Directional output distance functions: endogenous directions based on exogenous normalization constraints

In response to a question raised by Knox Lovell, we develop a method for estimating directional output distance functions with endogenously determined direction vectors based on exogenous normalization constraints. This is reminiscent of the Russell measure proposed by Färe and Lovell (J Econ Theory 19:150–162, 1978). Moreover it is related to the slacks-based directional distance function introduced by Färe and Grosskopf (Eur J Oper Res 200:320–322, 2010a, Eur J Oper Res 206:702, 2010b). Here we show how to use the slacks-based function to estimate the optimal directions.     

Modeling CRS bounded additive DEA models and characterizing their Pareto-efficient points

Dealing with weighted additive models in Data Envelopment Analysis guarantees that any projection of an inefficient unit belongs to the strong efficient frontier, among other interesting properties. Recently, constant returns to scale (CRS) range-bounded models have been introduced for defining a new additive-type efficiency measure (see Cooper et al. in J Prod Anal 35(2):85–94, 2011). This paper continues such earlier work further, considering a more general setting. In particular, we show that under free disposability of inputs and outputs, CRS bounded additive models require a double set of slacks. The second set of slacks allows us to properly characterize all the Pareto-efficient points associated to the bounded technology. We further introduce the CRS partially-bounded additive models.     

Properties of inefficiency indexes on ?input, output? space

We analyze efficiency measurement in the full á\langleinput, output?\rangle space. We posit four types of axioms: indication (of efficient production bundles), monotonicity, independence of units of measurement, and continuity (in technologies as well as input and output quantities). Impossibility results establish a tension between indication and continuity. We focus on seven well-known inefficiency indexes from the operations-research and economics literature, establishing the properties they satisfy—and do not satisfy—on a general class of technologies satisfying minimal regularity conditions and on the subset of these technologies satisfying convexity. We also discuss several other indexes that are dominated by or very similar to these seven indexes. The set of properties satisfied by these indexes elucidates the trade-offs faced in selecting among the indexes.     

Boundary problems with the “Russell” graph measure of technical efficiency: a refinement

In an influential paper, Färe and Lovell (J Econ Theory 19:150–162, 1978) proposed an (input based) technical efficiency index designed to correct two fundamental inadequacies of the Debreu-Farrell index: its failure to satisfy (1) indication (the index is equal to 1 if and only if the input bundle is technically efficient) and (2) weak monotonicity (an increase in any one input quantity cannot increase the value of the index). Färe et al. (1985) extended the index to measure efficiency in the full space of input and output quantities. Unfortunately, this index fails to satisfy not only indication and monotonicity at the boundary (of output space), but also weak monotonicity. We show, however, that a simple modification of the index corrects these flaws. To demonstrate the tractability of our proposal, we apply it to baseball batting performance, in which zero outputs occur frequently.     

A Quasi-Malmquist Productivity Index

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of one-sided efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi-Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking.     

Axiomatic foundations of efficiency measurement on data-generated technologies

We assess the ability of three well-known technical efficiency indexes, the Debreu-Farrell index, the Färe–Lovell index, and the Zieschang index, to satisfy the Färe–Lovell axioms and continuity axioms (for technologies as well as input quantities) on the class of technologies generated by standard mathematical-programming methods of measuring efficiency: data envelopment analysis (DEA) and free-disposal-hull (FDH) analysis. Our principal conclusions are that (a) restriction to these data-based technologies adds continuity in input quantities to the properties satisfied by the Färe–Lovell and the Zieschang indexes (thus eliminating a salient advantage of the Debreu–Farrell index), but (b) none of the indexes satisfies all Färe–Lovell axioms (nor all continuity axioms) on either DEA or FDH technologies, and hence (c) trade-offs among the indexes remain. These findings provide motivation for the search for an index that does satisfy these axioms on DEA and FDH technologies.     

