Aggregate Growth Model Research Articles

Unification of aggregate growth models by emergence from cellular and intracellular mechanisms.

Multicellular aggregate growth is regulated by nutrient availability and removal of metabolites, but the specifics of growth dynamics are dependent on cell type and environment. Classical models of growth are based on differential equations. While in some cases these classical models match experimental observations, they can only predict growth of a limited number of cell types and so can only be selectively applied. Currently, no classical model provides a general mathematical representation of growth for any cell type and environment. This discrepancy limits their range of applications, which a general modelling framework can enhance. In this work, a hybrid cellular Potts model is used to explain the discrepancy between classical models as emergent behaviours from the same mathematical system. Intracellular processes are described using probability distributions of local chemical conditions for proliferation and death and simulated. By fitting simulation results to a generalization of the classical models, their emergence is demonstrated. Parameter variations elucidate how aggregate growth may behave like one classical growth model or another. Three classical growth model fits were tested, and emergence of the Gompertz equation was demonstrated. Effects of shape changes are demonstrated, which are significant for final aggregate size and growth rate, and occur stochastically.

Aggregate growth models from a Schumpeterian perspective

The paper presents a critical assessment of the Schumpeterian macroeconomic approach to economic growth. Taking as reference a representative sample of important works within this tradition, the paper identifies the main contributions and limitations of the macroeconomic Schumpeterian literature to understanding economic growth. More specifically, the literature review carried out in this paper focuses on three of Schumpeter’s ideas that have become particularly influential in macroeconomic growth theory: (i) the role of technological transfer in productivity growth in follower countries; (ii) the importance of research intensity for technical progress; and (iii) the prominence of technological competitiveness for trade performance. The contribution of the paper is twofold: (i) it provides an organized review of the macroeconomic literature until its present state; and (ii) it indicates important gaps in this literature that should be the focus of further research.

Continental-scale tree-ring-based projection of Douglas-fir growth: Testing the limits of space-for-time substitution.

A central challenge in global change research is the projection of the future behavior of a system based upon past observations. Tree-ring data have been used increasingly over the last decade to project tree growth and forest ecosystem vulnerability under future climate conditions. But how can the response of tree growth to past climate variation predict the future, when the future does not look like the past? Space-for-time substitution (SFTS) is one way to overcome the problem of extrapolation: the response at a given location in a warmer future is assumed to follow the response at a warmer location today. Here we evaluated an SFTS approach to projecting future growth of Douglas-fir (Pseudotsuga menziesii), a species that occupies an exceptionally large environmental space in North America. We fit a hierarchical mixed-effects model to capture ring-width variability in response to spatial and temporal variation in climate. We found opposing gradients for productivity and climate sensitivity with highest growth rates and weakest response to interannual climate variation in the mesic coastal part of Douglas-fir's range; narrower rings and stronger climate sensitivity occurred across the semi-arid interior. Ring-width response to spatial versus temporal temperature variation was opposite in sign, suggesting that spatial variation in productivity, caused by local adaptation and other slow processes, cannot be used to anticipate changes in productivity caused by rapid climate change. We thus substituted only climate sensitivities when projecting future tree growth. Growth declines were projected across much of Douglas-fir's distribution, with largest relative decreases in the semiarid U.S. Interior West and smallest in the mesic Pacific Northwest. We further highlight the strengths of mixed-effects modeling for reviving a conceptual cornerstone of dendroecology, Cook's 1987 aggregate growth model, and the great potential to use tree-ring networks and results as a calibration target for next-generation vegetation models.

Aggregate Growth and Internal Structures of Chondrite Parent Bodies Forming from Dense Clumps

Abstract The major components of chondrites are chondrules and matrix. Measurements of volatile abundance in Semarkona chondrules suggest that chondrules formed in a dense clump that had a higher solid density than the gas density in the solar nebula. We investigate collisions between chondrules and matrix in the surface region of dense clumps using fluffy aggregate growth models. Our simulations show that the collisional growth of aggregates composed of chondrules and matrix takes place in the clumps well before they experience gravitational collapse. The internal structure of chondrite parent bodies (CPBs) can be thereby determined by aggregate growth. We find that the aggregate growth generates two scales within CPBs. The first scale is involved with the small-scale distribution of chondrules and determined by the early growth stage, where chondrules accrete aggregates composed of matrix grains. This accretion can reproduce the thickness of the matrix layer around chondrules found in chondrites. The other scale is related to the large-scale distribution of chondrules. Its properties (e.g., the abundance of chondrules and the overall size) depend on the gas motion within the clump, which is parameterized in this work. Our work thus suggests that the internal structure of CPBs may provide important clues about their formation conditions and mechanisms.

Enhancing Gravity Thickener Feedwell Design and Operation for Optimal Flocculation through the Application of Computational Fluid Dynamics

ABSTRACT As the expectations for more consistent and higher density thickened and paste tailings in the minerals industry increase, so do the demands on flocculation performance within gravity thickeners. Low solids feed suspensions are delivered at a high velocity to center feedwells, which not only serve to dissipate the feed’s momentum and evenly distribute the solids, but are also the primary means by which polymer flocculant solutions are distributed across the fine particle to form fast settling (but fragile) aggregates. Computational fluid dynamics (CFD) is a powerful tool for optimizing the design and performance of unit operations used to achieve particle aggregation and sedimentation. Early CFD feedwell modeling gave predictions on the solids and fluid flows, which were useful for identifying discharge asymmetry and short-circuiting currents, but did not give major insights into aggregation states. Incorporating a population balance (PB) model of aggregate growth and breakage made it possible to capture the critical impacts of shear, residence time and solids concentration that characterize polymer-bridging flocculation, in particular the potential for prolonged higher shear conditions to give excessive breakage. This created a unique capability for understanding the complex balance between the hydrodynamic and physical chemistry requirements for flocculation, enabling systematic CFD studies of different design and operation elements. Some of the main conclusions on feedwell design optimization are outlined. Potential future applications of CFD outputs in feed-forward thickener control are also discussed.

