inference in dynamic models containing surprise variables abstract some new results on calculating moving average representation mar coefficients and their limiting distribution from estimated vector arma processes are presented the technique is applied to the problem of estimating the coefficients of unanticipated or surprise variables in a single equation for a multi period expectations horizon the method naturally conditions the expectations on all past values of the process and avoids the necessity of using two step regression procedures and adjusting the resulting standard errors

kernel weighted gmm estimators for linear time series models abstract this paper analyzes the higher order asymptotic properties of generalized method of moments gmm estimators for linear time series models using many lags as instruments a data dependent moment selection method based on minimizing the approximate mean squared error is developed in addition a new version of the gmm estimator based on kernel weighted moment conditions is proposed it is shown that kernel weighted gmm estimators can reduce the asymptotic bias compared to standard gmm estimators kernel weighting also helps to simplify the problem of selecting the optimal number of instruments a feasible procedure similar to optimal bandwidth selection is proposed for the kernel weighted gmm estimator

estimating dynamic equilibrium models using mixed frequency macro and financial data abstract we provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency along with macro series at standard lower frequency our formulation of the macro finance model in continuous time conveniently accounts for the difference in observation frequency we suggest the use of martingale estimating functions mef to infer the structural parameters of the model directly through a nonlinear scheme this method is compared to regression based methods and the generalized method of moments gmm we illustrate our approaches by estimating various versions of the ak vasicek model with mean reverting interest rates we provide asymptotic theory and monte carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of us macro and financial data

non parametric hypothesis testing procedures and applications to demand analysis abstract this paper proposes a test of the hypothesis that a possibly vector valued regression function g lies in a particular compact family of functions f where f is not necessarily a finite dimensional parametric family under the assumption of a known covariance matrix of the errors the test is shown to be consistent for a broad range of alternatives and an upper bound on the significance level is established it is shown how the test may be used to test the utility maximization hypothesis and homotheticity and the paper indicates how to apply the test to a broad range of other non parametric hypotheses

asymptotic properties of monte carlo estimators of diffusion processes abstract this paper studies the limit distributions of monte carlo estimators of diffusion processes we examine two types of estimators based on the euler scheme one applied to the original processes the other to a doss transformation of the processes we show that the transformation increases the speed of convergence of the euler scheme we also study estimators of conditional expectations of diffusions after characterizing expected approximation errors we construct second order bias corrected estimators we also derive new convergence results for the mihlstein scheme illustrations of the results are provided in the context of simulation based estimation of diffusion processes

smoothed gmm for quantile models abstract we consider estimation of finite dimensional parameters identified by general conditional quantile restrictions including instrumental variables quantile regression within a generalized method of moments framework moment functions are smoothed to aid both computation and precision consistency and asymptotic normality are established under weaker assumptions than previously seen in the literature allowing dependent data and nonlinear structural models simulations illustrate the finite sample properties an in depth empirical application estimates the consumption euler equation derived from quantile utility maximization advantages of quantile euler equations include robustness to fat tails decoupling risk attitude from the elasticity of intertemporal substitution and error free log linearization

two step two stage least squares estimation in models with rational expectations abstract the paper develops a two step estimator for use in rational expectations models with autocorrelated residuals and predetermined but not strictly exogenous instruments the estimator extends the applicability of mccallum s 1976 error in variablesapproach to estimating such models and is asymptotically efficient in a class of intrumental variables estimators as an application we use instrumental variables techniques to estimate taylor s 1979 rational expectations macroeconomic model of the united states

efficiency bounds implied by multiperiod conditional moment restrictions abstract in this article we study a class of econometric models that imply a set of multiperiod conditional moment restrictions these restrictions depend on an unknown parameter vector we construct an extensive class of consistent asymptotically normal estimators of this parameter vector and calculate the greatest lower bound for the asymptotic covariance matrices of estimators in this class in so doing we extend results reported by hansen 1985 and stoica soderstrom and friedlander 1985 by allowing for more general forms of nonlinearities and temporal dependence many dynamic econometric models imply that the expectation of a function of a currently observed data vector and an unknown parameter vector conditioned on information available at some point in the past is 0 we focus on models in which the conditioning information is lagged more than one time period as in the models considered by barro 1981 dunn and singleton 1986 eichenbaum and hansen 1987 eichenbaum hansen and singleto

