a note on the equivalence of specification tests in the two factor multivariate variance components model abstract this note offers a generalization of hausman and taylor s equivalence of specification tests in the single equation variance error components model to the two factor multivariate variance components case the relationship between the specification tests and the hypothesis test in the model proposed by mundlak is also discussed

iterative time limited signal restoration the purpose of this paper is to show that time limited restoration of shift invariant blurred signals can be done by means of fixed point solutions of contraction mappings under rather general conditions for the distortion operator all our results are valid for multidimensional signals an application of these results to the iterative extrapolation of band limited discrete images is shown

robust linear static panel data models using e contamination abstract the paper develops a general bayesian framework for robust linear static panel data models using e contamination a two step approach is employed to derive the conditional type ii maximum likelihood ml ii posterior distribution of the coefficients and individual effects the ml ii posterior means are weighted averages of the bayes estimator under a base prior and the data dependent empirical bayes estimator two stage and three stage hierarchy estimators are developed and their finite sample performance is investigated through a series of monte carlo experiments these include standard random effects as well as mundlak type chamberlain type and hausman taylor type models the simulation results underscore the relatively good performance of the three stage hierarchy estimator within a single theoretical framework our bayesian approach encompasses a variety of specifications while conventional methods require separate estimators for each case

a two stage estimator for probit models with structural group effects this paper outlines a two stage technique for estimation and inference in probit models with structural group effects the structural group specification belongs to a broader class of random components models in particular individuals in a given group share a common component in the specification of the conditional mean of a latent variable for a number of computational reasons existing random effects models are impractical for estimation and inference in this type of problem our two stage estimator provides an easily estimable alternative to the random effects specification in addition we conduct a monte carlo simulation comparing the performance of alternative es timators and find that the two stage estimator is superior both in terms of estimation and inference to traditional estimators

extrapolation algorithms for discrete signals with application in spectral estimation in this paper we present some new algorithms useful for extrapolation and spectral estimation of band limited sequences in one and two dimensions first we show that many of the existing extrapolation algorithms for noiseless observations are unified under the criterion of minimum norm least squares mnls extrapolation for example the iterative algorithms proposed in 2 and 8 10 are shown to be special cases of a one step gradient algorithm which has linear convergence convergence and other numerical properties are improved by going to a conjugate gradient algorithm for noisy observations these algorithms could be extended by considering a mean square extrapolation criterion which gives rise to a mean square extrapolation filter and also to a recursive extrapolation filter examples and application of these methods are given extension of these algorithms is made for problems where the signal is known to be periodic a new set of functions called the periodic discrete prolate spheroidal sequences p dpss analogous to dpss 21 22 are introduced and their properties are studied finally several of these algorithms are generalized to two dimensions and the relevant equations are given

omitted variables in multilevel models statistical methodology for handling omitted variables is presented in a multilevel modeling framework in many nonexperimental studies the analyst may not have access to all requisite variables and this omission may lead to biased estimates of model parameters by exploiting the hierarchical nature of multilevel data a battery of statistical tools are developed to test various forms of model misspecification as well as to obtain estimators that are robust to the presence of omitted variables the methodology allows for tests of omitted effects at single and multiple levels the paper also introduces intermediate level tests these are tests for omitted effects at a single level regardless of the presence of omitted effects at a higher level a simulation study shows not surprisingly that the omission of variables yields bias in both regression coefficients and variance components it also suggests that omitted effects at lower levels may cause more severe bias than at higher levels important factors resulting in bias were found to be the level of an omitted variable its effect size and sample size a real data study illustrates that an omitted variable at one level may yield biased estimators at any level and in this study one cannot obtain reliable estimates for school level variables when omitted child effects exist however robust estimators may provide unbiased estimates for effects of interest even when the efficient estimators fail and the one degree of freedom test helps one to understand where the problem is located it is argued that multilevel data typically contain rich information to deal with omitted variables offering yet another appealing reason for the use of multilevel models in the social sciences

