nonsmooth backfitting for the excess risk additive regression model with two survival time scales we consider an extension of aalen s additive regression model allowing covariates to have effects that vary on two different time scales the two time scales considered are equal up to a constant that varies for each individual such as for example follow up time and age in medical studies or calendar time and age in longitudinal studies the model has been introduced in scheike 2001 where it was solved via smoothing techniques we present a new backfitting 20 algorithm estimating the structured model without having to use smoothing estimators of the cumulative regression functions on the two time scales are suggested by solving local estimating equations jointly on the two time scales we provide large sample properties and simultaneous confidence bands the model is applied to data on myocardial infarction providing a separation of the two effects stemming from time since diagnosis and age

likelihood gradient evaluation using square root covariance filters using the array form of numerically stable square root implementation methods for kalman filtering formulas we construct a new square root algorithm for the log likelihood gradient score evaluation this avoids the use of the conventional kalman filter with its inherent numerical instabilities and improves the robustness of computations against roundoff errors the new algorithm is developed in terms of covariance quantities and based on the ldquocondensed formrdquo of the array square root filter

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

a lagrange multiplier test for cross sectional dependence in a fixed effects panel data model abstract it is well known that the standard breusch and pagan 1980 lm test for cross equation correlation in a sur model is not appropriate for testing cross sectional dependence in panel data models when the number of cross sectional units n is large and the number of time periods t is small in fact a scaled version of this lm test was proposed by pesaran 2004 and its finite sample bias was corrected by pesaran et al 2008 this was done in the context of a heterogeneous panel data model this paper derives the asymptotic bias of this scaled version of the lm test in the context of a fixed effects homogeneous panel data model this asymptotic bias is found to be a constant related to n and t which suggests a simple bias corrected lm test for the null hypothesis additionally the paper carries out some monte carlo experiments to compare the finite sample properties of this proposed test with existing tests for cross sectional dependence

bootstrapping factor augmented regression models abstract this paper proposes and theoretically justifies bootstrap methods for regressions where some of the regressors are factors estimated from a large panel of data we derive our results under the assumption that t n c where 0 c n and t are the cross sectional and the time series dimensions respectively thus allowing for the possibility that the factor estimation error enters the limiting distribution of the ols estimator as an asymptotic bias term as was recently discussed by ludvigson and ng 2011 we consider general residual based bootstrap methods and provide a set of high level conditions on the bootstrap residuals and on the idiosyncratic errors such that the bootstrap distribution of a rotated ols estimator is consistent we subsequently verify these conditions for a simple wild bootstrap residual based procedure

estimation of a multiplicative covariance structure in the large dimensional case abstract we propose a kronecker product model for correlation or covariance matrices in the large dimensional case the number of parameters of the model increases logarithmically with the dimension of the matrix we propose a minimum distance md estimator based on a log linear property of the model as well as a one step estimator which is a one step approximation to the quasi maximum likelihood estimator qmle we establish rates of convergence and central limit theorems clt for our estimators in the large dimensional case a specification test and tools for kronecker product model selection and inference are provided in a monte carlo study where a kronecker product model is correctly specified our estimators exhibit superior performance in an empirical application to portfolio choice for s p500 daily returns we demonstrate that certain kronecker product models are good approximations to the general covariance matrix

theory and methods of panel data models with interactive effects this paper considers the maximum likelihood estimation of the panel data models with interactive effects motivated in economics and other social sciences a notable feature of the model is that the explanatory variables are correlated with the unobserved effects the usual within group estimator is inconsistent existing methods for consistent estimation are either designed for panel data with short time periods or are less efficient the maximum likelihood estimator has desirable properties and is easy to implement as illustrated by the monte carlo simulations this paper develops the inferential theory for the maximum likelihood estimator including consistency rate of convergence and the limiting distributions we further extend the model to include time invariant regressors and common regressors cross section invariant the regression coefficients for the time invariant regressors are time varying and the coefficients for the common regressors are cross sectionally varying

confidence intervals for diffusion index forecasts and inference for factor augmented regressions we consider the situation when there is a large number of series n e ach witht observations and each series has some predictive ability for some variable of interest a methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components and then to augment an otherwise standard regression with the estimated factors in this paper we show that the least squares estimates obtained from these factor augmented regressions are t consistent and asymptotically normal if t n 0 the conditional mean predicted by the estimated factors is min t n consistent and asymptotically normal except when t n goes to zero inference should take into account the effect of estimated regressors on the estimated conditional mean we present analytical formulas for prediction intervals that are valid regardless of the magnitude of n t and that can also be used when the factors are nonstationary

estimating and accounting for unobserved covariates in high dimensional correlated data many high dimensional and high throughput biological datasets have complex sample correlation structures which include longitudinal and multiple tissue data as well as data with multiple treatmen

