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

on constructing matrices with prescribed singular values and diagonal elements abstract similar to the well known schur horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a hermitian matrix the sing thompson theorem characterizes the relationship between the diagonal entries and the singular values of an arbitrary matrix it is noted in this paper that based on the induction principle such a matrix can be constructed numerically by a fast recursive algorithm provided that the given singular values and diagonal elements satisfy the sing thompson conditions

using sample survey weights in multiple regression analyses of stratified samples abstract the rationale for the use of sample survey weights in a least squares regression analysis is examined with respect to four increasingly general specifications of the population regression model the appropriateness of the weighted regression estimate depends on which model is chosen a proposal is made to use the difference between the weighted and unweighted estimates as an aid in choosing the appropriate model and hence the appropriate estimator when applied to an analysis of the familial and environmental determinants of the educational level attained by a sample of young adults the methods lead to a revision of the initial additive model in which interaction terms between county unemployment and race as well as between sex and mother s education are included

asymptotic properties of weighted m estimators for variable probability samples i provide a systematic treatment of the asymptotic properties of weighted m estimators under variable probability stratified sampling the characterization of the sampling scheme and representation of the objective function allow for a straightforward analysis simple consistent asymptotic variance matrix estimators are proposed for a large class of problems when stratification is based on exogenous variables i show that the unweighted m estimator is more efficient than the weighted estimator under a generalized conditional information matrix equality when population frequencies are known a more efficient weighting is possible i also show how the results carry over to multinomial sampling

a fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values the weyl horn theorem characterizes a relationship between the eigenvalues and the singular values of an arbitrary matrix based on that characterization a fast recursive algorithm is developed to construct numerically a matrix with prescribed eigenvalues and singular values besides being of theoretical interest the technique could be employed to create test matrices with desired spectral features numerical experiment shows this algorithm to be quite efficient and robust

efficient estimation and stratified sampling abstract in this paper we investigate estimation of a class of semi parametric models the part of the model that is not specified is the marginal distribution of the explanatory variables the sampling is stratified on the dependent variables implying that the explanatory variables are no longer exogenous or ancillary we develop a new estimator for this estimation problem and show that it achieves the semi parametric efficiency bound for this case in addition we show that the estimator applies to a number of sampling schemes that have previously been treated separately

companions on artin stacks deligne s conjecture that ell adic sheaves on normal schemes over a finite field admit ell companions was proved by l lafforgue in the case of curves and by drinfeld in the case of smooth schemes in this paper we extend drinfeld s theorem to smooth artin stacks and deduce deligne s conjecture for coarse moduli spaces of smooth artin stacks we also extend related theorems on frobenius eigenvalues and traces to artin stacks

estimation of reliability in field performance studies likelihood based methods are developed for the analysis of field performance studies with particular attention centered on the estimation of regression coefficients in parametric models failure record data are those in which the time to failure and the regressor variables are observed only for those items that fail in some prespecified follow up or warranty period 0 t it is noted that for satisfactory inference about baseline failure rates or regression effects it is usually necessary to supplement the failure record data either by incorporating specific prior information about x or by taking a supplementary sample of items that survive t general methods are outlined and specific formulas for various likelihood based methods are obtained when the failure time model is exponential or weibull in these models the methods are compared with respect to asymptotic efftciency of estimation several extensions to more complicated sampling plans are considered

the generalized triangular decomposition given a complex matrix h we consider the decomposition h qrp where r is upper triangular and q and p have orthonormal columns special instances of this decomposition include the singular value decomposition svd and the schur decomposition where r is an upper triangular matrix with the eigenvalues of h on the diagonal we show that any diagonal for r can be achieved that satisfies weyl s multiplicative majorization conditions k k k k i 1 r i i 1 1 k k k i 1 r i i 1 i where k is the rank of h i is the i th largest singular value of h and r i is the i th largest in magnitude diagonal element of r given a vector r which satisfies weyl s conditions we call the decomposition h qrp where r is upper triangular with prescribed diagonal r the generalized triangular decomposition gtd a direct nonrecursive algorithm is developed for computing the gtd this algorithm starts with the svd and applies a series of permutations and givens rotations to obtain the gtd the numerical stability of the gtd update step is established the gtd can be used to optimize the power utilization of a communication channel while taking into account quality of service requirements for subchannels another application of the gtd is to inverse eigenvalue problems where the goal is to construct matrices with prescribed eigenvalues and singular values

