higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

stability of linear stochastic 2 d homogeneous systems the two dimensional stably excited random sequence is introduced properties of the two dimensional stably excited random sequence are discussed some sufficient conditions are obtained to guarantee the stability of the linear stochastic 2 d homogeneous systems the two dimensional stably excited random sequence is introduced and some properties are discussed in this paper then the stability of the linear stochastic 2 d homogeneous systems is studied and some sufficient conditions to guarantee its stability are obtained

cross section regression with common shocks this paper considers regression models for cross section data that exhibit cross section dependence due to common shocks such as macroeconomic shocks the paper analyzes the properties of least squares ls estimators in this context the results of the paper allow for any form of cross section dependence and heterogeneity across population units the probability limits of the ls estimators are determined and necessary and sufficient conditions are given for consistency the asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling the t wald and f statistics are found to have asymptotic standard normal x 2 and scaled x 2 distributions respectively under the null hypothesis when the conditions required for consistency of the parameter under test hold however the absolute values of t wald and f statistics are found to diverge to infinity under the null hypothesis when these conditions fail confidence intervals exhibit similarly dichotomous behavior hence common shocks are found to be innocuous in some circumstances but quite problematic in others models with factor structures for errors and regressors are considered using the general results conditions are determined under which consistency of the ls estimators holds and fails in models with factor structures the results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units

strongly consistent model order selection for estimating 2 d sinusoids in colored noise the problem of jointly estimating the number as well as the parameters of 2 d sinusoidal signals observed in the presence of an additive colored noise field is considered we begin by establishing the strong consistency of the nonlinear least squares estimator of the parameters of 2 d sinusoids when the number of sinusoidal signals assumed in the field is incorrect based on these results we prove the strong consistency of a new family of model order selection rules

strong consistency of the over and underdetermined lse of 2 d exponentials in white noise we consider the problem of least squares estimation of the parameters of two dimensional 2 d exponential signals observed in the presence of an additive noise field when the assumed number of exponentials is incorrect we consider both the case where the number of exponential signals is underestimated and the case where the number of exponential signals is overestimated in the case where the number of exponential signals is underestimated we prove the almost sure convergence of the least squares estimates lse to the parameters of the dominant exponentials in the case where the number of exponential signals is overestimated the estimated parameter vector obtained by the least squares estimator contains a subvector that converges almost surely to the correct parameters of the exponentials

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

estimation of close sinusoids in colored noise and model discrimination this paper considers the estimation of the two close dominant frequencies in the signal when it is known a priori that the observation is a sum of two close sinusoids and an additive colored noise whose spectral density is unknown earlier attempts have assumed the additive noise to be independent next we develop decision rules for checking whether the observed signal has only one sinusoid or two close sinusoids all of the earlier studies assumed that there are two close sinusoids in the signal another model discrimination problem considered is the determination of the causal structure of the observed periodicity a rule is given to test whether the observation comes from a sinusoid plus additive noise possible colored or the observation comes from a stationary autoregressive model we also present a numerical study showing the efficacy of the robust estimation procedure for estimating the two frequencies and the decision rules for checking the number of dominant frequencies and the causal mechanism finally we compare the proposed method to well known methods used for two close sinusoids in white noise

dynamic spatial panel models networks common shocks and sequential exogeneity this paper considers a class of generalized methods of moments gmm estimators for general dynamic panel models allowing for weakly exogenous covariates and cross sectional dependence due to spatial lags unspecified common shocks and time varying interactive effects we significantly expand the scope of the existing literature by allowing for endogenous time varying spatial weight matrices without imposing explicit structural assumptions on how the weights are formed an important area of application is in social interaction and network models where our specification can accommodate data dependent network formation we consider an exemplary social interaction model and show how identification of the interaction parameters is achieved through a combination of linear and quadratic moment conditions for the general setup we develop an orthogonal forward differencing transformation to aid in the estimation of factor components while maintaining orthogonality of moment conditions this is an important ingredient to a tractable asymptotic distribution of our estimators in general the asymptotic distribution of our estimators is found to be mixed normal due to random norming however the asymptotic distribution of our test statistics is still chi square