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

estimation and inference of change points in high dimensional factor models abstract in this paper we consider the estimation of break points in high dimensional factor models where the unobserved factors are estimated by principal component analysis pca the factor loading matrix is assumed to have a structural break at an unknown time we establish the conditions under which the least squares ls estimator is consistent for the break date our consistency result holds for both large and small breaks we also find the ls estimator s asymptotic distribution simulation results confirm that the break date can be accurately estimated by the ls even if the magnitudes of breaks are small in two empirical applications we implement the method to estimate break points in the u s stock market and u s macroeconomy respectively

semi parametric single index panel data models with interactive fixed effects theory and practice abstract in this paper we propose a single index panel data model with unobserved multiple interactive fixed effects this model has the advantages of being flexible and of being able to allow for common shocks and their heterogeneous impacts on cross sections thus making it suitable for the investigation of many economic issues the asymptotic theories are established accordingly our monte carlo simulations show that our methodology works well for large n and t cases in our empirical application we illustrate our model by analysing the returns to scale of large commercial banks in the u s

recursive estimation in large panel data models theory and practice abstract bai 2009 proposes recursive estimation for panel data models with interactive effects we study the behaviours of this recursive estimator the recursive formula is established that shows the behaviours of recursive estimators depend on the initial estimator the population structure and the iterative steps under some general scenarios we find that the recursive estimator becomes consistent after the first iteration from any initials we also obtain the optimal number of iterative steps under some prescribed conditions the central limit theorem of the recursive estimator is established when the initial estimator is ols various simulations are conducted to support our theoretical findings

estimating and testing a quantile regression model with interactive effects this paper proposes a quantile regression estimator for a panel data model with interactive effects potentially correlated with the independent variables we provide conditions under which the slope parameter estimator is asymptotically gaussian monte carlo studies are carried out to investigate the finite sample performance of the proposed method in comparison with other candidate meth ods we discuss an approach to testing the model specification against a competing fixed effects specification the paper presents an empirical application of the method to study the effect of class size and class composition on educational attainment the findings show that i a change in the gender composition of a class impacts differently low and high performing students ii while smaller classes are beneficial for low performers larger classes are beneficial for high performers iii reductions in class size do not seem to impact mean and median student performance iv the fixed effects specification is rejected in favor of the interactive effects specification

sieve estimation of panel data models with cross section dependence abstract in this paper we consider the problem of estimating semiparametric panel data models with cross section dependence where the individual specific regressors enter the model nonparametrically whereas the common factors enter the model linearly we consider both heterogeneous and homogeneous regression relationships when both the time and cross section dimensions are large we propose sieve estimators for the nonparametric regression functions by extending pesaran s 2006 common correlated effect cce estimator to our semiparametric framework asymptotic normal distributions for the proposed estimators are derived and asymptotic variance estimators are provided monte carlo simulations indicate that our estimators perform well in finite samples

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

constrained estimators and consistency of a regression model on a lexis diagram this article considers a regression model on a lexis diagram of an a p table with a single response in each cell following a distribution in the exponential family a regression model on the fixed effects of a rows p columns and a p 1 diagonals induces a singular design matrix and yields multiple estimators leading to parameter identifiability problem in age period cohort analysis in social sciences demography and epidemiology where assessment of secular trend in age period and birth cohort of social events e g violence and diseases e g cancer is of interest similar problems also exist in other settings such as in supersaturated designs in this article we study the finite sample properties of the multiple estimators propose a penalized profile likelihood method to study the consistency and asymptotic bias and demonstrate the results through simulations and data analysis as a by product the identifiability problem is addressed with consistent estimation for model parameters an