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

a compact algorithm for evaluating linear prolate functions linear prolate functions lpfs are a set of bandlimited functions constructed to be invariant to the fourier transform and orthonormal on the real line for the given bandwidth their unique properties make lpfs useful in signal processing a method is described to evaluate the lps by solving the eigensystem of the corresponding differential equation the eigenvectors of this system provide the coefficients of the representation of the required functions into a series of spherical bessel functions the method omits several cumbersome steps inherent to previous algorithms without loss of accuracy

estimation of a fixed effect cobb douglas system using panel data abstract this paper considers the estimation of a model consisting of a cobb douglas production function and the associated first order conditions for cost minimization there is a fixed individual firm effect in each equation and the availability of panel data is assumed the conditional mle is derived and shown to be mle after a within transformation it can be written explicitly as a corrected ols estimator or as an iv estimator in the special case in which the errors in the production function are independent of the errors in the first order conditions the conditional mle does not require input price data

semiparametric efficient estimation of ar 1 panel data models this study focuses on the semiparametric efficient estimation of random effect panel models containing ar 1 disturbances we also consider such estimators when the effects and regressors are correlated hausman and taylor 1981 we introduce two semiparametric efficient estimators that make minimal assumptions on the distribution of the random errors effects and the regressors and that provide semiparametric efficient estimates of the slope parameters and of the effects our estimators extend the previous work of park and simar j amer statist assoc 89 1994 929 park et al j econometrics 84 1998 273 and adams et al j business econom statist 17 1999 349 theoretical derivations are supplemented by monte carlo simulations we also provide an empirical illustration by estimating relative efficiencies from a stochastic distance function for the u s banking industry over the 1980s and 1990s in markets where regulatory constraints have been lessened or done away with the deregulatory dynamic market shocks may not be adjusted to immediately and may induce a serial correlation pattern in firm s use of best practice banking technologies our semiparametric estimators have an important role in providing robust point estimates and inferences of the productivity and efficiency gains due to such economic reforms

linear prediction of bandlimited processes with flat spectral densities lyman et al 2000 developed some important properties of a continuous time linear predictor applied to a bandlimited random process and discussed how such a prediction could be applied to the problem of mobile radio fading in this paper we solve explicitly for the optimal predictor in the mean square sense when the process spectral density is not within the band limits and the predictor impulse response is energy constrained as basis functions we use time shifted versions of the prolate spheroidal wave functions leading to a simple algebraic optimization problem that is solved using a lagrange multiplier we show how to use the solution to compute the minimum mean squared prediction error under the energy constraint then we discuss the case of a bandlimited process embedded in white noise showing how to determine if a certain mean squared prediction error can be attained

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

pooling an experimental study of alternative testing and estimation procedures in a two way error component model abstract this paper considers a two way error component model with no lagged dependent variable and investigates the performance of various testing and estimation procedures applied to this model by means of monte carlo experiments the following results were found 1 the chow test performed poorly in testing the stability of cross section regressions over time and in testing the stability of time series regression across regions 2 the roy zellner test performed well and is recommended for testing the poolability of the data 3 the hausman specification test employed to test the orthogonality assumption gave a low frequency of type i errors 4 the lagrange multiplier test employed to test for zero variance components did well except in cases where it was badly needed 5 the problem of negative estimates of the variance components was found to be more serious in the two way model than in the one way model however replacing the negative variance estimates by zero did not have a serious effect on the performance of the second round gls estimates of the regression coefficients 6 as in the one way model all the two stage estimation methods performed reasonably well 7 better estimates of the variance components did not necessarily lead to better second round gls estimates of the regression coefficients

panel data models with spatially correlated error components abstract in this paper we consider a panel data model with error components that are both spatially and time wise correlated the model blends specifications typically considered in the spatial literature with those considered in the error components literature we introduce generalizations of the generalized moments estimators suggested in kelejian and prucha 1999 a generalized moments estimator for the autoregressive parameter in a spatial model international economic review 40 509 533 for estimating the spatial autoregressive parameter and the variance components of the disturbance process we then use those estimators to define a feasible generalized least squares procedure for the regression parameters we give formal large sample results for the proposed estimators we emphasize that our estimators remain computationally feasible even in large samples

min max linear estimation of band limited sequences in the presence of random noise corresp a problem in band limited signal estimation is presented the signal is assumed to be a band limited sequence subject to an energy constraint the observed signal components are assumed to be corrupted by the components of a discrete time stochastic noise process with zero mean and known antocorrelations the error metric is the energy in a fixed linear combination of the error components linear estimators are considered and an explicit expression for the optimal in a min max sense estimation scheme is derived an interesting feature of the optimal estimation scheme derived in this correspondence is that it is identical to one based on stochastic models for both the signal and the noise

