Hölder continuity of the policy function approximation in the value function approximation

We show that given a value function approximation V of a strongly concave stochastic dynamic programming problem (SDDP), the associated policy function approximation is Hölder continuous in V.     

An iterative approach to the estimation of the abatement costs of harmful emissions

The ability to quantify tradeoffs involved in the process of reducing harmful emissions is essential to successful policy-making in the environmental planning area. The approach by Färe et al. (J Econom 126: 469–492, 2005) to computing point estimates of the marginal abatement costs (MACs) of reducing pollution by estimating the directional output distance function has been gaining popularity in recent years. The contribution of this study is to compute MACs as slopes of the iterated parametric production possibilities frontier (PPF) estimated on the basis of the set of efficient projections of observable output combinations obtained from the parameters of directional output distance function. Policy makers are thus provided with the general shape of the production possibilities set for a polluting technology rather than with a set of point estimates of the MACs. We apply our methodology to a balanced panel of seven Korean manufacturing sectors spanning the period between 1999 and 2009, obtaining theoretically consistent concave PPFs based on a large set of directional output distance vectors. Finally, we estimate the parameters of a directional output distance function corresponding to the iterated PPF.     

Hölderian properties of partial sums of regression residuals

In this paper we investigate Hölder convergence of polygonal line process based on residuals of linear regression model. Bootstrap counterpart is also studied. Our results provide additional tools for testing epidemic type structural changes in regression models.     

Probabilistic characterization of directional distances and their robust versions

In this work, we analyze the performance of production units using the directional distance function which allows to measure the distance to the frontier of the production set along any direction in the inputs/outputs space. We show that this distance can be expressed as a simple transformation of radial or hyperbolic distance. This formulation allows to define robust directional distances in the lines of α-quantile or order-m partial frontiers and also conditional directional distance functions, conditional to environmental factors. We propose simple methods of estimation and derive the asymptotic properties of our estimators.     

A global Malmquist-Luenberger productivity index

This paper introduces an alternative environmentally sensitive productivity growth index, which is circular and free from the infeasibility problem. In doing so, we integrated the concept of the global production possibility set and the directional distance function. Like the conventional Malmquist-Luenberger productivity index, it can also be decomposed into sources of productivity growth. The suggested index is employed in analyzing 26 OECD countries for the period 1990–2003. We also employed the conventional Malmquist-Luenberger productivity index, the global Malmquist productivity index and the conventional Malmquist productivity index for comparative purposes in this empirical investigation.     

The directional profit efficiency measure: on why profit inefficiency is either technical or allocative

The directional distance function encompasses Shephard’s input and output distance functions and also allows nonradial projections of the assessed firm onto the frontier of the technology in a preassigned direction. However, the criteria underlying the choice of its associated directional vector are numerous. When market prices are observed and firms have a profit maximizing behavior, it seems natural to choose as the directional vector that projecting inefficient firms towards profit maximizing benchmarks. Based on that choice of directional vector, we introduce the directional profit efficiency measure and show that, in this general setting, profit inefficiency can be categorized as either technical, for firms situated within the interior of the technology, or allocative, for firms lying on the frontier. We implement and illustrate the analytical model by way of Data Envelopment Analysis techniques, and introduce the necessary optimization programs for profit inefficiency measurement.     

Optimal strategies in linear multisector models: Value function and optimality conditions

In this paper we study an optimal control problem with mixed constraints related to a multisector linear model with endogenous growth. The main aim is to establish a set of necessary and a set of sufficient conditions which are the basis for studying the qualitative properties of optimal trajectories. The presence of possibly degenerate mixed constraints, the unboundedness and non-strict convexity of the Hamiltonian, make the problem difficult to deal with. We develop first the dynamic programming approach, proving that the value function is a bilateral viscosity solution to the associated Hamilton–Jacobi–Bellman (HJB) equation. Then, using our results, we give a set of sufficient and a set of necessary optimality conditions which involve so-called co-state inclusion: this can be interpreted as the existence of a dual path of prices supporting the optimal path.     

Persistence in corporate networks

We examine the bipartite graphs of German corporate boards in 1993, 1999 and 2005, focusing on their projections onto directors (the “personal” network) and onto companies (the “institutional” network). The novel feature here is our focus on the temporal evolution of the two projections. The personal networks exhibit cores of highly central directors who are densely connected among themselves, while the institutional networks show a persistent core of large corporations whose identity remains mostly the same. This results in the persistent presence of a core network of very large corporations, despite substantial turnover in the identity of directors and significant changes in Germany’s corporate governance during the investigated period. Our findings strongly suggest that core persistence originates from the board appointment decisions of the very largest corporations and is largely independent of personal destinies.     