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

origins of the limited information maximum likelihood and two stage least squares estimators theil basmann and sargan are often credited with the development of the two stage least squares tsls estimator of the coefficients of one structural equation in a simultaneous equations model however anderson and rubin had earlier derived the asymptotic distribution of the limited information maximum likelihood liml estimator by finding the asymptotic distribution of what is essentially the tsls estimator

stable and finite morse index solutions of toda system abstract we prove a liouville type theorem and a partial regularity result for stable and finite morse index solutions of toda system the main tools are integral estimates a monotonicity formula and blowing down analysis for such systems they may be split into two sub systems during the blowing down process some e regularity theorems are developed to deal with this problem

partial regularity of stable solutions to the supercritical equations and its applications abstract we prove the partial regularity of stable solutions of supercritical elliptic equations as an application we prove that any smooth stable entire solution to supercritical equations with p in a suitable range is radially symmetric

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

maximum likelihood parameter estimation of discrete homogeneous random fields with mixed spectral distributions this paper presents a maximum likelihood solution to the general problem of fitting a parametric model to observations from a single realization of a real valued 2 d homogeneous random field with mixed spectral distribution on the basis of a 2 d wold like decomposition the field is represented as a sum of mutually orthogonal components of three types purely indeterministic harmonic and evanescent the proposed algorithm provides a complete solution to the joint estimation problem of the random field components by introducing appropriate parameter transformations the highly nonlinear least squares problem that results from the maximization of the likelihood function is transformed into a separable least squares problem in this new problem the solution for the unknown spectral supports of the harmonic and evanescent components reduces the problem of solving for the transformed parameters of the field to linear least squares solution of the transformation equations provides a complete solution of the field model parameter estimation problem

arbitrage factor structure and mean variance analysis on large asset markets we examine the implications of arbitrage in a market with many assets the absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous hence there exist unique portfolios that represent these functionals these portfolios span the mean variance efficient set we resolve the question of when a market with many assets permits so much diversification that risk free investment opportunities are available ross 12 14 showed that if there is a factor structure then the mean returns are approximately linear functions of factor loadings we define an approximate factor structure and show that this weaker restriction is sufficient for ross result if the covariance matrix of the asset returns has only k unbounded eigenvalues then there is an approximate factor structure and it is unique the corresponding k eigenvectors converge and play the role of factor loadings hence only a principal component analysis is needed in empirical work

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

specification test for panel data models with interactive fixed effects abstract in this paper we propose a consistent nonparametric test for linearity in a large dimensional panel data model with interactive fixed effects both lagged dependent variables and conditional heteroskedasticity of unknown form are allowed in the model we estimate the model under the null hypothesis of linearity to obtain the restricted residuals which are then used to construct the test statistic we show that after being appropriately centered and standardized the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of pitman local alternatives by using the concept of conditional strong mixing that was recently introduced by prakasa rao 2009 to improve the finite sample performance we propose a bootstrap procedure to obtain the bootstrap p value a small set of monte carlo simulations illustrates that our test performs well in finite samples an application to an economic growth panel dataset indicates significant nonlinear relationships between economic growth initial income level and capital accumulation

linear regression for panel with unknown number of factors as interactive fixed effects in this paper we study the least squares ls estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects assuming that the number of factors used in estimation is larger than the true number of factors in the data we establish the limiting distribution of the ls estimator for the regression coefficients as the number of time periods and the number of cross sectional units jointly go to infinity the main result of the paper is that under certain assumptions the limiting distribution of the ls estimator is independent of the number of factors used in the estimation as long as this number is not underestimated the important practical implication of this result is that for inference on the regression coefficients one does not necessarily need to estimate the number of interactive fixed effects consistently

least squares estimation of 2 d sinusoids in colored noise asymptotic analysis this paper considers the problem of estimating the parameters of real valued two dimensional 2 d sinusoidal signals observed in colored noise this problem is a special case of the general problem of estimating the parameters of a real valued homogeneous random field with mixed spectral distribution from a single observed realization of it the large sample properties of the least squares ls estimator of the parameters of the sinusoidal components are derived making no assumptions on the type of the probability distribution of the observed field it is shown that if the disturbance field satisfies a combination of conditions comprised of a strong mixing condition and a condition on the order of its uniformly bounded moments the normalized estimation error of the ls estimator is consistent asymptotically normal with zero mean and a normalized asymptotic covariance matrix for which a simple expression is derived it is further shown that the ls estimator is asymptotically unbiased the normalized asymptotic covariance matrix is block diagonal where each block corresponds to the parameters of a different sinusoidal component assuming further that the colored noise field is gaussian the ls estimator of the sinusoidal components is shown to be asymptotically efficient