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

efficient estimation of general dynamic models with a continuum of moment conditions there are two difficulties with the implementation of the characteristic function based estimators first the optimal instrument yielding the ml efficiency depends on the unknown probability density function second the need to use a large set of moment conditions leads to the singularity of the covariance matrix we resolve the two problems in the framework of gmm with a continuum of moment conditions a new optimal instrument relies on the double indexing and as a result has a simple exponential form the singularity problem is addressed via a penalization term we introduce hac type estimators for non markov models a simulated method of moments is proposed for non analytical cases

ccs with hennessy s merge has no finite equational axiomatization this paper confirms a conjecture of bergstra and klop s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by hennessy in 1981 to the recursion free fragment of milner s calculus of communicating systems is not finitely based modulo bisimulation equivalence thus hennessy s merge cannot replace the left merge and communication merge operators proposed by bergstra and klop at least if a finite axiomatization of parallel composition modulo bisimulation equivalence is desired

spurious inference in reduced rank asset pricing models this note studies some seemingly anomalous results that arise in possibly misspecified reduced rank linear asset pricing models estimated by the continuously updated generalized method of moments when a spurious factor that is a factor that is uncorrelated with the returns on the test assets is present the test for correct model specification has asymptotic power that is equal to the nominal size in other words applied researchers will erroneously conclude that the model is correctly specified even when the degree of misspecification is arbitrarily large the rejection probability of the test for overidentifying restrictions typically decreases further in underidentified models where the dimension of the null space is larger than 1

probabilistic index models summary we present a semiparametric statistical model for the probabilistic index which can be defined as p y y a where y and y a are independent random response variables associated with covariate patterns x and x a respectively a link function defines the relationship between the probabilistic index and a linear predictor asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory the model is illustrated with several examples and the estimation theory is validated in a simulation study

testing nonnested euler conditions with quadrature based methods of approximation abstract singleton 1985 proposed a test of the validity of an euler equation specification which incorporates information on a nonnested set of euler equations from an alternative economic model the information about the alternative model is introduced into the testing framework by constructing a sequence of local alternatives to the euler equations of the maintained model which are in the direction of the euler equations of the alternative model singleton s test is easy to apply but is designed to have power against an alternative that in many cases does not have a straightforward economic interpretation in this paper we reexamine the construction of local alternatives to euler equations we compare singleton s approach with a method based on perturbing the data generation process dgp of the maintained model in the direction of the dgp of the alternative model the second approach leads to tests which are always of interest but require the complete specification of the dgp in this paper we derive a test for discriminating between two nonnested sets of euler conditions which have been estimated us ing generalized method of moments gmm the test is based on the encompassing principle of cox 1961 and mizon and richard 1986 and uses tauchen s 1986 quadrature based nethods for approximating the expectation of nonlinear functions of stationary random variables singleton s empirical examples are also reconsidered

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

are consumption based intertemporal capital asset pricing models structural abstract hansen and singleton 1982 and dunn and singleton 1986 have found supporting evidence for the overidentifying restrictions of two empirical consumption based asset pricing models when estimated with a particular set of single asset returns in this paper we submit these models to further scrutiny by testing whether they exhibit structural stability a series of tests recently developed by ghysels and hall 1990 are applied and a test for structuralinvariance is introduced based on the likelihood ratio type test procedure of eichenbaum hansen and singleton 1988 there are a number of reasons why structural stability tests are particularly appropriate for diagnostic testing of euler equation models namely 1 the lucas econometric policy evaluation critique 2 euler equations are only a partial description of the data generating process and parameter stability is one of the few assumptions imposed in their estimation via the generalized method of moments and finally 3 it is demonstrated that hansen s overidentifying restrictions test has no power against a class of local alternatives characterized by a parameter drift

estimation of affine asset pricing models using the empirical characteristic function abstract the known functional form of the conditional characteristic function ccf of discretely sampled observations from an affine diffusion is used to develop computationally tractable and asymptotically efficient estimators of the parameters of affine diffusions and of asset pricing models in which the state vectors follow affine diffusions both time domain estimators based on fourier inversion of the ccf and frequency domain estimators based directly on the ccf are constructed a method of moments estimator based on the ccf is shown to approximate the efficiency of maximum likelihood for affine diffusion and asset pricing models

