semi nonparametric estimation of binary response models with an application to natural resource valuation abstract a semi nonparametric binary response model is estimated to obtain the willingness to pay for the environmental quality improvement when the willingness to pay is restricted to be nonnegative the model estimation is straightforward by using conventional maximum likelihood software because the semi nonparametric model is the generalization of the parametric model the generality can be assessed by a likelihood ratio test by using an existing referendum survey data set it is shown that the semi nonparametric estimation provides a significant improvement over the parametric estimation the willingness to pay is sensitive to the distribution assumption

the laurent series approach to structural modeling abstract caves and christensen 1980 have provided a procedure for displaying the regular regions of a flexible functional form in the 2 good homothetic and nonhomothetic cases and in the 3 good homothetic case we extend the procedure to the nonhomothetic 3 good case and we apply the extended procedure to the translog generalized leontief and minflex laurent flexible functional forms in addition we acquire the regular regions for the minflex laurent model in the 2 good nonhomothetic case and superimpose the resulting regions on those already found by caves and christensen for the translog and generalized leontief models we find that the new minflex laurent model generally has the largest regular regions of the three flexible functional forms in addition the regular region of the minflex laurent model is found to expand as real income increases as a result that model is particularly well suited for use with time series data which typically is characterized by positive long term growth trends in real income in such applications all recent data and future forecasts can be expected to lie within the regular region of the minflex laurent model although it is possible for some of the earliest data to fall outside that regular region the model s regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets the regular region of each of the three models moves when the model s parameters are changed with the generalized leontief or translog model the regular region s shape location and size are unpredictable without prior knowledge of the model s parameters with either of those models the intersection of the model s regular regions as the parameters are changed is contained within a very small neighborhood of the one point at which we require the model to be regular with the minflex laurent model the primary properties of the regular regions are invariant to the values of the parameters and the intersection of the displayed regular regions is a very large unbounded set the width of that intersection increases without limit as real income increases

nombres de weil sommes de gauss et annulateurs galoisiens for an abelian number field k containing a primitive p rm th root of unity p an odd prime and satisfying certain technical conditions we parametrize the bbb z p rm g k bbb q annihilators of the minus part a k of the p class group by means of modules of jacobi sums using a reflection theorem and bloch kato s reciprocity law we then determine the fitting ideal of the plus part a k in terms of twisted gauss sums

seminonparametric bayesian estimation of the asymptotically ideal production model abstract recently it has been shown that seminonparametric methods can be used to produced high quality approximations to a firm s technology unlike the local approximations provided by the conventional class of flexible functional forms seminonparametric methods generate global spans within large classes of functions however that approach usually spans a much larger space than the neoclassical function space relevant to most production modeling an exception is the asymptotically ideal model aim generated from the muntz szatz series expansion since every basis function in that expansion is within the neoclassical function space a straightforward method exists for imposing neoclassical regularity when all factors are substitutes since the relevant constraints are inequality restrictions we implement the approach using bayesian methods to avoid the problems of sampling distribution truncation that would occur from sampling theoretic methods we further discuss the relevant extensions that would permit complementary factors nonconstant returns to scale and technological change

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 normality and consistency of semi nonparametric regression estimators using an upwards f test truncation rule abstract the consistency and asymptotic normality of semi nonparametric regression estimators are shown when the truncation parameter is selected by an upwards f test moreover the same statements are also shown to apply to a large class of linear estimators the article concludes with a discussion of f test critical value settings and includes results from a simulation study which demonstrates that confidence interval coverage can be increased by varying the critical values in a nonstandard way

a reexamination of diffusion estimators with applications to financial model validation time homogeneous diffusion models have been widely used for describing the stochastic dynamics of the underlying economic variables recently stanton proposed drift and diffusion estimators based on a higher order approximation scheme and kernel regression method he claimed that higher order approximations must outperform lower order approximations and concluded nonlinearity in the instantaneous return function of short term interest rates to examine the impact of higher order approximations we develop general and explicit formulas for the asymptotic behavior of both drift and diffusion estimators we show that these estimators will reduce the numerical approximation errors in asymptotic biases but their asymptotic variances escalate nearly exponentially with the order of approximation simulation studies also confirm our asymptotic results this variance inflation problem arises not only from nonparametric fitting but also from parametric fitting stanton s work also postulates the interesting qu