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

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

panel data models with interactive fixed effects and multiple structural breaks abstractin this article we consider estimation of common structural breaks in panel data models with unobservable interactive fixed effects we introduce a penalized principal component ppc estimation procedure with an adaptive group fused lasso to detect the multiple structural breaks in the models under some mild conditions we show that with probability approaching one the proposed method can correctly determine the unknown number of breaks and consistently estimate the common break dates furthermore we estimate the regression coefficients through the post lasso method and establish the asymptotic distribution theory for the resulting estimators the developed methodology and theory are applicable to the case of dynamic panel data models simulation results demonstrate that the proposed method works well in finite samples with low false detection probability when there is no structural break and high probability of correctly estimating the break numbers when the structural breaks exist we finall

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

a heteroskedasticity robust breusch pagan test for contemporaneous correlation in dynamic panel data models abstract this paper proposes a heteroskedasticity robust breusch pagan test of the null hypothesis of zero cross section or contemporaneous correlation in linear panel data models without necessarily assuming independence of the cross sections the procedure allows for either fixed strictly exogenous and or lagged dependent regressor variables as well as quite general forms of both non normality and heteroskedasticity in the error distribution the asymptotic validity of the test procedure is predicated on the number of time series observations t being large relative to the number of cross section units n in that either i n is fixed as t or ii n 2 t 0 as both t and n diverge jointly to infinity given this it is not expected that asymptotic theory would necessarily provide an adequate guide to finite sample performance when t n is small because of this we also propose and establish asymptotic validity of a number of wild bootstrap schemes designed to provide improved inference when t n is small across a variety of experimental designs a monte carlo study suggests that the predictions from asymptotic theory do in fact provide a good guide to the finite sample behaviour of the test when t is large relative to n however when t and n are of similar orders of magnitude discrepancies between the nominal and empirical significance levels occur as predicted by the first order asymptotic analysis on the other hand for all the experimental designs the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels when t n is small with a recursive design wild bootstrap scheme performing best in general and providing quite close agreement between the nominal and empirical significance levels of the test even when t and n are of similar size moreover in comparison with the wild bootstrap version of the original breusch pagan test godfrey and yamagata 2011 our experiments indicate that the corresponding version of the heteroskedasticity robust breusch pagan test appears reliable as an illustration the proposed tests are applied to a dynamic growth model for a panel of 20 oecd countries

unequal spacing in dynamic panel data identification and estimation abstract we propose conditions under which parameters of fixed effect dynamic models are identified with unequally spaced panel data under predeterminedness weak stationarity and empirically testable rank conditions ar 1 parameters are identified given the availability of two pairs of two consecutive time gaps which generalizes two pairs of two consecutive time periods this result extends to models with multiple covariates higher order autoregressions and partial linearity applying our method to the nls original cohorts older men where personal interviews took place in 1966 67 and 69 we analyze the earnings dynamics in the old time and compare the results with more recent ones

a diagnostic criterion for approximate factor structure abstract we build a simple diagnostic criterion for approximate factor structure in large panel datasets given observable factors the criterion checks whether the errors are weakly cross sectionally correlated or share at least one unobservable common factor interactive effects a general version allows to determine the number of omitted common factors also for time varying structures the empirical analysis runs on ten thousand us stocks from january 1968 to december 2011 for monthly returns we select time invariant specifications with at least four financial factors and a scaled three factor specification for quarterly returns we cannot select macroeconomic models without the market factor

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

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

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

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

inference on factor structures in heterogeneous panels this paper develops an estimation and testing framework for a stationary large panel model with observable regressors and unobservable common factors we allow for slope heterogeneity and for correlation between the common factors and the regressors we propose a two stage estimation procedure for the unobservable common factors and their loadings based on common correlated effects estimator and the principal component estimator we also develop two tests for the null of no factor structure one for the null that loadings are cross sectionally homogeneous and one for the null that common factors are homogeneous over time our tests are based on using extremes of the estimated loadings and common factors the test statistics have an asymptotic gumbel distribution under the null and have power versus alternatives where only one loading or common factor differs from the others monte carlo evidence shows that the tests have the correct size and good power

a randomized sequential procedure to determine the number of factors this paper proposes a procedure to estimate the number of common factors k in a static approximate factor model the building block of the analysis is the fact that the first k eigenvalues of the covariance matrix of the data diverge whilst the others stay bounded on the grounds of this we propose a test for the null that the i th eigenvalue diverges using a randomised test statistic based directly on the estimated eigenvalue the test only requires minimal assumptions on the data and no assumptions are required on factors loadings or idiosyncratic errors the randomised tests are then employed in a sequential procedure to determine k

