gmm with many moment conditions this paper provides a first order asymptotic theory for generalized method of moments gmm estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak examples in which these asymptotics are relevant include instrumental variable iv estimation with many possibly weak or uninformed instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments under certain regularity conditions the gmm estimators are shown to converge in probability but not necessarily to the true parameter and conditions for consistent gmm estimation are given a general framework for the gmm limit distribution theory is developed based on epiconvergence methods some illustrations are provided including consistent gmm estimation of a panel model with time varying individual effects consistent limited information maximum likelihood estimation as a continuously updated gmm estimator and consistent iv structural estimation using large numbers of weak or irrelevant instruments some simulations are reported

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

the optimal choice of moments in dynamic panel data models this paper derives an approximation of the mean square error mse of the gmm estimator in dynamic panel data models the approximation is based on higher order asymptotic theory under double asymptotics while first order theory under double asymptotics provides information about the bias it does not provide enough information about the variance of the estimator higher order theory enables us to obtain information about the variance from this result a procedure for choosing the number of instruments is proposed the simulations confirm that the proposed procedure improves the precision of the estimator

existence of bv solutions for a non conservative constrained aw rascle zhang model for vehicular traffic abstract the main aim of this paper is to study the aw rascle zhang arz model with non conservative local point constraint on the density flux introduced in 10 its motivation being for instance the modeling of traffic across a toll gate we prove the existence of weak solutions under assumptions that result to be more general than those required in 11 more precisely we do not require that the waves of the first characteristic family have strictly negative speeds of propagation the result is achieved by showing the convergence of a sequence of approximate solutions constructed via the wave front tracking algorithm the case of solutions attaining values at the vacuum is considered we also present an explicit numerical example to describe some qualitative features of the solutions

hypothesis testing in linear regression when k n is large abstract this paper derives the asymptotic distribution of the f test for the significance of linear regression coefficients as both the number of regressors k and the number of observations n increase together so that their ratio remains positive in the limit the conventional critical values for this test statistic are too small and the standard version of the f test is invalid under this asymptotic theory this paper provides a correction to the f statistic that gives correctly sized tests both under this paper s limit theory and also under conventional asymptotic theory that keeps k finite this paper also presents simulations that indicate the new statistic can perform better in small samples than the conventional test the statistic is then used to reexamine olivei and tenreyro s results from olivei g tenreyro s 2007 the timing of monetary policy shocks the american economic review 97 636 663 and sala i martin s results from sala i martin x x 1997 i just ran two million regressions the american economic review 87 2 178 183

functorial tropicalization of logarithmic schemes the case of constant coefficients the purpose of this article is to develop foundational techniques from logarithmic geometry in order to define a functorial tropicalization map for fine and saturated logarithmic schemes in the case of constant coefficients our approach crucially uses the theory of fans in the sense of kato and generalizes thuillier s retraction map onto the non archimedean skeleton in the toroidal case for the convenience of the reader many examples as well as an introductory treatment of the theory of kato fans are included

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

first steps in tropical intersection theory we establish first parts of a tropical intersection theory namely we define cycles cartier divisors and intersection products between these two without passing to rational equivalence and discuss push forward and pull back we do this first for fans in mathbb r n and then for abstract cycles that are fans locally with regard to applications in enumerative geometry we finally have a look at rational equivalence and intersection products of cycles and cycle classes in mathbb r n

on the asymptotics of constrained m estimation limit theorems for an m estimate constrained to lie in a closed subset of r d are given under two different sets of regularity conditions a consistent sequence of global optimizers converges under chernoff regularity of the parameter set a n consistent sequence of local optimizers converges under clarke regularity of the parameter set in either case the asymptotic distribution is a projection of a normal random vector on the tangent cone of the parameter set at the true parameter value limit theorems for the optimal value are also obtained agreeing with chernoff s result in the case of maximum likelihood with global optimizers

near exogeneity and weak identification in generalized empirical likelihood estimators many moment asymptotics abstract this paper investigates the generalized empirical likelihood gel estimators when there are local violations of the exogeneity condition near exogeneity in the case of many weak moments we also examine the tradeoff between the degree of violation of the exogeneity and the number of nearly exogenous instruments in this respect this paper extends many weak moment asymptotics of newey and windmeijer 2009a the overidentifying restrictions test can detect both mild and large violations of exogeneity in the case of minor violations the anderson rubin 1949 and wald tests are not size distorted

