they follow unit root processes and for both cases derive the asymptotic distribution of the pmg estimators as t tends to infinity we also provide two empirical applications aggregate consumption functions for 24 organization for economic cooperation and development economies over th

a transformation that will circumvent the problem of autocorrelation in an error component model abstract this paper derives a simple transformation which will transform serially correlated error components disturbances into spherical disturbances although and 1 are well known in the literature see lillard and willis 1978 the derivation of 1 2 has many advantages i it transforms gls into a wls procedure and therefore simplifies the computation ii it provides natural estimates of the variance components iii the transformation obtained can be easily extended to handle more general error processes on the remainder disturbances this is illustrated for the ar 1 model ar 2 model and the specialized ar 4 model for quarterly data also for the ar 1 model this transformation is extended to handle alternative assumptions on the initial observation this paper also shows that breusch s 1987 results on maximum likelihood estimation for the random error component model extend to the case of serial correlation in the remainder term this suggests an iterative gls procedure for obtaining the maximum likelihood estimates

multivariate regression models for panel data abstract the paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x the relationship is very strong when x is continuous weaker when x is discrete and non existent as the order of the distributed lag becomes infinite the individual specific random variables introduce nonlinearity and heteroskedasticity so the paper provides an appropriate framework for the estimation of multivariate linear predictors restrictions are imposed using a minimum distance estimator it is generally more efficient than the conventional estimators such as quasi maximum likelihood there are computationally simple generalizations of two and three stage least squares that achieve this efficiency gain some of these ideas are illustrated using the sample of young men in the national longitudinal survey the paper reports regressions on the leads and lags of variables measuring union coverage smsa and region the results indicate that the leads and lags could have been generated just by a random intercept this gives some support for analysis of covariance type estimates these estimates indicate a substantial heterogeneity bias in the union smsa and region coefficients

large deviations for wigner s law and voiculescu s non commutative entropy we study the spectral measure of gaussian wigner s matrices and prove that it satisfies a large deviation principle we show that the good rate function which governs this principle achieves its minimum value at wigner s semicircular law which entails the convergence of the spectral measure to the semicircular law as a conclusion we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about voiculescu s non commutative entropy

a bivariate autoregressive linear mixed effects model for the analysis of longitudinal data in clinical studies dependent bivariate continuous responses may approach equilibrium over time we propose an autoregressive linear mixed effects model for bivariate longitudinal data in which the current responses are regressed on the previous responses of both variables fixed effects and random effects the equilibria are modeled using fixed and random effects this model is a bivariate extension of the model for univariate longitudinal data given by funatogawa et al statist med 2007 26 2113 2130 as an illustration of the approach we analyze parathyroid hormone and serum calcium measurements in the treatment of secondary hyperparathyroidism in chronic hemodialysis patients

jackknife and analytical bias reduction for nonlinear panel models fixed effects estimators of panel models can be severely biased because of the well known incidental parameters problem we show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large t we give bias corrections for averages over the fixed effects as well as model parameters we find large bias reductions from using these approaches in examples we consider asymptotics where t grows with n as an approximation to the properties of the estimators in econometric applications we show that if t grows at the same rate as n the fixed effects estimator is asymptotically biased so that asymptotic confidence intervals are incorrect but that they are correct for the panel jackknife we show t growing faster than n 1 3 suffices for correctness of the analytic correction a property we also conjecture for the jackknife

bias in dynamic panel estimation with fixed effects incidental trends and cross section dependence abstract explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size n the results extend earlier work by nickell 1981 biases in dynamic models with fixed effects econometrica 49 1417 1426 and later authors in several directions that are relevant for practical work including models with unit roots deterministic trends predetermined and exogenous regressors and errors that may be cross sectionally dependent the asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient another finding of interest is that when there is cross section error dependence the probability limit of the dynamic panel regression estimator is a random variable rather than a constant which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where n is very large some proposals for bias correction are suggested and finite sample performance is analyzed in simulations