asymptotic optimality of generalized cl cross validation and generalized cross validation in regression with heteroskedastic errors abstract the problem considered here is that of using a data driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter in contrast to other papers on this subject we consider models with heteroskedastic errors the results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators nearest neighbor estimators and local regression estimators among others generalized c l gc l cross validation cv and generalized cross validation gcv procedures are analyzed the gc l and cv criteria are shown to be asymptotically optimal under general conditions a feasible version of gc l however is available only in some applications the gcv criterion is found to be asymptotically optimal only under a condition that is satisfied in some applications but not in others for example it is satisfied in the nearest neighbor estimation context but not in the series estimation local regression estimation or model selection contexts thus the cv criterion is the only feasible criterion of the three that is asymptotically optimal under general conditions the proofs rely heavily on results of li 1987

on deviations between neoclassical and gft based true cost of living indexes derived from the same demand function system abstract given that a generalized fechner thurstone gft direct utility function and a neoclassical direct utility function yield exactly the same system of demand functions then for which combinations of a regions of the domain of neoclassical parameters and b price and total expenditure regimes do the alternative true cost of living indexes tcli s and their sensitivities to changes in casual factors differ significantly practical neoclassical alternatives to the gft based non parametric tcli s are limited to parametric tcli s based on the class of implicit utility models discussed by barnett this paper describes the design and results of a simulation experiment which generated alternative tcli s under different parameter specifications focus of appraisal is on specifications which produced realistic demand elasticities and large deviations between tcli s

spline smoothing the equivalent variable kernel method on considere une approche spline pour la regression non parametrique et l estimation de courbe on montre que dans un certain sens le lissage spline correspond approximativement au lissage par une methode du noyau avec une largeur de bande dependant de la densite locale des points du plan de regression

the mm me ml el ef and gmm approaches to estimation a synthesis abstract the 20th century began on an auspicious statistical note with the publication of karl pearson s philos mag ser 50 1900 157 goodness of fit test which is regarded as one of the most important scientific breakthroughs the basic motivation behind this test was to see whether an assumed probability model adequately described the data at hand pearson philos trans roy soc london ser a 185 1894 71 also introduced a formal approach to statistical estimation through his method of moments mm estimation ronald a fisher while he was a third year undergraduate at the gonville and caius college cambridge suggested the maximum likelihood estimation mle procedure as an alternative to pearson s mm approach in 1922 fisher published a monumental paper that introduced such basic concepts as consistency efficiency sufficiency and even the term parameter with its present meaning fisher philos trans roy soc london ser a 222 1922 309 provided the analytical foundation of mle and studied its efficiency relative to the mm estimator fisher j roy statist soc 87 1924a 442 established the asymptotic equivalence of minimum 2 and ml estimators and wrote in favor of using minimum 2 method rather than pearson s mm approach recently econometricians have found working under assumed likelihood functions restrictive and have suggested using a generalized version of pearson s mm approach commonly known as the gmm estimation procedure as advocated in hansen econometrica 50 1982 1029 earlier godambe ann math statist 31 1960 1208 and durbin j roy statist soc ser b 22 1960 139 developed the estimating function ef approach to estimation that has been proven very useful for many statistical models a fundamental result is that score is the optimum ef ferguson ann math statist 29 1958 1046 considered an approach very similar to gmm and showed that estimation based on the pearson 2 statistic is equivalent to efficient gmm golan et al maximum entropy econometrics robust estimation with limited data wiley new york 1996 developed entropy based formulation that allowed them to solve a wide range of estimation and inference problems in econometrics more recently imbens et al econometrica 66 1998 333 kitamura and stutzer econometrica 65 1997 861 and mittelhammer et al econometric foundations cambridge university press cambridge 2000 put gmm within the framework of empirical likelihood el and maximum entropy me estimation it can be shown that many of these estimation techniques can be obtained as special cases of minimizing cressie and read j roy statist soc ser b 46 1984 440 power divergence criterion that comes directly from the pearson 1900 2 statistic in this way we are able to assimilate a number of seemingly unrelated estimation techniques into a unified framework

estimating substitution elasticities with the fourier cost function some monte carlo results abstract the fourier flexible form possesses desirable asymptotic properties that are not shared by other flexible forms such as the translog generalized leontief and generalized box cox one of them is that an elasticity of substitution can be estimated with negligible bias in sufficiently large samples regardless of what the true form actually is save that it be smooth enough this article reports the results of an experiment designed to determine whether or not this property obtains in samples of the sizes customarily encountered in practice a three input homothetic version of the generalized box cox cost function was used to generate technologies that were oriented in a two dimensional design space according to a central composite rotatable design the two factors of the design were the box cox parameter and a measure of the dispersion of the substitution matrix the fourier cost function was used to estimate the substitution elasticities at each design point and the bias at each point was estimated using the monte carlo method a response surface over the entire design space was fitted to these estimates an examination of the surface reveals that the bias is small over the entire design space roughly speaking the estimates of elasticities of substitution are unbiased to three significant digits using the fourier flexible form no matter what the true technology our conclusion is that the small bias property of the fourier form does obtain in samples of reasonable size this claim must be tampered by the usual caveats associated with inductive inference

