Biproportional Method Research Articles

Apportionment with parity constraints

In the classic apportionment problem, the goal is to decide how many seats of a parliament should be allocated to each party as a result of an election. The divisor methods solve this problem by defining a notion of proportionality guided by some rounding rule. Motivated by recent challenges in the context of electoral apportionment, we consider the question of how to allocate the seats of a parliament under parity constraints between candidate types (e.g., an equal number of men and women elected) while at the same time satisfying party proportionality. We study two different approaches to solve this question. We first provide a theoretical analysis of a recently devised mechanism based on a greedy approach. We then propose and analyze a mechanism that follows the idea of biproportionality introduced by Balinski and Demange. In contrast with the classic biproportional method by Balinski and Demange, this mechanism is ruled by two levels of proportionality: Proportionality is satisfied at the level of parties by means of a divisor method, and then biproportionality is used to decide the number of candidates allocated to each type and party. A typical benchmark used in the context of two-dimensional apportionment is the fair share (a.k.a matrix scaling), which corresponds to an ideal fractional biproportional solution. We provide lower bounds on the distance between these two types of solutions, and we explore their consequences in the context of two-dimensional apportionment.

Constructing Retrospective Time Series of Russian Input-Output Accounts Based on the NACE/CPA Classifications

Time series of Input-Output (IO) accounts at current and constant prices are widely applied to study the dynamics and structure of economic activity within country and conduct cross-country comparisons and analyses of globalization processes as well as their impacts. For these purposes IO accounts have to adhere to a uniform nomenclature of products and economic activities in accordance with international standards. Unfortunately, Russian statistics currently do not satisfy this condition. The first Russian IO accounts for 2011, built in accordance with international standards, will be published only at the end of 2015 (previously published tables for 1995-2003 were built in the classifications "inherited" from the Soviet period). The IO accounts for 2012 and subsequent years will be built by extrapolating the cost structure of products and services for 2011. However, it leaves the open question of extending the time series of these tables for the retrospective period prior to 2011. As international experience shows, this type of calculation was predominantly conducted by research organizations and universities. Given this, the National Research University Higher School of Economics has been developing a methodology for constructing a retrospective time series of a part of the IO accounts (use tables and valuation matrices) from 2010, in order to experimentally test them, and apply them to the official IO accounts for 2011. The following results were obtained from our study. First, we proposed a two-step procedure to transform IO accounts for 2003 from the Soviet into the OKVED/OKPD classifications. Second, we used a two-stage biproportional method generalizing the RAS procedure to construct a time series of IO accounts for the subsequent period using the 2003 transformed IO accounts as the starting point. Finally, we recalculated a part of the IO accounts (use tables) at the previous year prices.

A Bayesian Approach to the Balancing of Statistical Economic Data

This paper addresses the problem of balancing statistical economic data, when data structure is arbitrary and both uncertainty estimates and a ranking of data quality are available. Using a Bayesian approach, the prior configuration is described as a multivariate random vector and the balanced posterior is obtained by application of relative entropy minimization. The paper shows that conventional data balancing methods, such as generalized least squares, weighted least squares and biproportional methods are particular cases of the general method described here. As a consequence, it is possible to determine the underlying assumptions and range of application of each traditional method. In particular, the popular biproportional method is found to assume that all source data has the same relative uncertainty. Finally, this paper proposes a simple linear iterative method that generalizes the biproportional method to the data balancing problem with arbitrary data structure, uncertainty estimates and multiple data quality levels.

Normal People in Clinical Practice: A General Factor of Personality in Biproportional Scaling and Its Practical Relevance