independence of l in lafforgue s theorem abstract let x be a smooth curve over a finite field of characteristic p let l p be a prime number and let l be an irreducible lisse q l sheaf on x whose determinant is of finite order by a theorem of l lafforgue for each prime number l p there exists an irreducible lisse q l sheaf l on x which is compatible with l in the sense that at every closed point x of x the characteristic polynomials of frobenius at x for l and l are equal we prove an independence of l assertion on the fields of definition of these irreducible l adic sheaves l namely that there exists a number field f such that for any prime number l p the q l sheaf l above is defined over the completion of f at one of its l adic places

gmm redundancy results for general missing data problems we consider questions of efficiency and redundancy in the gmm estimation problem in which we have two sets of moment conditions where two sets of parameters enter into one set of moment conditions while only one set of parameters enters into the other we then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest and the second set of moment conditions is for the selection process we use these results to explain the counterintuitive result in the literature that under an ignorability assumption that justifies gmm with weighted moment conditions weighting using estimated probabilities of selection is better than weighting using the true probabilities we also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid and we show that when weighting is not needed for consistency it is also not useful for efficiency

group majorization the convex hulls of sets of matrices and the diagonal element singular value inequalities abstract a group induced preorder on matrix space permits the description of the convex hulls of sets of proper and improper real matrices with given singular values and also permits a new proof of the necessity of the known relations between the diagonal elements and singular values of a real matrix

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

multivariate regression models for panel data abstract the paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x the relationship is very strong when x is continuous weaker when x is discrete and non existent as the order of the distributed lag becomes infinite the individual specific random variables introduce nonlinearity and heteroskedasticity so the paper provides an appropriate framework for the estimation of multivariate linear predictors restrictions are imposed using a minimum distance estimator it is generally more efficient than the conventional estimators such as quasi maximum likelihood there are computationally simple generalizations of two and three stage least squares that achieve this efficiency gain some of these ideas are illustrated using the sample of young men in the national longitudinal survey the paper reports regressions on the leads and lags of variables measuring union coverage smsa and region the results indicate that the leads and lags could have been generated just by a random intercept this gives some support for analysis of covariance type estimates these estimates indicate a substantial heterogeneity bias in the union smsa and region coefficients

partially generalized least squares and two stage least squares estimators abstract a class of partially generalized least squares estimators and a class of partially generalized two stage least squares estimators in regression models with heteroscedastic errors are proposed by using these estimators a researcher can attain higher efficiency than that attained by the least squares or the two stage least squares estimators without explicitly estimating each component of the heteroscedastic variances however the efficiency is not as high as that of the generalized least squares or the generalized two stage least squares estimator calculated using the knowledge of the true variances hence the use of the term partial

the potential for efficiency gains in estimation from the use of additional moment restrictions it is frequently assumed that in generalised method of moments estimation the explicit utilization of valid additional moment restrictions will lead to asymptotic efficiency gains in this paper i develop a general framework for examining the possibility of such efficiency gains using this framework i then consider in more detail the potential for efficiency gains from utilizing a constant conditional disturbance variance restriction when estimating a single equation from a nonlinear simultaneous equations model sem by nonlinear two stage least squares 2sls in general such efficiency gains will arise however for a linear sem with constant disturbance covariances and zero third moments no efficiency gains arise for fairly general instrument sets this generalises in certain respects the usual result that 2sls is asymptotically efficient for estimating a single equation from a linear sem with independently identically distributed normal disturbances

attaining the optimal gaussian diffusion acceleration sampling from probability distributions in high dimensional spaces is generally impractical diffusion processes with invariant equilibrium distributions can be used as a means to generate approximations an important task in such an endeavor is to design an equilibrium preserving drift to accelerate the convergence starting from a reversible diffusion it is desirable to depart for non reversible dynamics via a perturbed drift so that the convergence rate is maximized with the common equilibrium in the gaussian diffusion acceleration this problem can be cast as perturbing the inverse of a given covariance matrix by skew symmetric matrices so that all resulting eigenvalues have identical real part this paper describes two approaches to obtain the optimal rate of gaussian diffusion the asymptotical approach works universally for arbitrary ornstein uhlenbeck processes whereas the direct approach can be implemented as a fast divide and conquer algorithm a comparison with recently proposed lelievre nier pavliotis algorithm is made