nonparametric function estimation subject to monotonicity convexity and other shape constraints this paper uses free knot and fixed knot regression splines in a bayesian context to develop methods for the nonparametric estimation of functions subject to shape constraints in models with log concave likelihood functions the shape constraints we consider include monotonicity convexity and functions with a single minimum a computationally efficient mcmc sampling algorithm is developed that converges faster than previous methods for non gaussian models simulation results indicate the monotonically constrained function estimates have good small sample properties relative to i unconstrained function estimates and ii function estimates obtained from other constrained estimation methods when such methods exist also asymptotic results show the methodology provides consistent estimates for a large class of smooth functions two detailed illustrations exemplify the ideas

the global properties of the minflex laurent generalized leontief and translog flexible functional forms caves and christensen 16 have provided a procedure for displaying the regular regions of a flexible functional form in the 2 good homothetic and nonhomothetic cases and in the 3 good homothetic case we extend the procedure to the nonhomothetic 3 good case and we apply the extended procedure to the translog generalized leontief and minflex laurent flexible functional forms in addition we acquire the regular regions for the minflex laurent model in the 2 good nonhomothetic case and superimpose the resulting regions on those already found by caves and christensen for the translog and generalized leontief models we find that the new minflex laurent model generally has the largest regular regions of the three fiexible functional forms in addition the regular region of the minflex laurent model is found to expand as real income increases as a result that model is particularly well suited for use with time series data which typically is characterized by positive long term growth trends in real income in such applications all recent data and future forecasts can be expected to lie within the regular region of the minflex laurent model although it is possible for some of the earliest data to fall outside that regular region the model s regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets the regular region of each of three models moves when the model s parameters are changed with the generalized leontief or translog model the regular region s shape location and size are unpredictable without prior knowledge of the model s parameters with either of those two models the intersection of the model s regular regions as the parameters are changed is contained within a very small neighborhood of the one point at which we require the model to be regular with the minflex laurent model the primary properties of the regular regions are invariant to the values of the parameters and the intersection of the displayed regular regions is a very large unbounded set the width of that intersection increases without limit as real income increases

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

the dihedral lie algebras and galois symmetries of pi_1 l mathbb p 0 infty cup mu_n we describe the image of the absolute galois group acting on the pro l completion of the fundamental group of the mathbb g m minus n th roots of unity we relate the structure of the image with geometry and topology of modular varieties for the congruence subgroups gamma 1 m n of rm gl m mathbb z for m 1 2 3 ldots

efficiency of weighted average derivative estimators and index models weighted average derivatives are useful parameters for semiparametric index models and nonparametric demand analysis this paper gives efficiency results for average derivative estimators including formulating estimators that have high efficiency our analysis is carried out in three steps first we derive the efficiency bound for weighted average derivatives of conditional location functionals such as the conditional mean and median second we derive the efficiency bound for semiparametric index models where the location measure depends only on indices or linear combinations of the regressors third we compare the bound for index models with the asymptotic variance of weighted average derivative estimators of the index coefficients we characterize the form of the optimal weight function when the distribution of the regressors is elliptically symmetric in more general cases we discuss how to combine estimators with different weight functions to achieve efficiency we derive a general condition for approximate efficiency of pooled minimum chi square estimators for index model coefficients based on weighted average derivatives finally we discuss ways of selecting the type and number of weighting functions to achieve high efficiency

exponential series estimator of multivariate densities abstract we present an exponential series estimator ese of multivariate densities which has an appealing information theoretic interpretation for a d dimensional random variable x with density p 0 the ese takes the form p x exp i 1 0 m 1 i d 0 m d i i x where i are some real valued linearly independent functions defined on the support of p 0 we derive the convergence rate of the ese in terms of the kullback leibler information criterion the integrated squared error and some other metrics we also derive its almost sure uniform convergence rate we then establish the asymptotic normality of p we undertake two sets of monte carlo experiments the first experiment examines the ese performance using mixtures of multivariate normal densities the second estimates copula density functions the results demonstrate the efficacy of the ese an empirical application on the joint distributions of stock returns is presented