state sensitivity evaluation within ud based array covariance filters this technical note addresses the ud factorization based kalman filtering kf algorithms using this important class of numerically stable kf schemes we extend its functionality and develop an elegant and simple method for computation of sensitivities of the system state to unknown parameters required in a variety of applications for instance it can be used for efficient calculations in sensitivity analysis and in gradient search optimization algorithms for the maximum likelihood estimation the new theory presented in this technical note is a solution to the problem formulated by bierman in which has been open since 1990s as in the cited paper our method avoids the standard approach based on the conventional kf and its derivatives with respect to unknown system parameters with its inherent numerical instabilities and hence improves the robustness of computations against roundoff errors

forecasting with the age period cohort model and the extended chain ladder model we consider forecasting from age period cohort models as well as from the extended chain ladder model the parameters of these models are known only to be identified up to linear trends forecasts from such models may therefore depend on arbitrary linear trends a condition for invariant forecasts is proposed a number of standard forecast models are analysed

asymptotics for in sample density forecasting this paper generalizes recent proposals of density forecasting models and it develops theory for this class of models in density forecasting the density of observations is estimated in regions where the density is not observed identification of the density in such regions is guaranteed by structural assumptions on the density that allows exact extrapolation in this paper the structural assumption is made that the density is a product of one dimensional functions the theory is quite general in assuming the shape of the region where the density is observed such models naturally arise when the time point of an observation can be written as the sum of two terms e g onset and incubation period of a disease the developed theory also allows for a multiplicative factor of seasonal effects seasonal effects are present in many actuarial biostatistical econometric and statistical studies smoothing estimators are proposed that are based on backfitting full asymptotic theory is derived for them a practical example from the insurance business is given producing a within year budget of reported insurance claims a small sample study supports the theoretical results

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

over dispersed age period cohort models summarywe consider inference and forecasting for aggregate data organised in a two way table with age and cohort as indices but without measures of exposure this is modelled using a poisson likelihood with an age period cohort structure for the mean while allowing for over dispersion we propose a repetitive structure that keeps the dimension of table fixed while increasing the latent exposure for this we use a class of infinitely divisible distributions which include a variety of compound poisson models and poisson mixture models this results in asymptotic f inference and t forecast distributions

the estimation of age period and cohort effects for vital rates in models for vital rates which include effects due to age period and cohort there is aliasing due to a linear dependence among these three factors this dependence arises both when age and period intervals are equal and when they are not one solution to the dependence is to set an arbitrary constraint on the parameters estimable functions of the parameters are invariant to the particular constraint applied for evenly spaced intervals deviations from linearity are estimable but only a linear function of the three slopes is estimable when age and period intervals have different widths further aliasing occurs it is assumed that the number of deaths in the numerator of the rate equation has a poisson distribution the calculations are illustrated with data on mortality from prostate cancer among nonwhites in the u s

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

on the role of the rank condition in cce estimation of factor augmented panel regressions a popular approach to factor augmented panel regressions is the common correlated effects cce estimator of pesaran 2006 this paper points to a problem with the cce approach that appears in the empirically relevant case when the number of factors is strictly less than the number of observables used in their estimation specifically the use of too many observables causes the second moment matrix of the estimated factors to become asymptotically singular an issue that has not yet been appropriately accounted for the purpose of the present paper is to fill this gap in the literature

forecasting using principal components from a large number of predictors this article considers forecasting a single time series when there are many predictors n and time series observations t when the data follow an approximate factor model the predictors can be summarized by a small number of indexes which we estimate using principal components feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both n and t grow large the estimated factors are shown to be consistent even in the presence of time variation in the factor model

a cubature h filter and its square root version in this paper we present a nonlinear state estimation algorithm based on the fusion of an extended h eh f and a cubature kalman filter ckf the resulting estimator is called a cubature h filter the recently developed ckf is a gaussian approximation of a bayesian filter and its performance over non gaussian noises may degrade in contrast the h filter is capable of estimating the states of linear systems with non gaussian noises and the extended h filter eh f can estimate the states of non linear and non gaussian systems similar to the h filter an eh f also does not make any assumptions about the statistics of the process or measurement noise but it does require jacobians during the state estimation of nonlinear systems which degrade the overall performance when the nonlinearities are severe the cubature h filter is developed to have the desirable features of both ckf and eh f for numerical accuracy a square root version of the cubature h filter is developed using j unitary transform

generalized linear time series regression we consider a cross section model that contains an individual component a deterministic time trend and an unobserved latent common time series component we show the following oracle property the parameters of the latent time series and the parameters of the deterministic time trend can be estimated with the same asymptotic accuracy as if the parameters of the individual component were known we consider this model in two settings least squares fits of linear specifications of the individual component and the parameters of the deterministic time trend and more generally quasilikelihood estimation in a generalized linear time series model