The closest strong efficient targets in the FDH technology: an enumeration method

This paper is concerned with the identification of the closest strong efficient target of a Decision Making Unit (DMU) in the Free Disposal Hull (FDH) technology in Data Envelopment Analysis (DEA). The paper uses the geometrical properties of the FDH Production Possibility Set (PPS) to design and test an enumeration algorithm to obtain the minimum distance from a DMU to the strong efficient frontier of the PPS, corresponding to each of the various returns to scale assumptions. The proposed method solves some simple optimization problems whose optimal solutions are obtained by calculating a limited number of ratios. Then, an attempt will be made to mitigate the problem of the lack of unit and translation invariance of the selected distances by considering weighted norms. Finally, the applicability of the presented method is illustrated by a numerical example using real data.

     

Hyperbolic Efficiency and Parametric Distance Functions: With Application to Spanish Savings Banks

Distance functions are gaining relevance as alternative representations of production technologies, with growing numbers of empirical applications being made in the productivity and efficiency field. Distance functions were initially defined on the input or output production possibility sets by Shephard (1953, 1970) and extended to a graph representation of the technology by Färe, Grosskopf and Lovell (1985) through their graph hyperbolic distance function. Since then, different techniques such as non parametric-DEA and parametric-SFA have been used to calculate these distance functions. However, in the latter case we know of no study in which the restriction to input or output orientation has been relaxed. What we propose is to overcome such restrictiveness on dimensionality by defining and estimating a parametric hyperbolic distance function which simultaneously allows for the maximum equiproportionate expansion of outputs and reduction of inputs. In particular, we introduce a translog hyperbolic specification that complies with the conventional properties that the hyperbolic distance function satisfies. Finally, to illustrate its applicability in efficiency analysis we implement it using a data set of Spanish savings banks.     

A bargaining set for roommate problems

Since stable matchings may not exist, we propose a weaker notion of stability based on the credibility of blocking pairs. We adopt the weak stability notion of Klijn and Massó (2003) for the marriage problem and we extend it to the roommate problem. We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution concept based on the credibility of the deviations for the roommate problem: the bargaining set. We show that weak stability is not sufficient for a matching to be in the bargaining set. We generalize the coincidence result for marriage problems of Klijn and Massó (2003) between the bargaining set and the set of weakly stable and weakly efficient matchings to roommate problems. Finally, we prove that the bargaining set for roommate problems is always non-empty by making use of the coincidence result.     

Comparison of test vs. control treatments using distance optimality criterion

We consider the problem of comparison of one test treatment (τ₀) with a set of v control treatments (τ₁, τ₂, …, τ_v) using distance optimality [DS-optimality] criterion introduced by Sinha (1970) in some treatment-connected design settings. It turns out that the nature of DS-optimal designs is quite similar to that for the usual A−, D− and E− optimality criteria. However, the optimality problem is quite complicated in most situations. First we deal with the CRD model and derive DS-optimal allocations for a given set of treatments. The results are almost identical to the A-optimal allocations for such problems. Then we consider a block design set-up and examine the nature of DS-optimal designs. In the process, we introduce the method of weighted coverage probability and maximize the resulting expression to obtain an optimal design. Received: December 1999     

Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure

We show that the monotonicity condition is conceptually important in Stochastic Frontier Analysis (SFA). Despite its importance, most empirical studies do not impose monotonicity—probably because existing approaches are rather complex and laborious. Therefore, we propose a three-step procedure that is much simpler than existing approaches. We demonstrate how monotonicity of a translog function can be imposed regionally at a connected set (region) of input quantities. Our method can be applied not only to impose monotonicity on translog production frontiers but also to impose other restrictions on cost, distance, or profit frontiers.     

Modelling and predicting recorded property crime trends in England and Wales—a retrospective

In 1999 the Home Office published, for the first time ever, 3-year ahead projections of property crime in England and Wales. The projections covered the period 1999–2001 and indicated strong upward pressure after five full years of falling crime. This pressure was generated by three factors: the number of young men in the general population, the state of the economy and the fact that property crime appeared to be well below its underlying trend level. The projections received a mixed response, with some agreeing that crime was set to rise while questioning the scale of any increase, to others who doubted the value of this type of econometric modelling. In fact, property crime did increase in 1999, although not at the rate suggested by the models—and indeed levels of burglary continued to fall. This paper addresses some of the reasons for this disparity as well as considering various criticisms of the Home Office approach.     