improving point and interval estimators of monotone functions by rearrangement suppose that a target function is monotonic and an available original estimate of this target function is not monotonic rearrangements univariate and multivariate transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function furthermore suppose an original confidence interval which covers the target function with probability at least 1 is defined by an upper and lower endpoint functions that are not monotonic then the rearranged confidence interval defined by the rearranged upper and lower endpoint functions is monotonic shorter in length in common norms than the original interval and covers the target function with probability at least 1 we illustrate the results with a growth chart example

a cup product in the galois cohomology of number fields this paper is devoted to the consideration of a certain cup product in the galois cohomology of an algebraic number field with restricted ramification let n be a positive integer let k be a number field containing the group n of nth roots of unity and let s be a finite set of primes including those above n and all real archimedean places let gk s denote the galois group of the maximal extension of k unramified outside s inside a fixed algebraic closure of k we consider the cup product h gk s n h gk s n h gk s 2 n

nonparametric and distribution free estimation of the binary threshold crossing and the binary choice models in this paper it is shown that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term this identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term the estimator is shown to be strongly consistent and a two step procedure for its calculation is developed the paper also includes examples of economic models that satisfy the conditions that are necessary to apply the results

a pro l version of the congruence subgroup problem for mapping class groups of genus one abstract let l be a prime number in the present paper we discuss a pro l version of the congruence subgroup problem for mapping class groups of genus one our main result is that the pro 2 version has an affirmative answer but the pro l version for l 11 has a negative answer

nonparametric policy analysis abstract this article considers the problem of predicting the mean effect of a change in the distribution of certain policy related variables on a dependent variable y this is conventionally done using a parametric model if however the conditional expectation of y given policy and nonpolicy variables x is unaltered by the policy intervention and if the support of x after the policy intervention lies within the support of x before the intervention then this analysis can be performed nonparametrically the proposed nonparametric estimator is developed for the model yj g xj a dj uj where g is a continuous unknown function of the continuous variables x dj is an m vector of dummy variables a is an m vector of unknown parameters representing fixed cell specific effects and uj is an error term with e uj xj dj 0 the estimand is b eg xj eg xj where x and x respectively denote the values of x before and after the policy intervention a nonparametric estimator bn is propo

specification testing in discretized diffusion models theory and practice we propose two new tests for the specification of both the drift and the diffusion functions in a discretized version of a semiparametric continuous time financial econometric model theoretically we establish some asymptotic consistency results for the proposed tests practically a simple selection procedure for the bandwidth parameter involved in each of the proposed tests is established based on the assessment of the power function of the test under study to the best of our knowledge this is the first approach of this kind in specification of continuous time financial econometrics the proposed theory is supported by good small and medium sample studies

calculation of maximum entropy distributions and approximation of marginalposterior distributions abstract it is shown how members of the broad class of cobb koppstein chen probability density functions can be generated by maximizing shannon s entropy subject to appropriate side conditions a particular member of the class the quartic exponential distribution is obtained by maximizing shannon s entropy subject to the conditions that the probability density function integrate to one and have given first four moments an algorithm for computing the quartic exponential distribution is provided and applied to approximate marginal posterior probability densities these approximations are compared with those provided by the pearson density function approximation procedure and exact densities obtained by numerical integration it is found that the maximum entropy method performs very well

the rank of demand systems theory and nonparametric estimation w m gorman s 1981 concept of engel curve rank is extended to apply to any demand system rank is shown to have implications for specification separability and aggregation of demands a simple nonparametric test of rank using engel curve data is described and applied to u s and u k consumer survey data the test employs a new general method for testing the rank of estimated matrices the results are used to assess theoretical and empirical aggregation error in representative consumer models and to explain a representative consumer paradox copyright 1991 by the econometric society

on bayesian analysis and computation for functions with monotonicity and curvature restrictions our goal is inference for shape restricted functions our functional form consists of finite linear combinations of basis functions prior elicitation is difficult due to the irregular shape of the parameter space we show how to elicit priors that are flexible theoretically consistent and proper we demonstrate that uniform priors over coefficients imply priors over economically relevant quantities that are quite informative and give an example of a non uniform prior that addresses this issue we introduce simulation methods that meet challenges posed by the shape of the parameter space we analyze data from a consumer demand experiment