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

sum rules for jacobi matrices and their applications to spectral theory we discuss the proof of and systematic application of case s sum rules for jacobi matrices of special interest is a linear combination of two of his sum rules which has strictly positive terms among our results are a complete classification of the spectral measures of all jacobi matrices j for which j j 0 is hilbert schmidt and a proof of nevai s conjecture that the szego condition holds if j j 0 is trace class

testing serial correlation in semiparametric panel data models we propose three test statistics for testing serial correlation in a semiparametric partially linear panel data model that could allow lagged dependent variables as explanatory variables the first is for testing zero first order serial correlation the second for testing higher order serial correlations and the third testing for individual effects the test statistics are shown to have asymptotic normal or chi square distributions under the null hypothesis of a martingale difference error process we conduct some monte carlo experiments to examine the finite sample performances of the proposed tests we also discuss the generalization to testing serial correlation in a nonparametric framework

an autoregressive linear mixed effects model for the analysis of longitudinal data which include dropouts and show profiles approaching asymptotes we are interested in longitudinal data of a continuous response that show profiles with an initial sharp change and approaching asymptotes for each patient and many patients drop out with a reason related to the response in this paper we focus on a model that assumes a dropout process is missing at random mar in this dropout process we can obtain consistent maximum likelihood estimators as long as both the mean and covariance structures are correctly specified however parsimonious covariance structures for the profiles approaching asymptotes are unclear an autoregressive linear mixed effects model can express the profile with random individual asymptotes we show that this model provides a new parsimonious covariance structure the covariance structure at steady state is compound symmetry and the other elements of the covariance depend on the measurement points in simulation studies the estimate of the asymptote is unbiased in mar dropouts but biased in non ignorable dropouts we also applied this model to actual schizophrenia trial data

consistent model and moment selection procedures for gmm estimation with application to dynamic panel data models this paper develops consistent model and moment selection criteria for gmm estimation the criteria select the correct model specification and all correct moment conditions asymptotically the selection criteria resemble the widely used likelihood based selection criteria bic hqic and aic the latter is not consistent the gmm selection criteria are based on the j statistic for testing over identifying restrictions bonus terms reward the use of fewer parameters for a given number of moment conditions and the use of more moment conditions for a given number of parameters the paper also considers a consistent downward testing procedure the paper applies the model and moment selection criteria to dynamic panel data models with unobserved individual effects the paper shows how to apply the selection criteria to select the lag length for lagged dependent variables to detect the number and locations of structural breaks to determine the exogeneity of regressors and or to determine the existence of correlation between some regressors and the individual effect to illustrate the finite sample performance of the selection criteria and the testing procedures and their impact on parameter estimation the paper reports the results of a monte carlo experiment on a dynamic panel data model

choosing a spanning tree for the integer lattice uniformly consider the nearest neighbor graph for the integer lattice zd in d dimensions for a large finite piece of it consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees as the piece gets larger this approaches a limiting measure on the set of spanning graphs for zd this is shown to be a tree if and only if d 4 in this case the tree has only one topological end that is there are no doubly infinite paths when d 2 5 the spanning forest has infinitely many components almost surely with each component having one or two topological ends

estimation and hypothesis testing for collections of autoregressive time series summary the analysis of a number of independent first order autoregressive time series is considered in a normal theory context a model is studied which allows for nonstationary and nonidentical distribution of the series caused by both fixed effect and random effect components

unified m estimation of fixed effects spatial dynamic models with short panels abstract it is well known that quasi maximum likelihood qml estimation of dynamic panel data dpd models with short panels depends on the assumptions on the initial values and a wrong treatment of them will result in inconsistency and serious bias the same issues apply to spatial dpd sdpd models with short panels in this paper a unified m estimation method is proposed for estimating the fixed effects sdpd models containing three major types of spatial effects namely spatial lag spatial error and space time lag the method is free from the specification of the distribution of the initial observations and robust against nonnormality of the errors consistency and asymptotic normality of the proposed m estimator are established a martingale difference representation of the underlying estimating functions is developed which leads to an initial condition free estimate of the variance of the m estimators monte carlo results show that the proposed methods have excellent finite sample performance

inference for unit roots in dynamic panels where the time dimension is fixed this paper derives similar asymptotic unit root tests for first order autoregressive panel data models assuming that the time dimension of the panel is fixed it is shown that the limiting distributions of the test statistics are normal the assumption that the time dimension is fixed allows us to derive analytical expressions for the moments of the distributions similarity with respect to the initial conditions of the data generating process is achieved by including fixed effect dummy variables in the regression model while similarity with respect to fixed effects in the data generating process is achieved by including a linear deterministic trend for each individual unit of the panel when fixed effects or individual trends are included as regressors the least squares estimator of the autoregressive parameter is inconsistent and thus the test statistics must be appropriately adjusted monte carlo evidence suggests that the proposed tests have empirical size that is very close to the nominal five percent level and substantially more power than the corresponding unit root tests for the single time series case

