generalised weak disposability and efficiency measurement in environmental technologies abstract weak disposability based models of environmental technologies typically assume equiproportionate trade offs between desired and undesired outputs we postulate a generalised version of weak disposability allowing for different types of trade offs between good and bad outputs and derive a new technology called piecewise cobb douglas environmental technology whose envelopments capture all three types of production structures concavity linearity and convexity to measure environmental performance with reference to this technology we develop radial and non radial directional hyperbolic distance functions we demonstrate that the value of these functions can be simply computed via the directional distance function as linear programs we use data from 112 us power plants to illustrate our approach

a comparison of parametric and non parametric distance functions with application to european railways abstract in this paper we use multi output distance functions to investigate technical inefficiency in european railways the principle aim of the paper is to compare the results obtained from the three alternative methods of estimating multi output distance functions namely the construction of a parametric frontier using linear programming data envelopment analysis dea and corrected ordinary least squares cols input orientated output orientated and constant returns to scale crs distance functions are estimated and compared the results indicate a strong degree of correlation between the input and output orientated results for each of the three methods there are also significant correlations observed between the results obtained using the alternative estimation methods the strongest correlations being between the parametric linear programming and the cols methods finally the paper concludes with the suggestion that a combination of the technical efficiency scores obtained from the three different methods be used as the preferred set of scores this idea is borrowed from the time series forecasting literature

nonparametric least squares estimation of a multivariate convex regression function this paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional we characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided we also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization computation and consistency of its least squares estimator

generalized quadratic revenue functions abstract in this paper we focus on the specification of revenue functions in their dual price space we consider two distance functions the shephard output distance function and the directional output distance function and define both in price space the former is multiplicative in nature and satisfies homogeneity whereas the latter is additive and satisfies the translation property functional equation methods yield the translog specification in the case of the shephard distance function and a quadratic specification in the case of the directional distance function monte carlo evidence suggests that the quadratic specification outperforms the translog in large samples and in true models with plenty of curvature

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

some properties of wkb series we investigate some properties of the wkb series for arbitrary analytic potentials and then specifically for potentials xn n even where more explicit formulae for the wkb terms are derived our main new results are i we find the explicit functional form for the general wkb terms k where one has only to solve a general recursion relation for the rational coefficients ii we give a systematic algorithm for an essential simplification of the integrated wkb terms k dx that enter the energy eigenvalue equation and iii we derive almost explicit formulae for the wkb terms for the energy eigenvalues of the homogeneous power law potentials v x xn where n is even

globally flexible functional forms the neural distance function the output distance function is a key concept in economics however its empirical estimation often violates properties dictated by neoclassical production theory in this paper we introduce the neural distance function ndf which constitutes a global approximation to any arbitrary production technology with multiple outputs given by a neural network nn specification the ndf imposes all theoretical properties such as monotonicity curvature and homogeneity for all economically admissible values of outputs and inputs fitted to a large data set for all us commercial banks 1989 2000 the ndf explains a very high proportion of the variance of output while keeping the number of parameters to a minimum and satisfying the relevant theoretical properties all measures such as total factor productivity tfp and technical efficiency te are computed routinely next the ndf is compared with the translog popular specification and is found to provide very satisfactory results as it possesses the properties thought as desirable in neoclassical production theory in a way not matched by its competing specification

positive solutions of a singular nonlinear third order two point boundary value problem abstract in this paper some existence results of positive solutions for the following singular nonlinear third order two point boundary value problem x t t f t x t 0 a t b x a x b x b 0 are established where c a b 0 f c a b 0 0 t may be singular at t a b and f t x may be singular at x 0

a superlative indicator for the luenberger hicks moorsteen productivity indicator theory and application abstract consisting of the difference between an output indicator and an input indicator the luenberger hicks moorsteen lhm productivity indicator allows straightforward interpretation however its computation requires estimating distance functions that are inherently unknown this paper shows that a computationally simple bennet indicator is a superlative indicator for the lhm indicator when one can assume profit maximizing behavior and the input and output directional distance functions can be represented up to the second order by a quadratic functional form we also show that the luenberger and lhm approximating bennet indicators coincide for an appropriate choice of directional vectors focusing on a large sample of italian food and beverages companies for the years 1995 2007 we empirically investigate the extent to which this theoretical equivalence translates into similar estimates we find that the bennet indicator is a close empirical alternative to the lhm indicator for the sample