panel estimators and the identification of firm specific efficiency levels in parametric semiparametric and nonparametric settings abstract the paper analyzes a number of competing approaches to modeling efficiency in panel studies the specifications considered include the fixed effects stochastic frontier the random effects stochastic frontier the hausman taylor random effects stochastic frontier and the random and fixed effects stochastic frontier with an ar 1 error i have summarized the foundations and properties of estimators that have appeared elsewhere and have described the model assumptions under which each of the estimators have been developed i discuss parametric and nonparametric treatments of time varying efficiency including the battese coelli estimator and linear programming approaches to efficiency measurement monte carlo simulation is used to compare the various estimators and to assess their relative performances under a variety of misspecified settings a brief illustration of the estimators is conducted using u s banking data

panel data models with multiple time varying individual effects abstract this paper considers a panel data model with time varying individual effects the data are assumed to contain a large number of cross sectional units repeatedly observed over a fixed number of time periods the model has a feature of the fixed effects model in that the effects are assumed to be correlated with the regressors the unobservable individual effects are assumed to have a factor structure for consistent estimation of the model it is important to estimate the true number of individual effects we propose a generalized methods of moments procedure by which both the number of individual effects and the regression coefficients can be consistently estimated some important identification issues are also discussed our simulation results indicate that the proposed methods produce reliable estimates

the truncated k moment problem for closure of open sets we solve the truncated k moment problem when k subseteq r n is the closure of a not necessarily bounded open set which includes the important cases k r n and k r n that is we completely characterize the interior of the convex cone of finite sequences that have a representing measure on k subseteq r n it is in fact the domain of the legendre fenchel transform associated with a certain convex function and so in this context detecting whether a sequence is in the interior of this cone reduces to solving a finite dimensional convex optimization problem this latter problem is related to maximum entropy methods for approximating an unknown density from knowing only finitely many of its moments interestingly the proposed approach is essentially geometric and of independent interest as it also addresses the abstract problem of characterizing the interior of a convex cone c which is the conical hull of a set continuously parametrized by a compact set m subset r n or m subseteq s n 1 where m is the closure of an open subset of r n resp s n 1 as a by product we also obtain a barrier function for the cone c

maximum likelihood estimation of random effects models abstract iterated gls has a remarkable property when applied to the random effects model in its usual parameterization the values for the parameter that measures relative variance obtained through successive iterations form a monotonic sequence this property provides convenient checks for multiple maxima of the likelihood function and for existence of a local maximum that satisfies the non negativity condition

a general representation theorem for partially ordered commutative rings an extension of the kadison dubois representation theorem is proved this extends both the classical version 3 and the preordering version given by jacobi in 5 it is then shown how this can be used to sharpen the results on representations of strictly positive polynomials given by jacobi and prestel in 6

specification testing in panel data with instrumental variables i show that specification tests for correlated fixed effects developed by hausman and taylor extend in an analogous way to panel data sets with endogenous regressors given panel data different sets of instrumental variables can be used to construct the test for a simple class of models the test in many cases is asymptotically more efficient if an incomplete set of instruments is used however in small samples one may do better using the complete set of instruments monte carlo results demonstrate the likely gains for different assumptions about the degree of between and within variance in the data

multilevel modeling with correlated effects when there exist omitted effects measurement error and or simultaneity in multilevel models explanatory variables may be correlated with random components and standard estimation methods do not provide consistent estimates of model parameters this paper introduces estimators that are consistent under such conditions by employing generalized method of moments gmm estimation techniques in multilevel modeling the authors present a series of estimators along a robust to efficient continuum this continuum depends on the assumptions that the analyst makes regarding the extent of the correlated effects it is shown that the gmm approach provides an overarching framework that encompasses well known estimators such as fixed and random effects estimators and also provides more options these gmm estimators can be expressed as instrumental variable iv estimators which enhances their interpretability moreover by exploiting the hierarchical structure of the data the current technique does not require additional variables unlike traditional iv methods further statistical tests are developed to compare the different estimators a simulation study examines the finite sample properties of the estimators and tests and confirms the theoretical order of the estimators with respect to their robustness and efficiency it further shows that not only are regression coefficients biased but variance components may be severely underestimated in the presence of correlated effects empirical standard errors are employed as they are less sensitive to correlated effects when compared to model based standard errors an example using student achievement data shows that gmm estimators can be effectively used in a search for the most efficient among unbiased estimators

grouped effects estimators in fixed effects models abstract we consider estimation of nonlinear panel data models with common and individual specific parameters fixed effects estimators are known to suffer from the incidental parameters problem which can lead to large biases in estimates of common parameters pooled estimators which ignore heterogeneity across individuals are also generally inconsistent we assume that individuals in the data are grouped on multiple levels where groups are defined by some observable external classification we consider group effects estimators where individual specific parameters are assumed common across groups at some level we provide conditions under which group effects estimates of common parameters are asymptotically unbiased and normal the conditions suggest a tradeoff between two sources of bias one due to incidental parameters and the other due to misspecification of unobserved heterogeneity