To investigate the clinical relevance of absolute scaling in personality assessment, Hofstee and Ten Berge's (2004) biproportional scaling method was applied to 3 clinical samples and compared with relative scaling in traditional analyses. In the first sample, 80 psychotherapy clients provided self-reports as well as reports by 3 informants, resulting in 320 ratings of the Dutch short form of the MMPI (NVM). In the second sample, 96 psychotherapy clients provided self-reports and informant reports, resulting in 384 Five-Factor Personality Inventory (FFPI) ratings. In the third sample, 95 clients provided self-reports and informant reports, resulting in 380 ratings of the NEO Five-Factor Inventory (NEO–FFI). In Part I of the study, the personality structure based on biproportional scaling was examined by replicating Hofstee, Barelds, and Ten Berge (2006). In Part II, this personality structure as well as self-informant distances and self-informant likenesses were related to symptoms, personality pathology, and level of functioning. The results confirmed the presence of a general factor of personality in absolute scaling, which appears to reflect social fitness and the absence of severe psychopathology. This factor was significantly associated with fewer symptoms and better functioning in all 3 samples. The personality pathology results were only significant in the FFPI sample. Self-informant distance and self-informant likeness were primarily associated with symptoms. A relationship between poor social fitness and insecure early attachment was suggested in 3 case studies.

Joint estimation of supply and use tables

AbstractWe apply the RAS updating idea for the joint estimation of supply and use tables (SUTs). In contrast to standard input‐output techniques, our approach does not require the availability of total outputs by product for the projection year(s). This condition is usually not met in practice. The algorithm, called the SUT‐RAS method, jointly estimates SUTs that are immediately consistent. It is applicable to different settings of SUTs, such as the frameworks with basic prices and purchasers' prices, and a setting in which use tables are separated into domestic and imported uses. Our empirical evaluations show that the SUT‐RAS method improves upon existing short‐cut methods in projection of Spanish SUTs.ResumenAplicamos la idea de actualización con RAS para la estimación conjunta de cuadros de oferta y utilización (COU). En contraste con las técnicas estándar de input‐output, nuestro enfoque no requiere la disponibilidad del total de outputs por producto para el año(s) proyectado(s). En la práctica, esta condición normalmente no se satisface. El algoritmo, denominado método COU‐RAS, estima conjuntamente aquellos COU que son inmediatamente uniformes. Es aplicable a diferentes contextos de COU, tales como marcos con precios básicos y precios de comprador, y el caso en el que los cuadros de uso están separados entre usos interiores e importados. Nuestras evaluaciones empíricas muestran que el método SUT‐RAS representa una mejora respecto a métodos abreviados en la proyección de COU españoles.

Joint Estimation of Supply and Use Tables

We propose a new biproportional method specifically designed for joint projection of Supply and Use tables (SUTs). In contrast to standard input-output techniques, this method does not require the availability of total outputs by product for the projection year(s), a condition which is not often met in practice. The algorithm, called the SUT-RAS method, jointly estimates SUTs that are immediately consistent. It is applicable to different settings of SUTs, such as the frameworks with basic prices and purchasers’ prices, and a setting in which Use tables are separated into domestic and imported uses. Our empirical evaluations show that the SUT-RAS method performs quite well compared to widely used short-cut methods.

A bi-proportional method applied to the Spanish Congress

A bi-proportional divisor method is applied to allocate the seats of the 2004 Spanish Congress, thus achieving proportionality relative to the population counts in the fifty-two districts, as well as proportionality relative to the vote counts for the political parties. Also, advantages and disadvantages of the method are discussed.

Impacts of Aggregation on Relative Performances of Nonsurvey Updating Techniques And Intertemporal Stability of Input–Output Coefficients

In many instances, and for variety of reasons, input–output researchers are compelled to both employ mechanical techniques to update older survey-based tables as well as using more aggregated ones. This combination, however, gives rise to several concerns. The present paper is an attempt to investigate two such questions. First, the effects of aggregation on the accuracy ranking of selected updating methods, and second, the effects of aggregation on intertemporal stability of the input–output coefficients. To probe these issues, three updating methods were selected. These methods are NAIVE or constant coefficient hypothesis, RAS or biproportional method, and LaGrangian optimization technique. Two survey-based tables from the former Soviet Union along with the selected updating techniques are used to generate updated target year’s direct and inverse transaction matrices at four aggregation levels. Comparison of the resultant estimates at these four levels of aggregation with their counterparts in the actual benchmark table reveals that a higher level of aggregation neither affects the rankings of the updating methods nor does it universally and unequivocally leads to a higher degree of intertemporal stability of input–output coefficients.

