The dynamic variable input-output model: An advancement from the Leontief dynamic input-output model

The Dynamic Variable Input-Output (VIO) model extends the static single regional version of the Multiregional Variable Input-Output (MRVIO) model which is a general equilibrium model applied to the Leontief Input-Output model. The Dynamic VIO model which incorporates time dimensions can describe the real situation more accurately while maintaining the computational simplicity. Under the model, the investment expenditures are directly linked with the profit maximizing behavior of firms. Both technical coefficients and capital stock requirement coefficients include price terms, and they become variable instead of being fixed.  By gathering investment terms together instead of separating them as is done in Leontief's Dynamic output equation, we not only preserve the consistency between time-specific dynamic multipliers and total dynamic multipliers, but also get over the shortcoming of the negative occurences of the Leontief's multiplier matrices, particularly the impact (initial period) multiplier matrix.  Using the 15 sector interindustry transaction table derived from the 1987 U.S. benchmark input-output table, we estimate dynamic output and income multipliers for all industries.  Empirical results show that, over all industries, dynamic total multipliers of the Dynamic VIO model are larger than static multipliers of the static Household Interactive VIO (HIVIO) model. Static multipliers of the static Household Interactive VIO (HIVIO) model which lie between Leontief's static type I and type II multipliers are exactly the same as the impact (initial period) multiplier of the Dynamic VIO model. Similarly, dynamic total multipliers of the Dynamic VIO model are larger than those of the Leontief static type I and type II multipliers, and multipliers of the Leontief dynamic (in nested form) IO model. Thereby, the study demonstrates that the static HIVIO model and the Leontief IO models (both static and dynamic (in nested form)) underestimate actual impacts. The study also shows that the sum of all time-specific multipliers of the dynamic VIO model equals to dynamic total multiplier; thus, consistency is ensured in the dynamic multipliers of the Dynamic VIO model. The multipliers of the dynamic VIO model vary among different industries, and they decrease as the number of time lags increase with the initial period impact as the largest. The percent distributions of multipliers over time periods reveal that ripple effects of spending are mostly recognized during the first four periods. The dynamic multipliers of the Dynamic VIO model are useful information in evaluating the long-term economic effects of spending. Received: August 1996/Accepted: March 1999     

The Model Reference Adaptive System in the dynamic input-output model

In this paper we explore the use of the Model Reference Adaptive System (MRAS) in a dynamic socio-economic enviroment. We prove the existence of adaptation laws which ensure that the error equation in MRAS for a dynamic input-output model is asymptotically stable. The resulting theorems are appraised through some numerical simulations.     

Dynamic variable input-output (VIO) model and price-sensitive dynamic multipliers

The conventional multipliers of macro economic models, econometric models, Computable General Equilibrium (CGE) models with fixed industrial purchase I/O coefficients, and Leontief Input-Output (I/O) models are price-insensitive. On the other hand, the multipliers of the Dynamic Variable Input-Output (VIO) model have the advantage of being price-sensitive. The Dynamic VIO model extends the static single regional version of the Multi-Regional Variable Input-Output (MRVIO) model, which is a hybrid of Computable General Equilibrium (CGE) model and the further developed Leontief's dynamic Input-Output (I/O) model. The Dynamic VIO model, which incorporates time dimensions, can describe the actual situations more accurately while maintaining computational simplicity. Under this model, both technical coefficients and capital stock requirement coefficients include price terms, and they become variable instead of being fixed. By using the 15 sector industrial transaction table derived from the 1987 U.S. Benchmark input-output table, and by assuming constant technology during the years of 1987–1991, I estimate the dynamic equilibrium price changes due to wage rate changes and measure the effects of the relative equilibrium price changes on output, income, and employment multipliers that are spread over the time periods. The dynamic multipliers of the Dynamic VIO model include both pure spending effect and substitution effect in the presence of input cost changes such as wage rate changes. The substitution effect is the relative equilibrium price change effect, and it occurs due to the substituting behavior of firms and consumers seeking cheaper products. Actual economic impacts that we observe in a given time period, as the result of government spendings, are the total cumulative effects of the current and previous time periods. The empirical analysis shows that wage rate changes during 1987 through 1991 give statistically significant effect on mean equilibrium price changes for the total of five years and for each time period except the immediate time period (lag 0) under 1% level of significance. As for the immediate time period (lag 0), mean equilibrium prices are same between the two groups of wage rate-change and no-wage rate-change cases. Nevertheless, equilibrium price changes affect output, income, and employment multipliers significantly. Hypothesis tests show that significant differences exist in mean output, income, and employment multipliers between the two groups of wage rate-change and no-wage rate-change cases for each time lag (1–4) and for the total of five time lags. The dependent t-test is applied to the paired data. The study concludes that substitution effects do alter mean output, income, and employment multipliers for each time lag (1–4) and for the total of all five time lags under 1% level of significance. Furthermore, the study finds that mean multipliers of output, income, and employment under the wage rate-change case are smaller than those under the no-wage rate-change case. For the immediate time period (lag 0), the significance level should be increased to 2%, 13%, and 5%, respectively, to support the claim that mean multipliers of output, income, and employment are different between the two groups, and that mean multipliers of output, income, and employment of the wage rate-change case are smaller than those of the no-wage-rate change case. These strong empirical results demonstrate the capability and usefulness of the Dynamic VIO model for measuring government spending effects in terms of price-sensitive dynamic multipliers. Received: May 2000 / Accepted: August 2003 I am grateful to Roger R. Stough and three anonymous referees for valuable comments and suggestions. If there is any error, it is solely mine.     