numerical treatment of sth order boundary value problems by solving second kind fredholm integral equations a nystrom method is proposed for solving fredholm integral equations equivalent to boundary value problems of order s with complete differential equations the stability and the convergence of the proposed procedure are proved some numerical examples are provided in order to illustrate the accuracy of the method and to compare the procedure with some other ones given in the literature

technical efficiency estimation with multiple inputs and multiple outputs using regression analysis regression and linear programming provide the basis for popular techniques for estimating technical efficiency regression based approaches are typically parametric and can be both deterministic or stochastic where the later allows for measurement error in contrast linear programming models are nonparametric and allow multiple inputs and outputs the purported disadvantage of the regression based models is the inability to allow multiple outputs without additional data on input prices in this paper deterministic cross sectional and stochastic panel data regression models that allow multiple inputs and outputs are developed notably technical efficiency can be estimated using regression models characterized by multiple input multiple output environments without input price data we provide multiple examples including a monte carlo analysis

wkb approach applied to 1d time dependent nonlinear hamiltonian oscillators we present a simple wkb like approach to obtain approximate analytic solutions to a certain class of time dependent nonlinear 1d hamiltonian oscillators the case of homogeneous power law potentials is solved explicitly in a closed form in the leading order the accuracy of the approximation is surprisingly good and we illustrate it in the case of the quartic oscillator

sensitivity analysis of efficiency scores how to bootstrap in nonparametric frontier models efficiency scores of production units are generally measured relative to an estimated pro duction frontier nonparametric estimators dea fdh are based on a finite sample of observed production units the bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier the main point in order to validate the bootstrap is to define a reasonable data generating process in this complex framework and to propose a reasonable estimator of it this paper provides a general methodology of bootstrapping in nonparametric frontier models some adapted methods are illustrated in analyzing the bootstrap sampling variations of input efficiency measures of electricity plants

the numerical solution of third order boundary value problems using quintic splines we present a fourth order method based on quintic splines for the solution of third order linear and non linear boundary value problems bvps of the form y f x y a

bayesian measurement of productivity and efficiency in the presence of undesirable outputs crediting electric utilities for reducing air pollution abstract many studies have measured productivity change and efficiency when an undesirable output is a by product we flexibly treat the bad as a technology shifter of an input distance function and model a system of nonlinear equations subject to endogeneity theory dictates that we impose monotonicity on all inputs outputs and the bad since a bayesian full information likelihood approach can easily be misspecified we utilize the kim j econometrics 107 2002 175 limited information likelihood lil derived by minimizing the entropy distance subject to the moment conditions from the generalized method of moments gmm estimator this represents an extension of the bayesian method of moments approach of zellner and chen macroeconom dyn 5 2001 673 zellner and tobias int econom rev 42 2001 121 and zellner in bayesian analysis in econometrics and statistics the zellner view and papers edward elgar cheltenham 1997 j econometrics 83 1998 185 which uses entropy maximization but does not incorporate a specific likelihood using bayes theorem we combine traditional priors with the lil which has a mode at the standard multiple equation gmm estimator yielding a limited information posterior distribution we generalize the approach of kim j econometrics 107 2002 175 by incorporating an unknown covariance matrix in a gibbs sampling framework and applying the methodology to nonlinear equations this allows us to estimate shadow prices technical efficiency and productivity change for a panel of electric utilities yielding results that differ substantially from those obtained using standard gmm

notes on technical efficiency estimation with multiple inputs and outputs collier johnson and ruggiero 2011 deal with the problem of estimating technical efficiency using regression analysis that allows multiple inputs and outputs this revives an old problem in the analysis of production in this note we provide an alternative maximum likelihood estimator that addresses the concerns a monte carlo experiment shows that the technique works well in practice a test for homotheticity a critical assumption in collier johnson and ruggiero 2011 is constructed and its behavior is examined using monte carlo simulation and an empirical application to european banking