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

arco an artificial counterfactual approach for high dimensional panel time series data abstract we consider a new flexible and easy to implement method to estimate thecausal effects of an intervention on a single treated unit when a control group is not available and which nests previous proposals in the literature it is a two step methodology where in the first stage a counterfactual is estimated based on a large dimensional set of variables from a pool of untreated units by means of shrinkage methods such as the least absolute shrinkage and selection operator lasso in the second stage we estimate the average intervention effect on a vector of variables which is consistent and asymptotically normal our results are valid uniformly over a wide class of probability laws we show that these results hold even when the exact date of the intervention is unknown tests for multiple interventions and for contamination effects are derived by a simple transformation of the variables it is possible to test for multivariate intervention effects on several moments of the variables of interest existing methods in the literature usually test for intervention effects on a single variable and assume that the time of the intervention is known in addition high dimensionality is frequently ignored and inference is either conducted under a set of more stringent hypotheses and or by permutation tests a monte carlo experiment evaluates the properties of the method in finite samples and compares it with other alternatives as an application we evaluate the effects on inflation gdp growth retail sales and credit of an anti tax evasion program

time displaced interactions classical dynamics and path integral quantization the path integral was created to quantize systems whose dynamics are nonlocal in time and for which a hamiltonian formulation could not be found in this article we quantize a linear oscillator with an interaction that depends on the oscillator s position at past and future times the central issue is the classical boundary value problem for such an oscillator because two time functional boundary conditions are used to implement the quantization we take up related questions such as causality in this context and the general issue of stability for forward and inward data specifications

explicit evaluation of a path integral with memory kernel an explicit expression is presented for the path integral of an harmonic oscillator interacting with itself in the past the time dependence of the memory kernel is assumed to be exponential the relation with the feynman trial action for the variational calculation of the polaron ground state energy is discussed

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

new square root algorithms for kalman filtering presents some new square root algorithms that allow more reliable computation of the state estimates using as far as possible quantities obtained via orthogonal operations new algorithms are given for covariance quantities and information quantities and a new combined algorithm is also presented

kalman filter sensitivity evaluation with orthogonal and j orthogonal transformations this technical note addresses the array square root kalman filtering smoothing algorithms with the conventional orthogonal and j orthogonal transformations in the adaptive filtering context j orthogonal matrices arise in computation of the square root of the covariance or smoothed covariance by solving an equation of the form cct ddt bbt the latter implies an application of the qr decomposition with j orthogonal transformations in each iteration step in this paper we extend functionality of array square root kalman filtering schemes and develop an elegant and simple method for computation of the derivatives of the filter variables to unknown system parameters required in a variety of applications for instance our result can be implemented for an efficient sensitivity analysis and in gradient search optimization algorithms for the maximum likelihood estimation of unknown system parameters it also replaces the standard approach based on direct differentiation of the conventional kalman filtering equations with their inherent numerical instability and hence improves the robustness of computations against roundoff errors

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

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

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

identification of the age period cohort model and the extended chain ladder model we consider the identification problem that arises in the age period cohort models as well as in the extended chain ladder model we propose a canonical parameterization based on the accelerations of the trends in the three factors this parameterization is exactly identified and eases interpretation estimation and forecasting the canonical parameterization is applied to a class of index sets which have trapezoidal shapes including various lexis diagrams and the insurance reserving triangles

explicit evaluation of certain gaussian functional integrals arising in problems of statistical physics an explicit formula is presented for a conditional wiener integral the integrand of which is an exponential of a general quadratic functional of the path the functional integrals arising in non markovian gaussian approximations to various problems of statistical physics e g theory of the large polaron theory of disordered systems are easily recovered as special cases

gls estimation of dynamic factor models in this article a simple two step estimation procedure of the dynamic factor model is proposed the estimator allows for heteroscedastic and serially correlated errors it turns out that the feasible two step estimator has the same limiting distribution as the generalized least squares gls estimator assuming that the covariance parameters are known in a monte carlo study of the small sample properties we find that the gls estimators may be substantially more efficient than the usual estimator based on principal components furthermore it turns out that the iterated version of the estimator may feature considerably improved properties in sample sizes usually encountered in practice