non parametric unconditional quantile estimation for efficiency analysis with an application to federal reserve check processing operations abstract this paper examines the technical efficiency of us federal reserve check processing offices over 1980 2003 we extend results from park et al park b simar l weiner c 2000 fdh efficiency scores from a stochastic point of view econometric theory 16 855 877 and daouia and simar daouia a simar l 2007 nonparametric efficiency analysis a multivariate conditional quantile approach journal of econometrics 140 375 400 to develop an unconditional hyperbolic quantile estimator of efficiency our new estimator is fully non parametric and robust with respect to outliers when used to estimate distance to quantiles lying close to the full frontier it is strongly consistent and converges at rate root n thus avoiding the curse of dimensionality that plagues data envelopment analysis dea estimators our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices

maximum entropy estimation of density and regression functions abstract this paper presents an information efficient technique to determine the functional forms of density and regression functions by maximizing entropy subject to given side conditions a flexible functional form approach is established as special cases of this approach exponential polynomial cobb douglas translog generalized cobb douglas generalized leontief fourier flexible form and minflex laurent series etc can be derived in a monte carlo experiment the maximum entropy regression method shows good performance in terms of goodness of fit boxplots and isoquants produced by the maximum entropy method are compared with those produced by other well known functions

asymptotic normality of series estimators for nonparametric and semiparametric regression models this paper establishes the asymptotic normality of series estimators for nonparametric regression models gallant s fourier flexible form estimators trigonometric series estimators and polynomial series estimators are prime examples of the estimators covered by the results the results apply to a wide variety of estimates in the regression model under consideration including derivatives and integrals of the regression function the errors in the model may be homoskedastic or heteroskedastic the paper also considers series estimators for additive interactive regression semiparametric regression and semiparametric index regression models and shows them to be consistent and asymptotically normal copyright 1991 by the econometric society

consistent model specification tests for time series econometric models in this paper we consider general hypothesis testing problems for nonparametric and semiparametric time series econometric models we apply the general methodology to construct a consistent test for omitted variables and a consistent test for a partially linear model the proposed tests are shown to have asymptotic normal distributions under their respective null hypotheses we also discuss the problems of testing portfolio conditional mean variance efficiency and testing a semiparametric single index model monte carlo simulations are conducted to examine the finite sample performances of the nonparametric omitted variable test and the test for a partially linear specification

on the asymptotic normality of fourier flexible form estimates abstract rates of increase in the number of parameters of a fourier factor demand system that imply asymptotically normal elasticity estimates are characterized this is the multivariate analog of work by andrews 1991 our proof strategy is new and consists of relating the minimum eigenvalue of the sample sum of squares and cross products matrix to the minimum eigenvalue of the population matrix via a uniform strong law with rate that is established using results from the empirical processes literature in its customary form the minimum eigenvalue of the fourier sum of squares and cross products matrix considered as a function of the number of parameters decreases faster than any polynomial the consequence is that the rate at which parameters may increase is slower than any fractional power of the sample size in this case we get the same rate as andrews when our results are applied to multivariate regressions with a minimum eigenvalue that is bounded or declines at a polynomial rate the rate on the parameters is a fractional power of the sample size in this case our method of proof gives faster rates than andrews andrews results cover the heteroskedastic case ours do not

imposing curvature restrictions on flexible functional forms abstract a general computational method for estimating the parameters of a flexible functional form subject to convexity quasi convexity concavity or quasi concavity at a point at several points or over a region is set forth and illustrated with an example

estimation of some partially specified nonlinear models abstract this paper presents a procedure for analyzing a partially specified nonlinear regression model in which the nuisance parameter is an unrestricted function of a subset of regressors the procedure does not require parameteric modeling of the nuisance parameter but assumes that the model can be transformed into a partially specified linear equation by inverting some nonlinear functions the model parameters are estimated by applying robinson s 1988a procedure and the estimator is show to be n consistent and asymptotically normal one attraction of the estimator is that is to computationally simple requiring no more than least squares regressions a simulation study indicates that the estimator has practical values

on the bias in flexible functional forms and an essentially unbiased form the fourier flexible form abstract the fourier flexible form and its derived expenditure system are introduced subject to smoothness conditions on the consumer s true indirect utility function the consumer s true expenditure system must be of the fourier form over the region of interest in an empirical investigation arbitrarily accurate finite parameter approximations of the consumer s true expenditure system are obtained by dropping all high order terms of the fourier expenditure system past an appropriate truncation point the resulting finite parametersystem is tractable in empirical studies the reader who is primarily interested in applications need only read the second and fifth sections the remainder of the article is concerned with the verification of these claims and an investigation of some aspects of the bias in translog specifications