Optimal rules and robust Bayes estimation of a Gamma scale parameter

For estimating an unknown scale parameter of Gamma distribution, we introduce the use of an asymmetric scale invariant loss function reflecting precision of estimation. This loss belongs to the class of precautionary loss functions. The problem of estimation of scale parameter of a Gamma distribution arises in several theoretical and applied problems. Explicit form of risk-unbiased, minimum risk scale-invariant, Bayes, generalized Bayes and minimax estimators are derived. We characterized the admissibility and inadmissibility of a class of linear estimators of the form $cX\,{+}\,d$ , when $X\sim \varGamma (\alpha ,\eta )$ . In the context of Bayesian statistical inference any statistical problem should be treated under a given loss function by specifying a prior distribution over the parameter space. Hence, arbitrariness of a unique prior distribution is a critical and permanent question. To overcome with this issue, we consider robust Bayesian analysis and deal with Gamma minimax, conditional Gamma minimax, the stable and characterize posterior regret Gamma minimax estimation of the unknown scale parameter under the asymmetric scale invariant loss function in detail.     

Communications About Resilience Enhancing Activities By English Local Authorities

Abstract

The Civil Contingencies Act (2004 Civil Contingencies Act. 2004. Contingency Planning Regulations 2005, London: The Stationery Office. No. 2042 Statutory Instruments [Google Scholar]) in the United Kingdom introduced new responsibilities for public authorities regarding Business Continuity Management (BCM) and other emergency planning activities. Using content analysis techniques, this study examined thirty-four English county councils' websites to examine the extent to which this online medium communicated these new responsibilities to stakeholders. Using key-word-in-context (KWIC) and content clustering, this exploratory study found that local authorities' websites were far from generic in their web-based communications about their new Civil Contingencies Act responsibilities and BCM activities, and it reveals a number of differing website traits, motivations and orientations.     

An aggregate quantity framework for measuring and decomposing productivity change

Total factor productivity (TFP) can be defined as the ratio of an aggregate output to an aggregate input. This definition naturally leads to TFP indexes that can be expressed as the ratio of an output quantity index to an input quantity index. If the aggregator functions satisfy certain regularity properties then these TFP indexes are said to be multiplicatively complete. This paper formally defines what is meant by completeness and reveals that (1) the class of multiplicatively complete TFP indexes includes Laspeyres, Paasche, Fisher, T?rnqvist and Hicks-Moorsteen indexes, (2) the popular Malmquist TFP index of Caves et al. (Econometrica 50(6):1393?C1414, 1982a) is incomplete, implying it cannot always be interpreted as a measure of productivity change, (3) all multiplicatively complete TFP indexes can be exhaustively decomposed into measures of technical change and efficiency change, and (4) the efficiency change component can be further decomposed into measures of technical, mix and scale efficiency change. Artificial data are used to illustrate the decomposition of Hicks-Moorsteen and Fisher TFP indexes.     

Note on the existence and modulus of continuity of the {\textit{SLE}}_8 curve

We review one method for estimating the modulus of continuity of a Schramm–Loewner evolution (SLE) curve in terms of the inverse Loewner map. Then we prove estimates about the distribution of the inverse Loewner map, which underpin the difficulty in bounding the modulus of continuity of SLE for $\kappa =8$ . The main idea in the proof of these estimates is applying the Girsanov theorem to reduce the problem to estimates about one-dimensional Brownian motion.     

A directional slacks-based measure of technical inefficiency

Radial measures of efficiency estimated using linear programming (LP) methods can be biased since slack in the constraints defining the technology suggests that at least one input can be reduced, or one output can be expanded, even though a firm is deemed to be “technically efficient.” In this paper, we propose a directional slacks-based measure of technical inefficiency to account for the potential of slack in technological constraints. When no such slacks exist, directional slacks-based inefficiency collapses to the directional technology distance function. Our proposed measure helps to generalize some of the existing slacks-based measures of inefficiency. We examine the financial services provided by Japanese cooperative Shinkin banks, and estimate their inefficiency during the period 2002–2005. This inefficiency declined slightly during the period. We thus propose that slack is an important source of inefficiency which is often not captured by the directional technology distance function.     