powers of totally positive subgroups of fields abstract for a formally real field f a totally positive co torsion subgroup s of f and m 1 we prove that s m s m this extends a result of becker we prove several refinements of this fact related to higher pythagoras numbers real holomorphy rings and sums with mixed powers

optimal estimation for band limited signals including time domain considerations the problem of estimation for band limited signals is investigated the desired estimate is based on a finite number of time samples taken from a measurement interval of length t m with no additional information the estimate must be based on these samples alone when the signal is band limited with normalized bandwidth this provides additional information which is used to improve the estimate by extrapolating the signal an extrapolation based on the measured time samples and the known bandwidth is concentrated in time about the measurement interval the length of this effective extrapolation interval is t l approx t m 2 beta several band limited estimation methods of this type have been described a new estimation method for band limited signals is described which is also based on a time concentrated extrapolation of the measurements this new method improves estimates by specifically incorporating the interval t l into the problem formulation and thereby improving the extrapolation on this relevant interval estimation error bounds and examples are presented in comparing these two types of band limited estimation procedures estimation with imperfect data is considered sensitivity of the band limited methods to errors in the data is discussed estimation with smoothing is utilized in reducing the effects of this noise

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

comments and corrections on on the eigenvectors of symmetric toeplitz matrices the necessary and sufficient condition for a matrix to be doubly symmetric as stated in the above paper is questioned it is proved that the condition under consideration is necessary but not sufficient somecounterexamples are provided to substantiate the claim in fact what appears to be a new class of matrices possessing some interesting properties is discussed

grouped data estimation and testing in simple labor supply models abstract inappropriate identifying assumptions and measurement error in hourly wage data may account for the poor performance of some empirical labor supply models this paper discusses an efficient generalization of wald s method of fitting straigth lines that is robust to measurement error imposes mild identifying assumptions and is useful for the estimation of labor supply models with panel data a two stage least squares tsls equivalent of the efficient wald estimator is presented and a tsls overidentification test statistic is shown to be a test statistic for the equality of alternative wald estimates of the same parameter in an emperical example estimated labor supply elasticities range from 0 6 to 0 8 a test for measurement error based on the difference between efficient wald and analysis of covariance estimators is also proposed application of the test indicates that measurement error may be responsible for low or negative estimates of labor supply elasticities

the impact of a hausman pretest on the size of a hypothesis test the panel data case the size properties of a two stage test in a panel data model are investigated where in the rst stage a hausman 1978 speci cation test is used as a pretest of the random eects speci cation and in the second stage a simple hypothesis about a component of the parameter vector is tested using a t statistic that is based on either the random eects or the xed eects estimator depending on the outcome of the hausman pretest it is shown that the asymptotic size of the two stage test depends on the degree of time variation in the regressors and on the variance of the error term relative to the variance of the individual speci c eect and equals 1 for empirically relevant speci cations of the parameter space monte carlo simulations document that the size distortion is well re ected in nite samples the size distortion is caused mainly by the poor power properties of the pretest that lead to frequent unjusti ed inference based on the random eects estimator in the second stage however it is also shown that the conditional size of the test conditional on the hausman pretest rejecting the pretest null hypothesis exceeds the nominal level of the test given the results in the paper the recommendation then is to use a t statistic based on the xed eects estimator instead of using the two stage procedure

two step estimation of panel data models with censored endogenous variables and selection bias this paper presents some two step estimators for a wide range of parametric panel data models with censored endogenous variables and sample selection bias our approach is to derive estimates of the unobserved heterogeneity responsible for the endogeneity selection bias to include as additional explanatory variables in the primary equation these are obtained through a decomposition of the reduced form residuals the panel nature of the data allows adjustment and testing for two forms of endogeneity and or sample selection bias furthermore it incorporates roles for dynamics and state dependence in the reduced form finally we provide an empirical illustration which features our procedure and highlights the ability to test several of the underlying assumptions

