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.     

Biproportional Techniques in Input-Output Analysis: Table Updating and Structural Analysis

This paper introduces the rest of this issue of Economic Systems Research, which is dedicated to the contributions of Sir Richard Stone, Michael Bacharach, and Philip Israilevich. It starts out with a brief history of biproportional techniques and related matrix balancing algorithms. We then discuss the RAS algorithm developed by Sir Richard Stone and others. We follow that by evaluating the interpretability of the product of the adjustment parameters, generally known as R and S. We then move on to discuss the various formal formulations of other biproportional approaches and discuss what defines an algorithm as 'biproportional'. After mentioning a number of competing optimization algorithms that cannot fall under the rubric of being biproportional, we reflect upon how some of their features have been included into the biproportional setting (the ability to fix the value of interior cells of the matrix being adjusted and of incorporating data reliability into the algorithm). We wind up the paper by pointing out some areas that could use further investigation.     

投入产出表、社会核算矩阵的更新方法研究

本文将现有的众多矩阵更新技术纳入约束最优化的数学建模框架中,并统一进行了若干扩展,特别地,在约束条件存在冲突时通过引入误差精度调整项,使得原本不可行的矩阵更新问题能够求解,以扩大其适用范围。然后使用中国2002年和2007年的投入产出表对6种扩展修正后的矩阵更新方法进行了实证比较,结果显示无论是基于流量还是基于系数形式,或是对矩阵进行聚合处理,更新矩阵时ERAS的表现始终是最优的,ENSD其次,两者差距较小;而EAD方法表现较差。     

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.     

Updating Choquet beliefs

We apply Pires’s coherence property between unconditional and conditional preferences that admit a CEU representation. In conjunction with consequentialism (only those outcomes on states which are still possible can matter for conditional preference) this implies that the conditional preference may be obtained from the unconditional preference by taking the Full Bayesian Update of the capacity.     

Biproportional Methods of Structural Change Analysis: A Typological Survey

Analysts often are interested in learning how much an exchange system has changed over time or how two different exchange systems differ. Identifying structural difference in exchange matrices can be performed using either 'directed' or 'undirected' methods. Directed methods are based on the computation and comparison of column- or row-normalizations of the matrices. The choice of row or column for the normalization implies a specific direction of the exchanges, so that the column-wise normalized results should not be compared to the row-wise normalized results. In this category fall the simple comparison of coefficient matrices and the causative method. Undirected methods do not impose such underlying constraints on exchanges. Hence, I present a set of undirected methods that can be used to compare structural matrices: the biproportional ordinary filter, the biproportional mean filter and the bi-Markovian filter. While doing so, I recall why the bicausative method must be dismissed. I then classify the methods according to their orientation and data needs, and illustrate how the results can differ from one method to the next using French tables for 1980 and 1997.     

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'.     

An Algorithm for Balancing Commodity-flow Systems

In many cases there is a need to balance commodity-flow system data quickly and with limited resources. In order to compile new supply and use tables and investment matrices consistent with revised national accounts data, it can be necessary to apply some sort of automatic balancing technique. The paper proposes an algorithm that, contrary to RAS, can balance a commodity-flow system with unequal net row and column sums. The algorithm is applied to a recent revision of Danish capital stock estimates.     

Comparison of Two Methods of Identifying Input-Output Coefficients for Exogenous Estimation

Input-output (IO) updating research indicates substantial improvements in the forecasts when some of the coefficients have been exogenously estimated and included in the updating process. Several methods for identifying the appropriate subsets have been proposed. The present paper attempts to assess the relative performances of two such approaches: 'the largest coefficients' and 'the most important parameters' criteria. Utilizing these criteria, a set of coefficients from the 1966 IO table of the former Soviet Union were selected and exogenously determined. The remaining coefficients were updated to 1972 by means of naive, RAS, and Lagrangian techniques. Comparison of the results with the 1972 benchmark table provided the desired answers.     

投入产出表和社会核算矩阵更新研究评述

本文对投入产出(IO)表和社会核算矩阵(SAM)更新方法进行了归类和比较评述。主要观点:第一,已有的IO表或SAM更新方法主要分为统计学方法、优化法和宏观经济学分析方法;第二,以现代经济学为基础的更新技术应引起高度重视;第三,在非普查年份,统计部门应制度化地开展重点IO系数调查,并将相关数据及时公开化;第四,在实际操作中应正确认识更新中已知信息的地位,并注意更新中的保号性问题。     

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.     

The Solution of Updating or Regionalizing a Matrix with both Positive and Negative Entries

Normally, when updating or regionalizing input-output matrices with negative entries, the negative numbers are first brought outside the matrix, then the matrix is updated or regionalized, then the negative numbers are added back to the result. This is theoretically, and sometimes also empirically, a rather unsatisfactory procedure. This paper proposes a theoretically sound alternative for the presently used ad hoc procedure. Based on the first-order conditions of a restated information loss problem, we generalize the RAS-procedure using reciprocals of the exponential transformations of the related Lagrange multipliers. The diagonal matrices that update or regionalize a given matrix optimally are the solutions of a fixed-point problem. To derive a numerical solution, the paper presents the GRAS-algorithm, which is illustrated in terms of a simple updating example.     

Updating an Input–Output Matrix with Sign-preservation: Some Improved Objective Functions and their Solutions

This paper presents an easy-to-use method for updating input–output (IO) matrices with sign-preservation by combining Lagrangian multipliers and penalty functions. Biproportional methods such as the representative RAS are very simple and popular because a target matrix can be obtained simply by iterative computation. However, they cannot reasonably deal with matrices that include negative entries. Although a generalized version, GRAS, can do so, its objective function is questionable. In contrast, some non-biproportional methods such as those that take weighted or unweighted squared differences between the target and original matrix as objective functions can deal with negative entries, but it is difficult to guarantee the signs of entries. In this study, GRAS and some conventional objective functions were improved and their solutions for preserving the signs of entries are presented. Comparisons of applying these objective functions to a simple example show that both the Improved Normalized Squared Differences (INSD) function and the Improved GRAS (IGRAS) function yield a good target matrix and are close to each other; we suggest that INSD or IGRAS be used for updating IO transaction matrices in practice.