optimal phase description of chaotic oscillators we introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones on chaotic attractors possessing a general phase description we define the optimal isophases as poincare surfaces showing return times as constant as possible the dynamics of the resultant optimal phase is maximally decoupled from the amplitude dynamics and provides a proper description of the phase response of chaotic oscillations the method is illustrated with the rossler and lorenz systems

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

gmm with many moment conditions this paper provides a first order asymptotic theory for generalized method of moments gmm estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak examples in which these asymptotics are relevant include instrumental variable iv estimation with many possibly weak or uninformed instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments under certain regularity conditions the gmm estimators are shown to converge in probability but not necessarily to the true parameter and conditions for consistent gmm estimation are given a general framework for the gmm limit distribution theory is developed based on epiconvergence methods some illustrations are provided including consistent gmm estimation of a panel model with time varying individual effects consistent limited information maximum likelihood estimation as a continuously updated gmm estimator and consistent iv structural estimation using large numbers of weak or irrelevant instruments some simulations are reported

efficient estimation of auto regression parameters and innovation distributions for semiparametric integer valued ar p models summary integer valued auto regressive inar processes have been introduced to model non negative integer valued phenomena that evolve over time the distribution of an inar p process is essentially described by two parameters a vector of auto regression coefficients and a probability distribution on the non negative integers called an immigration or innovation distribution traditionally parametric models are considered where the innovation distribution is assumed to belong to a parametric family the paper instead considers a more realistic semiparametric inar p model where there are essentially no restrictions on the innovation distribution we provide an semiparametrically efficient estimator of both the auto regression parameters and the innovation distribution

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

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

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

additive rank one preservers on block triangular matrix spaces in this note we address a description of the general form of additive rank one preservers on block triangular matrix spaces over an arbitrary field as an application we characterize additive mappings preserving rank additivity on block triangular matrix algebras

instrumental variable estimation of an error components model on propose des estimateurs efficaces en considerant des hypotheses alternatives sur les sources d endogeneite et les proprietes de variance covariance des perturbations

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

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

a disaggregate negative binomial regression procedure for count data analysis various research areas face the methodological problems presented by nonnegative integer count data drawn from heterogeneous populations we present a disaggregate negative binomial regression procedure for analysis of count data observed for a heterogeneous sample of cross sections possibly over some fixed time periods this procedure simultaneously pools or groups cross sections while estimating a separate negative binomial regression model for each group an e m algorithm is described within a maximum likelihood framework to estimate the group proportions the group specific regression coefficients and the degree of overdispersion in event rates within each derived group the proposed procedure is illustrated with count data entailing nonnegative integer counts of purchases events for a frequently bought consumer good

efficient estimation using panel data in an important recent paper hausman and taylor 1981 hereafter ht considered the instrumental variable estimation of a regression model using panel data when the individual effects may be correlated with a subset of the explanatory variables they provided a simple consistent estimator and an efficient estimator more recently amemiya and macurdy 1986 hereafter am have suggested an alternative estimator which is more efficient than the ht estimator under certain conditions and given stronger assumptions than ht made however the relationship between the ht and am papers is less clear than it might be in part because of notational differences between the two papers in this paper we clarify the relationship between the ht and am estimators and we show that the difference between these estimators lies in the treatment of the time varying explanatory variables which are uncorrelated with the effects ht use each such variable as two instruments means and deviations from means while am use such variables as t 1 instruments as deviations from means and also separately for each of the t available time periods this enables us to make clear the conditions under which the am estimator is more efficient than the ht estimator we also present each estimator in a form which allows it to be calculated using standard instrumental variables two stage least squares software following the am path one step further we then define a third bms estimator which under yet stronger assumptions is more efficient than the am estimator both ht and am use as instruments the deviations from means of the time varying variables which are correlated with the effects a more efficient estimator may be obtained by using separately the t 1 linearly independent values of these deviations from individual means consistency requires that these be legitimate instruments and whether this is so depends on why these time varying variables are correlated with the effects for example if such correlation arises solely because of a time invariant component which is removed in taking deviations from individual means these instruments are legitimate