simultaneous selection and weighting of moments in gmm using a trapezoidal kernel abstract this paper proposes a novel procedure to estimate linear models when the number of instruments is large at the heart of such models is the need to balance the trade off between attaining asymptotic efficiency which requires more instruments and minimizing bias which is adversely affected by the addition of instruments two questions are of central concern 1 what is the optimal number of instruments to use 2 should the instruments receive different weights this paper contains the following contributions toward resolving these issues first i propose a kernel weighted generalized method of moments gmm estimator that uses a trapezoidal kernel this kernel turns out to be attractive to select and weight the number of moments second i derive the higher order mean squared error of the kernel weighted gmm estimator and show that the trapezoidal kernel generates a lower asymptotic variance than regular kernels finally monte carlo simulations show that in finite samples the kernel weighted gmm estimator performs on par with other estimators that choose optimal instruments and improves upon a gmm estimator that uses all instruments

stable pair tropical and log canonical compactifications of moduli spaces of del pezzo surfaces we give a functorial normal crossing compactification of the moduli space of smooth cubic surfaces entirely analogous to the grothendieck knudsen compactification m 0 n subset overline m 0 n

empirical likelihood estimation and consistent tests with conditional moment restrictions this paper is about efficient estimation and consistent tests of conditional moment restrictions we use unconditional moment restrictions based on splines or other approximating functions for this purpose empirical likelihood estimation is particularly appropriate for this setting because of its relatively low bias with many moment conditions we give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size we also give results for generalized empirical likelihood generalized method of moments and nonlinear instrumental variable estimators

tropicalizing the space of admissible covers we study the relationship between tropical and classical hurwitz moduli spaces following recent work of abramovich caporaso and payne we outline a tropicalization for the moduli space of generalized hurwitz covers of an arbitrary genus curve our approach is to appeal to the geometry of admissible covers which compactify the hurwitz scheme we study the relationship between a combinatorial moduli space of tropical admissible covers and the skeleton of the berkovich analytification of the classical space of admissible covers we use techniques from non archimedean geometry to show that the tropical and classical tautological maps are compatible via tropicalization and that the degree of the classical branch map can be recovered from the tropical side as a consequence we obtain a proof at the level of moduli spaces of the equality of classical and tropical hurwitz numbers

conditional moment models under semi strong identification we consider conditional moment models under semi strong identification identification strength is directly defined through the conditional moments that flatten as the sample size increases our new minimum distance estimator is consistent asymptotically normal robust to semi strong identification and does not rely on the choice of a user chosen parameter such as the number of instruments or some smoothing parameter heteroskedasticity robust inference is possible through wald testing without prior knowledge of the identification pattern simulations show that our estimator is competitive with alternative estimators based on many instruments being well centered with better coverage rates for confidence intervals

efficient gmm estimation of spatial dynamic panel data models with fixed effects abstract in this paper we derive the asymptotic properties of gmm estimators for the spatial dynamic panel data model with fixed effects when n is large and t can be large but small relative to n the gmm estimation methods are designed with the fixed individual and time effects eliminated from the model and are computationally tractable even under circumstances where the ml approach would be either infeasible or computationally complicated the ml approach would be infeasible if the spatial weights matrix is not row normalized while the time effects are eliminated and would be computationally intractable if there are multiple spatial weights matrices in the model also consistency of the mle would require t to be large and not small relative to n if the fixed effects are jointly estimated with other parameters of interest the gmm approach can overcome all these difficulties we use exogenous and predetermined variables as instruments for linear moments along with several levels of their neighboring variables and additional quadratic moments we stack up the data and construct the best linear and quadratic moment conditions an alternative approach is to use separate moment conditions for each period which gives rise to many moments estimation we show that these gmm estimators are n t consistent asymptotically normal and can be relatively efficient we compare these approaches on their finite sample performance by monte carlo

jackknife instrumental variable estimation with heteroskedasticity we present a new jackknife estimator for instrumental variable inference with unknown heteroskedasticity it weighs observations such that many instruments consistency is guaranteed while the signal component in the data is maintained we show that this results in a smaller signal component in the many instruments asymptotic variance when compared to estimators that neglect a part of the signal to achieve consistency both many strong instruments and many weak instruments asymptotic distributions are derived using high level assumptions that allow for instruments with identifying power that varies between explanatory variables standard errors are formulated compactly we review briefly known estimators and show in particular that our symmetric jackknife estimator performs well when compared to the hlim and hful estimators of hausman et al in monte carlo experiments