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

maximum likelihood parameter estimation of textures using a wold decomposition based model we present a solution to the problem of modeling parameter estimation and synthesis of natural textures the texture field is assumed to be a realization of a regular homogeneous random field which can have a mixed spectral distribution on the basis of a 2 d wold like decomposition the field is represented as a sum of a purely indeterministic component a harmonic component and a countable number of evanescent fields we present a maximum likelihood solution to the joint parameter estimation problem of these components from a single observed realization of the texture field the proposed solution is a twostage algorithm in the first stage we obtain an estimate for the number of harmonic and evanescent components in the field and a suboptimal initial estiqate for the parameters of their spectral supports in the second stage we refine these initial estimates by iterative maximization of the likelihood function of the observed data by introducing appropriate parameter transformations the highly nonlinear least squares problem that results from the maximization of the likelihood function is transformed into a separable least squares problem in this new problem the solution for the unknown spectral supports of the harmonic and evanescent components reduces the problem of solving for the transformed parameters of the field to linear least squares solution of the transformation equations then provides a complete solution of the field model parameter estimation problem the wold based model and the resulting analysis and synthesis algorithms are seen applicable to a wide variety of texture types found in natural images the support or shape of the analyzed texture patch may be arbitrary our model is very efficient in terms of the number of parameters required to represent and faithfully reconstruct the original texture

two dimensional harmonic retrieval and its time domain analysis technique the two dimensional harmonic retrieval is examined in theory by confirming that the 2 d sinusoids in white noise are modeled as a special 2 d autoregressive moving average arma process whose ar parameters are identical to the ma ones a new analysis technique for resolving 2 d sinusoids in white noise is proposed

liouville type theorems for stable solutions of the weighted elliptic system abstract we examine the weighted elliptic system u 1 x 2 2 v v 1 x 2 2 u p in r n and prove liouville type theorems for the classical positive and nonnegative stable solutions in higher dimension in particular there are no positive stable solutions for any n 12 5 p 1 and 0 our proof is based on a combination of the bootstrap argument souplet s inequality and intermediate stability criterion which is used to obtain sharp results

liouville theorems for stable solutions of biharmonic problem we prove some liouville type results for stable solutions to the biharmonic problem delta 2 u u q u 0 in mathbb r n where 1 q infty for example for n ge 5 we show that there are no stable classical solution in mathbb r n when frac n 4 n 4 q le left frac n 8 n right 1

generalized method of moments with many weak moment conditions using many moment conditions can improve efficiency but makes the usual generalized method of moments gmm inferences inaccurate two step gmm is biased generalized empirical likelihood gel has smaller bias but the usual standard errors are too small in instrumental variable settings in this paper we give a new variance estimator for gel that addresses this problem it is consistent under the usual asymptotics and under many weak moment asymptotics is larger than usual and is consistent we also show that the kleibergen 2005 lagrange multiplier and conditional likelihood ratio statistics are valid under many weak moments in addition we introduce a jackknife gmm estimator but find that gel is asymptotically more efficient under many weak moments in monte carlo examples we find that t statistics based on the new variance estimator have nearly correct size in a wide range of cases

multiplicity of solutions for a fourth order equation with power type nonlinearity let b be the unit ball in mathbb r n n 3 and n be the exterior unit normal vector on the boundary we consider radial solutions to delta 2 u lambda 1 rm sign p u p quad rm in b quad u 0 quad frac partial u partial n 0 quad rm on partial b where 0 for positive p we assume 5 n 12 and p frac n 4 n 4 or n 13 and frac n 4 n 4 0 such that if s there exists a radial weakly singular solution for s there exist infinitely many regular radial solutions and the number of radial regular solutions goes to infinity as s

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

texture decomposition by harmonics extraction from higher order statistics in this paper a method of harmonics extraction from higher order statistics hos is developed for texture decomposition we show that the diagonal slice of the fourth order cumulants is proportional to the autocorrelation of a related noiseless sinusoidal signal with identical frequencies we propose to use this fourth order cumulants slice to estimate a power spectrum from which the harmonic frequencies can be easily extracted hence a texture can be decomposed into deterministic components and indeterministic components as in a unified texture model through a wold like decomposition procedure the simulation and experimental results demonstrated that this method is effective for texture decomposition and it performs better than traditional lower order statistics based decomposition methods