Alternative Input-Output Matrix Updating Formulations

There has been a recent resurgence of interest in biproportional adjustment methods for updating and interpreting change in matrix representations of regional structures, most commonly input-output accounts. Although the biproportional method, commonly called the RAS technique in the input-output literature, has been shown to have a number of theoretically appealing properties, various alternatives do exist. In this paper, we develop and empirically assess a number of alternatives, comparing performance and examining the attributes of these adjustment methods. Two of these are sign-preserving updating methods for use when tables contain both positive and negative entries. One of these is shown to generate less information gain than does a generalized RAS method that Junius & Oosterhaven (2003) formulated to deal with matrices with both positive and negative values. Overall, while the RAS method continues to be commonly used and its choice is often rational, alternative methods can perform as well or better along certain dimensions and in certain contexts.

Input Coefficient Change Using Biproportional Econometric Adjustment Functions

This paper deals with the issue of updating input-output (I-O) coefficients within a large-scale disaggregated econometric macro-model of the Austrian economy. Capturing the changes in input coefficients over time is an important issue in I-O modelling due to a lack of recent benchmark I-O tables in most countries. Different approaches for updating these coefficients can be found in the literature, such as adjusting input coefficients 'along the row' and variable input coefficients 'along the column' stemming from factor input equations derived from production or cost functions. This paper combines these two approaches, yielding a biproportional method. For the adjustment, 'along the column' econometric factor input functions are used to derive a sum of non-energy intermediate inputs. For the adjustment 'along the row' the starting point is a set of adjustment functions described in the literature: special emphasis is placed on econometric specification and 'cointegration accounting'.

A note on a Lagrangian derivation of a general multi-propotional scaling algorithm

This note describes an efficient minimum information loss solution to the general multi-proportional updating problem. The method provides a robust algorithm which allows additional constraints on groups of elements on the interior of the matrix to be applied, and multi-regional economies to be adjusted simulteneously. A Lagrangian derivation of the scaling algorithm is presented, and the conditions for the existence, uniqueness and convergence of the iterative solutions are explained. The method overcomes restrictions on the bi-proportional method and its extensions.

Biproportional Method for Analysing Interindustry Dynamics: the Case of France

Two elements are being presented in this paper: (1) A new and original method for analysing matrix dynamics, called the synthetical biproportional projector method (SBP), which can be used to project input–output tables and compare one with another. (2) Some results for France for the important period 1970–85. The paper starts with the observation that no systematic study of the change in the French productive structure as displayed In the input–output tables (tableaux entries-sorties in France) has ever been made. This is unfortunate, since a complete series of data is now available concerning a key period of the French economic evolution including the petroleum crisis, European integration and so on. It thus appeared that such a study could be undertaken using an original method of intertemporal comparison of the 16 matrices corresponding to the period 1970–85. The method and some of the results are briefly summarized.

A direct method for speeding up the convergence of the furness biproportional method

This paper describes a direct non-iterative balancing technique which could be used as a complementary part to the Furness method to speed up the convergence to the final solution. This is particularly useful when the convergence of the Furness iterations is uneconomically slow and/or when high balancing accuracy is needed. The direct method however, might be used as a substitute to the Furness method in evaluating the consequences of a few alternative sets of small variations in the marginal totals of a two dimensional array.

Exploratory analyses of interregional migration tables: an Austrian example

Mackinnon R. D. and Skarke A. M. (1977) Exploratory Analyses of Interregional Migration Tables: an Austrian Example, Reg. Studies 11, 99–111. Four different techniques of a rather simple type are used to analyze recent interregional migration flows in Austria. Purely descriptive methods are used to reduce the large data set to proportions which facilitate interpretation. Methods of Markov and matrix growth operator type are used to project future spatial redistribution of population arising from both migration and differences in the rates of natural increase. A least squares approach is used to measure the attractiveness and emissiveness of regions based on a revealed preference rationale. Finally, the biproportional method of updating economic input-output and transportation origin-destination tables is used to generate the most plausible changes in migration propensities which would give rise to a specified target population distribution.