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

low rank update of singular values the notion of a low rank update arises in many important applications this paper deals with the inverse problem of updating a rectangular matrix by additive low rank matrices so as to reposition the associated singular values the setting is analogous to the classical pole assignment problem where eigenvalues of a square matrix are relocated precise and easy to check necessary and sufficient conditions under which the problem is solvable are completely characterized generalizing some traditional weyl inequalities for singular values the constructive proof makes it possible to compute such a solution numerically a pseudo algorithm is outlined

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

maximum entropy autoregressive conditional heteroskedasticity model abstract in many applications it has been found that the autoregressive conditional heteroskedasticity arch model under the conditional normal or student s t distributions are not general enough to account for the excess kurtosis in the data moreover asymmetry in the financial data is rarely modeled in a systematic way in this paper we suggest a general density function based on the maximum entropy me approach that takes account of asymmetry excess kurtosis and also of high peakedness the me principle is based on the efficient use of available information and as is well known many of the standard family of distributions can be derived from the me approach we demonstrate how we can extract information functional from the data in the form of moment functions we also propose a test procedure for selecting appropriate moment functions our procedure is illustrated with an application to the nyse stock returns the empirical results reveal that the me approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively

least squares regression with data arising from stratified samples of the dependent variable regression analysis is being widely used in the analysis of survey data in situations where complex sampling designs are employed often the selection procedure is based on values of the independent variables in which case standard regression methods apply however the literature abounds with examples where the selection procedure is based on values of the dependent variable for example demets halperin 1977 consider the relationship between serum cholesterol the dependent variable and dietary cholesterol the independent variable from an initial large random sample a smaller subsample was selected with the procedure that only persons with very high or very low initial serum cholesterol were chosen for subsequent measurement of the regression variables in a study of the relationship of blood pressure the dependent variable and certain anthropometric factors in adolescents kotchen et al 1980 performed follow up on a subsample of a previous survey in which individuals in the original highest and lowest blood pressure groups were deliberately oversampled a regression analysis was subsequently performed using standard least square methods finally hausman wise 1982 discuss income maintenance experiments in econometrics where high income families were undersampled from the population in a situation where income is the dependent variable of a subsequent regression analysis there are many reasons why complex sampling designs may be used on the basis of the dependent variable y for example an initial goal of the study may be to estimate the mean of y with high precision for which stratified sampling on the basis of y values may be useful subsequently regression analysis with y as the dependent variable may be desired secondly oversampling extreme values of y is a method of reducing the variances of estimated regression coefficients in cases where it may not be feasible to use traditional efficient designs based on the independent variables for such sampling situations it is now well known that in general ordinary least squares regression estimates will be biased even asymptotically see for example holt smith winter 1980 and nathan holt 1980 various adjusted estimators have been considered which we discuss briefly below

specification test on mixed logit models abstract this paper proposes a specification test of the mixed logit models by generalizing hausman and mcfadden 1984 test we generalize the test even further by considering a model developed by berry et al 1995

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

inference in panel data models under attrition caused by unobservables this paper concerns identification and estimation of a finite dimensional parameter in a panel data model under nonignorable sample attrition attrition can depend on second period variables which are unobserved for the attritors but an independent refreshment sample from the marginal distribution of the second period values is available this paper shows that under a quasi separability assumption the model implies a set of conditional moment restrictions where the moments contain the attrition function as an unknown parameter this formulation leads to i a simple proof of identification under strictly weaker conditions than those in the existing literature and more importantly ii a sieve based root n consistent estimate of the finite dimensional parameter of interest these methods are applicable to both linear and nonlinear panel data models with endogenous attrition and analogous methods are applicable to situations of endogenously missing data in a single cross section the theory is illustrated with a simulation exercise using current population survey data where a panel structure is introduced by the rotation group feature of the sampling process