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

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

a monotonicity formula and a liouville type theorem for a fourth order supercritical problem we consider liouville type and partial regularity results for the nonlinear fourth order problem

comment on iv estimation of panels with factor residuals by d robertson and v sarafidis abstract this comment discusses two issues related to the paper by robertson and sarafidis 2014 hereafter rs the first issue is the potential incidental parameters problem that may arise when data are cross sectionally heteroskedastic the second issue is an identification problem in the estimation of panel models with weakly exogenous instrumental variables

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

a regularity theory of biharmonic maps in this article we prove the regularity of weakly biharmonic maps of domains in euclidean four space into spheres as well as the corresponding partial regu larity result of stationary biharmonic maps of higher dimensional domains into spheres c 1999 john wiley sons inc in this article we consider for simplicity the class of bihar monic maps from eu clidean domains to spheres we realize the standard spheres s k as unit vectors in r k 1 and consider maps u s k as vector valued functions that are contained in s k the energy functional for biharmonic maps is then j uj 2 dx a locally de fined biharmonic map is a map that is critical with respect to c ompactly supported variations we note that in the case where the domain has dimension four this en ergy functional is conformally invariant and hence conformal maps of euclidean four space are biharmonic in this sense we remark that this definition of bihar monic map depends on the embedding of the target space in euclidean space we

nearly efficient estimation of time series models with predetermined but not exogenous instruments particularly under the assumption of rational expectations a model may have serially correlated errors and those errors may be uncorrelated with contemporaneous and lagged values of a predetermined instrument yet the instruments may not be strictly exogenous this paper proposes a method for transforming such a model to one without serial correlation while keeping the instrument predetermined standard theory of instrumental variables estimation then applies furthermore it turns out that for transformations of the class proposed asymptotic distribution theory is the same whether the serial correlation properties of the errors are known a priori or estimated as the number of lagged values of the predetermined variables used as instruments increases the asymptotic variance of the standard instrumental variables estimator applied to the transformed model approaches that of the optimal estimator proposed by hansen and sargent 8 in a number of recently developed macroeconomic models behavioral equations arise in which error terms can be asserted on the basis of economic arguments to be uncorrelated with some set of instrumental variables at a certain set of dates but not to be uncorrelated with the instruments at all dates examples of such

two dimensional robust spectrum estimation robust estimation is studied of two dimensional 2 d power spectra of signals which are adequately represented by gaussian random field models but for which there are imperfect observations two situations of particular interest occur when the contaminating noise is additive and when the contaminating noise appears in the innovations in these cases the observed data are not gaussian and conventional procedures are no longer efficient to estimate the parameters of the signal model from the contaminated data two procedures are described which were originally proposed for estimation of scale and location from independent data and adapted to one dimensional autoregression parameter estimation by previous researchers the first algorithm is a robustification of least squares and equivalent to an iterated weighted least squares problem where the weights are data dependent the second algorithm is an iterative procedure known as a filter cleaner experiments using the robust procedures with synthetic data are reported and the results compared to a conventional method of model based spectrum estimation

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

consistent moment selection procedures for generalized method of moments estimation this paper considers a generalized method of moments gmm estimation problem in which one has a vector of moment conditions some of which are correct and some incorrect the paper introduces several procedures for consistently selecting the correct moment conditions the procedures also can consistently determine whether there is a sufficient number of correct moment conditions to identify the unknown parameters of interest the paper specifies moment selection criteria that are gmm analogues of the widely used bic and aic model selection criteria the latter is not consistent the paper also considers downward and upward testing procedures all of the moment selection procedures discussed in this paper are based on the minimized values of the gmm criterion function for different vectors of moment conditions the procedures are applicable in time series and cross sectional contexts application of the results of the paper to instrumental variables estimation problems yields consistent procedures for selecting instrumental variables

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

the evanescent field transform for estimating the parameters of homogeneous random fields with mixed spectral distributions parametric modeling and estimation of complex valued homogeneous random fields with mixed spectral distributions is a fundamental problem in two dimensional 2 d signal processing the parametric model under consideration results from the 2 d wold type decomposition of the random field the same model naturally arises as the physical model in problems of space time adaptive processing of airborne radar a computationally efficient algorithm for estimating the parameters of the field components is presented the algorithm is based on a nonlinear operator that uniquely maps each evanescent component to a single exponential the exponential s spatial frequency is a function of the spectral support parameters of the evanescent component hence employing this operator the problem of estimating the spectral support parameters of an evanescent field is replaced by the simpler problem of estimating the spatial frequency of a 2 d exponential the properties of the operator are analyzed the algorithm performance is illustrated and investigated using monte carlo simulations