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

marginal and dynamic regression models for longitudinal data regression models for longitudinal data often employ random effects and serial correlation to account for residual variation between and within subjects most of these models are marginal models separating the mean and covariance parameters this paper discusses the use of dynamic models in which a lagged response serves as a predictor and compares these to marginal models regression parameters have a different interpretation in dynamic models as they describe changes in response levels rather than the levels themselves lagged predictors are also useful with longitudinal data explicitly quantifying the effect of previous levels of risk factors these models are explored through analysis of data from the childhood respiratory study modelling lung function fev1 levels as a function of age height sex and smoking status in children measured over a five year period copyright 2001 john wiley sons ltd

a note on autoregressive error components models abstract the purpose of this paper is to shed some light on the asymptotic behavior of a wide class of estimators for a dynamic error components model when only the number of individuals tends to infinity the number of time periods being kept fixed in particular it is shown that this asymptotic behavior is highly dependent on the assumption about the initial observations and that it offers very good approximations to the small sample behavior of the various estimators under consideration

generalized method of moments specification testing abstract this paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions it shows that any such test may fail against general misspecification that causes estimator inconsistency the mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived applications to testing for exogeneity of a set of instrumental variables are presented

dimension of the loop erased random walk in three dimensions we measure the fractal dimension of loop erased random walk lerw in three dimensions and estimate that it is 1 624 00 0 000 05 lerw is closely related to the uniform spanning tree and the abelian sandpile model we simulated lerw on both the cubic and face centered cubic lattices the corrections to scaling are slightly smaller for the face centered cubic lattice

estimating systems of equations with different instruments for different equations abstract for applications where different instruments are required for different equations this paper offers a relatively primitive set of assumptions under which the nonlinear three stage least squares estimator is the asymptotically efficient generalized method of moments estimator these conditions can be verified for a general class of panel data models under reasonable assumptions about the dynamics in the model on the other hand the 3sls estimator is necessarily inefficient for models such as hedonic price systems and for certain simultaneous equations models with measurement error or omitted variables in some equations

iv gmm or likelihood approach to estimate dynamic panel models when either n or t or both are large abstract we examine the asymptotic properties of iv gmm or mle to estimate dynamic panel data models when either n o r t or both are large we show that the anderson and hsiao 1981 1982 simple instrumental variable estimator iv or maximizing the likelihood function with initial value distribution properly treated quasi maximum likelihood estimator is asymptotically unbiased when either n or t or both tend to infinity on the other hand the qmle mistreating the initial value as fixed is asymptotically unbiased only if n is fixed and t is large if both n and t are large and n t c c 0 c as t it is asymptotically biased of order n t we also explore the source of the bias of the arellano and bond 1991 type gmm estimator we show that it is asymptotically biased of order t n if t n c c 0 c as n even if we restrict the number of instruments used monte carlo studies show that whether an estimator is asymptotically biased or not has important implications on the actual size of the conventional t test

robust standard errors in transformed likelihood estimation of dynamic panel data models with cross sectional heteroskedasticity abstract this paper extends the transformed maximum likelihood approach for estimation of dynamic panel data models by hsiao et al 2002 to the case where the errors are cross sectionally heteroskedastic this extension is not trivial due to the incidental parameters problem and its implications for estimation and inference we approach the problem by working with a mis specified homoskedastic model and then show that the transformed maximum likelihood estimator continues to be consistent even in the presence of cross sectional heteroskedasticity we also obtain standard errors that are robust to cross sectional heteroskedasticity of unknown form by means of monte carlo simulations we investigate the finite sample behavior of the transformed maximum likelihood estimator and compare it with various gmm estimators proposed in the literature simulation results reveal that in terms of median absolute errors and accuracy of inference the transformed likelihood estimator outperforms the gmm estimators in almost all cases