directional distance functions and slacks based measures of efficiency abstract in this paper we introduce a sbm slacks based measure of efficiency based on directional distance functions this measure is contrasted with the sbm due to professor tone tone k 2001 a slacks based measure of efficiency in data envelopment analysis european journal of operational research 130 498 509

statistical inference for dea estimators of directional distances in productivity and efficiency analysis the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set the most familiar non parametric methods use farrell debreu shephard or hyperbolic radial measures these approaches require that inputs and outputs be non negative which can be problematic when using financial data recently chambers et al 1998 have introduced directional distance functions which can be viewed as additive rather than multiplicative measures efficiency directional distance functions are not restricted to non negative input and output quantities in addition the traditional input and output oriented measures are nested as special cases of directional distance functions consequently directional distances provide greater flexibility however until now only free disposal hull fdh estimators of directional distances and their conditional and robust extensions have known statistical properties simar and vanhems 2012 this paper develops the statistical properties of directional d estimators which are especially useful when the production set is assumed convex we first establish that the directional data envelopment analysis dea estimators share the known properties of the traditional radial dea estimators we then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance estimation of confidence intervals and bias correction the methods are illustrated in some empirical examples

how to generate regularly behaved production data a monte carlo experimentation on dea scale efficiency measurement abstract monte carlo experimentation is a well known approach used to test the performance of alternative methodologies under different hypotheses in the frontier analysis framework whatever the parametric or non parametric methods tested experiments to date have been developed assuming single output multi input production functions the data generated have mostly assumed a cobb douglas technology among other drawbacks this simple framework does not allow the evaluation of dea performance on scale efficiency measurement the aim of this paper is twofold on the one hand we show how reliable two output two input production data can be generated using a parametric output distance function approach a variable returns to scale translog technology satisfying regularity conditions is used for this purpose on the other hand we evaluate the accuracy of dea technical and scale efficiency measurement when sample size and output ratios vary our monte carlo experiment shows that the correlation between true and estimated scale efficiency is dramatically low when dea analysis is performed with small samples and wide output ratio variations

using information about technologies markets and firm behaviour to decompose a proper productivity index this paper uses distance functions to define new output and input quantity indexes that satisfy important axioms from index number theory e g identity transitivity proportionality and time space reversal dividing the output index by the input index yields a new productivity index that can be decomposed into a measure of technical change a measure of environmental change and several measures of efficiency change a problem with this new index is that it cannot be computed without estimating the production frontier the paper shows how assumptions concerning technologies markets and firm behaviour can be used to inform the estimation process the focus is on the asymptotic properties of least squares estimators when the explanatory variables in the production frontier model are endogenous in this case the ordinary least squares estimator is usually inconsistent however there is one situation where it is super consistent a fully modified ordinary least squares estimator is also available in this case to illustrate the main ideas the paper uses us state level farm data to estimate a stochastic production frontier the parameter estimates are then used to obtain estimates of the economically relevant components of productivity change

exact analysis of adiabatic invariants in the time dependent harmonic oscillator the theory of adiabatic invariants has a long history and important applications in physics here we treat exactly the general time dependent 1d harmonic oscillator which cannot be solved in general we follow the time evolution of an initial ensemble of phase points with sharply defined energy e0 and calculate rigorously the distribution of energy e1 after time t and all its moments especially its average value and variance 2 using wkb theory we get the exact result for the leading asymptotic behaviour of 2

a novel fixed point iteration method for the solution of third order boundary value problems in this work a new alternative uniformly convergent iterative scheme is presented and applied for the solution of an extended class of linear and nonlinear third order boundary value problems that arise in physical applications the method is based on embedding green s functions into well known fixed point iterations including picard s and krasnoselskii mann s schemes convergence of the numerical method is proved by manipulating the contraction principle the effectiveness of the proposed approach is established by implementing it on several numerical examples including linear and nonlinear third order boundary value problems the results show highly accurate approximations when compared to exact and existing numerical solutions