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

efficient estimation of heterogeneous coefficients in panel data models with common shocks this paper investigates efficient estimation of heterogeneous coefficients in panel data models with common shocks which have been a particular focus of recent theoretical and empirical literature we propose a new two step method to estimate the heterogeneous coefficients in the first step the maximum likelihood ml method is first conducted to estimate the loadings and idiosyncratic variances the second step estimates the heterogeneous coefficients by using the structural relations implied by the model and replacing the unknown parameters with their ml estimates we establish the asymptotic theory of our estimator including consistency asymptotic representation and limiting distribution the two step estimator is asymptotically efficient in the sense that it has the same limiting distribution as the infeasible generalized least squares gls estimator intensive monte carlo simulations show that the proposed estimator performs robustly in a variety of data setups

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

bounds on the accuracy of estimating the parameters of discrete homogeneous random fields with mixed spectral distributions this paper considers the achievable accuracy in jointly estimating the parameters of a real valued two dimensional 2 d homogeneous random field with mixed spectral distribution from a single observed realization of it on the basis of a 2 d wold like decomposition the field is represented as a sum of mutually orthogonal components of three types purely indeterministic harmonic and evanescent an exact form of the cramer rao lower bound on the error variance in jointly estimating the parameters of the different components is derived it is shown that the estimation of the harmonic component is decoupled from that of the purely indeterministic and the evanescent components moreover the bound on the parameters of the purely indeterministic and the evanescent components is independent of the harmonic component numerical evaluation of the bounds provides some insight into the effects of various parameters on the achievable estimation accuracy

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

limit theory for panel data models with cross sectional dependence and sequential exogeneity abstract the paper derives a general central limit theorem clt and asymptotic distributions for sample moments related to panel data models with large n the results allow for the data to be cross sectionally dependent while at the same time allowing the regressors to be only sequentially rather than strictly exogenous the setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and or from the presence of common factors the latter leads to the need for random norming the limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied we prove such a central limit theorem by first extending results for stable convergence in hall and heyde 1980 to non nested martingale arrays relevant for our applications we illustrate our result by establishing a generalized estimation theory for gmm estimators of a fixed effect panel model without imposing i i d or strict exogeneity conditions we also discuss a class of maximum likelihood ml estimators that can be analyzed using our clt

some nonexistence theorems for semilinear fourth order equations in this paper we analyse the semilinear fourth order problem 2 u g u in exterior domains of n assuming the function g is nondecreasing and continuous in 0 and positive in 0 we show that positive classical supersolutions u of the problem which additionally verify u 0 exist if and only if n 5 and int 0 delta displaystyle g s over s 2 n 2 n 4 rm d s lt infty for some 0 when only radially symmetric solutions are taken into account we also show that the monotonicity of g is not needed in this result finally we consider the same problem posed in n and show that if g is additionally convex and lies above a power greater than one at infinity then all positive supersolutions u automatically verify u 0 in n and they do not exist when the previous condition fails

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

the gel fand problem for the biharmonic operator we study stable and finite morse index solutions of the equation delta 2 u e u if the equation is posed in mathbb r n we classify radial stable solutions we then construct nonradial stable solutions and we prove that unlike the corresponding second order problem no liouville type theorem holds unless additional information is available on the asymptotics of solutions at infinity thanks to this analysis we prove that stable solutions of the equation on a smoothly bounded domain supplemented with navier boundary conditions are smooth if and only if n leqq 12 we find an upper bound for the hausdorff dimension of their singular set in higher dimensions and conclude with an a priori estimate for solutions of bounded morse index provided they are controlled in a suitable morrey norm