A multiregional,multiproduct, household interactive,variable input-output model

This paper introduces a multiregional, multiproduct, household interactive, variable input-output (MMHIVIO) model. The MMHIVIO model is a general equilibrium model which captures the interactions and the optimizing behavior of consumers and producers in the space economy. It is not only consistent with the theories of consumer and producer behavior, it also makes it relatively easy to solve because it reduces to several blocks of linear systems of equations. The model is used to evaluate the economic effects of the Ohio River Navigation System.     

Interregional migration in an extended input-output model

"This article develops a two-region version of an extended input-output model that disaggregates consumption among employed, unemployed, and inmigrant households, and which explicitly models the influx into a region of migrants to take up a proportion of any jobs created in the regional economy. The model is empirically tested using real data for the Scotland (UK) regions of Strathclyde and Rest-of-Scotland. Sets of interregional economic, demographic, demo-economic, and econo-demographic multipliers are developed and discussed, and the effects of a range of economic and demographic impacts are modeled. The circumstances under which Hawkins-Simon conditions for non-negativity are breached are identified, and the limits of the model discussed."     

Dynamic multipliers for a regional input-output model

Regional multiplier is a very useful and popular tool in economic study of a region. However, conventional regional multiplier derived from a static input-output model fails to provide time path of the impact over period. In many cases, it restricts the impact within a year period. To alleviate the problem, this paper introduces a regional dynamic multiplier which makes the impact to spread out over period. In the absence of the technical change, each period multiplier added up to the static multiplier. Utilizing Oklahoma data, the paper estimates the capital coefficients and the dynamic multipliers of Oklahoma regional economy. Finally, it provides a comparative study of dynamic multipliers for various industries.The author is grateful to Professor Wassily Leontief who generously sent him the U.S. Capital Coefficient data and to the referees for their valuable suggestions. This research was supported in part by the Center for Economic and Management Research, the University of Oklahoma. Mr. Chun K. Chang and Mr. Ui Nam Choi provided computer assistance and data gathering works. The final revision was done at Harvard University.     

A price-responsive framework for interregional input-output

In interregional analysis, supply models are based typically on defined sets of ‘representative firms’ with given ‘averaged’ technological and cost coefficients, such that, when aggregated as identical units into both sectors and regions, they reproduce the total output of each sector in each region. Then, deterministic models obtain profit-maximising patterns of input demands and corresponding output, prior to aggregating these quantities as if the firms were truly identical and homogeneous. In this paper, the above optimisation models are replaced by a probabilistic framework, which nevertheless guarantees convergence to the above classical deterministic solutions in the limit. The models are estimated on ‘observed’ flows, technological coefficients and prices, and a CES function (optionally) handles substitution between primary factors. These new input-output models become explicitly price-responsive, allowing tatonnement with spatial models of final demand. Received: June 1996 / Accepted: February 1997     

Regionalizing national projections with a multiregional input-output model linked to a demographic model

Multiregional input-output has long been recognized as a tool that provides an appropriate framework for considering regional growth and development questions, but implementation problems have impeded utilization of this methodology. This paper discusses how several of these problems have been partially overcome with a multiregional economic-demographic model of the Southwest. The model is used to regionalize projections from a national dynamic input-output model.     

A fugacity based continuous and dynamic fate and transport model for river networks and its application to Altamaha River

In this paper, a continuous and dynamic fugacity-based contaminant fate and transport model is developed. The dynamic interactions among all phases in the physical domain are addressed through the use of the fugacity approach instead of the use of concentration as the unknown variable. The full form of Saint Venant equations is used in order to solve for the hydrodynamic conditions in the river network. Then a fugacity-based advection-dispersion equation is modeled to examine the fate and transport of contaminants in the river network for all phases.The fugacity-based, dynamic and continuous contaminant fate and transport model developed here is applied to Altamaha River in Georgia, USA to demonstrate its use in environmental exposure analysis. Altamaha River is the largest river system east of Mississippi which offers habitat for many species, including about 100 rare endangered species, along its 140 mile course. Polychlorinated biphenyls (PCBs), a highly hydrophobic and toxic chemical ubiquitous in nature, and atrazine, the most commonly-used agricultural pesticide are modeled as contaminants in this demonstration. Through this approach the concentration distribution of PCBs and atrazine in the water column of Altamaha River as well as the sediments can be obtained with relative ease, which is an improvement over concentration based analysis of phase distribution of contaminants.     