unbiased determination of production technologies abstract to determine whether an industry exhibits constant returns to scale whether the production function is homothetic or whether inputs are separable a common approach is to specify a cost function estimate its parameters using data such as prices and quantities of inputs and then test the parametric restrictions corresponding to constant returns a homothetic technology or separability statistically such inferences are valid if the true cost function is a member of the parametric class considered otherwise the inference is biased that is the true rejection probability is not necessarily adequately approximated by the nominal size of the statistical test the use of fixed parameter flexible functional forms such as the translog the generalized leontief or the box cox will not alleviate this problem the fourier flexible form differs fundamentally from other flexible forms in that it has a variable number of parameters and a known bound depending on the number of parameters on the error as measured by the sobolev norm of approximation to an arbitrary cost function thus it is possible to construct statistical tests for constant returns a homothetic technology or separability which are asymptotically size by letting the number of parameters of the fourier flexible form depend on sample size that is the true rejection probability converges to the nominal size of the test as sample size tends to infinity the rate of convergence depends on the smoothness of the true cost function the more times is differentiable the true cost function the faster the convergence the method is illustrated using the data on aggregate u s manufacturing of berndt and wood 1975 1979 and berndt and khaled 1979

on a high dimensional model representation method based on copulas abstract this article provides an alternative to high dimensional model representation using a copula approximation of an unknown functional form we apply our methodology in the context of an extensive monte carlo study and to a sample of large us commercial banks in the monte carlo experiment the approximations errors of the copula approach are small and behave randomly in our empirical application we find that the copula approximation performs much better in terms of bayes factors for model comparison compared to high dimensional model representation which in turn provides better results when compared with standard flexible functional forms like the translog the minflex laurent and the generalized leontief or a multilayer perceptron moreover the choice of approximation has significant implications for productivity and its components returns to scale technical inefficiency technical change and efficiency change

profinite braid groups galois representations and complex multiplications in this paper we consider two closely correlated subjects one is a pro i analogue of the braid group and the other is a construction of the universal 1 adic power series for complex multiplications of fermat type or equivalently for jacobi sums both arise from and constitute a first step in the study of the canonical representation of the absolute galois group gq gal q q in the outer automorphism group of the profinite fundamental group of pq o 1 oo

on galois representations arising from towers of coverings of p1 0 1 we propose a new way to describe universally thel adic galois representations associated to each almost pro l tower of etale coverings ofp1 0 1 this generalizes our universal power series for jacobi sums cf i which arises from the tower of fermat curves of degreeln n and contains the case of the tower of modular curves of level 2mln m fixed n as another important special case as a fundamental tool we shall establish and use an almost pro l version of the theorems of blanchfield and of lyndon in fox free differential calculus

on bayesian modeling of fat tails and skewness abstract we consider a bayesian analysis of linear regression models that can account for skewed error distributions with fat tails the latter two features are often observed characteristics of empirical datasets and we formally incorporate them in the inferential process a general procedure for introducing skewness into symmetric distributions is first proposed even though this allows for a great deal of flexibility in distributional shape tail behavior is not affected applying this skewness procedure to a student t distribution we generate a skewed student distribution which displays both flexible tails and possible skewness each entirely controlled by a separate scalar parameter the linear regression model with a skewed student error term is the main focus of the article we first characterize existence of the posterior distribution and its moments using standard improper priors and allowing for inference on skewness and tail parameters for posterior inference with this model we suggest

semiparametric estimation of monotone and concace utility functions for polychotomous choice models this paper introduces a semiparametric estimation method for polychotomous choice models the method does not require a parametric structure for the systematic subutility of observable exogenous variables the distribution of the random terms is assumed to be known up to a finite dimensional parameter vector in contrast previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified the systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory the estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent a computational technique to calculate the estimators is developed copyright 1991 by the econometric society

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

nonparametric pricing of interest rate derivative securities we propose a nonparametric estimation procedure for continuous time stochastic models because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process we leave the volatility function unrestricted and estimate it nonparametrically only discrete data are used but the estimation procedure still does not rely on replacing the continuous time model by some discrete approximation instead the drift and volatility functions are forced to match the densities of the process we estimate the stochastic differential equation followed by the short term interest rate and compute nonparametric prices for bonds and bond options

