MATRIX BALANCING UNDER CONFLICTING INFORMATION

We have developed a generalised iterative scaling method (KRAS) that is able to balance and reconcile input–output tables and SAMs under conflicting external information and inconsistent constraints. Like earlier RAS variants, KRAS can: (a) handle constraints on arbitrarily sized and shaped subsets of matrix elements; (b) include reliability of the initial estimate and the external constraints; and (c) deal with negative values, and preserve the sign of matrix elements. Applying KRAS in four case studies, we find that, as with constrained optimisation, KRAS is able to find a compromise solution between inconsistent constraints. This feature does not exist in conventional RAS variants such as GRAS. KRAS can constitute a major advance for the practice of balancing input–output tables and Social Accounting Matrices, in that it removes the necessity of manually tracing inconsistencies in external information. This quality does not come at the expense of substantial programming and computational requirements (of conventional constrained optimisation techniques).     

The RAS Approach in Updating Input–Output Matrices: An Instrumental Variable Interpretation and Analysis of Structural Change

The main purposes of the paper are to reconsider the rationale of the RAS method, and to attempt to improve on its interpretation and usefulness. The substitution and fabrication factors in the RAS method are interpreted as statistical estimates obtained by the method of instrumental variables. This enables the computation of asymptotic standard errors for the factors and the relative precision of the predicted technical coefficients. Furthermore, an adjustment cost minimization model to describe how a sector determines its substitution and fabrication factors is presented. The solutions of the model provide another rationale for the RAS method, and the associated Lagrangian multipliers can be useful for assessing structural constraints and structural change.     

Using Weighted Least Squares to Deflate Input–Output Tables

This article proposes a balancing procedure for the deflation of input–output (I-O) tables from the viewpoint of users. This is a ‘subjective’ variant of the Weighted Least Squares (WLS) method, already known in the literature. It is argued that it is more flexible than other methods, and it is shown that SWLS subsumes the first-order approximation of RAS as a special case. Flexibility is due to the facts that (a) users can attach differential ‘reliability’ weights to first (unbalanced) estimates, depending on the confidence they have in the different parts of their pre-balancing work, (b) differently from RAS, one is not bound to take any row or column total as exogenously given, and (c) additional constraints can be added to it. The article describes also how SWLS was utilised to estimate a yearly (1959–2000) series of constant-price I-O tables for the Italian economy.     

On estimating trade flows in interregional input output models

Non-survey techniques have previously been devised for adjusting regional technical requirements matrices so as to account for commodity imports. Surrogates such as the location quotient have been utilised for estimating trading coefficients in a regional input output table. Extensions of these techniques to an interregional system are generally considered. It is shown that non-survey techniques are conceptually improved as a result of this extension. Particular regard is given to calibration methods that achieve consistency between estimates of exports and imports within an interregional system. The RAS method and some variants are compared and an additive algorithm is demonstrated to be efficient for this purpose.     

Estimating International Interindustry Linkages: Non-survey Simulations of the Asian-Pacific Economy

This paper evaluates a recently published semi-survey international input–output table for nine East-Asian countries and the USA with four non-survey estimation alternatives. A new generalized RAS procedure is used with stepwise increasing information from both import and export statistics as optimisation constraints on the four non-survey tables. The results show that the estimated table improves when increasing information from both sources is used, despite the well known inconsistencies between import and export data in trade statistics. It is concluded that the new procedure can be useful as a critical analysis of newly published (semi-)survey international tables and/or as an early updating tool during the construction process.     

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.     

Updating and Estimating a Social Accounting Matrix Using Cross Entropy Methods

The problem in estimating a social accounting matrix (SAM) for a recent year is to find an efficient and cost-effective way to incorporate and reconcile information from a variety of sources, including data from prior years. Based on information theory, the paper presents a flexible 'cross entropy' (CE) approach to estimating a consistent SAM starting from inconsistent data estimated with error, a common experience in many countries. The method represents an efficient information processing rule-using only and all information available. It allows incorporating errors in variables, inequality constraints, and prior knowledge about any part of the SAM. An example is presented, applying the CE approach to data from Mozambique, using a Monte Carlo approach to compare the CE approach to the standard RAS method and to evaluate the gains in precision from utilizing additional information.     

A comparison of shift-share and the RAS adjustment

It is argued that the RAS procedure applied to regions and industries performs a function similar to that of the shift-share technique, and that RAS has the advantage of a justification based on concepts from information theory.     

Completing Input–Output Tables using Partial Information,with an Application to Canadian Data

This paper develops a three-stage extension of the standard biproportional RAS algorithm-an extension that we label TRAS-to incorporate information in addition to row and column margins. The TRAS algorithm is tested using pseudo-censored input–output tables and is shown to produce more accurate estimates than does the RAS algorithm.     

An Algorithm for the Consistent Inclusion of Partial Information in the Revision of Input-Output Tables

TRAS is a natural extension of RAS that utilizes information in addition to row and column totals to produce updated matrices that are consistent with known cells and aggregates of known cells. This paper provides a simple restatement of the TRAS algorithm developed in Gilchrist & St. Louis (1999) and then tests its effectiveness by applying TRAS to the matrices obtained after RAS adjustments have been completed. The incremental gains from the TRAS adjustments were statistically significant.     

Estimation and inference under economic restrictions

Estimation of economic relationships often requires imposition of constraints such as positivity or monotonicity on each observation. Methods to impose such constraints, however, vary depending upon the estimation technique employed. We describe a general methodology to impose (observation-specific) constraints for the class of linear regression estimators using a method known as constraint weighted bootstrapping. While this method has received attention in the nonparametric regression literature, we show how it can be applied for both parametric and nonparametric estimators. A benefit of this method is that imposing numerous constraints simultaneously can be performed seamlessly. We apply this method to Norwegian dairy farm data to estimate both unconstrained and constrained parametric and nonparametric models.     