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

latent change in recurrent choice data this paper introduces dynamic latent class models for the analysis and interpretation of stability and change in recurrent choice data these latent class models provide a nonparametric representation of individual taste differences changes in preferences are modeled by allowing for individual level transitions from one latent class to another over time the most general model facilitates a saturated representation of class membership changes several special cases are presented to obtain a parsimonious description of latent change mechanisms an easy to implement em algorithm is derived for parameter estimation the approach is illustrated by a detailed analysis of a purchase incidence data set

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

consistent estimation of linear panel data models with measurement error abstract measurement error causes a bias towards zero when estimating a panel data linear regression model the panel data context offers various opportunities to derive instrumental variables allowing for consistent estimation we consider three sources of moment conditions i restrictions on the covariance matrix of the errors in the equations ii nonzero third moments of the regressors and iii heteroskedasticity and nonlinearity in the relation between the error ridden regressor and another error free regressor in simulations these approaches appear to work well

efficient estimation of dynamic panel data models alternative assumptions and simplified estimation abstract this paper considers the estimation of dynamic models for panel data it shows how to count and express the moment conditions implied by a variety of covariance restrictions these conditions can be imposed in a gmm framework many of the moment conditions are nonlinear in the parameters we derive a simple linearized estimator that is asymptotically as efficient as the nonlinear gmm estimator and convenient tests of the validity of the nonlinear restrictions

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

mixed inar 1 poisson regression models analyzing heterogeneity and serial dependencies in longitudinal count data this paper presents finite mixture versions of integer valued autoregressive inar poisson regression models for investigating regularity and predictability of purchase behavior over time the approach facilitates the analysis of heterogeneity and serial correlation effects as well as conditional and marginal analyses of the effects of covariates an application to scanner panel data of detergents yields substantive insights into sources of autodependencies in individual category purchases

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

maximum likelihood estimation and inference methods for the covariance stationary panel ar 1 unit root model abstract this paper considers maximum likelihood ml based estimation and inference procedures for linear dynamic panel data models with fixed effects the paper first studies the asymptotic properties of macurdy s macurdy t 1982 the use of time series processes to model the time structure of earnings in a longitudinal data analysis journal of econometrics 18 83 114 first difference maximum likelihood fdml estimator for the covariance stationary panel ar 1 unit root model with fixed effects viz y i t y i t 1 1 i e i t under a variety of asymptotic plans subsequently the paper shows through monte carlo simulations for panels of various dimensions the favourable finite sample properties of the fdmle for as compared to those of a number of alternative fixed effects ml estimators for under covariance stationarity and normality of the data the paper also discusses panel unit root test procedures that are based on the fdmle a monte carlo study conducted for one version of these tests reveals that it has very good size and power properties in comparison with alternative panel unit root tests

modeling household purchase behavior with logistic normal regression the successful development of marketing strategies requires the accurate measurement of household preferences and their reaction to variables such as price and advertising manufacturers for examp

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

rank one preserving r linear maps on spaces of self adjoint operators on complex hilbert spaces abstract let h be a complex hilbert space and let s a h be the space of all self adjoint operators on h let denote the subset of s a h consisting of all rank one operators a map l from s a h to itself is called a rank one preserver on s a h if l and is said to be r linear if l a b l a l b and l ka kl a for any k r and a b s a h where r is the field of real numbers we give a complete classification of all r linear and weakly continuous rank one preservers on s a h moreover we also determine the general form of all r linear and weakly continuous rank preservers respectively rank one idempotence preservers on s a h

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

econometric models for count data with an application to the patents r d relationship this paper focuses on developing and adapting statistical models of counts nonnegative integers in the context of panel data and using them to analyze the relationship between patents and r d expenditures since a variety of other economic data come in the form of repeated counts of some individual actions or events the methodology should have wide applications the statistical models we develop are applications and generalizations of the poisson distribution two important issues are i given the panel nature of our data how can we allow for separate persistent individual fixed or random effects ii how does one introduce the equivalent of disturbances in the equation into the analysis of poisson and other discrete probability functions the first problem is solved by conditioning on the total sum of outcomes over the observed years while the second problem is solved by introducing an additional source of randomness allowing the poisson parameter to be itself randomly distributed and compounding the two distributions lastly we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models

