THE SENSITIVITY OF INPUT-OUTPUT MULTIPLIERS*

The present paper derives analytical expressions for the sensitivity of input-output multipliers to errors in the data. The effects on the simple output multipliers are investigated for additive errors, multiplicative errors in the columns, multiplicative errors in the rows, error rectangles, the error couple and the single error, and price changes. In contrast to earlier investigations, the results are not obtained from the Leontief inverse. The present approach focusses on the effects of errors on the eigenvector corresponding to the dominant eigenvalue. It is indicated how similar expressions may be derived for several other multipliers.     

THE ROLE OF ERROR STRUCTURE IN SIMULATIONS ON REGIONAL INPUT-OUTPUT ANALYSIS*

Previous simulation experiments on regional input-output analysis have concluded that regional purchase coefficients are more important than technical coefficients in contributing to multiplier accuracy. This paper shows that the multiplicative error structure used in those experiments may have biased the results. A new error structure, combining a multiplicative and an additive component is introduced, and simulations are conducted on randomly generated models. The analysis shows that the results are sensitive to the relative magnitudes of the two error components, as well as to the closure of the model.     

我国城乡关系的定量研究——基于城乡投入产出表的视角

城乡关系是地理学研究的重要议题。本文运用城乡投入产出模型,构建了"乡村支持城镇、城镇反哺乡村"的定量模型,分析了我国1987-2012年间城乡间的经济联系。结果发现,从经济联系角度看,虽然城镇对乡村的反哺作用有了较大的提升,但总体上我国城乡关系仍处于乡村支持城镇阶段。乡村对其他服务业（如教育、医疗）的消费是导致乡村支持城镇的主要来源,且其作用有增大趋势。而城镇对农业的消费、对建筑业的投资以及纺织服装业的出口是城镇反哺乡村最主要的经济活动。因此,减轻乡村居民在其他服务业领域的支出负担,刺激城镇居民对乡村农产品的消费,保持建筑业投资力度,扩大纺织服装行业的出口水平有利于提升我国城镇反哺乡村的水平。     

UPPER BOUNDS ON THE SIZES OF INTERREGIONAL FEEDBACKS IN MULTIREGIONAL INPUT-OUTPUT MODELS*

ABSTRACT. Upper bounds are presented for a measure of the overall percentage error caused in a multiregional input-output model when interregional feedback effects are ignored. This error figure is thus a measure of the magnitude of interregional linkages. The upper bounds are expressed as a function of the levels of self-sufficiency in the regions in the model and of the norms of the regional technical coefficients matrices. Experimental results are presented for a variety of examples that are thought to reflect real-world situations, and it is clear that in many cases the upper bound (and hence the error) is extremely small. The implication is that single-region input-output models may be adequate for a variety of questions.     

ANALYSIS OF SETTLEMENT SYSTEMS IN A MOUNTAIN REGION

In a continuing study of settlement systems using space imagery and aerial photography, systems of settlement and central places are analyzed on the basis of the intensity of transport movements between places. Central places are assigned to different categories according to the patterns of transport linkages in their tributary areas. Relationships between the maximum extent of zones of influence and the population of central places are discussed. The concept of developmental phase of a settlement system is introduced. For previous articles by the author, see S.G., Jan. 1975 and Oct. 1976. [The study area, though not identified, is in the Altay Mountains.]     

ACCOUNTING FOR NEIGHBORING EFFECTS IN MEASURES OF SPATIAL CONCENTRATION*

ABSTRACT A common problem with spatial economic concentration measures based on areal data (e.g., Gini, Herfindhal, entropy, and Ellison‐Glaeser indices) is accounting for the position of regions in space. While they purport to measure spatial clustering, these statistics are confined to calculations within individual areal units. They are insensitive to the proximity of regions or to neighboring effects. Clearly, since spillovers do not recognize areal units, economic clusters may cross regional boundaries. Yet with current measures, any industrial agglomeration that traverses boundaries will be chopped into two or more pieces. Activity in adjacent spatial units is treated in exactly the same way as activity in far‐flung, nonadjacent areas. This paper shows how popular measures of spatial concentration relying on areal data can be modified to account for neighboring effects. With a U.S. application, we also demonstrate that the new instruments we propose are easy to implement and can be valuable in regional analysis.     