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

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

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

a simple consistent bootstrap test for a parametric regression function abstract a simple consistent test is considered and a bootstrap method is proposed for testing a parametric regression functional form it is shown that the bootstrap method gives a more accurate approximation to the null distribution of the test than the asymptotic normal theory result we also propose a consistent test for testing a parametric partially linear model versus a semiparametric partially linear alternative monte carlo simulations suggest that the bootstrap test performs well based on wild bootstrap critical values

a nonparametric test of weak separability and consumer preferences abstract two stochastic nonparametric procedures are developed to evaluate the significance of violations of weak separability when the data have measurement error we show that the necessary and sufficient weak separability conditions of varian varian h 1983 nonparametric tests of consumer behavior review of economic studies 50 99 110 must also satisfy the afriat inequalities the tests detect weak separability with high probability for weakly separable data in addition the procedures correctly reject weak separability for both nonseparable and random utility simulated data sets the tests also fail to reject weak separability for a monetary and consumption data set which suggests that measurement error may be the source of the observed violations

introduction to internally consistent modeling aggregation inference and policy abstract this special issue of the journal of econometrics honors william a barnett s exceptional contributions to unifying economic theory with rigorous statistical inference to interpret economic data and inform public policy it is devoted to papers that advance microeconometrics macroeconometrics and financial econometrics to build models to interpret evidence

the galois action and cohomology of a relative homology group of fermat curves abstract for an odd prime p satisfying vandiver s conjecture we give explicit formulae for the action of the absolute galois group g q p on the homology of the degree p fermat curve building on work of anderson further we study the invariants and the first galois cohomology group which are associated with obstructions to rational points on the fermat curve

asymptotically distribution free tests for the volatility function of a diffusion abstract this paper develops two tests for parametric volatility function of a diffusion model based on khmaladze 1981 s martingale transformation the tests impose no restrictions on the functional form of the drift function and are shown to be asymptotically distribution free the tests are consistent against a large class of fixed alternatives and have nontrivial power against a class of root n local alternatives the paper also extends the tests of volatility to testing for joint specifications of drift and volatility monte carlo simulations show that the tests perform well in finite samples the proposed tests are then applied to testing models of short term interest using data of treasury bill rate and eurodollar deposit rate the empirical results show that the commonly used ckls volatility function of chan et al 1992 fits volatility function poorly and none of the parametric interest rate models considered in the paper fit data well

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

bootstrap specification tests for diffusion processes this paper discusses specification tests for diffusion processes in the one dimensional case our proposed test is closest to the nonparametric test of ait sahalia rev financ stud 9 1996 385 however we compare cdfs instead of densities in the multidimensional and or multifactor case our proposed test is based on comparison of the empirical cdf of actual data and the empirical cdf of simulated data asymptotically valid critical values are obtained using an empirical process version of the block bootstrap which accounts for parameter estimation error an example based on a simple version of the cox et al econometrica 53 1985 385 model is outlined and related monte carlo experiments are carried out

maximum entropy in the problem of moments the maximum entropy approach to the solution of underdetermined inverse problems is studied in detail in the context of the classical moment problem in important special cases such as the hausdorff moment problem we establish necessary and sufficient conditions for the existence of a maximum entropy solution and examine the convergence of the resulting sequence of approximations a number of explicit illustrations are presented in addition to some elementary examples we analyze the maximum entropy reconstruction of the density of states in harmonic solids and of dynamic correlation functions in quantum spin systems we also briefly indicate possible applications to the lee yang theory of ising models to the summation of divergent series and so on the general conclusion is that maximum entropy provides a valuable approximation scheme a serious competitor of traditional pade like procedures

estimation and moment recursion relations for multimodal distributions of the exponential family abstract multimodal generalizations of the normal gamma inverse gamma and beta distributions are introduced within a unified framework these multimodal distributions belonging to the exponential family require fewer parameters than corresponding mixture densities and have unique maximum likelihood estimators simple moment recursion relations which make maximum likelihood estimation feasible also yield easily computed estimators that themselves are shown to be consistent and asymptotically normal lastly a statistic for bimodality based on cardan s discriminant for a cubic shape polynomial is introduced

fundamental groups of moduli and the grothendieck teichmuller group let mo denote the moduli space of riemann spheres with n ordered marked points in this article we define the group out of quasispecial symmetric outer automorphisms of the algebraic fundamental group 1r1 mo n for all n 4 to be the group of outer automorphisms respecting the conjugacy classes of the inertia subgroups of irl m4 n and commuting with the group of outer automorphisms of rl mo n obtained by permuting the marked points our main result states that outd is isomorphic to the grothendieck teichmiiller group gt for all n 5

the global properties of the two minflex laurent flexible functional forms abstract the minflex laurent flexible functional form is a special case of a second order laurent series expansion the minflex laurent when constructed in square roots is called the minflex laurent ml generalized leontief the minflex laurent ml translog model is the minflex laurent in logarithms we find that the regular region of the ml translog is most often even larger than that of the ml generalized leontief model except when substitutability is very low we previously have shown that the regular region of the ml generalized leontief is substantially larger than that of the usual translog and generalized leontief models