energy decay rate of wave equations with indefinite damping abstract we consider the one dimensional wave equation with an indefinite sign damping and a zero order potential term using a shooting method we establish the asymptotic expansion of eigenvalues and eigenvectors of the damped wave equation for a large class of coefficients in addition if the damping coefficient is more positive than negative we prove that the energy of system decays uniformly exponentially to zero this sharp result generalizes a previous work of freitas and zuazua 1996

min max optimal instrumental variable estimation method for multivariate linear time series systems a min max optimal instrumental variable iv estimation method for multivariate linear time series systems is presented a monte carlo study is performed to assess the merits of the min max optimal iv method using two different parametrizations of the multivariate time series system the analysis indicates that the proposed estimation method yields accurate estimation results at modest computational cost

another heteroskedasticity and autocorrelation consistent covariance matrix estimator abstract a t consistent estimator of a heteroskedasticity and autocorrelation consistent covariance matrix estimator is proposed and evaluated the relevant applications are ones in which the regression disturbance follows a moving average process of known order in a system of l equations this am l estimator entails estimation of the moving average coefficients of an l dimensional vector simulations indicate that the ma l estimator s finite sample performance is better than that of the estimators of andrews and monahan 1992 and newey and west 1994 when cross products of instruments and disturbances are sharply negatively autocorrelated comparable or slightly worse otherwise

exponential stability of an abstract nondissipative linear system in this paper we consider an abstract linear system with perturbation of the form frac dy dt ay varepsilon by on a hilbert space cal h where a is skew adjoint b is bounded and varepsilon is a positive parameter motivated by a work of freitas and zuazua on the one dimensional wave equation with indefinite viscous damping p freitas and e zuazua j differential equations 132 1996 pp 338 352 we obtain a sufficient condition for exponential stability of the above system when b is not a dissipative operator we also obtain a hautus type criterion for exact controllability of system a g where g is a bounded linear operator from another hilbert space to cal h our result about the stability is then applied to establish the exponential stability of several elastic systems with indefinite viscous damping as well as the exponential stabilization of the elastic systems with noncolocated observation and control

energy methods for quasilinear hyperbolic initial boundary value problems applications to elastodynamics the aim of this paper is to show how energy methods can be used to establish local in time existence of smooth solutions to certain initial boundary value problems for systems of quasilinear hyperbolic partial differential equations our particular objective is to treat the equations of nonlinear elastodynamics

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

optimal instrumental variable estimates of the ar parameters of an arma process the modified yule walker myw equations for estimating the ar parameters of an arma process are presented as a special case of an instrumental variable iv method the consistency and accuracy of the ar parameter estimates are studied it is shown that estimation accuracy increases monotonically with the number of myw equations for an optimal choice of the weighting matrix used in the least squares solution of these equations the asymptotic error covariance of the optimal iv method equals that of the prediction error method the results of this paper verify experimental results reported in the literature regarding the performance of the myw method and provide the necessary accuracy analysis furthermore they suggest several simple asymptotically efficient multistep algorithms for estimating the ar parameters which are presented in a companion paper

estimating stochastic volatility diffusion using conditional moments of integrated volatility we exploit the distributional information contained in high frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions the estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility the realization of which is effectively approximated by the sum of the squared high frequency increments of the process our simulation evidence indicates that the resulting gmm estimator is highly reliable and accurate our empirical implementation based on high frequency five minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps

generalized spectral estimation of the consumption based asset pricing model this paper provides a framework for estimating parameters of a wide class of dynamic rational expectations models in the frequency domain the approach is particularly useful for models that are meant to match the data only in limited ways specifically this holds when interest is focused on a subset of frequencies the estimation strategy generalizes band spectrum regression to more general settings and allows for more general loss functions a noteworthy special case involves whitening estimators which force estimated innovations to be close to white noise these estimators can be understood as minimizing a set of moment conditions which grows with sample size and which are typically implied by re models

semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions abstract this paper computes the semiparametric efficiency bound for finite dimensional parameters identified by models of sequential moment restrictions containing unknown functions our results extend those of chamberlain 1992b and ai and chen 2003 for semiparametric conditional moment restrictions with identical information sets to the case of nested information sets and those of chamberlain 1992a and brown and newey 1998 for models of sequential moment restrictions without unknown functions to cases with unknown functions of possibly endogenous variables our results are applicable to semiparametric panel data models and two stage plug in problems as an important example we compute the efficiency bound for a weighted average derivative of a nonparametric instrumental variables regression npiv and find that simple plug in npiv estimators are not efficient we present an optimally weighted orthogonalized sieve minimum distance estimator that achieves the semiparametric efficiency bound