o k floquet multipliers in the determination of the asymptotic stability and bifurcation behaviour of periodic orbits it is necessary to accurately compute the floquet multipliers having modulus nearly 1 and to determine the number of multipliers that lie well inside and well outside the unit circle current numerical methods for computing floquet multipliers suffer a loss of accuracy in two cases of importance namely when the multiplier at 1 is nearly defective and when there are large multipliers an alternative approach is proposed which can be derived from a reexamination of the underlying algebraic eigenvalue problem and which is suitable for systems of ordinary differential equations numerical results indicate that avoiding the explicit construction of a matrix commonly called the circuit matrix and using known properties of a fixed floquet multiplier at 1 will circumvent the difficulties mentioned above convergence results are given

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

testing for overdispersion in poisson and binomial regression models abstract in this article a method for obtaining tests for overdispersion with respect to a natural exponential family is derived the tests are designed to be powerful against arbitrary alternative mixture models where only the first two moments of the mixed distribution are specified various tests for extra poisson and extra binomial variation are obtained as special cases the use of a particular test may be motivated by a consideration of the mechanism through which the overdispersion may arise the common occurrence of extra poisson and extra binomial variation has been noted by several authors however the poisson and binomial models remain valid in many instances and because of their simplicity and appeal it is of real interest to ascertain when they apply this paper develops a unifying theory for testing for overdispersion and generalizes tests previously derived including those by fisher 1950 collings and margolin 1985 and prentice 1986 it also shows the pearson statistic to be a sc

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

individual effects and dynamics in count data models in this paper we examine the panel data estimation of dynamic models for count data that include correlated fixed effects and predetermined variables use of a linear feedback model is proposed a quasi differenced gmm estimator is consistent for the parameters in the dynamic model but when series are highly persistent there is a problem of weak instrument bias an estimator is proposed that utilises pre sample information of the dependent count variable which is shown in monte carlo simulations to possess desirable small sample properties the models and estimators are applied to data on us patents and r d expenditure

pseudo maximum likelihood methods applications to poisson models pseudo maximum likelihood techniques are applied to basic poisson models and to poisson models with specification errors in the latter case it is shown that consistent and asymptotically normal estimators can be obtained without specifying the p d f of the disturbances these estimators are compared both from the finite sample and the asymptotic point of view quasi generalized pml estimators which asymptotically dominate all pml estimators are also proposed finally bivariate and panel data poisson models are discussed the analysis of economic behavior often leads to the study of characteristics taking a small number of positive values the classical linear model is not adapted to explain how such discrete variables depend on other quantitative or qualitative variables the reasons are similar to those usually given in the case of an endogenous qualitative variable the shape of the observation set does not correspond to a linear model the assumption of normality of the disturbances cannot be made since the endogenous variables take a small number of values with strictly positive probabilities and the prediction formulae which are deduced from a linear model give impossible values in the models considered in the literature to describe discrete variables cox and lewis 2 el sayyad 3 frome kutner and beauchamp 4 gilbert 5 hausman hall and griliches 8 see also lancaster 12 the endogenous variable is assumed to have a poisson distribution conditional upon the exogenous variables the parameter of this distribution is a function of the values of the exogenous variables the choice of such a model is justified if the dependent variable counts the occurrence of a given event during a fixed period and if the usual assumptions of the poisson process are satisfied for instance the model is adapted to describe daily numbers of oil tankers arrivals in a port the number of accidents at work by factory or the number of patents applied for and received by firms hausman hall and griliches 8

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

gmm estimators with improved finite sample properties using principal components of the weighting matrix with an application to the dynamic panel data model gmm estimators have poor finite sample properties in highly overidentified models with many moment conditions the optimal weighting matrix is poorly estimated we suggest using principal components of the weighting matrix this effectively drops some of the moment conditions our simulations done in the context of the dynamic panel data model show that the resulting gmm estimator has better finite sample properties than the usual two step gmm estimator in the sense of smaller bias and more reliable standard errors