accurate state estimation in continuous discrete stochastic state space systems with nonlinear or nondifferentiable observations this paper presents a novel method of nonlinear kalman filtering which unifies the best features of the accurate continuous discrete extended and cubature kalman filters more precisely the time updates in the discussed state estimator are done as those in the first filter whereas the measurement updates are conducted with use of the third degree spherical radial cubature rule applied for approximating the arisen gaussian weighted integrals all this allows accurate predictions of the state mean and covariance matrix to be combined with accurate measurement updates moreover the new filter is particularly effective for continuous discrete stochastic systems with nonlinear and or nondifferentiable observations the efficiency of this mixed type method is shown in comparison to the performance of the original accurate continuous discrete extended and cubature kalman filters in severe conditions of tackling a seven dimensional radar tracking problem where an aircraft executes a coordinated turn with sufficiently long sampling times

large panels with common factors and spatial correlation this paper considers the statistical analysis of large panel data sets where even after condi tioning on common observed eects the cross section units might remain dependently distrib uted this could arise when the cross section units are subject to unobserved common eects and or if there are spill over eects due to spatial or other forms of local dependencies the paper provides an overview of the literature on cross section dependence introduces the con cepts of time speci c weak and strong cross section dependence and shows that the commonly used spatial models are examples of weak cross section dependence it is then established that the common correlated eects cce estimator of panel data model with a multifactor error structure recently advanced by pesaran 2006 continues to provide consistent estimates of the slope coe cient even in the presence of spatial error processes small sample properties of the cce estimator under various patterns of cross section dependence including spatial forms are investigated by monte carlo experiments results show that the cce approach works well in the presence of weak and or strong cross sectionally correlated errors we also explore the role of certain characteristics of spatial processes in determining the performance of cce estimators such as the form and intensity of spatial dependence and the sparseness of the spatial weight

maximum likelihood estimation using square root information filters the maximum likelihood parameter estimation algorithm is known to provide optimal estimates for linear time invariant dynamic systems however the algorithm is computationally expensive and requires evaluations of the gradient of a log likelihood function and the fisher information matrix by using the square root information filter a numerically reliable algorithm to compute the required gradient and the fisher information matrix is developed the algorithm is a significant improvement over the methods based on the conventional kalman filter the square root information filter relies on the use of orthogonal transformations that are well known for numerical reliability this algorithm can be extended to real time system identification and adaptive control

a varying coefficient panel data model with fixed effects theory and an application to us commercial banks in this paper we propose a semiparametric varying coefficient categorical panel data model in which covariates variables affecting the coefficients are purely categorical this model has two features first fixed effects are included to allow for correlation between individual unobserved heterogeneity and the regressors second it allows for cross sectional dependence through a general spatial error dependence structure we derive a semiparametric estimator for our model by using a modified within transformation and then show the asymptotic and finite properties for this estimator under large n and t the monte carlo study shows that our methodology works well for both large n and t and large n and small t cases finally we illustrate our model by analyzing the effects of state level banking regulations on the returns to scale of commercial banks in the us our empirical results suggest that returns to scale is higher in more regulated states than in less regulated states

cross sectional averages versus principal components in spite of the increased use of factor augmented regressions in recent years little is known regarding the relative merits of the two main approaches to estimation and inference namely the cross sectional average and principal component estimators by providing a formal comparison of the approaches the current paper fills this gap in the literature

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

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

time series modelling with semiparametric factor dynamics high dimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors the inference on the whole system is then based on the low dimensional time series analysis such high dimensional problems occur frequently in many different fields of science in this article we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods this more flexible modeling approach poses an important question is it justified from an inferential point of view to base statistical inference on the estimated times series factors we show that the difference of the inference based on the estimated time series and true unobserved time series is asymptotically negligible our results justify fitting vector autoregressive processes to the estimated factors which allows one to study the dynamics of the whole high dimensional system with a low dimensional representation we illustrate the theory with a simulati

asymptotic distribution of factor augmented estimators for panel regression abstract in this paper we derive an asymptotic theory for linear panel regression augmented with estimated common factors we give conditions under which the estimated factors can be used in place of the latent factors in the regression equation for the principal components estimate of the factor space it is shown that these conditions are satisfied when t n 0 and n t 3 0 under regularity monte carlo studies verify the asymptotic theory

