Mathematical Models in Input-Output Economics

This paper describes the mathematical basis for input-output economics, the major types of models, and the underlying economic theory. The features of these models that make them especially well suited for understanding the connections between the economy and the environment are emphasized throughout. These include the dual physical and price representations and the representation of resource inputs as factors of production, whether they are priced or not. The basic static physical and price models are described, along with their major properties and associated databases. The most important approaches to analysis involve multipliers, decomposition, and scenario analysis. Going beyond the basic static framework requires the progressive closure of the model by making exogenous variables endogenous while maintaining simplicity, transparency, and the distinctive feature of an input-output model: the simultaneous determination of solutions at the sectoral level and the economy-wide level. Closures for household activities and for investment are described by way of example. The major extensions of the basic model accommodate the representation of pollutant emissions and policies for constraining them, dynamic models, and multi-regional models, the latter including a new version of a world model that solves for bilateral trade flows and region-specific prices based on comparative advantage with factor constraints. The concluding section describes the challenges currently being addressed within the field. An annotated bibliography provides references for further reading and includes both classic articles and a representation of recent research.

CHOICE OF FLEXIBLE FUNCTIONAL FORMS: REVIEW AND APPRAISAL

Choice between alternative flexible functional forms has received little explicit treatment in many empirical agricultural studies. Theoretical criteria and empirical techniques for choosing between flexible functional forms are reviewed. Theoretical topics include definitions of flexibility, mathematical expansions, separability, and regular regions. Empirical techniques examined are Monte Carlo analysis, parametric modeling, bayesian inference, and nonnested hypothesis testing. Comparison of the full range of theoretical and empirical aspects may provide more credible and reliable empirical estimates when consumer or producer duality assumptions are appropriate in agricultural applications.Research Methods/ Statistical Methods,

Income distributions in input-output models

The analysis of income distribution (ID) has traditionally been of prime importance for economists and policy-makers. However, the standard input-output (I-O) model is not particularly well equipped for studying current issues such as the consequences of decreasing access to primary inputs or the effects of specific redistributive policies. This paper addresses this gap in the existing literature. We propose that IDs can excellently be studied by restructuring the I-O relations. A new coefficients matrix is defined, the so-called augmented input coefficients matrix. This matrix is the sum of the intermediate input coefficients matrix and newly constructed matrices of sector-specific input coefficients that represent the existing distribution of income. We show that shifts in the distribution can be modelled by attributing weights to these matrices and vary these according to system-specific rules. Numerical illustrations based on the existing literature are given throughout the paper

Using a Linear Regression Approach to Sequential Interindustry Model for Time-Lagged Economic Impact Analysis

The input-output (IO) model is a powerful economic tool with many extended applications. However, one of the widely criticized drawbacks is its rather lengthy time lag in data preparation, making it impossible to apply IO in high-resolution time-series analysis. The conventional IO model is thus unfortunately unsuited for time-series analysis. In this study, we present an innovative algorithm that integrates linear regression techniques into a derivative of the IO method, the Sequential Interindustry Model (SIM), to overcome the inherent shortcomings of statistical lags in conventional IO studies. The regressed relationship can thus be used to predict, in the short term, the accumulated chronological impacts induced by fluctuations in sectorial economic demands under disequilibrium conditions. A simulated calculation is presented to serve as an illustration and verification of the new method. In the future, this application can be extended beyond economic studies to broader problems of system analysis

Solving the Reswitching Paradox in the Sraffian Theory of Capital

The possibility of the reswitching of techniques in Piero Sraffa’s intersectoral model, namely the recurring capital-intensive techniques with monotonic changes in the interest rate, is traditionally considered as a paradoxical violation of the assumed convexity of technology putting at stake the viability of the neoclassical theory of production. It is argued here that this phenomenon can be rationalized within the neoclassical paradigm. Sectoral interdependencies can give rise to the well-known price Wicksell effect, which is the revaluation of capital goods due to changes in relative prices triggered by monotonic variations in income distribution. The reswitching of techniques is, therefore, the result of cost-minimizing technical choices facing returning ranks of relative input prices in full consistency with the pure marginalist theory of factor rewards. The theoretical analysis proposed in this article is applied empirically to the counterexamples of various case studies presented in the literature

Mathematical Models in Input-Output Economics

This paper describes the mathematical basis for input-output economics, the major types of models, and the underlying economic theory. The features of these models that make them especially well suited for understanding the connections between the economy and the environment are emphasized throughout. These include the dual physical and price representations and the representation of resource inputs as factors of production, whether they are priced or not. The basic static physical and price models are described, along with their major properties and associated databases. The most important approaches to analysis involve multipliers, decomposition, and scenario analysis. Going beyond the basic static framework requires the progressive closure of the model by making exogenous variables endogenous while maintaining simplicity, transparency, and the distinctive feature of an input-output model: the simultaneous determination of solutions at the sectoral level and the economy-wide level. Closures for household activities and for investment are described by way of example. The major extensions of the basic model accommodate the representation of pollutant emissions and policies for constraining them, dynamic models, and multi-regional models, the latter including a new version of a world model that solves for bilateral trade flows and region-specific prices based on comparative advantage with factor constraints. The concluding section describes the challenges currently being addressed within the field. An annotated bibliography provides references for further reading and includes both classic articles and a representation of recent research

Vintage capital growth theory: Three breakthroughs

Vintage capital growth models have been at the heart of growth theory in the 60s. This research line collapsed in the late 60s with the so-called embodiment controversy and the technical sophisitication of the vintage models. This paper analyzes the astonishing revival of this literature in the 90s. In particular, it outlines three methodological breakthroughs explaining this resurgence: a growth accounting revolution, taking advantage of the availability of new time series, an optimal control revolution allowing to safely study vintage capital optimal growth models, and a vintage human capital revolution, along with the rise of economic demography, accounting for the vintage structure of human capital similarly to physical capital age structuring. The related literature is surveyed.Vintage capital, embodied technical progress, growth accounting, optimal control, endogenous growth, vintage human capital, demography.

Centered solutions for uncertain linear equations

Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we derive convex representations for united and tolerable solution sets. Secondly, to obtain centered solutions for uncertain linear equations, we develop a new method based on adjustable robust optimization (ARO) techniques to compute the maximum size inscribed convex body (MCB) of the set of the solutions. In general, the obtained MCB is an inner approximation of the solution set, and its center is a potential solution to the system. We use recent results from ARO to characterize for which convex bodies the obtained MCB is optimal. We compare our method both theoretically and numerically with an existing method that minimizes the worst-case violation. Applications to the input–output model, Colley’s Matrix Rankings and Article Influence Scores demonstrate the advantages of the new method