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

estimating the parameters of a convolution by maximum likelihood abstract in the present age of computer sophistication computational difficulty is no longer a justification for seeking alternative and inefficient estimation procedures in place of maximum likelihood estimation particularly when there are only two or three parameters to be estimated convolution densities are an example where this has occurred it is shown that in a large class of such densities the maximum likelihood equations can be reduced by one thus for a two parameter family only a single equation need be solved iteratively the required formulas are derived the problem of basing inferences on the resulting maximum likelihood estimates is briefly discussed

efficient estimation of panel data models with strictly exogenous explanatory variables abstract with panel data exogeneity assumptions imply many more moment conditions than standard estimators use however many of the moment conditions may be redundant in the sense that they do not increase efficiency if so we may establish the standard estimators efficiency we prove efficiency results for gls in a model with unrestricted error covariance matrix and for 3sls in models where regressors and errors are correlated such as the hausman taylor model for models with correlation between regressors and errors and with unrestricted error covariance structure we provide a simple estimator based on a gls generalization of deviations from means

on the identifiability of finite mixtures of distributions corresp finite mixtures of the following ten families of univariate distributions are shown to be identifiable logarithmic series discrete rectangular rectangular first law of laplace noncentral x 2 logistic generalized logistic generalized hyperbolic secant inverse gaussian and random walk a generalized version of a theorem given by teicher is used to show that the finite mixtures of the following multivariate distributions are also identifiable negative binomial logarithmic series poisson normal inverse gaussian and random walk

new methods for calculating the stability of periodic solutions abstract systems of autonomous first order ordinary differential equations are considered dimension n the stability of periodic solutions is determined by the eigenvalues of the monodromy matrix m a standard way of calculating m requires storage proportional to n 2 in this paper new algorithms for calculating m are proposed one algorithm requires storage proportional to n another algorithm involves nearly no work provided the periodic solution was calculated by shooting features of the new algorithms are discussed

testing for individual effects in autoregressive models abstract this note describes a test for the presence of individual effects in dynamic models the test employs restrictions on sample moments implied by the absence of individual effects testing the assumption of unobserved heterogeneity is desirable because estimation methods which control for heterogeneity are typically more complicated and require more data than would be required without individual effects the test is easily implemented as the calculation of statistics follows directly from a linear instrumental variables estimation technique the test is illustrated in the context of estimating a dynamic wage equation using data from the panel study of income dynamics

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

iv estimation of panels with factor residuals this paper considers panel data regression models with weakly exogenous or endogenous regressors and residuals generated by a multi factor error structure in this case the standard dynamic panel estimators fail to provide consistent estimates of the parameters we propose a new estimation approach based on instrumental variables which retains the traditional attractive features of method of moments estimators one novelty of our approach is that we introduce new parameters to represent the unobserved covariances between the instruments and the factor component of the residual these parameters are typically estimable when n is large some important estimation and identification issues are studied in detail the finite sample performance of the proposed estimators is investigated using simulated data the results show that the method produces reliable estimates of the parameters over various parametrizations and is robust to large values of the autoregressive parameter and or the variance of the factor loadings

an analytical and numerical study of the bifurcations in a system of linearly coupled oscillators abstract we study a two parameter family of ordinary differential equations in r 4 that governs the dynamics of two coupled planar oscillators each oscillator has a unique periodic solution that is attracting and the uncoupled product system has a unique invariant torus that is attracting the torus persists for weak coupling and contains two periodic solutions when the coupling is linear and conservative one of these in which the oscillators are synchronized persists and is stable for all coupling strengths the other in which the oscillators are radiant out of phase disappears either in a hopf bifurcation or when fixed points appear on the orbit at a critical ratio of the coupling strength to the frequency the out of phase oscillation is unstable except on an open set in the frequency coupling strength plane which contains moderate values of both parameters furthermore there are tori bifurcating from the out of phase solution which means according to the arnol d theory for hopf bifurcations in maps that there may be periodic solutions of arbitrarily large period and chaotic solutions as well numerous other bifurcations occur and there are a number of higher codimension singularities in a large region of the frequency coupling parameter plane stable steady states coexist with stable periodic solutions

concomitant variable latent class models abstract this article introduces and illustrates a new type of latent class model in which the probability of latent class membership is functionally related to concomitant variables with known distribution the function or so called submodel may be logistic exponential or another suitable form concomitant variable models supplement latent class models incorporating grouping by providing more parsimonious representations of data for some cases also concomitant variable models are useful when grouping models involve a greater number of parameters than can be meaningfully fit to existing data sets although parameter estimates may be calculated using standard iterative procedures such as the newton raphson method sample analyses presented here employ a derivative free approach known as the simplex method a general procedure for imposing linear constraints on the parameter estimates is introduced a data set involving arithmetic test items in a mastery testing context is used to illustrate fitting a