optimal instrumental variables estimation for arma models in this paper a new class of instrumental variables iv estimators for linear processes and in particular arma models is developed previously iv estimators based on lagged observations as instruments have been used to account for unmodelled ma q errors in the estimation of the ar parameters here it is shown that these iv methods can be used to improve efficiency of linear time series estimators in the presence of unmodelled conditional heteroskedasticity moreover an iv estimator for both the ar and ma part is developed estimators based on a gaussian likelihood are inefficient members of the class of iv estimators analyzed here when the innovations are conditionally heteroskedastic

stability results for the wave equation with indefinite damping abstract the one dimensional wave equation with damping of indefinite sign in a bounded interval with dirichlet boundary conditions is considered it is proved that solutions decay uniformly exponentially to zero provided the damping potential is in thebv class has positive average is small enough and satisfies a finite number of further constraints guaranteeing that the derivative of the real part of the eigenvalues is negative when the damping vanishes this sharp result completes a previous one by the first author showing that an indefinite sign damping always produces unstable solutions if it is large enough and it answers by the afirmative to a conjecture concerning small damping terms the method of proof relies on the developments by s cox and the second author on the high frequency asymptotic expansion of the spectrum for damped wave equations and on the characterization of the decay rate in terms of the spectral abscissa

stabilization of the wave equations with potential and indefinite damping by means of global carleman type estimate we study the stabilization problem of the wave equations with potential and indefinite damping the energy decay rate of the system is given explicitly also we obtain an upper bound estimate on the negative damping to guarantee the energy of the system decays exponentially

free shuffle algebras in language varieties we give simple concrete descriptions of the free algebras in the varieties generated by the shuffle semirings l p 0 1 or the semirings r r 0 1 where p is the collection of all subsets of the free monoid and r is the collection of all regular subsets the operation x y is the shuffle product

a method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators abstract for many time series estimation problems there is an infinite dimensional class of generalized method of moments estimators that are consistent and asymptotically normal this paper suggests a procedure for calculating the greatest lower bound for the asymptotic covariance matrices of such estimators the analysis focuses on estimation problems in which the data are generated by a stochastic process that is stationary and ergodic the calculation of the bound uses martingale difference approximations as suggested by gordon 1969 and a matrix version of hilbert space methods

the recognition of series parallel digraphs we present a linear time algorithm to recognize the class of vertex series parallel vsp digraphs our method is based on the relationship between vsp digraphs and the class of edge series paralle

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

perturbing the critically damped wave equation we consider the wave equation with viscous damping the equation is said to be critically damped when the damping is that value for which the spectral abscissa of the associated wave operator is minimized within the class of constant dampings the critically damped wave operator possesses a nonsemisimple eigenvalue we present a detailed study of the splitting of this eigenvalue under bounded perturbations of the damping and subsequently show that the critical choice is a local minimizes of the spectral abscissa over lines in the class of all bounded dampings

exponential stability of the plate equations with potential of second order and indefinite damping we study the exponential stability of the plate equations with potential of second order and indefinite sign damping term by means of a global carleman type estimate and the usual perturbation method we show that the energy of the system decays exponentially provided that the negative damping is sufficiently small both the energy decay rate and the upper bound estimate on the negative damping are given explicitly

full versus limited information estimation of a rational expectations model some numerical comparisons abstract this paper compares numerically the asymptotic distributions of parameter estimates and test statistics associated with two estimation techniques a a limited information one which uses instrumental variables to estimate a single equation hansen and singleton 1982 and b a full information one which uses a procedure asymptotically equivalent to maximum likelihood to simultaneously estimate multiple equations hansen and sargent 1980 the paper compares the two with respect to both 1 asymptotic efficiency under the null hypothesis of no misspecification and 2 asymptotic bias and power in the presence of certain local alternatives it is found that 1 full information standard errors are only moderately smaller than limited information standard errors and 2 when the model is misspecified full information tests tend to be more powerful and its parameter estimates tend to be more biased this suggests that at least in the model considered here the gains from the use of the less robust and computationally more complex full information technique are not particularly large

a remark on serial correlation in maximum likelihood abstract maximum likelihood estimation can be consistent and asymptotically normal despite serial correlation in the residuals the usual estimator of the asymptotic covariance of the parameter estimator is inconsistent but an alternative consistent estimator is derived