nonparametric tests of regularity farrell efficiency and goodness of fit abstract the goal of this paper is to reveal the links among several seemingly unrelated literatures 1 1 the nonparametric regularity test literature see afriat 1972 diewert and parkan 1983 hanoch and rothschild 1972 varian 1984 2 2 the efficiency measurement literature farrell 1957 is the classic reference but also included is what has been dubbed data envelopment analysis and 3 3 the goodness of fit approach associated with varian 1990 the unifying threads are the shephard type distance function and the mahler inequality mahler 1939 our synthesis yields regularity tests of cost minimization and technical change which are nonparametric yet provide information as to goodness of fit based on farrell type efficiency measures

a survey on parametric spline function approximation this survey paper contains a large amount of material and indeed can serve as an introduction to some of the ideas and methods for the solution of ordinary and partial differential equations starting from schoenberg s work quart appl math 4 1946 345 369 the parametric spline function which depends on a parameter w 0 is reduces to the ordinary cubic or quintic spline for w 0 a note on parametric spline function approximation which is special case of this work has been published in comp math applics 29 1995 67 73 this article deals with the odd order parametric spline relations

higher order emden fowler type equations via uniform haar wavelet resolution technique abstract a uniform haar wavelet collocation based method is proposed for finding the numerical results for a class of third order nonlinear emden fowler type singular differential equations with initial and boundary conditions at the point of singularity the coefficient of the such equation blows up that causes difficulties in capturing the numerical solutions near the point of singularity haar wavelet approach handles this peculiar situation efficiently the proposed method is employed to reduce the ivps bvps into the system of algebraic equations and the nonlinearity is taken care by newton raphson method it is demonstrated that the method is appropriate for both initial as well as boundary conditions as these conditions are taken care automatically some numerical examples have been illustrated in order to demonstrate the ease of implementation and applicability of the method the l 2 norm and absolute errors further help to manifest the improvement of the findings with the increase in resolution j we compare our results with other methods which exists in literature e g variation iteration method vim cubic b spline method differential transformation method dtm iterative decomposition method idm and modified adomian decomposition method madm the second order convergence and error analysis of the proposed method is established to depict the accuracy and stability of the proposed method

linear production functions and the data envelopment analysis abstract this paper shows that the data envelopment analysis or farrell method is not nonparametric in the sense that the method implicitly employs linear production functions frontiers to measure efficiency deriving positive multiplier linear production frontiers and grouping the dmus by their corresponding frontiers can simplify the estimation procedures when there are new dmus included and can easily determine how many inputs should be reduced or and how many outputs should be increased to make an inefficient dmu efficiently this procedure can also circumvent the problems of the non archimedean infinitesmal in the ccr literature it is also shown that because of the linear production functions both banker s and the banker charnes cooper methods fail in testing for returns to scale

measurement of technical inefficiency and total factor productivity growth a semiparametric stochastic input distance frontier approach and the case of lithuanian dairy farms abstract this paper presents a four component stochastic frontier model in which the frontier function is represented by an unknown smooth input distance function and inefficiency is decomposed into persistent and transient inefficiencies furthermore the pre truncation mean and variance of the transient inefficiency are functions of the environmental variables by differentiating the four component input distance frontier with respect to the time trend total factor productivity tfp growth is estimated under the semiparametric smooth coefficient framework and is decomposed into six components i e technical change scale component allocative component external component efficiency change and residual component the empirical example focuses on the lithuanian dairy sector with multiple outputs our results show that there are some persistent and transient inefficiencies in lithuanian dairy farms however these farms maintained tfp growth of 2 per annum on average during 2004 2016 and much of it is attributed to the technical change and scale components

exact energy distribution function in a time dependent harmonic oscillator following a recent work by robnik and romanovski 2006 j phys a math gen 39 l35 2006 open syst inf dyn 13 197 222 we derive an explicit formula for the universal distribution function of the final energies in a time dependent 1d harmonic oscillator whose functional form does not depend on the details of the frequency t and is closely related to the conservation of the adiabatic invariant the normalized distribution function is where e1 is the final energy is its average value and 2 is the variance of e1 and 2 can be calculated exactly using the wkb approach to all orders