A dynamic competition model for construction contractors

In construction, the issue of competition has been studied focusing on competitive bidding. The objective of most competitive bidding models is to find the optimum mark‐up to maximise the expected profit from a single firm's perspective. However, a firm's success depends on its long‐term interactions with the market and its competitors. To better understand competition in the market, there is a need to analyse competition from a dynamic market perspective. Building on previous models and relevant competition studies, a dynamic simulation model has been developed to provide an analytical framework for understanding dynamic competition. In this model, similar firms are equally exposed to demand uncertainties. Each applies its own policy, responding to market changes and to competitors' actions to optimise its market position. The firms' responses and their dynamic feedback are simulated and analysed. The results show how difficult it is for any firm to acquire a long‐term competitive advantage by means of bidding/marketing strategies—just as it is in the real world of price‐competitive contracting. Some considerations are presented for a single firm to develop a competitive strategy.     

A dynamic Mills heritage model with replaceable capital

A general equilibrium, linear programming model of urban land use formulated in the heritage of Edwin Mills is reformulated for dynamic solution. This multiperiod extension identifies discontinuous land use as an optimal market strategy under reasonably general conditions of economic change. Information about future economic conditions is assumed to be complete, and capital is assumed to be replaceable at finite cost. As a result, land uses and export mixes adjust over time in response to exogenous shifts in export prices. It is noted that discontinuous land uses can constitute long-run outcomes, and a distinction is drawn between the assumptions associated with static and long-run perspectives.     

A metropolitan input-output model: Multisectoral and multispatial relations of production,income formation,and consumption

This study formulates a metropolitan input-output model (hereafter MIO) that incorporates the multispatial and multisectoral nature of an urban economic system. Two main features can be highlighted which distinguish the MIO model from other input-output models as applied to the urban context. The MIO model integrates information on intrametropolitan flows of people, commodities and services through the embedding approach within an input-output framework. Accordingly, the model has been built in one methodological framework (input-output framework) and operated by using one calculation system (inversion of input coefficient matrix), taking interspatial and intersectoral linkages into consideration. Another unique characteristic of the proposed model is that the input coefficient matrix of the MIO model consists of three partitioned matrices that have different spatial dimensions: interindustrial technical coefficients by place of production; the income coefficients by place of residence, and consumption coefficients by place of consumption. The MIO model can be applied for the impact analysis of a variety of urban policy evaluations. The main sets of results are derived as outputs from the MIO model: gross output and employment by zone, by sector, by income group, and by repercussion type.The early version of this paper was presented at the Western Regional Science Association (WRSA), February 25-28, 2001, Palm Springs, CA. This Research was supported by the Chung-Ang University Special Research Grants in 1999.     

A qualitative input-output method to find basic economic structures

Structural analysis deals with economic systems as defined by the set of industries and the relationships between them. However, multi-sectoral models are often limited: when studying economic systems empirically it is difficult to distinguish a priori the subset of basic or important relationships between industries. This research note presents a method to find the core of a productive structure by employing the qualitative approach and avoiding exogenous criteria. Results are presented in a graph of relationships that characterise the productive structure as a whole. In effect, the figure provides information concerning the main paths of influence between sectors in the structure, as well as information regarding the complexity of the economic system.Received: 2 January 2001, Accepted: 25 July 2002, JEL Classification: C63, C67Francisco Zarco developed the computing programme employed in this research note. María Eugenia Veras assistance was most helpful. I am also grateful to two anonymous referees, who helped enormously to improve the note, as well as to the editor, who made invaluable suggestions for the sake of clarity. The usual disclaimer applies.     

The choice of an input-output table embedded in regional econometric input-output models

In this paper, we investigate the role of input-output data sources in regional econometric input-output models. While there has been a great deal of experimentation focused on the accuracy of alternative methods for estimating regional inputoutput coefficients, little attention has been directed to the role of accuracy when the input-output system is nested within a broader accounting framework. The issues of accuracy were considered in two contexts, forecasting and impact analysis focusing on a model developed for the Chicago region. We experimented with three input-output data sources: observed regional data, national input-output, and randomly generated inputoutput coefficients. The effects of different sources of input-output data on regional econometric input-output models revealed that there are significant differences in results obtained in both forecast and impact analyses. The adjustment processes inherent in the econometric input-output system did not mask the differences imbedded in input-output tables derived from different data sources. Since applications of these types of models involve both impact and forecasting exercises, there should be strong motivation for basing the syste on the most accurate set of input-output accounts.     

大跨度连续刚构桥有限元建模与动力特性分析

本文采用有限元软件ANSYS建立某大跨连续刚构桥有限元模型,通过该模型的模态分析结果和实桥的环境振动测试结果的比较,得出一些有意义结论。