econometrics and decision theory abstract the paper considers the role of econometrics in decision making under uncertainty this leads to a focus on predictive distributions the decision maker s subjective distribution is only partly specified it belongs to a set s of distributions s can also be regarded as a set of plausible data generating processes criteria are needed to evaluate procedures for constructing predictive distributions we use risk robustness and minimax regret risk relative to s to obtain procedures for constructing predictive distributions we use bayes procedures based on parametric models with approximate prior distributions the priors are nested with a first stage that incorporates qualitative information such as exchangeability and a second stage that is quite diffuse special points in the parameter space such as boundary points can be accommodated with second stage priors that have one or more mass points but are otherwise quite diffuse an application of these ideas is presented motivated by an individual s consumption decision the problem is to construct a distribution for that individual s future earnings based on his earnings history and on a longitudinal data set that provides earnings histories for a sample of individuals

two laplacians for the distance matrix of a graph abstract we introduce a laplacian and a signless laplacian for the distance matrix of a connected graph called the distance laplacian and distance signless laplacian respectively we show the equivalence between the distance signless laplacian distance laplacian and the distance spectra for the class of transmission regular graphs there is also an equivalence between the laplacian spectrum and the distance laplacian spectrum of any connected graph of diameter 2 similarities between n as a distance laplacian eigenvalue and the algebraic connectivity are established

distance spectra of graphs a survey abstract in 1971 graham and pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems they also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph computing the distance characteristic polynomial and its coefficients was the first research subject of interest thereafter the eigenvalues attracted much more attention in the present paper we report on the results related to the distance matrix of a graph and its spectral properties

on the distance spectrum of distance regular graphs abstract the distance matrix of a simple graph g is d g d i j where d i j is the distance between ith and jth vertices of g the spectrum of the distance matrix is known as the distance spectrum or d spectrum of g a simple connected graph g is called distance regular if it is regular and if for any two vertices x y g at distance i there are constant number of neighbors c i and b i of y at distance i 1 and i 1 from x respectively in this paper we prove that distance regular graphs with diameter d have at most d 1 distinct d eigenvalues we find an equitable partition and the corresponding quotient matrix of the distance regular graph which gives the distinct d eigenvalues we also prove that distance regular graphs satisfying b i c d 1 have at most d 2 2 distinct d eigenvalues applying these results we find the distance spectrum of some distance regular graphs including the well known johnson graphs finally we also answer the questions asked by lin et al 16

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

the skew energy of a digraph we are interested in the energy of the skew adjacency matrix of a directed graph d which is simply called the skew energy of d in this paper properties of the skew energy of d are studied in particular a sharp upper bound for the skew energy of d is derived in terms of the order of d and the maximum degree of its underlying undirected graph an infinite family of digraphs attaining the maximum skew energy is constructed moreover the skew energy of a directed tree is independent of its orientation and interestingly it is equal to the energy of the underlying undirected tree skew energies of directed cycles under different orientations are also computed some open problems are presented

asymptotic properties of a robust variance matrix estimator for panel data when t is large abstract i consider the asymptotic properties of a commonly advocated covariance matrix estimator for panel data under asymptotics where the cross section dimension n grows large with the time dimension t fixed the estimator is consistent while allowing essentially arbitrary correlation within each individual however many panel data sets have a non negligible time dimension i extend the usual analysis to cases where n and t go to infinity jointly and where t with n fixed i provide conditions under which t and f statistics based on the covariance matrix estimator provide valid inference and illustrate the properties of the estimator in a simulation study

signless laplacian energy of a graph and energy of a line graph abstract for a simple graph g of order n size m and with signless laplacian eigenvalues q 1 q 2 q n the signless laplacian energy q e g is defined as q e g i 1 n q i d where d 2 m n is the average vertex degree of g we obtain the lower bounds for q e g in terms of first zagreb index m 1 g maximum degree d 1 second maximum degree d 2 minimum degree d n and second minimum degree d n 1 as a consequence of these bounds we obtain several bounds for the energy e l g of the line graph l g of graph g in terms of various graph parameters like m 1 g the clique number n m etc which improve some recently known bounds

