THE BIAS OF THE MULTIPLIER MATRIX WHEN SUPPLY AND USE TABLES ARE STOCHASTIC

The literature on stochastic input–output (I–O) analysis has paid considerable attention to the bias in the Leontief inverse. This paper extends previous studies by assuming supply and use tables (SUTs rather than I–O tables or input coefficients matrices) to be stochastic. This is a natural starting point because SUTs have become the basic data sources for I–O applications. In a Monte Carlo simulation experiment, a given SUT is randomized in two different ways and the effects are determined for eight different multiplier matrices. The analysis is carried out for Spain, Italy, the Netherlands, Germany and Finland, using their SUTs for 2006. The findings indicate that, in general, biases are statistically significant but negligibly small. This corroborates earlier findings obtained for stochastic I–O tables.     

Adjustment of Input–Output Tables from Two Initial Matrices

The compilation of the information required to construct survey-based input–output (I–O) tables consumes resources and time to statistical agencies. Consequently, a number of non-survey techniques have been developed in the last decades to estimate I–O tables. These techniques usually depart from observable information on the row and column margins, and then the cells of the matrix are adjusted using as a priori information a matrix from a past period (updating) or an I–O table from the same time period (regionalization). This paper proposes the use of a composite cross-entropy approach that allows for introducing both types of a priori information. The suggested methodology is suitable to be applied only to matrices with semi-positive interior cells and margins. Numerical simulations and an empirical application are carried out, where an I–O table for the Euro Area is estimated with this method and the result is compared with the traditional projection techniques.     

A Test for a Functioning Market Economy: Seton'S Eigenprices of Turkey

We use Seton's eigenprices to see if some evidence can be found in support of the European Commission's official statement that the Turkish economy can be considered as a functioning market economy. Given an input–output flows matrix, there is a unique set of prices for outputs and production factors compatible with final demand, generating demand for factors. The findings based on Turkey's most recent I–O table and comparable I–O matrices for Romania and Poland (two EU members) in 2005 show that price distortions were on average five times larger in Turkey. Hence, based on price distortions alone, there was no solid evidence in support of the statement that Turkey had a functioning market economy.     

A general weighted least squares approach for the projection of input–output tables

In the context of input–output analysis, it is often necessary to update a matrix for a date when only the sum of its columns and rows are known. This projection problem is quite similar to temporal disaggregation. I borrow from this literature a class of solutions for which the exact result can be implemented without iteration. These solutions minimize the adjustment made to the out-of-date matrix and as such can be said optimal according to a chosen criteria. The framework I expose is flexible enough to encompass many of the existing methods and develop new ones. I propose one of such methods to project a matrix between two given benchmarks. I exemplify the technique on 35 years of input–output tables for France and show in particular that the issue of negative cells can be avoided.     

Technical Change in the Private Consumption Converter

The analysis of technological change is centered on the study of the evolution of technical coefficients in the input–output table. Complementary to this analysis, the household consumption expenditure matrix, relating consumption by commodities to consumption by purpose or by function, also incorporates some other aspects of technological change. Thus, the evolution in time of the coefficients of this consumption expenditure matrix will portray technological processes, implying substitutions between commodities to satisfy the different functions The substitution between consumption expenditure by functions is also to be taken into consideration, because it can influence, together with technological change, the use of commodities in the final demand. For Switzerland, a 1980–89 time series of household consumption expenditure matrices with 37 commodities and 58 functional consumption categories has been estimated using data from consumer expenditure surveys. In this paper, instruments generally applied to the analysis of changes in input–output technical coefficients are extended to these matrices, including methods that deal with biproportional processes of substitution.     

HOW MUCH DO EXPORTS CONTRIBUTE TO CHINA'S INCOME GROWTH?

It is a widespread belief that exports, in particular of ‘high-tech’ products, contribute much to China's income growth. This study addresses this issue by applying a structural decomposition analysis to input–output (I–O) data. We employ two extended I–O tables that distinguish processing trade from ordinary exports. The contribution of exports to the value-added growth from 2002 to 2007 is found to be overestimated by 32% when standard I–O tables are used rather than the extended I–O tables. Even more strikingly, the value-added growth that may be attributed to the exports of ‘high-tech’ telecommunication products is overestimated by no less than 63%. A serious overestimation of the contribution to income growth of certain products (such as high-tech products) sends out misleading signals to policymakers. When measured correctly, the true contribution appears to be substantially smaller than is generally believed to be.     