Numerical and analytical results for the transportation problem of Monge-Kantorovich

The Monge-Kantorovich transportation problem has a long and interesting history and has found a great variety of applications (see Rachev and Rüschendorf (1998a,b)). Some interesting characterizations of optimal solutions to the transportation problem (resp. coupling problems) have been found recently. For the squared distance and discrete distributions they relate optimal solutions to generalized Voronoi diagrams. Numerically we investigate the dependence of optimal couplings on variations of the coupling function. Numerical results confirm also a conjecture on optimal couplings in the one-dimensional case for nonconvex coupling functions. A proof of this conjecture is given under some technical conditions. Received: November 1999     

Scale and scope economies of Japanese private universities revisited with an input distance function approach

This paper examines the scale and scope economies of higher education institutions in Japan assuming the presence of productive inefficiency. The standard approach to testing the scope economies is to apply the cost function. However, the cost function approach often entails the difficulty of obtaining reliable data on input prices, especially the input prices of capital for higher education institutions. This paper proposes a duality approach based on the input distance function. The scope economies are tested under a necessary and sufficient condition by retrieving the costs of joint and separate production from the input distance function. We apply the testing procedure to data pertaining to 218 Japanese private universities in 1999 and 2004. The results indicate the scale economies and the scope diseconomies.     

Information criteria for impulse response function matching estimation of DSGE models

We propose new information criteria for impulse response function matching estimators (IRFMEs). These estimators yield sampling distributions of the structural parameters of dynamic stochastic general equilibrium (DSGE) models by minimizing the distance between sample and theoretical impulse responses. First, we propose an information criterion to select only the responses that produce consistent estimates of the true but unknown structural parameters: the Valid Impulse Response Selection Criterion (VIRSC). The criterion is especially useful for mis-specified models. Second, we propose a criterion to select the impulse responses that are most informative about DSGE model parameters: the Relevant Impulse Response Selection Criterion (RIRSC). These criteria can be used in combination to select the subset of valid impulse response functions with minimal dimension that yields asymptotically efficient estimators. The criteria are general enough to apply to impulse responses estimated by VARs, local projections, and simulation methods. We show that the use of our criteria significantly affects estimates and inference about key parameters of two well-known new Keynesian DSGE models. Monte Carlo evidence indicates that the criteria yield gains in terms of finite sample bias as well as offering tests statistics whose behavior is better approximated by the first order asymptotic theory. Thus, our criteria improve existing methods used to implement IRFMEs.     

Multiple Comparisons with the Best: Bayesian Precision Measures of Efficiency Rankings

A large literature measures the allocative and technical efficiency of a set of firms using econometric techniques to estimate stochastic production frontiers or distance functions. Typically, researchers compute only the precision of individual efficiency rankings. Recently, Horrace and Schmidt (Journal of Applied Economics 15, 1–26, 2000) have applied sampling theoretic statistical techniques known as multiple comparisons with a control (MCC) and multiple comparisons with the best (MCB) to make statistical comparisons of efficiency rankings. As an alternative, this paper offers a Bayesian multiple comparison procedure that we argue is simpler to implement, gives the researcher increased flexibility over the type of comparison, and provides greater, and more intuitive, information content. For these methods and a parametric bootstrap technique, we carry out multiple comparisons of technical efficiency rankings for a set of U.S. electric generating firms, estimated using a distance function framework. We find that the Bayesian method provides substantially more precise inferences than obtained using the MCB and MCC methods.Jel Classification: C11, C32, D24.     

An econometric approach to estimating support prices and measures of productivity change in public hospitals

In industry sectors where market prices for goods and services are unavailable, it is common to use estimated output and input distance functions to estimate rates of productivity change. It is also possible, but less common, to use estimated distance functions to estimate the normalised support (or efficient) prices of individual inputs and outputs. A problem that arises in the econometric estimation of these functions is that more than one variable in the estimating equation may be endogenous. In such cases, maximum likelihood estimation can lead to biased and inconsistent parameter estimates. To solve the problem, we use linear programming to construct a quantity index. The distance function is then written in the form of a conventional stochastic frontier model where the explanatory variables are unambiguously exogenous. We use this approach to estimate productivity indexes, measures of environmental change, levels of efficiency, and support prices for a sample of Australian public hospitals.     

Power and efficiency in production pillage games

A pillage game is a formal model of Hobbesian anarchy as a coalitional game. The technology of pillage is specified by a power function that determines the power of each coalition as a function of its members and their wealth. A coalition can despoil any other coalition less powerful than itself. The present paper studies the problem of achieving an efficient allocation of resources when the required reallocation changes the distribution of power. For example, land redistribution may increase total production, but may also deprive the original owners of the power they need to compel compensation. In this case the original owners would block the redistribution. Previous work on pillage games has focused on the stable set (von Neumann–Morgenstern solution) as a representation of a stable balance of power. However, the balance of power is typically too delicate to support all efficient allocations. The present paper shows that for a large class of power functions, a recently developed extension of the stable set, called the legitimate set, can be rich enough to support all efficient allocations.