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

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

bias reduction in nonlinear and dynamic panels in the presence of cross section dependence abstract fixed effects estimation of nonlinear dynamic panel models is subject to the incidental parameter issue leading to a biased asymptotic distribution while this problem has been studied extensively in the literature a general analysis allowing for both serial and cross sectional dependence is missing in this paper we investigate the large n t theory of the profile and integrated likelihood estimators allowing for dependence across both dimensions we show that under stronger dependence types the asymptotic bias disappears but a o p 1 t small sample bias remains we provide bias correction and inference methods and also obtain primitive conditions for asymptotic normality under various dependence settings

the time series and cross section asymptotics of dynamic panel data estimators in this paper we derive the asymptotic properties of within groups wg gmm and liml estimators for an autoregressive model with random effects when both t and n tend to infinity gmm and liml are consistent and asymptotically equivalent to the wg estimator when t n 0 the fixed t results for gmm and liml remain valid but wg although consistent has an asymptotic bias in its asymptotic distribution when t n tends to a positive constant the wg gmm and liml estimators exhibit negative asymptotic biases of order 1 t 1 n and 1 2n t respectively in addition the crude gmm estimator that neglects the autocorrelation in first differenced errors is inconsistent as t n c 0 despite being consistent for fixed t finally we discuss the properties of a random effects pseudo mle with unrestricted initial conditions when both t and n tend to infinity

cospectrality of graphs with respect to distance matrices abstract the distance distance laplacian and distance signless laplacian spectra of a connected graph g are the spectra of the distance distance laplacian and distance signless laplacian matrices of g two graphs are said to be cospectral with respect to the distance resp distance laplacian or distance signless laplacian matrix if they share the same distance resp distance laplacian or distance signless laplacian spectrum if a graph g does not share its spectrum with any other graph we say g is determined by its spectrum in this paper we are interested in the cospectrality with respect to the three distance matrices first we report on a numerical study in which we looked into the spectra of the distance distance laplacian and distance signless laplacian matrices of all the connected graphs on up to 10 vertices then we prove some theoretical results about what we can deduce about a graph from these spectra among other results we identify some of the graphs determined by their distance laplacian or distance signless laplacian spectra

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

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

bounds of graph energy in terms of vertex cover number abstract the energy e g of a graph g is the sum of the absolute values of all eigenvalues of g in this paper we give a lower bound and an upper bound for graph energy in terms of vertex cover number for a graph g with vertex cover number it is proved that 2 2 c e g 2 where c is the number of odd cycles in g and is the maximum vertex degree of g the lower bound is attained if and only if g is the disjoint union of some complete bipartite graphs with perfect matchings and some isolated vertices the upper bound is attained if and only if g is the disjoint union of copies of k 1 together with some isolated vertices

efficient estimation of panel data models with sequential moment restrictions abstract this paper considers asymptotically efficient estimation of the panel data models with sequential moment restrictions in an environment with i i d observations it is shown that the gmm estimator with an increasing set of instruments attains the semiparametric efficiency bound of the model the estimator considered here allows for the heteroscedasticity of the unknown form

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

beyond graph energy norms of graphs and matrices abstract in 1978 gutman introduced the energy of a graph as the sum of the absolute values of graph eigenvalues and ever since then graph energy has been intensively studied since graph energy is the trace norm of the adjacency matrix matrix norms provide a natural background for its study thus this paper surveys research on matrix norms that aims to expand and advance the study of graph energy the focus is exclusively on the ky fan and the schatten norms both generalizing and enriching the trace norm as it turns out the study of extremal properties of these norms leads to numerous analytic problems with deep roots in combinatorics the survey brings to the fore the exceptional role of hadamard matrices conference matrices and conference graphs in matrix norms in addition a vast new matrix class is studied a relaxation of symmetric hadamard matrices the survey presents solutions to just a fraction of a larger body of similar problems bonding analysis to combinatorics thus open problems and questions are raised to outline topics for further investigation

estimation of spatial autoregressive panel data models with fixed effects this paper establishes asymptotic properties of quasi maximum likelihood estimators for sar panel data models with fixed effects and sar disturbances a direct approach is to estimate all the parameters including the fixed effects because of the incidental parameter problem some parameter estimators may be inconsistent or their distributions are not properly centered we propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions for the model with individual effects only the direct approach does not yield a consistent estimator of the variance parameter unless t is large but the estimators for other common parameters are the same as those of the transformation approach we also consider the estimation of the model with both individual and time effects

on the laplacian eigenvalues of a graph and laplacian energy abstract let g be a simple graph with n vertices m edges maximum degree average degree d 2 m n clique number having laplacian eigenvalues 1 2 n 1 n 0 for k 1 k n let s k g i 1 k i and let 1 n 1 be the number of laplacian eigenvalues greater than or equal to average degree d in this paper we obtain a lower bound for s 1 g and an upper bound for s g in terms of m and clique number of the graph as an application we obtain the stronger bounds for the laplacian energy le g i 1 n i d which improve some well known earlier bounds