a test for model specification of diffusion processes we propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process the empirical likelihood is used to formulate a statistic for each kernel smoothing bandwidth which is effectively a studentized l2 distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process to reduce the sensitivity of the test on smoothing bandwidth choice the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths to better capture the finite sample distribution of the test statistic and data dependence the critical value of the test is obtained by a parametric bootstrap procedure properties of the test are evaluated asymptotically and numerically by simulation and by a real data example

fully nonparametric estimation of scalar diffusion models we propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process we show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter the asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens we prove almost sure consistency and weak convergence to mixtures of normal laws where the mixing variates depend on the chronological local time of the underlying diffusion process that is the random time spent by the process in the vicinity of a generic spatial point the estimation method and asymptotic results apply to both stationary and nonstationary recurrent processes

the three dimensional global properties of the minflex laurent generalized leontief and translog flexible functional forms abstract we use the caves and christensen procedure to produce the regular regions of three flexible functional forms generalized leontief translog and barnett s new minflexlaurent model we display the regular regions in six cases with three goods using both three dimensional color graphics and two dimensional sections we find that minflex laurent generally has the largest regular region in addition the regular regions of that model are the most stable in shape across the six cases and always expand as real income increases consequently that model is especially well suited for use with income trended time series data

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

likelihood based inference for regular functions with fractional polynomial approximations abstract this paper shows that regular fractional polynomials can approximate regular cost production and utility functions and their first two derivatives on closed compact subsets of the strictly positive orthant of euclidean space arbitrarily well these functions therefore can provide reliable approximations to demand functions and other economically relevant characteristics of tastes and technology using canonical cost function data it shows that full bayesian inference for these approximations can be implemented using standard markov chain monte carlo methods

stochastic specification and estimation of share equation systems abstract this paper discusses a theoretical justification for the stochastic specification of singular share equation systems commonly used in the analysis of producer and consumer behavior which is based on the use of a random objective function the restrictions on the share equations that are implied by this formulation are derived in addition it is shown that in this context additive error terms in share equation models generally can be expected to be heteroskedastic the issue of invariance of a minimum distance estimator to the equation dropped is also explored

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

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

two step estimation of heteroskedastic sample selection models abstract this paper considers two step estimation of a sample selection model in which there is heteroskedasticity of unknown form in the latent errors we propose an estimator which uses recent developments in nonparametric regression estimation involving series approximations the estimator is shown to be consistent and asymptotically normally distributed under reasonable conditions a small monte carlo experiment demonstrates the usefulness of the estimator and highlights the bias inherent in the usual heckman 1979 estimator when there is heteroskedasticity

syntomic regulators and special values of p adic l functions in this paper p adic analogs of the lichtenbaum conjectures are proven for abelian number fields f and odd prime numbers p which generalize leopoldt s p adic class number formula and express special values of p adic l functions in terms of orders of k groups and higher p adic regulators the approach uses syntomic regulator maps which are the p adic equivalent of the beilinson regulator maps they can be compared with etale regulators via the fontaine messing map and computations of bloch kato in the case that p is unramified in f lead to results about generalized coates wiles homomorphisms and cyclotomic characters

non linear regression with discrete explanatory variables with an application to the earnings function abstract in this paper it will be shown that regression models with discrete explanatory variables take the form of a polynominal of a linear function of the regressors a two stage estimation procedure and various model specification tests will be developed in close harmony with an empirical application to the earnings function

an adaptive empirical likelihood test for parametric time series regression models we propose an adaptive empirical likelihood el test for a parametric regression model against a class of alternatives for weakly dependent time series observations the test is formulated by maximizing a standardized version of the el statistic over a set of smoothing bandwidths it is demonstrated that the proposed test is able to distinguish the null hypothesis from a series of local alternatives at an optimal rate

maximum entropy in the finite stieltjes and hamburger moment problem a necessary and sufficient condition for the existence of the maximum entropy me function defined in an infinite or semiinfinite interval is provided the conclusions reached show that except in a few particular cases the necessary and sufficient conditions for the existence of maximum entropy function are identical to the conditions for the solution of the moment problem when the first m 1 moments are assigned even if the conclusions reached are very similar to the hausdorff case the specificity of the hamburger and stieltjes cases demands a different handling a sufficient condition for the entropy convergence of the resulting sequence of maximum entropy estimators to the entropy of the recovering function is also provided