inverse probability weighted estimation for general missing data problems abstract i study inverse probability weighted m estimation under a general missing data scheme examples include m estimation with missing data due to a censored survival time propensity score estimation of the average treatment effect in the linear exponential family and variable probability sampling with observed retention frequencies i extend an important result known to hold in special cases estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation for the treatment effect case the setup allows a general characterization of a double robustness result due to scharfstein et al 1999 rejoinder journal of the american statistical association 94 1135 1146

asymptotic inference from multi stage samples i develop a gmm based framework for asymptotic inference to analyze data from surveys whose designs involve stratification and clustering i set up the estimation problem derive the appropriate asymptotic distribution theory as the number of clusters per stratum tends to infinity and compute asymptotic standard errors that are robust to sample design effects the analysis is then extended to nonparametric regression and to semiparametric estimation based on u processes empirical illustrations are provided using consumption expenditure data from the complexly designed indian national household survey

on empirical likelihood statistical functions abstract we consider the empirical likelihood method for estimation of distribution and quantile functions where side information is incorporated through moment conditions we systematically study the asymptotic properties of the estimators such as the uniform strong laws of large numbers and weak convergence over classes of functions two monte carlo examples are also given to illustrate the practical utility of the method

local gmm estimation of time series models with conditional moment restrictions this paper investigates statistical properties of the local generalized method of moments lgmm estimator for some time series models defined by conditional moment restrictions first we consider markov processes with possible conditional heteroskedasticity of unknown forms and establish the consistency asymptotic normality and semi parametric efficiency of the lgmm estimator second we undertake a higher order asymptotic expansion and demonstrate that the lgmm estimator possesses some appealing bias reduction properties for positively autocorrelated processes our analysis of the asymptotic expansion of the lgmm estimator reveals an interesting contrast with the ols estimator that helps to shed light on the nature of the bias correction performed by the lgmm estimator the practical importance of these findings is evaluated in terms of a bond and option pricing exercise based on a diffusion model for spot interest rate

improved instrumental variables and generalized method of moments estimators this paper considers gmm estimation with moment conditions of the usual type plus extra moment conditions that do not depend on the parameters the extra moment conditions improve efficiency if they are correlated with the original set of moment conditions this is true in linear and nonlinear models but in linear models we provide simple explicit formulas for the improved estimators our results may be useful in rational expectations models in which an equation s error is a forecast error and the extra moment conditions would be forecast errors in related variables

independence of ell for the supports in the decomposition theorem in this article we prove a result on the independence of l for the supports of irreducible perverse sheaves occurring in the decomposition theorem as well as for the family of local systems on each support it generalizes gabber s result on the independence of l of intersection cohomology to the relative case

efficiency bounds for missing data models with semiparametric restrictions this paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random mar coincides with that of a particular augmented moment condition problem the augmented system consists of the inverse probability weighted ipw original moment restriction and an additional conditional moment restriction which exhausts all other implications of the mar assumption the paper also investigates the value of additional semiparametric restrictions on the conditional expectation function cef of the original moment function given always observed covariates in the program evaluation context for example such restrictions are implied by semiparametric models for the potential outcome cefs given baseline covariates the efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem some implications of these results for estimation are briefly discussed

chtoucas de drinfeld et correspondance de langlands on demontre la correspondance de langlands pour gl r sur les corps de fonctions la preuve generalise celle de drinfeld en rang 2 elle consiste a realiser la correspondance en rang r dans la cohomologie l adique des varietes modulaires de chtoucas de drinfeld de rang r

regression models for choice based samples with misclassification in the response variable abstract in this paper we provide a general framework to deal with the presence of misclassification in the response variable in choice based samples the contaminated data sampling distribution is written as a function of the error free conditional distribution of the dependent variable given the covariates and the conditional misclassification probabilities of the observable variable of interest given its latent values we propose an extension of imbens econometrica 60 1992 1187 efficient generalized method of moments to estimate this model and outline a specification test to detect the presence of this sort of measurement error the performance of both the estimators and the test is investigated in a monte carlo simulation study which shows very encouraging results