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

empirical likelihood block bootstrapping monte carlo evidence has made it clear that asymptotic tests based on generalized method of moments gmm estimation have disappointing size the problem is exacerbated when the moment conditions are serially correlated several block bootstrap techniques have been proposed to correct the problem including hall and horowitz 1996 and inoue and shintani 2006 we propose an empirical likelihood block bootstrap procedure to improve inference where models are characterized by nonlinear moment conditions that are serially correlated of possibly infinite order combining the ideas of kitamura 1997 and brown and newey 2002 the parameters of a model are initially estimated by gmm which are then used to compute the empirical likelihood probability weights of the blocks of moment conditions the probability weights serve as the multinomial distribution used in resampling the first order asymptotic validity of the proposed procedure is proven and a series of monte carlo experiments show it may improve test sizes over conventional block bootstrapping

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

additive preservers of rank on alternate matrix spaces over fields and applications abstract suppose f is any field and n is an integer with n 4 let k n f be the set of all n n alternate matrices over f and let k n f be the non associative ring formed by k n f under the usual addition and the multiplication defined by x y xyx for all x y k n f a pair of n n matrices a b is said to be rank additive if rank a b rank a rank b and rank subtractive if rank a b rank a rank b we say that an operator k n f k n f is additive if x y x y for any x y k n f a preserver of rank additivity respectively rank subtractivity on k n f if it preserves the set of all rank additive respectively rank subtractive pairs a preserver of rank on k n f if rank x rank x for every x k n f and a ring endomorphism of k n f if it is additive and satisfies x y x y for any x y k n f we determine the general form of all additive preservers of rank respectively rank additivity and rank subtractivity on k n f and characterize all ring endomorphisms of k n f

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

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

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

semiparametric bayesian inference in autoregressive panel data models this paper develops bayesian methods for inference in dynamic panel data models with individual effects and applies them to study longitudinal data on earnings from the panel study of income dynamics psid we study semiparametric versions of commonly used random effects autoregressive models in which the distribution of the disturbances is not restricted to fall in a parametric class to model the unknown distributions without resorting to strong parametric assumptions we draw upon recent advances in the theory and computation of nonparametric bayesian models using dirichlet process priors the overall approach can be viewed as an application of the general semiparametric bayesian approach of west muller and escobar 1994 which in turn makes use of results on bayesian density estimation by escobar 1994 and escobar and west 1995 most conventional panel data methods e g anderson and hsiao 1981 macurdy

panel data and unobservable individual effects abstract an important purpose in pooling time series and cross section data is to control for individual specific unobservable effects which may be correlated with other explanatory variables e g latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions using instrumental variables and the time invariant characteristics of the latent variable we derive 1 1 a test for the presence of this effect and for the over identifying restriction we use 2 2 necessary and sufficient conditions for identification of all the parameters in the model and 3 3 the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within groups estimator we calculate efficient estimates of a wage equation from the michigan income dynamics data which indicate substantial differences from within groups and balestra nerlove estimates particularly a significantly higher estimate of the returns to schooling