Who pays for whom? Elements of a macroeconomic approach to income inequality

National income is generated through national production in the form of ‘value added’; it is expended on goods and services in the form of ‘disposable’ or ‘net’ income. In this paper, I investigate what happens in between. The circuit of income flows generated in this way is comparable to the circuit of product flows, in its complexity. It can be analysed, so the tenet of the paper, in a similar way, by means of well-known tools of input–output (IO) analysis; this on the pre-condition, however, that you draw out the institutional framework of an economy in similar detail as is now customarily done for production units in IO analysis. Existing data do not suffice for the purpose, at present; this paper shows, by way of some exemplary calculations, what insight into the mechanism of national income distribution is gained if the necessary data, normally in the form of a large social accounting matrix, are provided.     

Using a Demand System to Estimate Extended Input–Output Multipliers

The interface between household income and expenditure has always been considered to be a key component in the construction of input–output models. However, it can be argued that households are too often treated as if they were just another in dustry in the input–output table. In this paper, we seek to address this problem by developing a new modelling framework in which a micro demand system is used to estim ate the relationship between income and expenditure. This demand system is conjoined with an input–output table for the UK economy, and the system as a whole is solved as a computable general equilibrium model. Comparisons are made between the Jacobian multipliers generated by this model and those derived from a more traditional input–output model in which the income-expenditure linkage is estimated using static coefficients.     

EXPANDING EXTRACTIONS

In this paper, we generalize hypothetical extraction techniques. We suggest that the effect of certain economic phenomena can be measured by removing them from an input–output (I–O) table and by rebalancing the set of I–O accounts. The difference between the two sets of accounts yields the phenomenon's effect (or importance). We suggest that the approach can be used to measure the effect of changes in intermediate output, which are otherwise not easily rationalized within a Leontief framework. Of course, it can also be used to estimate the possible effects of the shutdown of a particular establishment or other identifiable segment of an economy. We demonstrate some properties and potential of the approach using the annual 2006 US I–O accounts.     

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.     

Some Relationships between T-Accounts,Input–Output Tables and Social Accounting Matrices

Some relationships between the T-accounting format for presenting commodity balances; input–output (IO) tables; and social accounting matrices are discussed in this paper. The starting point is to recognize that IO tables do not contain all the information that is needed to complete a social accounting matrix (SAM), or, therefore, for the modelling of phenomena that depend on having a fully articulated SAM, such as the interdependence of the distribution of income and the structure of production. There is a need, therefore, to establish the character of the extra information that is required and this can be achieved by imposing the requirement that a SAM should be consistent with the basic cash identity that is fundamental to all social accounting. A second agendum is to develop the argument that, while T-accounts can, in principle, provide a database equivalent to that of a SAM, in practice, they are typically found to be an imperfect substitute. It is important, therefore, in designing a database, to go beyond the confines of an (extended) IO system and T-accounts. SAMs provide an appropriate framework for doing so.     

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'.     

ANALYSING THE STRUCTURE OF THE ECONOMY USING PHYSICAL INPUT–OUTPUT TABLES

Analyses using physical input–output tables (PIOTs) are key to understanding the physical metabolism of economies, since they relate production to the generation of emissions and use of resources. Two methods have been developed to calculate the primary resources and emissions associated with a given final demand. However, one of these alters the PIOT, revealing different technical coefficients and Leontief inverse matrices. Which method should be used for structural analysis? In this paper, I compare both methods, explain the structural differences between them and illustrate the latter through a backward linkage analysis. I find that only one method is suited to the analysis of the physical structure of the economy, since it comprehends both the production of goods and associated emissions. The method is identified as a new model capable of tracing by-products as final outputs. Finally, I generalise both methods to analyse PIOTs including several emission types.     