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

a reformulation of the hausman test for regression models with pooled cross section time series data abstract a hausman test has been typically used to determine the consistency of the gls estimator in static models with pooled cross section time series data based on a gmm approach we reformulate the hausman test and find that it incorporates and tests only a limited set of moment restrictions we also consider an alternative gmm statistic incorporating additional restrictions which has power toward additional sources of model misspecification our monte carlo experiments demonstrate that while both the hausman test and the alternative have good power detecting endogenous regressors the alternative dominates if coefficients of regressors are nonstationary

rank estimation of a generalized fixed effects regression model abstract this paper considers estimation of a fixed effects version of the generalized regression model of han 1987 journal of econometrics 35 303 316 the model allows for censoring places no parametric assumptions on the error disturbances and allows the fixed effects to be correlated with the covariates we introduce a class of rank estimators that consistently estimate the coefficients in the generalized fixed effects regression model the maximum score estimator for the binary choice fixed effects model is part of this class like the maximum score estimator the class of rank estimators converge at less than the n rate smoothed versions of these estimators however converge at rates approaching the n rate in a version of the model that allows for truncated data a sufficient condition for consistency of the estimators is that the error disturbances have an increasing hazard function

a linear time varying system framework for noniterative discrete time band limited signal extrapolation a technique for the analysis and design of noniterative algorithms for discrete time band limited signal extrapolation is described the approach involves modeling the extrapolation process as a linear time varying ltv system or filter together with a previously developed fourier theory for ltv systems this model provides a frequency domain transfer function representation for the extrapolation system this representation serves as a powerful tool for characterizing and comparing the reconstruction properties of several well known least squares optimal algorithms for band limited extrapolation moreover the frequency domain setting provides a conceptually attractive means for understanding the process of extrapolation itself additionally a least squares approximation methodology for designing ltv filters for band limited extrapolation is developed the design technique is shown to unify a broad class of algorithms for extrapolating discrete time data and further to provide a means for designing new and improved extrapolation algorithms

properties of ordinary least squares estimators in regression models with nonspherical disturbances abstract a general discussion is presented of the properties of the ols estimator in regression models where the disturbances do not have a scalar identity covariance matrix several new and interesting characterizations are provided together with a synthesis of existing results a distinguishing feature of the paper is the unified treatment of the issues of efficiency and inference the theoretical material is illustrated by examples covering a wide range of models of interest to applied econometricians

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

simultaneous equations and panel data abstract this paper considers a simultaneous equations model with panel data and unobservable individual effects in each structural equation the effects may be fixed or random in the fixed effects case a conditional likehood approach leads to the within transformation just as in the single equation setting in the random effects case we allow an arbitrary number of the exogenous variables to be correlated with the effects and provide efficient gmm estimators along the lines of two stage and three stage least squares the case of different instruments in different equations is also considered

simultaneous equations with error components abstract in this paper we derive a limited as well as a full information estimator for the structural parameters of a simultaneous equations model with error components under this model the gain in efficiency by performing these estimators rather than the classical two stage and three stage least squares procedures is demonstrated it is shown that the full information estimator will reduce to the limited information estimator when the disturbances of different structural equations are uncorrelated with each other but not necessarily when all structural equations are just identified this is different from the analogous situation in the classical case

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

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

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

stochastic production frontiers and panel data a latent variable framework abstract this paper deals with the issue of estimating production frontier and measuring efficiency from a panel data set first it proposes an alternate method for the estimation of a production frontier on a short panel data set the method is based on the so called mean and covariance structure analysis which is closely related to the generalized method of moments one advantage of the method is that it allows us to investigate the presence of correlations between individual effects and exogenous variables without the requirement of some available instruments uncorrelated with the individual effects as in instrumental variable estimation another advantage is that the method is well suited to a panel data set with a short number of periods second the paper considers the question of recovering individual efficiency levels from the estimates obtained from the mean and covariance structure analysis since individual effects are here viewed as latent variables they can be estimated as factor scores i e weighted sums of the observed variables we illustrate the proposed methods with the estimation of a stochastic production frontier on a short panel data of french fruit growers

the moment problem on compact semi algebraic sets in this chapter we begin the study of the multidimensional moment problem the passage to dimensions d 2 brings new difficulties and unexpected phenomena in sect 3 2 we derived solvability criteria of the moment problem on intervals in terms of positivity conditions it seems to be natural to look for similar characterizations in higher dimensions as well this leads us immediately into the realm of real algebraic geometry and to descriptions of positive polynomials on semi algebraic sets in this chapter we treat this approach for basic closed compact semi algebraic subsets of mathbb r d it turns out that for such sets there is a close interaction between the moment problem and positivstellensatze for strictly positive polynomials