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

sharp upper bounds on the distance energies of a graph abstract in this paper for a simple undirected connected graph sharp upper bounds on the distance energy distance laplacian energy and distance signless laplacian energy are obtained the graphs attaining the corresponding upper bound are characterized

on a conjecture for the signless laplacian eigenvalues abstract let g be a simple graph with n vertices and e g edges and q 1 g q 2 g q n g 0 be the signless laplacian eigenvalues of g let s k g i 1 k q i g where k 1 2 n f ashraf et al conjectured that s k g e g k 1 2 for k 1 2 n in this paper we give various upper bounds for s k g and prove that this conjecture is true for the following cases connected graph with sufficiently large k unicyclic graphs and bicyclic graphs for all k and tricyclic graphs when k 3 finally we discuss whether the upper bound given in this conjecture is tight or not for c cyclic graphs and propose some problems for future research

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

the generalized distance matrix abstract let d g and d i a g t r denote the distance matrix and diagonal matrix of the vertex transmissions of a simple connected graph g respectively the distance signless laplacian matrix of g is defined as d q g d i a g t r d g heretofore the spectral properties of d g and d q g have attracted much more attention in the present paper we propose to study the convex combinations d g of d i a g t r and d g defined as d g d i a g t r 1 d g 0 1 this study sheds new light on d g and d q g some spectral properties of d g are given and a few open problems are discussed furthermore we take effort to obtain some upper and lower bounds of spectral radius of d g finally the generalized distance spectra of some graphs obtained by operations are also studied

consistent reduced rank lmmse estimation with a limited number of samples per observation dimension an improved construction of the optimal reduced rank linear minimum mean square error mmse estimator of a signal waveform of interest is derived that is consistent under a limited number of samples per filtering degree of freedom the new filter design generalizes traditional filter realizations based on directly replacing the theoretical covariance matrix by its sample estimate and being consistent when all dimensions in the model but the number of samples remain bounded our solution not only generalizes the conventional estimator but also turns out to appropriately characterize model mismatch constraints due to finite sample size limitations of fundamental importance in practical situations the proposed implementation results from a generalized consistent estimation of the set of mmse filter subspace coefficients on the reduced dimensional subspace results are based on the theory of the spectral analysis of large dimensional random matrices in particular we build on the analytical description of the asymptotic spectrum of sample covariance type matrices in the limiting regime defined as both the number of samples and the observation dimension grow without bound at the same rate as a result the proposed mmse signal waveform estimator is shown to present a superior mean square error performance under a finite sample size by avoiding the breakdown experienced as the selected rank increases

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

on the sum of signless laplacian eigenvalues of a graph abstract for a simple graph g let e g denote the number of edges and s k g denote the sum of the k largest eigenvalues of the signless laplacian matrix of g we conjecture that for any graph g with n vertices s k g e g k 1 2 for k 1 n we prove the conjecture for k 2 for any graph and for all k for regular graphs the conjecture is an analogous to a conjecture by a e brouwer with a similar statement but for the eigenvalues of laplacian matrices of graphs

on generalized distance energy of graphs abstract for the distance matrix d g and diagonal matrix of the vertex transmissions t r g of a simple connected graph g the generalized distance matrix d g is the convex combinations of t r g and d g and is defined as d g t r g 1 d g for 0 1 if 1 2 n are the eigenvalues of d g we define the generalized distance energy of the graph g as e d g i 1 n i 2 w g n where w g is the wiener index of g this is analogous to the energies associated with the distance laplacian and distance signless laplacian matrices of g we obtain upper and lower bounds for the generalized distance energy of graphs in terms of various parameters associated with the structure of the graph g we show that for 1 2 1 the complete bipartite graph has the minimum generalized distance energy among all connected bipartite graphs and for 0 2 n 3 n 2 the star graph has the minimum generalized distance energy among all trees

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

linear regression limit theory for nonstationary panel data this paper develops a regression limit theory for nonstationary panel data with large numbers of cross section n and time series t observations the limit theory allows for both sequential limits wherein t followed by n and joint limits where t n simultaneously and the relationship between these multidimensional limits is explored the panel structures considered allow for no time series cointegration heterogeneous cointegration homogeneous cointegration and near homogeneous cointegration the paper explores the existence of long run average relations between integrated panel vectors when there is no individual time series cointegration and when there is heterogeneous cointegration these relations are parameterized in terms of the matrix regression coefficient of the long run average covariance matrix in the case of homogeneous and near homogeneous cointegrating panels a panel fully modified regression estimator is developed and studied the limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population