Stochastic comparisons of distorted distributions,coherent systems and mixtures with ordered components

A distribution function F is a generalized distorted distribution of the distribution functions \(F_1,\ldots ,F_n\) if \(F=Q(F_1,\ldots ,F_n)\) for an increasing continuous distortion function Q such that \(Q(0,\ldots ,0)=0\) and \(Q(1,\ldots ,1)=1\). In this paper, necessary and sufficient conditions for the stochastic (ST) and the hazard rate (HR) orderings of generalized distorted distributions are provided when the distributions \(F_1,\ldots ,F_n\) are ordered. These results are used to obtain distribution-free ordering properties for coherent systems with heterogeneous components. In particular, we determine all the ST and HR orderings for coherent systems with 1–3 independent components. We also compare systems with dependent components. The results on distorted distributions are also used to get comparisons of finite mixtures.     

Test by adaptive LASSO quantile method for real-time detection of a change-point

This article proposes a test statistic based on the adaptive LASSO quantile method to detect in real-time a change in a linear model. The model can have a large number of explanatory variables and the errors don’t satisfy the classical assumptions for a statistical model. For the proposed test statistic, the asymptotic distribution under \(H_0\) is obtained and the divergence under \(H_1\) is shown. It is shown via Monte Carlo simulations, in terms of empirical sizes, of empirical powers and of stopping time detection, that the useful test statistic for applications is better than other test statistics proposed in literature. Two applications on the air pollution and in the health field data are also considered.     

On theE-optimality of certain asymmetrical designs under mixed effects model

TheE-optimality of the following designs within the class of all proper and connected designs with givenb, k andv under mixed effects model are established.

1. A group divisible design with λ₂ = λ₁ + 1.
2. A group divisible design with λ₁ = λ₂ + 1 and group size 2.
3. A linked block design.
4. The dual of design (i)
5. The dual of design (ii).

All these designs are known to satisfy the same optimality property under fixed effects model whenk<v, while the design (i) is known to beE-optimal even whenk>v. From the results proved here, theE-optimality of designs (ii, (iii), (iv) and (v) under fixed effects model in the situation whenk >v also follows.     

Human resource development of professionals in an emerging economy: the case of the Tanzanian construction industry

The issues pertaining to human resource development (HRD) of professionals1 1 The term ‘professional’ is used in this paper to refer to architects, engineers and quantity surveyors who work in managerial and/or professional roles in construction and construction related firms in the Tanzanian construction industry. in emerging/developing economies have not received sufficient attention in the literature. This is in spite of the strategic importance of the role of competent professionals in economic development. Using the construction industry in Tanzania as a case study, this study provides a review of the extent of the neglect of HRD for professionals in emerging/developing economies and what needs to be done to address the problem. In particular, it explores why there is no systematic integrated industry-wide training programme for professionals in the industry. It reveals that the existing programmes are fragmented and lack overall strategy and continuity, coordination and sustainable funding. The lack of sustainable funding is identified as the main obstacle to both the creation and sustainability of a training programme for professionals. To overcome this problem, the study suggests the establishment of an industry-specific training levy for professionals. But it warns that in an emerging/developing country environment there is the need to ensure that both the training programme and the administration of finance are not derailed by bureaucratic bottlenecks and other constraints, such as corruption. This study is of both organization and public policy relevance and, in additions, attempts to fill the gap (indicated above) in the HRD literature.     

