Growth Rate Form Research Articles

A structured model for the spread of <em>Mycobacterium marinum</em>: Foundations for a numerical approximation scheme

We develop a finite difference scheme to approximate the solution of a novel size-structured mathematical model of the transmission dynamics of <em> Mycobacterium marinum</em> (Mm) in an aquatic environment. The model consists of a system of nonlinear hyperbolic partial differential equations coupled with three nonlinear ordinary differential equations. Existence and uniqueness results are established and convergence of the finite difference approximation to the unique bounded variation weak solution of the model is obtained. Numerical simulations demonstrating the accuracy of the method are presented. We also conducted preliminary studies on the key features of this model, such as various forms of growth rates (indicative of possible theories of development), and conditions for competitive exclusion or coexistence as determined by reproductive fitness and genetic spread in the population.

Productivity and R&D: an econometric evidence from Spanish firm-level data

This article analyses the relationship between productivity growth and R&D investments of Spanish manufacturing firms during the 1990s. The theoretical model is a version of the Cobb–Douglas production function in its growth rate form. The purpose is to estimate the rate of return to R&D expenditures. The econometric specification is a distributed lag model. The estimation applies the generalized method of moments method. The main empirical finding is that a positive and significant role is played by R&D expenditures on productivity growth. The rate of return to R&D expenditures is 26.598%.

The global trends of total factor productivity: evidence from the nonparametric Malmquist index approach

In this paper the Malmquist index of total factor productivity is applied to a sample of 87 countries observed over the period 1960-90. This index and the method needed to quantify it, the data envelopment analysis, has substantial advantages as compared to traditional growth accounting. Two of these advantages are that it does not rely on questionable equilibrium assumptions to merge multiple inputs into a single index and that the rate of total factor productivity growth can explicitly be decomposed into a measure of efficiency change and the rate of technological progress. Results are reported both in the form of growth rates and measures of relative productivity levels. In each case related labour productivity measures are calculated and the differences to the total factor productivity measures are analysed. Among the topics covered are the productivity slowdown, the Asian Miracle and the bimodality of the distribution of relative producitivity levels. JEL classification: C14, O33, O47

A Problem with Some Estimations and Interpretations of the Mark-up in Manufacturing Industry

This paper evaluates the methodological foundations of some recent attempts to estimate econometrically the degree of market power and the degree of returns to scale in manufacturing. The method discussed is based on estimating the aggregate production function in growth rate form. It is argued, following an argument made in another context by Phelps Brown, Shaikh & Simon, that as the data used in empirical analyses are in value terms (i.e. monetary values at constant prices), the parameter derived as a mark-up can be reinterpreted simply as a coefficient from the income accounting identity, which takes a value of unity subject to omitted variable bias. Thus, it cannot be unambiguously interpreted as a mark-up. It is also shown that the large estimates of the degree of increasing returns to scale are similarly flawed. The argument also has implications for understanding cyclical fluctuations of the Solow residual, which turns out to be largely the result of the procyclical fluctuations of the profit rate.We conclude by questioning whether the aggregate production function can ever be statistically tested or, in other words, whether it is capable of being refuted, as opposed to its parameters being merely estimated.

A size-distribution model with density-dependent growth rates

A size-distribution model incorporating density-dependent growth rates is proposed. The global existence and uniqueness of non-negative solutions are shown. The existence and stability of stationary solutions are also investigated. It is shown that the number of stationary solutions and their stability are completely determined by the density-dependent form of growth rates.