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

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

an autoregressive linear mixed effects model for the analysis of unequally spaced longitudinal data with dose modification the assessment of the dose response relationship is important but not straightforward when the therapeutic agent is administered repeatedly with dose modification in each patient and a continuous response is measured repeatedly we recently proposed an autoregressive linear mixed effects model for such data in which the current response is regressed on the previous response fixed effects and random effects the model represents profiles approaching each patient s asymptote takes into account the past dose history and provides a dose response relationship of the asymptote as a summary measure in an autoregressive model intermittent missing data mean the missing values in previous responses as covariates we previously provided the marginal unconditional on the previous response form of the proposed model to deal with intermittent missing data irregular timings of dose modification or measurement can also be treated as equally spaced data with intermittent missing values by selecting an adequately small unit of time the likelihood is however expressed by matrices whose sizes depend on the number of observations for a patient and the computational burden is large in this study we propose a state space form of the autoregressive linear mixed effects model to calculate the marginal likelihood without using large matrices the regression coefficients of the fixed effects can be concentrated out of the likelihood in this model by the same way of a linear mixed effects model as an illustration of the approach we analyzed immunologic data from a clinical trial for multiple sclerosis patients and estimated the dose response curves for each patient and the population mean

a cautionary note on the use of autoregressive models in analysis of longitudinal data rosner et al presented a simple easily implemented modelling method for retaining time order relationships in analyses of longitudinal data when successive measures are correlated evaluation of time order is particularly useful in epidemiologic studies concerned with exposure to potentially toxic substances and subsequent outcome but may also have use in more traditional growth studies that relate intake to subsequent development the analysis allows for unequally spaced measures and missing data the estimation method permits varying numbers of observations per subject and with measures equally spaced one can fit the model with use of ordinary least squares regression software we report on a potential false association that can result when both exposure and outcome are related to time we illustrate this problem with a small scale simulation and example we also note a more serious problem with rosner s approach in interpreting parameters although the model may be useful for prediction parameters depend on the autocorrelation and are not readily interpretable we recommend alternative modelling strategies be used when autocorrelation of errors is suspected

heterogeneity and selection in dynamic panel data abstract the data generating process dgp for generic dynamic panel data consists of a law of state dynamics g a selection or attrition rule h and an initial condition f i study nonparametric identifiability of this complete dgp g h f using short unbalanced panel data allowing for nonseparability between observed states and unobserved heterogeneity in each of g h and f for t 3 the dgp is identified by using a proxy variable for t 6 the three additional periods construct a proxy and thus the dgp is identified without an auxiliary variable

the scaling limit of loop erased random walk in three dimensions we show that the scaling limit exists and is invariant under dilations and rotations we give some tools that might be useful to show universality

large deviations and the lukic conjecture we use the large deviation approach to sum rules pioneered by gamboa nagel and rouault to prove higher order sum rules for orthogonal polynomials on the unit circle in particular we prove one half of a conjectured sum rule of lukic in the case of two singular points one simple and one double this is important because it is known that the conjecture of simon fails in exactly this case so this article provides support for the idea that lukic s replacement for simon s conjecture might be true

an em algorithm fitting first order conditional autoregressive models to longitudinal data abstract an em algorithm fits a state space formulation of the longitudinal regression model in which a continuous response depends on the lagged response and both time dependent and time independent covariates the baseline response depends only on covariates the model handles both missing data and gaussian measurement error on both response and continuous covariates the e step uses the kalman filter and associated filtering algorithms to update the unknown true response and predictor series for the observed data the m step uses standard closed form gaussian results standard errors come from the supplemented em sem algorithm the model accurately fits 6 years of pulmonary function measurements on 158 children with many missing observations

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

wavelet based testing for serial correlation of unknown form in panel models wavelet analysis is a new mathematical method developed as a unified field of science over the last decade or so as a spatially adaptive analytic tool wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks as can arise from persistent dependence seasonality and other kinds of periodicity this paper proposes a new class of generally applicable wavelet based tests for serial correlation of unknown form in the estimated residuals of a panel regression model where error components can be one way or two way individual and time effects can be fixed or random and regressors may contain lagged dependent variables or deterministic stochastic trending variables our tests are applicable to unbalanced heterogenous panel data they have a convenient null limit n 0 1 distribution no formulation of an alternative model is required and our tests are consistent against serial correlation of unknown form even in the presence of substantial in homogeneity in serial correlation across individuals this is in contrast to existing serial correlation tests for panel models which ignore inhomogeneity in serial correlation across individuals by assuming a common alternative and thus have no power against the alternatives where the average of serial correlations among individuals is close to zero we propose and justify a data driven method to choose the smoothing parameter the finest scale in wavelet spectral estimation making the tests completely operational in practice the data driven finest scale automatically converges to zero under the null hypothesis of no serial correlation and diverges to infinity as the sample size increases under the alternative ensuring the consistency of our tests simulation shows that our tests perform well in small and finite samples relative to some existing tests