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

on the covariance structure of earnings and hours changes this paper presents an empirical analysis of individual earnings and hours data from three different longitudinal surveys in the first part of the paper we catalog the main features of the covariance structure of earnings and hours changes we find that this structure is very similar across data sets and may be adequately summarized by a simple components of variance model in the second part of the paper we offer an interpretation of this model in terms of a simple life cycle labor supply model

derper an algorithm for the continuation of periodic solutions in ordinary differential equations abstract an algorithm for the continuation of periodic solutions of ode was derived and tested the algorithm is based on the shooting method and a standard continuation algorithm variational variables are used to compute the jacobi matrix the starting point on the periodic orbit is adaptively changed in the algorithm by fixing one component of the solution stability of periodic solutions along the continuous branch of solutions is determined by computing characteristic multipliers without difficulty the algorithm crosses limit points and at bifurcation points double period bifurcation points and points of tori bifurcation it proceeds along the original branch of solutions the usefulness of the algorithm is demonstrated in two examples one of them describes two stirred tank reactors with mutual mass exchange the other one is the lorenz model of turbulence

efficient probabilistic forecasts for counts summary efficient probabilistic forecasts of integer valued random variables are derived the optimality is achieved by estimating the forecast distribution non parametrically over a given broad model class and proving asymptotic non parametric efficiency in that setting the method is developed within the context of the integer auto regressive class of models which is a suitable class for any count data that can be interpreted as a queue stock birth and death process or branching process the theoretical proofs of asymptotic efficiency are supplemented by simulation results that demonstrate the overall superiority of the non parametric estimator relative to a misspecified parametric alternative in large but finite samples the method is applied to counts of stock market iceberg orders a subsampling method is used to assess sampling variation in the full estimated forecast distribution and a proof of its validity is given

additive preservers of rank additivity on the spaces of symmetric and alternate matrices denote the set of n n symmetric matrices resp alternate matrices over a field f by sn f resp kn f we characterize the bijective additive preservers of rank additivity on sn f and kn f the set sn f resp kn f forms a non associative ring with respect to the addition a b a b and the multiplication a b a b aba where a b sn f resp kn f the forms of any automorphism of the two non associative rings are also given

gmm estimation of linear panel data models with time varying individual effects abstract this paper considers models for panel data in which the individual effects vary over time the temporal pattern of variation is arbitrary but it is the same for all individuals the model thus allows one to control for time varying unobservables that are faced by all individuals e g macro economic events and to which individuals may respond differently a generalized within estimator is consistent under strong assumptions on the errors but it is dominated by a generalized method of moments estimator this is perhaps surprising because the generalized within estimator is the mle under normality the efficiency gains from imposing second moment error assumptions are evaluated they are substantial when the regressors and effects are weakly correlated

mixed poisson regression models with covariate dependent rates this paper studies a class of poisson mixture models that includes covariates in rates this model contains poisson regression and independent poisson mixtures as special cases estimation methods based on the em and quasi newton algorithms properties of these estimates a model selection procedure residual analysis and goodness of fit test are discussed a monte carlo study investigates implementation and model choice issues this methodology is used to analyze seizure frequency and ames salmonella assay data

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

linear additive preservers of ranks 2 and 4 on alternate matrix spaces over fields abstract let kn f be the linear space of all n n alternate matrices over a field f an operator f kn f kn f is said to be additive if f a b f a f b for any a b kn f linear if f is additive and f aa af a for every a f and a kn f and a preserver of ranks 2 and 4 on kn f if rank f x rank x for every x kn f with rank x 2 or 4 when n 4 we characterize all linear respectively additive preservers of ranks 2 and 4 on kn f over any field respectively any field that is not isomorphic to a proper subfield of itself furthermore it is also shown that the condition f is not isomorphic to a proper subfield of itself is necessary for the obtained conclusion on additive preservers of ranks 2 and 4 on kn f

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

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970

how informative is the initial condition in the dynamic panel model with fixed effects abstract i consider estimation of the autoregressive panel model with fixed effects yit ci yi t 1 eit i investigate the estimation method developed by blundell and bond 1998 which makes use of the stationarity of the initial levels i do it by numerically comparing the semiparametric information bounds for the case that incorporates the stationarity of the initial condition and for the case that does not it is found that the efficiency gain can be substantial

some general techniques on linear preserver problems abstract several general techniques on linear preserver problems are described the first one is based on a transfer principle in model theoretic algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0 the second one concerns the use of some simple geometric technique to reduce linear preserver problems to standard types so that known results can be applied the third one is about solving linear preserver problems on more general operator algebras by reducing the problems to idempotent preservers numerous examples will be given to demonstrate the proposed techniques