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

augmented factor models with applications to validating market risk factors and forecasting bond risk premia abstract we study factor models augmented by observed covariates that have explanatory powers on the unknown factors in financial factor models the unknown factors can be reasonably well explained by a few observable proxies such as the fama french factors in diffusion index forecasts identified factors are strongly related to several directly measurable economic variables such as consumption wealth variable financial ratios and term spread with those covariates both the factors and loadings are identifiable up to a rotation matrix even only with a finite dimension to incorporate the explanatory power of these covariates we propose a smoothed or projected principal component analysis pca i regress the data onto the observed covariates and ii take the principal components of the fitted data to estimate the loadings and factors this allows us to more accurately estimate the percentage of both explained and unexplained components in factors and thus to assess the explanatory power of covariates we show that both the estimated factors and loadings can be estimated with improved rates of convergence compared to the benchmark method the degree of improvement depends on the strength of the signals representing the explanatory power of the covariates on the factors the proposed estimator is robust to possibly heavy tailed distributions we apply the model to forecast us bond risk premia and find that the observed macroeconomic characteristics contain strong explanatory powers of the factors the gain of forecast is more substantial when the characteristics are incorporated to estimate the common factors than directly used for forecasts

tests of equal accuracy for nested models with estimated factors abstract in this paper we develop asymptotics for tests of equal predictive ability between nested models when factor augmented regressions are used to forecast we provide conditions under which the estimation of the factors does not affect the asymptotic distributions developed in clark and mccracken 2001 and mccracken 2007 this enables researchers to use the existing tabulated critical values when conducting inference despite the presence of estimated predictors as an intermediate result we derive the asymptotic properties of the principal components estimator over recursive windows we provide simulation evidence on the finite sample effects of factor estimation and apply the tests to the case of forecasting excess returns to the s p 500 composite index

numerical aspects of different kalman filter implementations a theoretical analysis is made of the error propagation due to numerical roundoff for four different kalman filter implementations the conventional kalman filter the square root covariance filter the square root information filter and the chandrasekhar square root filter an experimental analysis is performed to validate the new insights gained by the theoretical analysis

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

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

testing capital asset pricing models using functional coefficient panel data models with cross sectional dependence abstract this paper proposes a functional coefficient panel data model with cross sectional dependence motivated by re examining the empirical performance of conditional capital asset pricing model in order to characterize the time varying property of assets betas and alpha our proposed model allows the betas to be unknown functions of some macroeconomic and financial instruments moreover a common factor structure is introduced to characterize cross sectional dependence which is an attractive feature under a panel data regression setting as different assets or portfolios may be affected by same unobserved shocks compared to the existing studies such as the classic fama macbeth two step procedure our model can achieve substantial efficiency gains for inference by adopting a one step procedure using the entire sample rather than a single cross sectional regression at each time point we propose a local linear common correlated effects estimator for estimating time varying betas by pooling the data the consistency and asymptotic normality of the proposed estimators are established another methodological and empirical challenge in asset pricing is how to test the constancy of conditional betas and the significance of pricing errors we echo this challenge by constructing an l 2 norm statistic for functional coefficient panel data models allowing for cross sectional dependence we show that the new test statistic has a limiting standard normal distribution under the null hypothesis finally the method is applied to test the model in fama and french 1993 using fama french 25 and 100 portfolios sorted by size and book to market ratio respectively dated from july 1963 to july 2018

unbiased monte carlo evaluation of certain functional integrals abstract a monte carlo algorithm for the evaluation of certain functional integrals is introduced this algorithm is not based on the approximation of the functional integral by a finite dimensional integral unbiased estimators for the functional integrals are constructed and corresponding variance reduction techniques are considered numerical results of simulation studies are presented

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

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

gradient based parameter estimation in pairwise linear gaussian system this technical note addresses the gradient based parameter estimation problem for pairwise linear gaussian systems the new adaptive filtering scheme is based on gradient based optimization methods for estimating the uncertain system parameters and a robust square root variant of the pairwise kalman filter used for estimating the unknown states of the pairwise linear gaussian systems hence in the adaptive filtering techniques the dynamic state and system parameters are estimated simultaneously the method of the filter sensitivities computation required in gradient evaluation is derived in terms of square root factors of covariance matrices