new cubic b spline approximation for solving third order emden flower type equations abstract in this article the typical cubic b spline collocation method equipped with new approximations for second and third order derivatives is employed to explore the numerical solution of a class of third order non linear singular boundary value problems the singularity is removed by means of l hospital s rule the taylor s series expansion of the error term reveals that our new scheme is fifth order accurate the proposed technique is tested on several third order emden flower type equations and the numerical results are compared with those found in the current literature it is found that our new approximation technique performs superior to the existing methods due to its simple implementation straight forward interpolation and very less computational cost

directional distance functions optimal endogenous directions a substantial literature has dealt with the problem of estimating multiple input and multiple output production functions where inputs and outputs can be good and bad numerous studies can be found in the areas of productivity analysis industrial organization labor economics and health economics while many papers have estimated the more restrictive output and input oriented distance functions here we estimate a more general directional distance function a seminal paper on directional distance functions by chambers 1998 as well as papers by fare et al 1997 chambers et al 1998 fare and grosskopf 2000 grosskopf 2003 fare et al 2005 and hudgins and primont 2007 do not address the issue of how to choose an optimal direction set typically the direction is arbitrarily selected to be 1 for good outputs and 1 for inputs and bad outputs by estimating the directional distance function together with the first order conditions for cost minimization and profit maximization using bayesian methods we are able to estimate optimal firm specific directions for each input and output which are consistent with allocative and technical efficiency we apply these methods to an electric utility panel data set which contains firm specific prices and quantities of good inputs and outputs as well as the quantities of bad inputs and outputs estimated firm specific directions for each input and output are quite different from those normally assumed in the literature the computed firm specific technical efficiency technical change and productivity change based on estimated optimal directions are substantially higher than those calculated using fixed directions

estimation and confidence regions for parameter sets in econometric models this paper develops a framework for performing estimation and inference in econometric models with partial identification focusing particularly on models characterized by moment inequalities and equalities applications of this framework include the analysis of game theoretic models revealed preference restrictions regressions with missing and corrupted data auction models structural quantile regressions and asset pricing models specifically we provide estimators and confidence regions for the set of minimizers i of an econometric criterion function q in applications the criterion function embodies testable restrictions on economic models a parameter value that describes an economic model satisfies these restrictions if q attains its minimum at this value interest therefore focuses on the set of minimizers called the identified set we use the inversion of the sample analog q n of the population criterion q to construct estimators and confidence regions for the identified set and develop consistency rates of convergence and inference results for these estimators and regions to derive these results we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification

data envelopment analysis as nonparametric least squares regression data envelopment analysis dea is known as a nonparametric mathematical programming approach to productive efficiency analysis in this paper we show that dea can be alternatively interpreted as nonparametric least squares regression subject to shape constraints on the frontier and sign constraints on residuals this reinterpretation reveals the classic parametric programming model by aigner and chu aigner d s chu 1968 on estimating the industry production function amer econom rev 58 826 839 as a constrained special case of dea applying these insights we develop a nonparametric variant of the corrected ordinary least squares cols method we show that this new method referred to as corrected concave nonparametric least squares c2nls is consistent and asymptotically unbiased the linkages established in this paper contribute to further integration of the econometric and axiomatic approaches to efficiency analysis