Notes on consistency of some minimum distance estimators with simulation results

We focus on the minimum distance density estimators \({\widehat{f}}_n\) of the true probability density \(f_0\) on the real line. The consistency of the order of \(n^{-1/2}\) in the (expected) L\(_1\)-norm of Kolmogorov estimator (MKE) is known if the degree of variations of the nonparametric family \(\mathcal {D}\) is finite. Using this result for MKE we prove that minimum Lévy and minimum discrepancy distance estimators are consistent of the order of \(n^{-1/2}\) in the (expected) L\(_1\)-norm under the same assumptions. Computer simulation for these minimum distance estimators, accompanied by Cramér estimator, is performed and the function \(s(n)=a_0+a_1\sqrt{n}\) is fitted to the L\(_1\)-errors of \({\widehat{f}}_n\) leading to the proportionality constant \(a_1\) determination. Further, (expected) L\(_1\)-consistency rate of Kolmogorov estimator under generalized assumptions based on asymptotic domination relation is studied. No usual continuity or differentiability conditions are needed.     

On interdisciplinary movements: The development of a network of support around Foucaultian perspectives in accounting research

Abstract

This paper seeks to better understand interdisciplinary movements in the making. Our investigation focuses on the processes through which a network of support surrounding Michel Foucault's ideas originally developed in the sociological and organizational stream of accounting research. Drawing on the sociology of translation, we first examine how a network of support emerged around the journal Accounting, Organizations and Society (AOS), which is generally perceived as the main vector of dissemination of sociological and organizational accounting research. Our investigation then focuses on how Foucault's ideas, a few years after the founding of AOS, came to the attention of a group of accounting academics in the UK – a group in which the editor-in-chief of AOS was a key actor. We also examine how a network of support surrounding Foucault's ideas subsequently developed in the greater accounting research community. Our analysis emphasizes the role of epistemological uncertainty in the constitution of networks of support around journals and ideas, and the role of trials of strength (Latour, 1987 Latour, B. 1987. Science in Action, Cambridge, MA: Harvard University Press.  [Google Scholar]) in fuelling or mitigating this uncertainty, thereby influencing actors' interests and commitments to particular networks. Our analysis also highlights the critical role that imitation and social differentiation play in the travel of ideas between scientific fields and the creation of scientific knowledge.     

The effect of the regularity of the error process on the performance of kernel regression estimators

This article considers estimation of regression function $f$ in the fixed design model $Y(x_i)=f(x_i)+ \epsilon (x_i), i=1,\ldots ,n$ , by use of the Gasser and Müller kernel estimator. The point set $\{ x_i\}_{i=1}^{n}\subset [0,1]$ constitutes the sampling design points, and $\epsilon (x_i)$ are correlated errors. The error process $\epsilon $ is assumed to satisfy certain regularity conditions, namely, it has exactly $k$ ( $=\!0, 1, 2, \ldots $ ) quadratic mean derivatives (q.m.d.). The quality of the estimation is measured by the mean squared error (MSE). Here the asymptotic results of the mean squared error are established. We found that the optimal bandwidth depends on the $(2k+1)$ th mixed partial derivatives of the autocovariance function along the diagonal of the unit square. Simulation results for the model of $k$ th order integrated Brownian motion error are given in order to assess the effect of the regularity of this error process on the performance of the kernel estimator.     

GRAS versus minimizing absolute and squared differences: a comment

Junius and Oosterhaven (2003) Junius, T. and Oosterhaven, J. 2003. The solution of updating or regionalizing a matrix with both positive and negative entries. Economic Systems Research, 15: 87–96. [Taylor & Francis Online] [Google Scholar] developed the GRAS algorithm that minimizes the information gain when updating input–output tables with both positive and negative signs. Jackson and Murray (2004) Jackson, R. W. and Murray, A. T. 2004. Alternative input–output matrix updating formulations. Economic Systems Research, 16: 135–148. [Taylor & Francis Online] [Google Scholar], however, claim that minimizing squared differences in coefficients produces a smaller information gain, which is theoretically impossible. In this comment, calculation errors are sorted out from differences in measures, and it is shown that the information gain needs to be taken in absolute terms when increasing and decreasing cell values occur together. The numerical results show that GRAS outperforms both sign-preserving alternatives in all but one comparison of lesser economic importance. Moreover, as opposed to the result of Jackson and Murray, they show that minimizing absolute differences consistently outperforms minimizing squared differences, which overweighs large errors in small coefficients.