MULTIPLICATIVE DECOMPOSITION AND INDEX NUMBER THEORY: AN EMPIRICAL APPLICATION OF THE SATO–VARTIA DECOMPOSITION

In de Boer (2008), additive decompositions of aggregate changes in a variable into its factors were considered. We proposed using the ‘ideal’ Montgomery decomposition, developed in index number theory as an alternative to the commonly used methods in structural decomposition analysis, and applied it to the example analyzed by Dietzenbacher and Los (1998) (D&L). In this paper we consider multiplicative decompositions and show that the method proposed by D&L of taking the geometric mean of all elementary decompositions is ‘ideal’. However, it requires the computation of an ever-increasing number of decompositions when the number of factors increases. As an alternative, we propose using the Sato–Vartia decomposition, which is also ‘ideal’, but requires the computation of only one decomposition. Application to the example of D&L reveals that the two methods yield results that are very close to each other.     

Decomposing profit change: Konüs,Bennet and Luenberger indicators

We introduce complementary decompositions of profit change that, relying on the duality between the profit function and the directional distance function, shed light on the different sources of profit growth including measures of technical efficiency, allocative efficiency and technological change. Our decompositions extend the literature on Konüs and Bennet quantity and price indicators to profit change. The first decomposition is ‘exact’ in the sense of Diewert, by completely exhausting the sources of profit change into profit inefficiency change (including technical and allocative inefficiency change), technological change, and output and input price change. The second decomposition equates the Bennet quantity indicator to a productivity measure represented by the Luenberger indicator plus allocative inefficiency change. We deem it ‘complete’ because in contrast to the existing literature, it retains the information on allocative inefficiency change while preventing the existence of residual terms capturing price variations, whose meaningful interpretation has not been addressed until now. Our proposed solution takes advantage of the flexibility of the directional distance function when choosing a suitable directional vector. All decompositions have the same structural form and therefore their components can be compared to each other vis-à-vis, providing alternative measures of equivalent sources of profit growth.     

Short-Run Dynamics in Cointegrated Systems

In this paper we build a unifying framework under which the time-domain properties of the permanent-transitory decompositions available in the literature are investigated. Starting from the state space representation of a cointegrated system expressions are derived for the (common) trends and cycles of the Beveridge–Nelson decomposition involving quantities already available from the interim multiplier representation. The cycles result from both movements along the attractor and adjustment dynamics; the latter are shown to be the transitory component of the Gonzalo–Granger decomposition. The two decompositions are equivalent when the number of common cycles and trends add up to the dimension of the system. Algorithms for the extraction of the components are given and the results are illustrated with respect to a trivariate system consisting of US per capita GNP, Private Consumption and Investment.     

On the Decomposition by Subgroups of the Gini Index and Zenga's Uniformity and Inequality Indexes

Besides a brief historical outline of the Gini index decomposition proposals, we compare, in a subgroups framework, the decompositions of the Gini index and of the uniformity and inequality indexes recently proposed by Zenga. The two decompositions follow a similar scheme: in both cases the overall index can be at first expressed as a weighted average of convenient "cross" measures, with their own interpretation, and afterwards it is decomposed into a within and a between term by merely distinguishing measures evaluated within the same subgroup from the ones regarding different subgroups. This procedure does not depend on an a priori definition of the within or the between term and allows their contribution to be naturally evaluated preserving the structure of the index itself. In the last section the two decompositions are applied to the Italian net household wealth provided by the 2006 central Bank of Italy sample survey on household budgets.     