positivstellensatze for real function algebras we look for algebraic certificates of positivity for functions which are not necessarily polynomial functions similar questions were examined earlier by lasserre and putinar positivity and optimization for semi algebraic functions to appear proposition 1 and by putinar a striktpositivestellensatz for measurable functions corrected version to appear theorem 2 1 we explain how these results can be understood as results on hidden positivity the required positivity of the functions implies their positivity when considered as polynomials on the real variety of the respective algebra of functions this variety is however not directly visible in general we show how algebras and quadratic modules with this hidden positivity property can be constructed we can then use known results for example jacobi s representation theorem jacobi in math z 237 259 273 2001 theorem 4 or the krivine stengle positivstellensatz marshall in positive polynomials and sums of squares mathematical surveys and monographs 146 2008 page 25 to obtain certificates of positivity relative to a quadratic module of an algebra of real valued functions our results go beyond the results of lasserre and putinar for example when dealing with non continuous functions the conditions are also easier to check we explain the application of our result to various sorts of real finitely generated algebras of semialgebraic functions the emphasis is on the case where the quadratic module is also finitely generated our results also have application to optimization of real valued functions using the semidefinite programming relaxation methods pioneered by lasserre siam j optim 11 3 796 817 2001 lasserre in moments positive polynomials and their applications imperial college press london 2009 lasserre and putinar in positivity and optimization for semi algebraic functions to appear marshall in positive polynomials and sums of squares mathematical surveys and monographs 146 2008 page 25

spectral estimators that extend the maximum entropy and maximum likelihood methods the theory of best linear approximation in weighted l 2 spaces is used to obtain a general procedure the pdft for linearly reconstructing the fourier transform from sampled data the pdft can be used either directly to reduce sidelobe structure and to extrapolate the data or indirectly to obtain high resolution spectral estimators the direct and indirect pdft include as special cases many of the commonly used spectral techniques including burg s maximum entropy method capon s maximum likelihood method the spectral estimators based on bandlimited extrapolation the eigenvalue eigenvector methods for detecting sinusoids in noise pisarenko method schmidt s music eigenvector power beamforming and the best linear unbiased estimator blue for regression coefficients by exploiting their relationship to the linear pdft these nonlinear techniques can be analyzed in terms of linear approximation theory in addition to providing a unifying formulation for many different spectral estimators the pdft

minimum weighted norm interpolation of seismic records in seismic data processing we often need to interpolate and extrapolate data at missing spatial locations the reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired we propose a wavefield reconstruction scheme for spatially band limited signals the method entails solving an inverse problem where a wavenumber domain regularization term is included the regularization term constrains the solution to be spatially band limited and imposes a prior spectral shape the numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix vector multiplications implemented via the fast fourier transform fft is adopted the algorithm can be used to perform multidimensional reconstruction in any spatial domain

on the testing of correlated effects with panel data abstract using orthogonal deviations of the variables correlated effects biases are regarded as misspecification biases due to the exclusion of relevant variables in a standard regression model following this approach hausman and chamberlain type tests of correlated effects are obtained as wald tests in an extended model estimated by ols and robust generalisations are suggested alternative estimators which introduce restrictions in the regression of the effects on the explanatory variables are proposed finally the paper extends the results to dynamic models

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

estimating multi way error components models with unbalanced data structures abstract i develop simple matrix algebra techniques that simplify and unify much of the previous literature on estimating error components models ecms in fact the simple analytic results provided here are useful for analyzing a very broad set of models with complex error structures to illustrate the techniques i develop the algebra for three and four way ecms explicitly in addition i provide monte carlo simulation evidence on the performance of several estimators for the three way ecm and estimate the model using data from a retail market where the three dimensions of data variation are products selling in many locations over time

archimedean operator theoretic positivstellensatze abstract we prove a general archimedean positivstellensatz for hermitian operator valued polynomials and show that it implies the multivariate fejer riesz theorem of dritschel rovnyak and positivstellensatze of ambrozie vasilescu and scherer hol we also obtain several generalizations of these and related results the proof of the main result depends on an extension of the abstract archimedean positivstellensatz for algebras that is interesting in its own right

the statistical implications of preliminary specification error testing abstract this paper demonstrates that a preliminary test estimator based on a specification test of the type suggested by wu and hausman is dominated under a mean square error criterion by an instrumental variable estimator results are obtained by considering a numerical evaluation of the asymptotic risk function of the pre test estimator for various levels of the pre test and special circumstances in which the power function of the pre test becomes flat in the direction of the alternative hypothesis

nonparametric dynamic panel data models kernel estimation and specification testing abstract motivated by the first differencing method for linear panel data models we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogenous regressors the estimators utilize the additive structure of the first differenced model the fact that the two additive components have the same functional form and the unknown function of interest is implicitly defined as a solution of a fredholm integral equation of the second kind we establish the uniform consistency and asymptotic normality of the estimators we also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the l 2 distance of our nonparametric estimates and the parametric estimates under the linear restriction we derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of pitman local alternatives and prove its consistency against global alternatives simulations suggest that the proposed estimators and tests perform well for finite samples we apply our new method to study the relationships among economic growth the initial economic condition and capital accumulation and find a significant nonlinear relation between economic growth and the initial economic condition