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

the energy of a graph abstract the energy e g of a simple graph g is defined to be the sum of the absolute values of the eigen values of g if g is a k regular graph on n vertices then e g k k n 1 n k b 2 and this bound is sharp it is shown that for each 0 there exist infinitely many n for each of which there exists a k regular graph g of order n with k e g b 2 two graphs with the same number of vertices are equienergetic if they have the same energy we show that for any positive integer n 3 there exist two equienergetic graphs of order 4n that are not cospectral

common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors abstract this paper extends the common correlated effects cce approach developed by pesaran 2006 to heterogeneous panel data models with lagged dependent variables and or weakly exogenous regressors we show that the cce mean group estimator continues to be valid but the following two conditions must be satisfied to deal with the dynamics a sufficient number of lags of cross section averages must be included in individual equations of the panel and the number of cross section averages must be at least as large as the number of unobserved common factors we establish consistency rates derive the asymptotic distribution suggest using covariates to deal with the effects of multiple unobserved common factors and consider jackknife and recursive de meaning bias correction procedures to mitigate the small sample time series bias theoretical findings are accompanied by extensive monte carlo experiments which show that the proposed estimators perform well so long as the time series dimension of the panel is sufficiently large

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

the energy of graphs and matrices abstract given a complex m n matrix a we index its singular values as 1 a 2 a and call the value e a 1 a 2 a the energy of a thereby extending the concept of graph energy introduced by gutman let 2 m n a be an m n nonnegative matrix with maximum entry and a 1 n extending previous results of koolen and moulton for graphs we prove that e a a 1 m n m 1 a 2 2 a 1 2 m n n m m 2 furthermore if a is any nonconstant matrix then e a 1 a a 2 2 1 2 a 2 a finally we note that wigner s semicircle law implies that e g 4 3 o 1 n 3 2 for almost all graphs g

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

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

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

bounds for the signless laplacian energy the energy of a graph g is the sum of the absolute values of the eigenvalues of the adjacency matrix of g the laplacian respectively the signless laplacian energy of g is the sum of the absolute values of the differences between the eigenvalues of the laplacian respectively signless laplacian matrix and the arithmetic mean of the vertex degrees of the graph in this paper among some results which relate these energies we point out some bounds to them using the energy of the line graph of g most of these bounds are valid for both energies laplacian and signless laplacian however we present two new upper bounds on the signless laplacian which are not upper bounds for the laplacian energy

a lower bound for the energy of symmetric matrices and graphs the energy of a symmetric matrix is the sum of the absolute values of its eigenvalues we introduce a lower bound for the energy of a symmetric matrix partitioned into blocks this bound is related to the spectrum of its quotient matrix furthermore we study necessary conditions for the equality applications to the energy of the generalized composition of a family of arbitrary graphs are obtained a lower bound for the energy of a graph with a bridge is given some computational experiments are presented in order to show that in some cases the obtained lower bound is incomparable with the well known lower bound 2m where m is the number of edges of the graph

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

unified inference for nonlinear factor models from panels with fixed and large time span abstract we provide unifying inference theory for parametric nonlinear factor models based on a panel of noisy observations the panel has a large cross section and a time span that may be either small or large moreover we incorporate an additional source of information provided by noisy observations on some known functions of the factor realizations the estimation is carried out via penalized least squares i e by minimizing the l 2 distance between observations from the panel and their model implied counterparts augmented by a penalty for the deviation of the extracted factors from the noisy signals of them when the time dimension is fixed the limit distribution of the parameter vector is mixed gaussian with conditional variance depending on the path of the factor realizations on the other hand when the time span is large the convergence rate is faster and the limit distribution is gaussian with a constant variance in this case however we incur an incidental parameter problem since at each point in time we need to recover the concurrent factor realizations this leads to an asymptotic bias that is absent in the setting with a fixed time span in either scenario the limit distribution of the estimates for the factor realizations is mixed gaussian but is related to the limiting distribution of the parameter vector only in the scenario with a fixed time horizon although the limit behavior is very different for the small versus large time span we develop a feasible inference theory that applies without modification in either case hence the user need not take a stand on the relative size of the time dimension of the panel similarly we propose a time varying data driven weighting of the penalty in the objective function which enhances efficiency by adapting to the relative quality of the signal for the factor realizations