exponential decay of energy of evolution equations with locally distributed damping consider an evolution equation with energy dissipation frac partial partial t y x t ay x t by x t on a bounded x domain omega where by signifies a dissipative perturbation to an otherwise energy conserving system this dissipation may be due to medium impurities viscous effects or artificially imposed dampers and stabilizers it is distributed over only part of the domain omega the question of when the dissipation is effective enough to cause uniform exponential decay of energy is examined because of the locally distributed nature of energy dissipation the problem lacks coercivity and is not directly solvable by energy identities thus to get conditions sufficient for uniform exponential decay a different approach needs to be taken provided here is a set of tight sufficient conditions in terms of the influence of the dissipative operatorbon the separated eigenmodes or clustered eigenmodes ofa the main theorems are general enough to treat the wave and bea

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

bresse system with indefinite damping abstract we consider the bresse system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign presented only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 1 l 0 l a x d x 0 and a a l 2 for small enough in the arguments we shall also give a new proof of exponential stability for the constant case a a

seasonality and approximation errors in rational expectations models abstract a frequency domain representation of the approximation criterion that is implicit in gaussian maximum likelihood estimation is applied to study the effects of using seasonally adjusted versus seasonally unadjusted data to estimate rational expectations models three classes of economic mechanisms for generating seasonality are described approximating parameter estimates are computed numerically for several examples

timoshenko systems with indefinite damping abstract we consider the timoshenko system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign present only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 0 l a x d x 0 and a a l 2 for small enough the decay rate will be described explicitly in the arguments we shall also give a new proof of exponential stability for the constant case a a moreover we give a precise description of the decay rate and demonstrate that the system has the spectrum determined growth sdg property i e the type of the induced semigroup coincides with the spectral bound for its generator

the implications of periodically varying coefficients for seasonal time series processes abstract periodic arma processes have seasonally varying parameters superimposed on a conventional arma structure these varying parameters can arise when seasonality is incorporated into the theory of economic decision making analogously to the aggregate of component arma processes having a unvariate representation the periodic process has a corresponding arma representation this unvariate representation may however imply high orders and substantial dynamic misspecification in terms of forecast efficiency the true periodic dynamic process dominates its unvariate counterpart

exponential stability for wave equations with non dissipative damping abstract we consider the nonlinear wave equation u t t u x x a x u t 0 in a bounded interval 0 l r 1 the function a is allowed to change sign but has to satisfy a 1 l 0 l a x d x 0 for this non dissipative situation we prove the exponential stability of the corresponding linearized system for i possibly large a l with small a a l 2 and ii a class of pairs a l with possibly negative moment 0 l a x sin 2 x l d x estimates for the decay rate are also given in terms of a moreover we show the global existence of smooth small solutions to the corresponding nonlinear system if additionally the negative part of a is small enough

exponential stability of wave equations with potential and indefinite damping abstract first we consider the linear wave equation u t t u x x a x u t b x u 0 on a bounded interval 0 l r the damping function a is allowed to change its sign if a 1 l 0 l a x d x is positive and the spectrum of the operator x x b is negative exponential stability is proved for small a a l 2 explicit estimates of the decay rate are given in terms of a and the largest eigenvalue of x x b second we show the existence of a global small smooth solution of the corresponding nonlinear wave equation u t t u x x a x u t b x u 0 if additionally the negative part of a is small enough compared with

the equational theory of pomsets abstract pomsets have been introduced as a model of concurrency since a pomset is a string in which the total order has been relaxed to be a partial order in this paper we view them as a generalization of strings and investigate their algebraic properties in particular we investigate the axiomatic properties of pomsets sets of pomsets and ideals of pomsets under such operations as concatenation parallel composition union and their associated closure operations we find that the equational theory of sets pomsets under concatenation parallel composition and union is finitely axiomatizable whereas the theory of languages under the analogous operations is not a similar result is obtained for ideals of pomsets which incorporate the notion of subsumption which is also known as augmentation finally we show that the addition of any closure operation parallel or serial leads to nonfinite axiomatizability of the resulting equational theory

axiomatizing shuffle and concatenation in languages abstract we consider the varietylanggenerated by all language structures p 0 1 and the varietylg of ordered algebras generated by the structures p 0 1 wherep is the powerset of and whereb cis the complex concatenation of the languagesb c b cis their shuffle product andb cis their union we prove that for each finite seteof equations valid inlangthere is a finite modelseofein which some inequation valid inlg fails it follows that neither variety is finitely axiomatizable