Additive Structural Decomposition Analysis and Index Number Theory: An Empirical Application of the Montgomery Decomposition

In recent years, a large number of empirical articles on structural decomposition analysis, which aims at disentangling an aggregate change in a variable into its r factors, has been published in this journal. Commonly used methods are the average of the two polar decompositions and the average of all r! elementary decompositions (Dietzenbacher and Los, 1998 Dietzenbacher, E. and Los, B. 1998. Structural decomposition techniques: sense and sensitivity. Economic Systems Research, 10: 307–323. [Taylor & Francis Online] [Google Scholar], D&L). We propose to use instead the ‘ideal’ Montgomery decomposition, which means that it satisfies the requirement of factor reversal imposed in index number theory. We prefer it to the methods previously mentioned. The average of the two polar decompositions is not ‘ideal’, so that the outcome depends on the ordering of the factors. The average of all elementary decompositions is ‘ideal’, but requires the computation of an ever increasing number of decompositions when the number of factors increases. Application to the example of D&L (four factors) shows that the three methods yield results that are close to each other.     

The Decomposition of Malmquist Productivity Indexes

Two different Malmquist productivity indexes have been proposed. One I call partially oriented because it is either output- or input-oriented, and the other is simultaneously output- and input-oriented. The partially oriented Malmquist index owes some of its popularity to the fact that it has been decomposed to isolate various sources of productivity change. Conversely, the simultaneously oriented Malmquist index has not achieved popularity in part because it has not been decomposed. In this paper I evaluate alternative decompositions of the partially oriented Malmquist index, and I obtain a new decomposition of the simultaneously oriented Malmquist index. This new decomposition leads me to conclude that the latter index is deserving of greater attention than it has received to date.     

Isometric operators on Hilbert spaces and Wold decomposition of stationary time series

Wold Theorem plays a fundamental role in the decomposition of weakly stationary time series. It provides a moving average representation of the process under consideration in terms of uncorrelated innovations, whatever the nature of the process is. From an empirical point of view, this result enables to identify orthogonal shocks, for instance in macroeconomic and financial time series. More theoretically, the decomposition of weakly stationary stochastic processes can be seen as a special case of the Abstract Wold Theorem, that allows to decompose Hilbert spaces by using isometric operators. In this work we explain this link in detail, employing the Hilbert space spanned by a weakly stationary time series and the lag operator as isometry. In particular, we characterize the innovation subspace by exploiting the adjoint operator. We also show that the isometry of the lag operator is equivalent to weak stationarity. Our methodology, fully based on operator theory, provides novel tools useful to discover new Wold-type decompositions of stochastic processes, in which the involved isometry is no more the lag operator. In such decompositions the orthogonality of innovations is ensured by construction since they are derived from the Abstract Wold Theorem.     

Bayesian non-parametric signal extraction for Gaussian time series

We consider the problem of unobserved components in time series from a Bayesian non-parametric perspective. The identification conditions are treated as unknown and analyzed in a probabilistic framework. In particular, informative prior distributions force the spectral decomposition to be in an identifiable region. Then, the likelihood function adapts the prior decompositions to the data.     

Significant drivers of growth in Africa

We employ bootstrap techniques in a production frontier framework to provide statistical inference for each component in the decomposition of labor productivity growth, which has essentially been ignored in this literature. We show that only two of the four components (efficiency changes and human capital accumulation) have significantly contributed to growth in Africa. Although physical capital accumulation is the largest force, it is not statistically significant on average. Thus, ignoring statistical significance would falsely identify physical capital accumulation as a major driver of growth in Africa when it is not.     

Structural information in recursive VAR orderings

This paper investigates structural models that will permit a Cholesky decomposition of the covariance matrix of VAR residuals to identify some structural impulse response functions. Cholesky decompositions are found to be useful identification tools for the set of partially recursive structural models. A partially recursive structure is defined as any block recursive system where the equations in one block can be recursively ordered and where the structural shocks are uncorrelated. Using this class of models, we derive necessary and sufficient conditions for the moving average representation from a Cholesky decomposition to identify structure. The paper concludes by discussing implications of these results for empirical research.     