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

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 sinusoids from incomplete time series the gerchberg papoulis extrapolation algorithm was applied to the problem of recovering missing observations from incomplete time series it has been experimentally shown that with as few as 10 percent of data points and a priori information on the bandwidth it is possible to recover all the missing points in the time series the technique is illustrated by means of a pair of sinusoids sampled randomly it has been possible to estimate the entire time series with mean squaze error less than 0 0035 after 30 iterations the parameters of the sinusoids could be estimated with high accuracy

production frontiers with cross sectional and time series variation in efficiency levels abstract in this paper we consider the efficient instrumental variables estimation of a panel data model with heterogeneity in slopes as well as intercepts using a panel of u s airlines we apply our methodology to a frontier production function with cross sectional and temporal variation in levels of technical efficiency our approach allows us to estimate time varying efficiency levels for individual firms without invoking strong distributional assumptions for technical inefficiency or random noise we do so by including in the production function a flexible function of time whose parameterization depends on the firm we also generalize the results of hausman and taylor 1981 to exploit assumptions about the uncorrelatedness of certain exogenous variables with the temporal pattern of the firm s technical inefficiency our empirical analysis of the airline industry over two periods of regulation yields believable evidence on the pattern of changes in efficiency across regulatory environments

minimum energy band limited predictor with dynamic subspace selection for time variant flat fading channels in this paper we develop and analyze the basic methodology for minimum energy me band limited prediction of sampled time variant flat fading channels this predictor is based on a subspace spanned by time concentrated and band limited sequences the time concentration of these sequences is matched to the length of the observation interval and the band limitation is determined by the support of the doppler power spectral density of the fading process slepian showed that discrete prolate spheroidal dps sequences can be used to calculate the me band limited continuation of a finite sequence we utilize this property to perform channel prediction we generalize the concept of time concentrated and band limited sequences to a band limiting region consisting of disjoint intervals for a fading process with constant spectrum over its possibly discontiguous support we prove that the me band limited predictor is identical to a reduced rank maximum likelihood predictor which is a close approximation of a wiener predictor in current cellular communication systems the time selective fading process is highly oversampled the essential dimension of the subspace spanned by time concentrated and band limited sequences is in the order of two to five only the prediction error mainly depends on the support of the doppler spectrum we exploit this fact to propose low complexity time variant flat fading channel predictors using dynamically selected predefined subspaces the subspace selection is based on a probabilistic bound on the reconstruction error we compare the performance of the me band limited predictor with a predictor based on complex exponentials for a prediction horizon of one eights of a wavelength the numerical simulation results show that the me band limited predictor with dynamic subspace selection performs better than or similar to a predictor based on complex exponentials with perfectly known frequencies for a prediction horizons of three eights of a wavelength the performance of the me band limited predictor approaches that of a wiener predictor with perfectly known doppler bandwidth

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

specification issues and confidence intervals in unilateral price effects analysis this paper contributes to the economics and econometrics literature on unilateral effects analysis it introduces the rotterdam demand system considers the effect and importance of demand restrictions for minimizing the mean squared error of price simulations demonstrates that approximate price changes are often misleading indicators of exact price changes and uses bootstrap techniques to determine confidence intervals and standard errors for simulated price changes allowing determination not only of their economic significance but also of their statistical significance

quasi maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and t are large this paper investigates the asymptotic properties of quasi maximum likelihood estimators for spatial dynamic panel data with xed eects when both the number of individuals n and the number of time periods t are large we consider the case where t is asymptotically large relative to n the case where t is asymptotically proportional to n and the case where n is asymptotically large relative to t in the case where t is asymptotically large relative to n the estimators are p nt consistent and asymptotically normal with the limit distribution centered around 0 when n is asymptotically proportional to t the estimators are p nt consistent and asymptotically normal but the limit distribution is not centered around 0 and when n is large relative to t the estimators are consistent with rate t and have a degenerate limit distribution the estimators of the xed eects are p t consistent and asymptotically normal we also propose a bias correction for our estimators we show that when t grows faster than n 1 3 the correction will asymptotically eliminate the bias and yield a centered con dence interval