efficient two step estimation via targeting abstract the standard description of two step extremum estimation amounts to plugging in a first step estimator of nuisance parameters to simplify the optimization problem and then deducing a user friendly but potentially inefficient estimator for the parameters of interest in this paper we consider a more general setting of two step estimation where we do not necessarily have nuisance parameters but rather awkward occurrences of the parameters of interest the efficiency problem associated with two step estimators in this context is more difficult than with standard nuisance parameters as even if the true unknown value of the parameters were plugged in to alleviate the awkward occurrences of the parameters the resulting second step estimator may not be efficient in addition standard approaches to restore efficiency for two step procedures may not work due to a consistency issue to alleviate this potential issue we propose a new computationally simple two step estimation procedure that relies on targeting and penalization to enforce consistency with the second step estimators maintaining asymptotic efficiency we compare this new method with existing iterative methods in the framework of copula models and asset pricing models simulation results illustrate that this new method performs better than existing iterative procedures and is nearly computationally equivalent

qml estimation of dynamic panel data models with spatial errors abstract we propose quasi maximum likelihood qml estimation of dynamic panel models with spatial errors when the cross sectional dimension n is large and the time dimension t is fixed we consider both the random effects and fixed effects models and prove consistency and derive the limiting distributions of the qml estimators under different assumptions on the initial observations we propose a residual based bootstrap method for estimating the standard errors of the qml estimators monte carlo simulation shows that both the qml estimators and the bootstrap standard errors perform well in finite samples under a correct assumption on initial observations but may perform poorly when this assumption is not met

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

nonparametric identification of discrete choice models with lagged dependent variables abstract variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity kasahara and shimotsu 2009 browning and carro 2014 in some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates this paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates the identification argument is related to that of honore and lewbel 2002 in that it requires a special regressor lewbel 1998 but it does not assume an additively separable latent index identification requires only 3 time periods neither stationarity nor time homogeneity is imposed and the distribution of the initial condition is not restricted apart from conditions required for the special regressor i demonstrate the result through a monte carlo simulation

maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods abstract a transformed likelihood approach is suggested to estimate fixed effects dynamic panel data models conditions on the data generating process of the exogenous variables are given to get around the issue of incidental parameters the maximum likelihood mle and minimum distance estimator mde are suggested both estimators are shown to be consistent and asymptotically normally distributed a hausman type specification test is suggested to test the fixed versus random effects specification or conditions on the data generating process of the exogenous variables monte carlo studies are conducted to evaluate the finite sample properties of the mle mde instrumental variable estimator iv and linear generalized method of moments estimator gmm it is shown that the likelihood approach appears to dominate the gmm approach both in terms of the bias and root mean square error of the estimators and the size and power of the test statistics

an autoregressive linear mixed effects model for the analysis of longitudinal data which show profiles approaching asymptotes in longitudinal data a continuous response sometimes shows a profile approaching an asymptote for such data we propose a new class of models autoregressive linear mixed effects models in which the current response is regressed on the previous response fixed effects and random effects asymptotes can shift depending on treatment groups individuals and so on and can be modelled by fixed and random effects we also propose error structures that are useful in practice the estimation methods of linear mixed effects models can be used as long as there is no intermittent missing

influence diagnostics for linear longitudinal models abstract influence diagnostics are important for analyzing cross sectional regression studies because they allow the analyst to understand the impact of individual observations on the estimated regression model in this article we consider the role of influence diagnostics in subject specific longitudinal models diagnostics are proposed under both fixed and random subject effects our approach is based on subject deletion which in this setting involves deleting a group of correlated observations we develop partial influence statistics to understand the combined impact of observations from a subject on population parameters simple computational formulas make the procedures feasible finally we illustrate the use of our new influence statistics by examining a dataset to model a taxpayer s charitable givings

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

quantile regression for dynamic panel data with fixed effects abstract this paper studies a quantile regression dynamic panel model with fixed effects panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors to reduce the dynamic bias we suggest the use of the instrumental variables quantile regression method of chernozhukov and hansen 2006 along with lagged regressors as instruments in addition we describe how to employ the estimated models for prediction monte carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias and the empirical levels for prediction intervals are very close to nominal levels finally we illustrate the procedures with an application to forecasting output growth rates for 18 oecd countries