Robust growth-equity decomposition of change in poverty: The case of Iran (2000–2009)

This paper examines a robust nonparametric methodology for decomposition of change in poverty into growth and redistribution components. The decomposition is exact, symmetric and free of residual terms. It is equivalent to the Shapley value decomposition in this two-component case. We avoid parametric assumptions about the underlying distributions and Lorenz functions. All of the currently popular poverty measures may be decomposed as suggested in this paper. We identify the issues that arise with parametric approaches to decomposition. An empirical application is given based on recent data on real consumption in rural and urban areas of Iran in 2000, 2004 and 2009 (covering the country's third and fourth five-year development plans). We find that both ‘pure growth’ and ‘redistribution’ components are present in a striking change in poverty, especially among rural households. It would appear that stochastic dominance rankings of the consumption distributions make poverty analyses and decompositions robust to the choice of a poverty line, or poverty measure.     

An application of model-based estimation of unobserved components

The paper analyzes a real-world application of an ARIMA-based trend/seasonal/irregular estimation. The analysis illustrates two points of applied interest. First, it is seen how the decomposition of ARIMA models is sensitive to changes in the specification of the overall model. Alternative ARIMA models, which yield similar fits and forecasts, may produce remarkably different decompositions. Second, it is shown how the model-based approach provides tools for interpretation of the results. In particular, the comparison between the empirical autocorrelation of the estimated components and the theoretical autocorrelations of the model-based estimators can be used as an overall diagnostic check.     

Using Additional Information in Structural Decomposition Analysis: The Path-based Approach

Structural decomposition analysis (SDA) is a well-known methodology to assess the relative importance of effects that together constitute the actual change in a variable of interest. A widely recognized problem of SDA is that the results often depend strongly on the specific decomposition formula chosen, while numerous formulae are equivalent from a theoretical point of view. This ‘non-uniqueness’ problem is often solved rather pragmatically, by reporting an average over (a subset of) all possible formulae. In this paper, we propose an approach that uses maximum entropy econometrics techniques to select a specific decomposition formula if additional information on one or more (but not all) determinants is available. We illustrate the method empirically by investigating the sources of change in real labour costs by industry in Spain, 1980–1994.     

Input–Output Structural Decomposition Analysis: A Critical Appraisal

Over the past decade, input–output structural decomposition analysis (SDA) has developed into a major analytical tool. We review the development of SDA and its relationship to other methodologies. We present the fundamental principles of alternative approaches to deriving SDA estimating equations and explore the various decompositions of changes in IO tables. We also identify several complications and unresolved issues. Most importantly, we find that a rigorous grounding in economic theory is lacking for SDA, but we are able to offer some suggestions as to how it might be established.     

A nonparametric decomposition of the Mexican American average wage gap

This paper shows that average wage gap decompositions between any two groups of workers can be carried out using nonparametric wage structures. It also proposes an algorithm to correct for sample selection in nonparametric models known as tree structures. This paper studies the wage gap between third‐generation Mexican American and non‐Hispanic white workers in the southwest. It is shown that the decomposition heavily depends on functional assumptions, and that different aproaches to flexibility may render sufficiently good and similar results Copyright © 2008 John Wiley & Sons, Ltd.     

A Structural Decomposition Analysis of Pollution in the Netherlands

This paper reviews the results of a structural decomposition analysis in which the annual changes in a number of air pollutants and solid waste are decomposed according to their causes. The analysis in this paper is applied with the help of the so-called National Accounting Matrix including Environmental Accounts (NAMEA) for the Netherlands, covering annual data for the period 1987-1998. In a sensitivity analysis it is shown that the average of any pair of so-called 'mirror image' decomposition forms will substantially reduce the variation in the estimates. These mirror image couples are approximately just as reliable as the full average of all decomposition forms. Besides reliable results, the full average also foresees the mutual comparability between the distinguished change factors and is therefore applied in the empirical analyses presented in this paper. The results of these analyses contain the macro-economic developments, results on the industry level as well as a comprehensive overview of the origin and destination of pollution in the Dutch economy that includes the environmental consequences of consumption and international trade.     