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

bandlimited extrapolation using time bandwidth dimension the problem of extrapolating discrete index bandlimited signals from a finite number of samples is addressed in this paper the algorithm presented in this paper exploits the fact that the set of bandlimited signals that are also essentially time limited is approximated well by a low dimensional linear subspace this fact which is well known for one dimensional 1 d signals with contiguous passbands and time concentration intervals is established for a more general class of multidimensional m d signals with discontiguous passbands and discontiguous time concentration regions a criterion is presented for determining the dimension of the approximating subspace and the minimax optimal subspace itself based on knowledge of the passband time concentration regions energy concentration factor and bounds on the tolerable extrapolation error the extrapolation is constrained to lie in this subspace and parameters characterizing the extrapolation are obtained from the data by solving a linear system of equations for certain sampling patterns the system is ill conditioned and a second rank reduction is needed to reduce the deleterious effects of observation noise and modeling error a novel criterion for rank selection based on known bounds on noise power and modeling error is presented the effectiveness of the new algorithm and the rank selection criterion are demonstrated by means of computer simulations

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

a representation theorem for certain partially ordered commutative rings let a be a commutative ring with 1 let p subset a be a preordering of higher level i e 0 1 in p 1 not in p p p subset p p cdot p subset p and a 2n subset p for some n in n and let m subset a be an archimedean p module i e 1 in m 1 not in m m m subset m p cdot m subset m and forall a in a exists n in n n a in m we endow x m varphi in rm hom a r mid varphi m subset r with the weak topology with respect to all mappings widehat a x m rightarrow r widehat a varphi varphi a and consider the representation phi m a rightarrow cal c x m r a mapsto widehat a we find that x m is a non empty compact hausdorff space further we prove that

specification tests in simultaneous equations systems abstract this paper makes two contributions a it provides a new derivation of 2sls and 3sls estimators in which they are represented as restricted least squares and restricted generalized least squares respectively b in the convext thus created it provides a perfectly routine and flexible vehicle for carrying out identifiability and specification tests utilizing 2sls or 3sls estimators the tests in question are simple lagrange multiplier tests lmt carried out directly on the prior restrictions in contrast to the current literature which approaches the problem indirectly through tests on the implications of such prior restrictions on the reduced form in addition it provides a limited monte carlo study comparing the performance of the newly created tests to that of the hausman test ht

identification and sequential estimation of panel data models with insufficient exclusion restrictions abstract this paper presents estimators for nonparametric panel data models with additive fixed effects we analyze a model in which the entire regressor vector consisting of time varying as well as time invariant regressors is correlated with the individual fixed effect but there are insufficient exclusion restrictions to permit direct instrumental variables estimation of the model it is shown that when the model satisfies the additive interactive regression air representation of andrews and whang economic theory 6 1990 466 480 a sequential estimator consistently estimates the model the limiting distribution of scalar nonlinear functionals of the model is shown to be standard normal finite sample properties of the estimator are considered in a monte carlo simulation study and used to estimate the returns to education in a cohort of mature men from the national longitudinal survey

assessing cross sectional correlation in panel data abstract consider drawing a sample of n experimental units where each unit is observed over t time periods are the draws independent a test statistic introduced by breusch and pagan 1980 is one measure used to quantify the amount of cross sectional correlation it is effective when t is large relative to n and as shown by breusch and pagan has desirable asymptotic in t properties in this paper we consider the case often encountered in the analysis of panel data where n is large relative to t here the breusch and pagan statistic does not enjoy the same desirable asymptotic in n properties in fact we show that the asymptotic distribution depends on the parent population even under the hypothesis of no cross sectional correlations thus we introduce a distribution free statistic that does not have this drawback asymptotic properties of the new statistic are established when the data are drawn from identical distributions and when the statistic is evaluated using residuals from a complex model both the breusch and pagan statistic and the new statistic are shown to be members of a more general family by considering this generalization finite sample properties of members of the family are easily established further it turns out that a statistic introduced by friedman 1937 is another special case of this family

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

polynomial programming lp relaxations also converge we consider the global minimization of a multivariate polynomial on a compact semialgebraic set using a result of krivine j analyse math 12 1964 pp 307 326 c r acad sci paris 258 1964 pp 3417 3418 it is shown that lp relaxations based on products of the original constraints in the spirit of the reformulation linearization technique procedure of sherali and adams converge to the global optimum this extends to compact semialgebraic sets previous results known for polytopes and 0 1 programs the asymptotic behavior of the lp relaxations is also analyzed and it is shown that in important cases finite convergence cannot occur