statistical properties of 1d time dependent hamiltonian systems from the adiabatic limit to the parametrically kicked systems we consider 1d time dependent hamiltonian systems and their statistical properties namely the time evolution of microcanonical distributions whose properties are very closely related to the existence and preservation of the adiabatic invariants we review the elements of the recent developments by robnik and romanovski during 2006 2008 for the entirely general 1d time dependent linear oscillator and try to generalize the results to the 1d nonlinear hamilton oscillators in particular the power law potentials like e g the quartic oscillator furthermore we consider the limit opposite to the adiabatic limit namely parametrically kicked 1d hamiltonian systems even for the linear oscillator interesting properties are revealed an initial kick disperses the microcanonical distribution to a spread one but an anti kick at an appropriate moment of time can annihilate it kicking it back to the microcanonical distribution the case of periodic parametric kicking is also interesting finally we propose that in the parametric kicking of a general 1d hamilton system the average value of the adiabatic invariant always increases which we prove for the power law potentials we find that the approximation of kicking is good for quite long times of the parameter variation up to the order of not much less than one period of the oscillator we also look at the behavior of the quartic oscillator for the case of the kick and anti kick and also the periodic kicking

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

on endogenizing direction vectors in parametric directional distance function based models abstract empirical studies of production technologies using directional distance functions have traditionally resorted to ad hoc ways of choosing direction vectors for these functions yet it is well known that the assumptions placed on the direction vector can have a non negligible impact on the estimation results several recent studies have attempted to address this issue using econometric estimation and data envelopment analysis we demonstrate the use of parametric nonlinear programming to select the direction vector optimally data on the us electric power plants from early 2000s are used to show the difference between results obtained with endogenously determined direction vectors and ad hoc vectors

on the numerical integration of ordinary differential equations by symmetric composition methods differential equations of the form dot x x a b are considered where the vector fields a and b can be integrated exactly enabling numerical integration of x by composition of the flows of a and b various symmetric compositions are investigated for order complexity and reversibility free lie algebra theory gives simple formulae for the number of determining equations for a method to have a particular order a new more accurate way of applying the methods thus obtained to compositions of an arbitrary first order integrator is described and tested the determining equations are explored and new methods up to 100 times more accurate at constant work than those previously known are given

statistical properties of the energy in time dependent homogeneous power law potentials we study classical 1d hamilton systems with a homogeneous power law potential and their statistical behavior assuming a microcanonical distribution of the initial conditions and describing its change under a monotonically increasing time dependent function a t the prefactor of the potential using the nonlinear wentzel kramers brillouin like method of papamikos and robnik 2012 j phys a math theor 44 315102 and following a previous work by papamikos and robnik 2011 j phys a math theor 45 015206 we specifically analyze the mean energy the variance and the adiabatic invariant action of the systems for large time and we show that the mean energy and variance increase as powers of a t while the action oscillates and finally remains constant by means of a number of detailed case studies we show that the theoretical prediction is excellent which demonstrates the usefulness of the method in such applications

probabilistic characterization of directional distances and their robust versions in productivity analysis the performance of production units is measured through the distance of the individual decision making units dmu to the technology which is defined as the frontier of the production set most of the existing methods farrell debreu and shephard radial measures input or output oriented and hyperbolic distance functions rely on multiplicative measures of the distance and so require to deal with strictly positive inputs and outputs this can be critical when the data contain zero or negative values as in financial data bases for the measure of funds performances directional distance function is an alternative that can be viewed as an additive measure of e ciency we show in this paper that using a probabilistic formulation of the production process the directional distance can be expressed as simple radial or hyperbolic distance up to a simple transformation of the inputs outputs space this allows to propose simple methods of estimation but also to transfer easily most of the known properties of the estimators shared by the radial and hyperbolic distances in addition the formulation allows to define robust directional distances in the lines of quantileor order m partial frontiers finally we can also define conditional directional distance functions conditional to environmental factors to illustrate the methodology we show how it can be implemented using a mutual funds database

stochastic estimation of firm technology inefficiency and productivity growth using shadow cost and distance functions it is well known that a firm s technology allocative efficiency technical efficiency and productivity growth can be estimated using a shadow cost system comprised of a shadow cost function and its share equations whose arguments are outputs and shadow input prices prices internal to the firm we provide a dual characterization to estimate these measures using a shadow distance system this system is comprised of a shadow distance function expressed in terms of shadow input quantities and output quantities plus the first order conditions from the cost minimization problem an advantage of the distance system over the cost system is that we obtain direct estimates of input inefficiency with the former but indirect estimates with the latter we also show how to express cost function derivatives in terms of distance function derivatives which allows calculation of returns to scale and price elasticities of demand from the estimated distance system using panel data on us electric utilities we estimate both systems and find a strong similarity between their associated measures