EVOLUTION OF URBAN SYSTEMS IN THE PARETO PLANE*

ABSTRACT Distributions of city sizes are usually characterized by their Pareto index. This, however, turns out to be a rather restrictive view, for the Pareto distribution is known to become singular whenever the Pareto index becomes smaller than one, a case which is fairly frequent in empirical distributions. We show that the introduction of finite Pareto distributions in which city sizes are bounded from above solves a number of difficulties encountered by the rank-size rule and by the unbounded Pareto distribution. Combined with the use of finite Pareto distributions, the green-belt model that has been introduced previously is reexamined. It implies definite constraints for the long-run evolution of urban systems; it is in the cases of countries experiencing a process of fast urbanization that these constraints are of greatest significance. The implications of the model are confronted with empirical evidence concerning the evolution of urban systems in major industrialized countries during the nineteenth and twentieth centuries.     

A LONG-RUN INTERPRETATION OF REGIONAL INPUT-OUTPUT ANALYSIS*

ABSTRACT. Regional input-output (I-O) analysis is traditionally motivated by a short-run, extreme Keynesian vision of markets. In this paper we argue that an appropriately formulated, investment-endogenous, I-O system replicates the long-run equilibria of a wide range of regional models, many of which do not operate as I-O systems in the short run. In particular, we use a computable general equilibrium (CGE) framework to illustrate the impact of an aggregate demand disturbance on an I-O and standard neoclassical model. When run forward over a number of periods, the results from the capacity-constrained neoclassical model asymptotically approach the I-O outcome. We use sensitivity analysis to examine the speed of adjustment of the neo-classical system and investigate barriers to the attainment of the I-O result.     

INTRODUCTION: PROCESSES OF CHANGE IN URBAN SYSTEMS*

ABSTRACT The twenty‐first century will be one of intensified urbanization, on a scale never before experienced. How do urban systems and individual cities change and develop? The social sciences have many different approaches to analyzing the economic, social, and spatial dimensions of urban change. We inventory some of these approaches and their implications for public policy toward cities, urban change, and economic development.     

MEASURES OF INCOME INEQUALITY AND SOCIAL POLARIZATION IN CANADIAN METROPOLITAN AREAS

Rising inequality and polarization of employment earnings have been clearly documented in Canada and most other developed economies in the 1990s. Following a critical discussion of the use of the Cini coefficient as a measure of inequality in geography, the level of inequality and social polarization of household incomes at the census tract level is assessed for Canada's 22 largest Census Metropolitan Areas. The distribution of household income among metropolitan census tracts is generally becoming more unequal. In addition, the proportion of households in middle-income census tracts is declining in most metropolitan centres, lending further support to arguments that Canada's middle class is in decline .
L'augmentation des intégalité et la polarisation des revenus d'emploi a été clairement documentee au Canada et dans la plupart des autres pays industrialises durant les annees 90. Á la suite d'une discussion critique sur l'utilisation du coefficient Gini comme mesure d'inégalite en geographie, on evalue le niveau d'inegalitéet la polarisation sociale des revenus menagers au niveau du secteur de recensement pour les 22 plus grandes regions metropolitaines de recensement au Canada. La distribution du revenu des menages parmi les secteurs de recensement metropolitains devient en général plus idgale. De plus, le fait que la proportion des menages parmi les secteurs de recensement d revenus moyens est d la baisse dans la plupart des regions métropolitaines soutient l'idee que la classe moyenne est en diminution.     

TRANSBOUNDARY INCOME AND EXPENDITURE FLOWS IN REGIONAL INPUT-OUTPUT MODELS*

ABSTRACT. Nearly all regional input-output models have been constructed without a proper accounting of inflows and outflows of personal income and personal consumption expenditures. Typically invoked is a no cross-payments assumption, analogous to the no cross-hauling assumption for commodities. We present a new accounting framework based on the classification of flows according to the location of income generation, receipt, and spending, and argue that only flows endogenous in all three respects should be part of a closed regional I-O model. We use the framework to compute the upward bias in multipliers in a typical regional I-O model. We also present several methods for estimating transboundary flows.     

THE PRIORITY OF LARGE CITIES IN ZIPF RANK-SIZE RULE SYSTEMS

The author seeks to establish possible reasons for differences in the rates of growth of towns within urban systems with rank-size regularities. It is shown that a system follows Zipf s law if the growth of population N _i of the towns of the system follows the regularity M(ΔN _i )/N _i ～ (In N _i - c) where M is the mathematical expectation, ΔN _i is an increment of Ni over a short period of time, ～ stands for “directly proportional,” and c is a constant.