Reconciling Domestication Techniques,the Notion of Re-exports and Some Comments on Regional Accounting

Recent work by Jackson (1998) subtly pointed out a means of forming direct input coefficient matrices from national technology that is different from that published elsewhere. In this paper, I rationalize his approach and also point out that prior approaches may still be useful in certain applications where the phenomenon of re-exports (imports that satisfy exports) are explicit in exports accounts. In the second half of this paper, I show some means of developing regional accounts, currently being used in the US, that are more elaborate than those Jackson discussed. For example, I substitute regional shares of employment with earnings shares to obtain productivity adjusted regional output. I also suggest using available regional value added and regional labour income when producing regional Use matrices.     

European Community Intercountry Input–Output Relations: Construction Method and Main Results for 1965–85

Eurostat constructs consolidated input–output (IO) tables for the European Community (EC) by means of an aggregation of the domestic and the intra-EC import matrices from the harmonized national IO tables. Intercountry EC IO tables can be constructed by disaggregating the intra-EC imports according to country of origin, with coefficients derived from international trade statistics. These procedures, however, produce inadequate outcomes for several reasons. The most important reason is that the imports are valued in ex-customs prices, instead of the theoretically more appropriate producers' prices. This paper analyzes the nature of these and other data problems, and describes a more extensive and satisfactory method to construct intercountry and consolidated EC IO tables. The empirical results are illustrated by an analysis of the domestic and intercountry intersectoral spillover effects for 1965–85.     

Important Coefficients and Structural Change: A Multi-layer Approach

Important coefficients within input–output matrices have been defined in terms of their so-called ‘tolerable limits’. Such coefficients have been utilized as a means to study economic structures. Important coefficients can also be useful for finding the characteristic production structure, based on endogenous information only. Graph theory provides the analytical methods to interpret the results. By applying the method to a series of matrices for one economy, it is possible to establish the structural evolution of that system.     

ON THE ECONOMIC INTERPRETATION OF THE BRÓDY CONJECTURE

The aim of the paper is to study the economic aspects of the Bródy conjecture: an increase in the size of a (random) input matrix causes a decline in the ratio of its subdominant and dominant eigenvalues and implies faster convergence to equilibrium [Bródy, A. (1997) The Second Eigenvalue of the Leontief Matrix. Economic Systems Research, 9, 253–258]. Simulation results provide evidence that this ratio depends inversely on the level of data aggregation and can therefore not be a good indicator of the speed of convergence of an economy to its equilibrium path. We show that this is consistent with findings based on actual input–output tables of EU member states. These results imply that theorems about the speed of convergence of random matrices are not useful in describing the cyclical dynamics of real economies.     

Extending the input–output model with assets

In this paper, the input–output model is extended with assets. It allows us to examine the various assets that are held and used in production. The requirements of assets that must be held by each sector can thus be specified. Extending the input–output model with assets provides a better alternative to the capital stock matrix in the standard Systems of National Accounts. The input–output model is extended by taking the depreciation of fixed assets into full account. This extension allows for the calculation of total holding coefficients that express the amount of assets that are required to be held in each sector in order to satisfy a unit of final demand. In addition, a dynamic version of the extended model is presented. The extended input–output model has been widely applied in China for various purposes.     

Issues in Assessing the Effect of Interindustry R&D Spillovers

This paper aims to clarify three issues concerning the weighting methodol ogy generally used to evaluate interindustry R&D spillovers. These issues concern the likely nature of the spillovers estimated through different types of supporting matrices; the similarity between input–output (IO), technology flows and technological proximity matrices; and the relevance of the assumption that a single matrix can be used for different countries. Data analyses of weighting components show that technology flows matrices are in an intermediate position between IO matrices and technological proximity matrices, but closer to the former. The various IO matrices, as well as the three technological proximity matrices, are very similar to each other. The panel data estimates of the effect of different types of interindustry R&D spillovers on industrial productivity growth in the G7 countries reject the hypotheses that a technology flows matrix can be approximated by an IO matrix and that a single IO matrix can be usedfor different countries. By transitivity, the procedure that comprises using a single technology flow for several countries is not reliable. The international comparison shows that each country benefits from different types of R&D externality. In Japan and, to a lesser extent, in the US, the rate of return to direct R&D is very high and is likely to compensate for relatively weak interindustry R&D spillover effects. In the five other industrialized countries, the reverse observation is true: strong social rates of return to R&D counterbal ance the poor performances of direct R&D.