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

covariance matrix estimation and the power of the overidentifying restrictions test class of heteroscedasticity and autocorrelation consistent covariance hacc matrix estimators that are now routinely used by practitioners in the calculation of the two step gmm estimator in applications it is customary to assume the model is correctly specified during the estimation and only to assess the specification after the second step using a statistic such as the overidentifying restrictions test one important consequence of this methodology is that the hacc estimator is calculated under the assumption that the model is correctly specified in this paper we examine the implications of model misspecification for the hacc covariance matrix estimator and the overidentifying restrictions test it is shown that the hacc estimator is asymptotically equivalent to the sum of two matrices one of these matrices is nonsingular and o 1 the other is of rank one and ob where b is the tt bandwidth used in the hacc estimator it is shown that this structure implies the inverse of the hacc estimator converges to a singular matrix as b with t and this t limiting matrix has rank q y 1 where q is the dimension of the moment condition it is shown that this limiting behavior translates into an overidentifying restrictions test that is ot rb in contrast it is shown that the overidentifying restrictions test is consistent pt and ot if the covariance matrix estimator is consistent under both null and alterna p tive this can be achieved by constructing the hacc estimator using the sample moment in mean deviation form 3

partial regularity of finite morse index solutions to the lane emden equation we prove regularity and partial regularity results for finite morse index solutions u h1 lp to the lane emden equation u u p 1u in

gmm estimation with cross sectional dependence this paper presents a spatial model of dependence among agents using a metric of economic distance measurements of this economic distance provide cross sectional data with a structure similar to that provided by the time index in time series data generalized method of moments estimators using such dependent data are shown to be consistent and asymptotically normal this paper presents a class of non parametric positive semi definite covariance matrix estimators that allow for general forms of dependence characterized by economic distance these covariance matrix estimators are shown to remain consistent when economic distances are not precisely observed

a unified texture model based on a 2 d wold like decomposition a unified texture model that is applicable to a wide variety of texture types found in natural images is presented this model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters the texture field is assumed to be a realization of a regular homogeneous random field which is characterized in general by a mixed spectral distribution the texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component the deterministic component is further orthogonally decomposed into a harmonic component and a generalized evanescent component both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component the model is very efficient in terms of the number of parameters required to faithfully represent textures reconstructed textures are practically indistinguishable from the originals

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

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

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

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

liouville type results for semi stable solutions of the weighted lane emden system abstract we examine the weighted lane emden system u 1 x 2 2 v p v 1 x 2 2 u q in r n where 1 p q and 0 and the weighted lane emden equation u 1 x 2 2 u p in r n where p 4 3 and 0 we prove that the system equation does not have the classical positive semi stable solution in dimension n 2 4 2 q 1 p q 1 0 n 2 2 2 p 1 p p 2 p in particular there is no positive semi stable solution of the weighted lane emden system if n 10 4 and 2 p q

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

efficiency bounds for semiparametric regression efficiency bounds for conditional moment restrictions with a nonparametric component are derived there is a given function of the data a random sample from a distribution f and a parameter the restriction is that a conditional expectation of this function is zero at some point in the parameter space the parameter has two parts a finite dimensional component and a general function evaluated at a subset of the conditioning variables an example is a regression function that is additive in parametric and nonparametric component as arises in sample selection models copyright 1992 by the econometric society

monotonicity formulas for extrinsic triharmonic maps and the triharmonic lane emden equation abstract we derive monotonicity formulas and e regularity results for extrinsic triharmonic maps and triharmonic lane emden equations as an application we prove partial regularity results for both types of equations in the supercritical regime

inferring the rank of a matrix abstract this paper considers methods of inference concerning the rank of matrix a based on an asymptotically normal estimate of and some identifiable specification for one such specification is 0 in which case one is interested in the rank of we first propose and examine the properties of a test of the hypothesis that the rank is of a given size against the alternative that the rank is larger we then look at the problem of estimating the rank of this matrix using model selection procedures and sequential hypothesis testing conditions for consistency of such procedures are obtained some economic applications are discussed and the various methods are compared in a monte carlo experiment

inferential theory for factor models of large dimensions this paper develops an inferential theory for factor models of large dimensions the principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator if normality is assumed we derive the rate of convergence and the limiting distributions of the estimated factors factor loadings and common components the theory is developed within the framework of large cross sections n and a large time dimension t to which classical factor analysis does not apply we show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of n and t the estimated factors and their loadings are generally normal although not always so the convergence rate of the estimated factors and factor loadings can be faster than that of the estimated common components these results are obtained under general conditions that allow for correlations and heteroskedasticities in both dimensions stronger results are obtained when the idiosyncratic errors are serially uncorrelated and homoskedastic a necessary and sufficient condition for consistency is derived for large n but fixed t

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