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

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

posterior consistency of nonparametric conditional moment restricted models this paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite dimensional parameter g0 we estimate it in a quasi bayesian way based on the limited information likelihood and investigate the impact of three types of priors on the posterior consistency i truncated prior priors supported on a bounded set ii thin tail prior a prior that has very thin tail outside a growing bounded set and iii normal prior with nonshrinking variance in addition g0 is allowed to be only partially identified in the frequentist sense and the parameter space does not need to be compact the posterior is regularized using a slowly growing sieve dimension and it is shown that the posterior converges to any small neighborhood of the identified region we then apply our results to the nonparametric instrumental regression model finally the posterior consistency using a random sieve dimension parameter is studied

gmm estimation of social interaction models with centrality this paper considers the specification and estimation of social interaction models with network structures and the presence of endogenous contextual correlated and group fixed effects when the network structure in a group is captured by a graph in which the degrees of nodes are not all equal the different positions of group members as measured by the bonacich 1987 centrality provide additional information for identification and estimation in this case the bonacich centrality measure for each group can be used as an instrument for the endogenous social effect but the number of such instruments grows with the number of groups we consider the 2sls and gmm estimation for the model the proposed estimators are asymptotically efficient respectively within the class of iv estimators and the class of gmm estimators based on linear and quadratic moments when the sample size grows fast enough relative to the number of instruments

compactifications of subvarieties of tori we study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non archimedean amoebas these compactifications have many nice properties for example any k boundary divisors intersect in codimension k we consider some examples including m 0 n subset overline m 0 n and more generally log canonical models of complements of hyperplane arrangements and compact quotients of grassmannians by a maximal torus

many ivs estimation of dynamic panel regression models with measurement error abstract in this paper we investigate a dynamic linear panel regression model with measurement error we consider the panel data estimation whose time dimension t is not small and comparable to the cross sectional dimension n first we show that the 2sls estimator suffers from the bias problem due to many instrumental variables using the alternative asymptotics where t 3 n goes to a constant as n t we characterize its asymptotic bias due to many ivs as a bias reduction method we investigate the jive and derive its limiting distribution under the alternative asymptotics

testing with many weak instruments abstract this paper establishes the asymptotic distributions of the likelihood ratio lr anderson rubin ar and lagrange multiplier lm test statistics under many weak iv asymptotics these asymptotics are relevant when the number of ivs is large and the coefficients on the ivs are relatively small the asymptotic results hold under the null and under suitable alternatives hence power comparisons can be made provided k 3 n 0 as n where n is the sample size and k is the number of instruments these tests have correct asymptotic size this holds no matter how weak the instruments are hence the tests are robust to the strength of the instruments the asymptotic power results show that the conditional lr test is more powerful asymptotically than the ar and lm tests under many weak iv asymptotics

estimation of a panel data model with parametric temporal variation in individual effects this paper is an extension of ahn et al j econom 101 2001 219 to allow a parametric function for time varying coefficients of the individual effects it provides a fixed effect treatment of models like those proposed by kumbhakar j econom 46 1990 201 and battese and coelli j prod anal 3 1992 153 we present a number of gmm estimators based on different sets of assumptions least squares has unusual properties its consistency requires white noise errors and given white noise errors it is less efficient than a gmm estimator we apply this model to the measurement of the cost efficiency of spanish savings banks

an efficient gmm estimator of spatial autoregressive models in this paper we consider gmm estimation of the regression and mrsar models with sar disturbances we derive the best gmm estimator within the class of gmm estimators based on linear and quadratic moment conditions the best gmm estimator has the merit of computational simplicity and asymptotic efficiency it is asymptotically as efficient as the ml estimator under normality and asymptotically more efficient than the gaussian qml estimator otherwise monte carlo studies show that with moderate sized samples the best gmm estimator has its biggest advantage when the disturbances are asymmetrically distributed when the diagonal elements of the spatial weights matrix have enough variation incorporating kurtosis of the disturbances in the moment functions will also be helpful

on rank estimators in increasing dimensions abstract the family of rank estimators including han s maximum rank correlation han 1987 as a notable example has been widely exploited in studying regression problems for these estimators although the linear index is introduced for alleviating the impact of dimensionality the effect of large dimension on inference is rarely studied this paper fills this gap via studying the statistical properties of a larger family of m estimators whose objective functions are formulated as u processes and may be discontinuous in increasing dimension set up where the number of parameters p n in the model is allowed to increase with the sample size n first we find that often in estimation as p n n 0 p n n 1 2 rate of convergence is obtainable second we establish bahadur type bounds and study the validity of normal approximation which we find often requires a much stronger scaling requirement than p n 2 n 0 third we state conditions under which the numerical derivative estimator of asymptotic covariance matrix is consistent and show that the step size in implementing the covariance estimator has to be adjusted with respect to p n all theoretical results are further backed up by simulation studies