On input-output type output multipliers from incomplete information

Incomplete knowledge of data usually hinders the establishment of detailed input-output tables. It is for this reason that up-dating procedures (RAS) as well as short-cut methods have been developed. In this paper the short-cut output multiplier formula by Drake (1976) is compared with the output multiplier involved in the RAS procedures. It will turn out that both these output multiplier estimates are two special cases of a more general class of estimating procedures. It is demonstrated by an empirical example how this generalized procedure should be applied in practice. The kind of reasoning underlying this paper can be extended to other problems of input-output analysis as well.     

Computing equilibria in dynamic models with occasionally binding constraints

We propose a method to compute equilibria in dynamic models with several continuous state variables and occasionally binding constraints. These constraints induce non-differentiabilities in policy functions. We develop an interpolation technique that addresses this problem directly: It locates the non-differentiabilities and adds interpolation nodes there. To handle this flexible grid, it uses Delaunay interpolation, a simplicial interpolation technique. Hence, we call this method Adaptive Simplicial Interpolation (ASI). We embed ASI into a time iteration algorithm to compute recursive equilibria in an infinite horizon endowment economy where heterogeneous agents trade in a bond and a stock subject to various trading constraints. We show that this method computes equilibria accurately and outperforms other grid schemes by far.     

基于Lingo和Matlab的空间桁架结构联合优化设计

本文研究了位移和应力约束下桁架结构的尺寸优化设计问题。首先,基于Matlab的有限元分析和符号计算功能,采用近似方法得到位移约束的显式函数,再结合桁架结构应力约束的计算公式,构造优化设计的数学模型,最后,采用Lingo和Matlab软件分别进行优化求解。数值算例的结果表明,两种方法得到的优化结果完全一致,都能明显的减轻设计结构的重量,且方法简单,易实施。     

企业社会责任信息披露能缓解融资约束吗？——基于A股上市公司的实证分析

目前,国内对于企业社会责任信息披露实施后果的研究还为数不多。本文从融资约束这一视角进行实证研究,以2010~2011年Ａ股上市公司为样本,考察了企业社会责任信息披露缓解融资约束的能力。研究结果显示,企业社会责任信息披露质量越高,面临的融资约束程度越低,并且企业社会责任信息披露缓解融资约束程度还受所有权性质和所在区域的影响。     

A MULTI-OBJECTIVE ASSESSMENT OF INPUT–OUTPUT MATRIX UPDATING METHODS

This paper shows that important insights can be lost when assessing the relative performance of balancing methods solely based on individual optima. This is demonstrated through a multi-objective assessment. A trade-off curve between RAS and sign-preserving absolute differences (SPAD) is obtained based on the 60×60 Norwegian 2001 input–output table. The trade-off curve takes on a form that is close to a step function. This demonstrates that the solution surface around the RAS and SPAD optimums are very flat. Solutions can be identified that improve on the other objective or measure with little or marginal cost to the original objective function. Motivation for the assessment is provided, the technique applied is presented and the implications of the findings are discussed in an input–output and industrial ecology context.     

Increasing the Timeliness of US Annual Input-Output Accounts

The timeliness of the US input-output (I-O) accounts is a major concern for policymakers and industry analysts, as well as academics. In response, the Bureau of Economic Analysis initiated research in 2001 to identify, develop and implement an estimating method for producing more timely and reliable annual I-O accounts than are currently available. The research included reviewing the frameworks and methods currently used by other statistical agencies and academic researchers, obtaining more timely industry source data, and developing enhanced methods and processes for the automated updating and balancing of annual I-O tables. The results of this research indicate that our new automated updating and balancing method can reduce the time lag for producing the annual I-O accounts from three years to one year without reducing quality. Our method is based on an adjusted RAS process that simultaneously balances the I-O table in producers' and purchasers' prices; uses more exogenous data; and processes tables at the most detailed level.     

Lingo和1stOpt在结构优化设计中的应用比较

本文研究了位移、应力和稳定约束下桁架结构的尺寸优化设计问题。首先,基于Matlab的有限元分析和符号计算功能,采用近似方法得到位移约束的显式函数,再结合桁架结构应力约束的计算公式,构造优化设计的数学模型,最后,采用Lingo和1stOpt软件对该问题分别进行优化求解并予以比较。数值算例的结果表明,两种方法得到的优化结果一致,都能明显的减轻设计结构的重量,且方法简单,易实施,但两种软件各有优缺点。     

Macro‐integration with inequality constraints: an application to the integration of transport and trade statistics

Macro‐integration is the process of combining data from several sources at an aggregate level. We review a Bayesian approach to macro‐integration with special emphasis on the inclusion of inequality constraints. In particular, an approximate method of dealing with inequality constraints within the linear macro‐integration framework is proposed. This method is based on a normal approximation to the truncated multivariate normal distribution. The framework is then applied to the integration of international trade statistics and transport statistics. By combining these data sources, transit flows can be derived as differences between specific transport and trade flows. Two methods of imposing the inequality restrictions that transit flows must be non‐negative are compared. Moreover, the figures are improved by imposing the equality constraints that aggregates of incoming and outgoing transit flows must be equal.     

BENCHMARKING LARGE ACCOUNTING FRAMEWORKS: A GENERALIZED MULTIVARIATE MODEL

We present a multivariate benchmarking model for achieving consistency between large quarterly and annual accounting frameworks. The method is based on a quadratic optimization problem, for which many efficient numeric solvers exist. The method combines several features, such as linear constraints, ratio constraints, weights, and inequalities, in one model. Therefore, a wide range of modelling possibilities is supported. This method is especially interesting for national statistical offices, to simplify their processes to achieve consistency between publications.