a bayesian approach to imposing curvature on distance functions the estimated parameters of output distance functions frequently violate the monotonicity quasi convexity and convexity constraints implied by economic theory leading to estimated elasticities and shadow prices that are incorrectly signed and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels we show how a bayesian approach can be used to impose these constraints on the parameters of a translog output distance function implementing the approach involves the use of a gibbs sampler with data augmentation a metropolis hastings algorithm is also used within the gibbs to simulate observations from truncated pdfs our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time invariant two models a fixed effects model and a random effects model are developed and applied to panel data on 17 european railways we observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed c 2004 elsevier b v all rights reserved

a penalized method for multivariate concave least squares with application to productivity analysis abstract we propose a penalized method for the least squares estimator of a multivariate concave regression function this estimator is formulated as a quadratic programing qp problem with o n2 constraints where n is the number of observations computing such an estimator is a very time consuming task and the computational burden rises dramatically as the number of observations increases by introducing a quadratic penalty function we reformulate the concave least squares estimator as a qp with only non negativity constraints this reformulation can be adapted for estimating variants of shape restricted least squares i e the monotonic concave convex least squares the experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem the matlab and r codes for implementing the penalized problems are provided in the paper

direction selection in stochastic directional distance functions abstract researchers rely on the distance function to model multiple product production using multiple inputs a stochastic directional distance function sddf allows for noise in potentially all input and output variables yet when estimated the direction selected will affect the functional estimates because deviations from the estimated function are minimized in the specified direction specifically the parameters of the parametric sddf are point identified when the direction is specified we show that the parameters of the parametric sddf are set identified when multiple directions are considered further the set of identified parameters can be narrowed via data driven approaches to restrict the directions considered we demonstrate a similar narrowing of the identified parameter set for a shape constrained nonparametric method where the shape constraints impose standard features of a cost function such as monotonicity and convexity our monte carlo simulation studies reveal significant improvements as measured by out of sample radial mean squared error in functional estimates when we use a directional distance function with an appropriately selected direction and the errors are uncorrelated across variables we show that these benefits increase as the correlation in error terms across variables increase this correlation is a type of endogeneity that is common in production settings from our monte carlo simulations we conclude that selecting a direction that is approximately orthogonal to the estimated function in the central region of the data gives significantly better estimates relative to the directions commonly used in the literature for practitioners our results imply that selecting a direction vector that has non zero components for all variables that may have measurement error provides a significant improvement in the estimator s performance we illustrate these results using cost and production data from samples of approximately 500 us hospitals per year operating in 2007 2008 and 2009 respectively and find that the shape constrained nonparametric methods provide a significant increase in flexibility over second order local approximation parametric methods

characteristics of a polluting technology theory and practice abstract we use a quadratic directional output distance function to measure the technical efficiency of 209 electric utilities that produce electricity and a polluting byproduct so 2 before 1993 and after 1997 implementation of phase i regulations of the acid rain program we also estimate the shadow price of so 2 and the output elasticity of substitution between electricity and so 2 and find that electric utilities can reduce emissions by 4000 6000 tons by reducing inefficiency the shadow price of so 2 increases from 1993 to 1997 and that the elasticity of substitution indicates that the ability to trade reductions in electricity production for reductions in so 2 emissions became more difficult between 1993 and 1997

flexible functional forms and global curvature conditions empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions lau and gallant and golub have worked out methods for imposing the appropriate curvature conditions locally but those local techniques frequently fail to yield satisfactory results we develop two methods for imposing curvature conditions globally in the context of cost function estimation the first method adopts lau s technique to a generalization of a functional form first proposed by mcfadden using this generalized mcfadden functional form it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally the second method adopts a technique used by mcfadden and barnett which is based on the fact that a non negative sum of concave functions will be concave our various suggested techniques are illustrated using the u s manufacturing data utilized by berndt and khaled