a dual approach to inference for partially identified econometric models abstract this paper considers inference for the set i of parameter values that minimize a criterion function chernozhukov et al 2007 cht develop a general theory of estimation and inference using the level set of a criterion function we establish a dual relationship between the level set estimator and its support function and show that the properly normalized support function provides alternative wald type inference methods these methods can be used to obtain confidence sets for i and points inside it for models with finitely many moment inequalities we show that our wald type statistic is asymptotically equivalent to cht s statistic under regularity conditions

choosing the number of instruments properties of instrumental variable estimators are sensitive to the choice of valid instruments even in large cross section applications in this paper we address this problem by deriving simple mean square error criteria that can be minimized to choose the instrument set we develop these criteria for two stage least squares 2sls limited information maximum likelihood liml and a bias adjusted version of 2sls b2sls we give a theoretical derivation of the mean square error and show optimality in monte carlo experiments we find that the instrument choice generally yields an improvement in performance also in the angrist and krueger 1991 returns to education application when the instrument set is chosen in the way we consider it turns out that both 2sls and liml give similar large returns to education

stable logarithmic maps to deligne faltings pairs i we introduce a new compactication of the space of relative stable maps this approach uses logarithmic geoemetry in the sense of kato fontaineillusie without taking expansions of the target the underlying structures of the stable logarithmic maps are stable in the usual sense

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

consistent estimation with a large number of weak instruments this paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables iv regression when the available instruments are weak and the number of instruments k n goes to infinity with the sample size we show that consistent estimation depends importantly on the strength of the instruments as measured by r the rate of growth of the so called concentration parameter and also on k n in particular when k n the concentration parameter can grow even if each individual instrument is only weakly correlated with the endogenous explanatory variables and consistency of certain estimators can be established under weaker conditions than have previously been assumed in the literature hence the use of many weak instruments may actually improve the performance of certain point estimators more specifically we find that the limited information maximum likelihood liml estimator and the bias corrected two stage least squares b2sls estimator are consistent when k n r n 0 while the two stage least squares 2sls estimator is consistent only if k n r n 0 as n these consistency results suggest that liml and b2sls are more robust to instrument weakness than 2sls

tropical compactification in log regular varieties in this article we define a natural tropicalization procedure for closed subsets of log regular varieties in the case of constant coefficients and study its basic properties this framework allows us to generalize some of tevelev s results on tropical compactification as well as hacking s result on the cohomology of the link of a tropical variety to log regular varieties

consistent estimation with many moment inequalities in this paper we consider estimation of the identified set when the number of moment inequalities is large relative to sample size possibly infinite many applications in the recent literature on partially identified problems have this feature including dynamic games set identified iv models and parameters defined by a continuum of moment inequalities in particular conditional moment inequalities we provide a generic consistency result for criterion based estimators using an increasing number of unconditional moment inequalities we then develop more specific results for set estimation subject to conditional moment inequalities we first derive the fastest possible rate for estimating the sharp identification region under smoothness conditions on the conditional moment functions we also give rate conditions for inference under local alternatives

cube root asymptotics we establish a new functional central limit theorem for empirical processes indexed by classes of functions in a neighborhood of a fixed parameter point an n 1 3 rescaling of the parameter is compensated for by an n 2 3 rescaling of the empirical measure resulting in a limiting gaussian process by means of a modified continuous mapping theorem for the location of the maximizing value we deduce limit theorems for several statistics defined by maximization or constrained minimization of a process derived from the empirical measure these statistics include the short rousseeuw s least median of squares estimator manski s maximum score estimator and the maximum likelihood estimator for a monotone density the limit theory depends on a simple new sufficient condition for a gaussian process to achieve its maximum almost surely at a unique point

gmm inference when the number of moment conditions is large abstract asymptotic theory typically presumes that the dimensionality of econometric models is independent of the sample size even though this presumption is often quite unrealistic in gmm estimation whenever optimal instruments are not available it can frequently be shown that adding over identifying restrictions moment conditions will increase asymptotic precision however the conventional asymptotics which underlies this view insists that the number of moment conditions remain finite even though the number of available moment conditions may grow without bound we consider the explicit dependence of the number of moment conditions or instruments q n on the sample size n and establish that under conventional regularity conditions for the estimation of a linear model with general heteroskedasticity q n 3 n 0 is a sufficient condition for the validity of conventional asymptotic inference about the gmm estimator