full versus limited information estimation of a rational expectations model this paper compares numerically the asymptotic distributions of parameter estimates and test statistics associated with two estimation techniques a a limited information one which uses instrumental variables to estimate a single equation hansen and singleton 1982 and b a full information one which uses a procedure asymptotically equivalent to maximum likelihood to simultaneously estimate multiple equations hansen and sargent 1980 the paper compares the two with respect to both 1 asymptotic efficiency under the null hypothesis of no misspecification and 2 asymptotic bias and power in the presence of certain local alternatives it is found that 1 full information standard errors are only moderately smaller than limited information standard errors and 2 when the model is misspecified full information tests tend to be more powerful and its parameter estimates tend to be more biased this suggests that at least in the model considered here the gains from the use of the less robust and computationally more complex full information technique are not particularly large

temporal aggregation of volatility models in this paper we consider temporal aggregation of volatility models we introduce semiparametric volatility models termed square root stochastic autoregressive volatility sr sarv which are characterized by autoregressive dynamics of the stochastic variance our class encompasses the usual garch models and various asymmetric garch models moreover our stochastic volatility models are characterized by multiperiod conditional moment restrictions in terms of observables the sr sarv class is a natural extension of the class of weak garch models this extension has four advantages i we do not assume that fourth moments are finite ii we allow for asymmetries skewness leverage effect that are excluded from weak garch models iii we derive conditional moment restrictions and iv our framework allows us to study temporal aggregation of igarch models

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

the large sample behaviour of the generalized method of moments estimator in misspecified models this paper presents the limiting distribution theory for the gmm estimator when the estimation is based on a population moment condition which is subject to non local or fixed misspecification it is shown that if the parameter vector is overidentified then the weighting matrix plays a far more fundamental role than it does in the corresponding analysis for correctly specified models specifically the rate of convergence of the estimator depends on the rate of convergence of the weighting matrix to its probability limit the analysis is presented for four particular choices of weighting matrix which are commonly used in practice in each case the limiting distribution theory is different and also different from the limiting distribution in a correctly specified model statistics are proposed which allow the researcher to test hypotheses about the parameters in misspecified models

an elasticity can be estimated consistently without a priori knowledge of functional form we consider an open question in applied price theory without a priori knowledge of a firm s cost function or a consumer s indirect utility function is it possible to estimate price and substitution elasticities consistently by observing a demand system as the work of white 30 guilkey lovell and sickles 19 and others has shown ordinary flexible functional forms such as the translog cannot achieve this objective we find that if one is prepared to assume that elasticities of substitution cannot oscillate wildly over the region of interest then consistent estimation is possible using the fourier flexible form provided the number of fitted parameters increases as the number of observations increases this result obtains with any of the commonly used statistical methods as for example multivariate least squares maximum likelihood and three stage least squares it obtains if the number of fitted parameters is chosen adaptively by observing the data or chosen deterministically according to some fixed rule we approach the problem along the classical lines of estimability considerations as used in the study of less than full rank linear statistical models and thereby discover that the problem has a fascinating structure which we explore in detail

estimation of jump tails we propose a new and flexible non parametric framework for estimating the jump tails of ito semimartingale processes the approach is based on a relatively simple to implement set of estimating equations associated with the compensator for the jump measure or its intensity that only utilizes the weak assumption of regular variation in the jump tails along with in fill asymptotic arguments for directly estimating the large jumps the procedure assumes that the large sized jumps are identically distributed but otherwise allows for very general dynamic dependencies in jump occurrences and importantly does not restrict the behavior of the small jumps nor the continuous part of the process and the temporal variation in the stochastic volatility on implementing the new estimation procedure with actual high frequency data for the s p 500 aggregate market portfolio we find strong evidence for richer and more complex dynamic dependencies in the jump tails than hitherto entertained in the literature

on the spectrum of evolution operators generated by hyperbolic systems abstract we prove that the asymptotic behavior of semigroups generated by mixed initial value problems for hyperbolic systems in one space variable is determined by the zeroes of the characteristic equation the proof is based on the following reduction principle we construct a reduced system which is much simpler than the given one such that the difference of the semigroups is a compact operator the construction of the reduced system is presented in the non autonomous case because it has implifications in the study of systems which are time periodic