Irregular workloads with MRP systems: Some causes and consequences

Material Requirements Planning (MRP) systems have been widely applied in industry to better manage multiproduct, multistage production environments. Although many applications have been quite successful, much is still left to the planner's intuition as to how to assure that master schedules, component lot sizes, and priorities realistically conform to the capacity limits at individual work centers. Capacity issues may indeed be the soft spot in MRP logic.This paper explores some possible causes of irregular workload patterns when using an MRP system. Better insight on which factors cause temporary bottlenecks could help managers better assess the vulnerability of their plants to this problem. It might also suggest ways of dampening peaks and valleys. The problem setting is a multistage environment; several products are made from various subassemblies and parts. Each shop order is routed through one or more capacitated work centers. An order is delayed either by temporary capacity shortages or the unavailability of components. Of course, the second delay can be caused by capacity problems previously encountered by the shop orders of its components.Seven experimental factors are tested with a large-scale simulator, and five performance measures are analyzed. The factors are the number of levels in the bill of material, the average load on the shop, the average lot size, the choice of priority rule, demand variability, the use of a gateway department, and the degree of equipment specialization. We have one measure of customer service, two for inventory, and two for workload. The workload measures are unconventional, since our interest is when workload variability occurs and how it affects inventory and customer service.The simulator has been developed over the course of eight years, and since this study has been further enhanced to handle many more factors. The simulator was validated recently with real data at two manufacturing plants. It is quite general, in that the bills of material, shop configuration, routings, worker efficiencies, and operating rules can be changed as desired.An initial screening experiment was performed, whereupon the average load and priority rules were not statistically significant at even the .05 level. A full factorial analysis with two replications was then conducted on the five remaining factors. Multivariate analysis of variance (MANOVA) and analysis of variance (ANOVA) statistical tests have been performed.The results confirm that workload variability can have a detrimental impact on customer service and inventory. The following structural changes to the manufacturing system can be beneficial, but tend to be more difficult to achieve. More BOM levels improve customer service, but increase inventory and capacity bottlenecks. Resource flexibility is a powerful tool to reduce workload variability. Capacity slack averaging much over 10% is wasteful, having no benefits for inventory and customer service. In general, revising the routing patterns only, such as creating more dominant paths, will not give big payoffs. The following procedural changes are easier to implement. Master schedules which smooth aggregate resources are an excellent device to reduce workload variability. Even with a smooth MPS, debilitating workload variability can still occur due to the design of the BOM, lot size, and leadtime offset parameters. Selecting a priority rule does not seem to be of overriding importance compared to master scheduling and component lot sizing. These findings must be considered within the context of the range of plant environments encompassed by this study.     

Towards an Ontology of Intellectual Property:

A bstract . Many world views and complicated laws within a society have evolved from simpler forms. In general, this process works well. However, on occasion the original basis, no matter how well it worked at inception, does not work well in later, more complex, or different societies. One such case is that of the current law of intellectual property, which does not seem to adapt well to the introduction of new technologies. This paper explores this problem and its causes, and then proposes some possible changes that might, with minimal disruption, minimize many of these difficulties in the future.     

Multivariate Wold decompositions: a Hilbert A-module approach

Decisions in Economics and Finance - Orthogonal decompositions are essential tools for the study of weakly stationary time series. Some examples are given by the classical Wold decomposition of...     

Just vote no! Union–busting in the European fast–food industry: the case of McDonald’s

This paper examines the problem of effectively regulating the labour relations practices of multinational corporations. It focuses on the activities of the McDonald’s Corporation in a number of European countries. The findings suggest that public and private codes of conduct have a very limited effect and that determined and well–resourced corporations can not only undermine regional forms of regulation—such as that provided by the European Union—but also, and to a considerable extent, national–level regulation. This is particularly evident in the area of independent trade union representation. Although its aim of avoiding collective bargaining and union recognition wherever possible is only partially successful, McDonald’s appears to have developed a number of highly effective strategies for limiting the presence of trade unions at restaurant level, particularly in avoiding or undermining statutory works councils and union representation rights.