A two-sector Kaleckian model of growth and distribution with endogenous productivity dynamics

This study extends a two-sector Kaleckian model of output growth and income distribution by incorporating endogenous labour productivity growth. The model is composed of investment goods and consumption goods production sectors. The impact of a change in wage and profit shares on capacity utilisation and output growth rates at the sectoral and aggregate levels are identified. The study reveals short-run cyclical capacity utilisation rates and productivity growth dynamics. Even if the short-run steady state is stable, the capital accumulation rate in the consumption goods sector must decrease more than that in the investment sector for long-run stability. When simultaneous rises in profit shares in both the sectors affect long-run aggregate economic growth differently at a steady state, the distributional interests between the same class in different sectors may hamper the long-run economic growth. A policy message is that the effect of income distribution on industrial output growth is not always beneficial. These phenomena are specific to two-sector models and cannot be observed when using conventional aggregate growth models.

WHO QUITS NEXT? FIRM GROWTH IN GROWING ECONOMIES

We document novel facts about the relationship between aggregate growth and firm dynamics using a large set of countries. We argue that firm employment patterns are not necessarily informative about cross‐country differences in aggregate growth because they are induced by changes in the productivity of a firm relative to others. In contrast, aggregate growth is linked to average firm‐level productivity growth and firm age. We formalize this intuition through a tractable model of endogenous aggregate growth and firm dynamics where firms realize positive returns to investment with some probability. We find that cross‐country disparities in this probability can account for two‐thirds of the variation in aggregate growth. (JEL D21, D22, E23, O4)

Suppes–Sen maximality of cyclical consumption: The neoclassical growth model

In this paper we demonstrate the existence of cyclical consumption that are maximal according to the Suppes–Sen grading principle for the Aggregative Growth Model. The paper demonstrates the optimality of cyclical consumption paths in the absence of discounting for the smooth neoclassical growth model. The process of this verification allows us to develop the theory of weakly maximal paths for a non-concave and discontinuous utility function extending previous results from Optimal Growth Theory.

Expectations, Means-Tested Subsidies, and Economic Performance during the Recession

The aggregate neoclassical growth model with only one impulse—means-tested subsidies whose replacement rates began rising at the end of 2007—produces time series for aggregate labor usage, consumption, investment, and real GDP that closely resemble actual US time series. Despite having no explicit financial market, the model has investment fall steeply during the recession not because of any distortions with the supply of capital, but merely because labor is falling and labor is complementary with capital in the production function. Through the lens of the model, the fact that real consumption fell significantly below trend during 2008 suggests that market participants were expecting labor usage to remain depressed for several years to come.

Controllable 5-sulfosalicylic acid assisted solvothermal synthesis of monodispersed superparamagnetic Fe3O4 nanoclusters with tunable size

Monodispersed Fe3O4 nanoclusters were synthesized in a one-pot solvothermal route with 5-sulfosalicylic acid (SSA) as the functional ligand in a mixed-solvent system of diethylene glycol/ethylene glycol (DEG/EG). Nucleation and aggregation growth model was responsible for the formation of secondary structure of the clusters. In the process, the size of the clusters can be effectively controlled by varying the amounts of SSA and the volume ratio of DEG/EG. The nanoclusters exhibited superparamagnetic properties with high saturation magnetization value of about 68.7emug−1 at room temperature. The water-soluble small-molecule SSA grafted on the surface of Fe3O4 nanocrystals rendered the superparamagnetic clusters dispersible in water, which is crucial for potential applications in biomedical fields.

Diffusion of innovations dynamics, biological growth and catenary function

The catenary function has a well-known role in determining the shape of chains and cables supported at their ends under the force of gravity. This enables design using a specific static equilibrium over space. Its reflected version, the catenary arch, allows the construction of bridges and arches exploiting the dual equilibrium property under uniform compression. In this paper, we emphasize a further connection with well-known aggregate biological growth models over time and the related diffusion of innovation key paradigms (e.g., logistic and Bass distributions over time) that determine self-sustaining evolutionary growth dynamics in naturalistic and socio-economic contexts. Moreover, we prove that the ‘local entropy function’, related to a logistic distribution, is a catenary and vice versa. This special invariance may be explained, at a deeper level, through the Verlinde’s conjecture on the origin of gravity as an effect of the entropic force.

Sectoral Dynamics and Business Cycles

I construct an index of sectoral dynamics to characterize changes in the sectoral composition of economic activity. There is evidence of asymmetry in different phases of business cycles with recessions being associated with larger changes in sectoral composition than expansions. I find that the correlation between dynamics in sectoral employment and aggregate output has weakened since the 1990s. Also, sectoral changes appear to be smaller and spread across more sectors, while their contribution to aggregate volatility has been increasing. I also perform a simulation exercise and replicate these documented facts. The results suggest that shifts in the sectoral composition of the economy likely contribute to the formation of business cycles. Also the duration of recessions implied by the impulse response functions from a VAR model of sectoral dynamics and aggregate output growth matches the duration of recessions observed in the data.

Asia Rising: Growth and Resilience in an Uncertain Global Economy

Asia Rising: Growth and Resilience in an Uncertain Global Economy. Edited by Hal Hill and Maria Socorro Gochoco-Bautista. Cheltenham, UK: Edward Elgar and Asian Development Bank, 2013. Pp. xvi + 424. Asia Rising takes stock of Asian economies in the aftermath of the 2008-09 Global Financial Crisis (GFC) and evaluates challenges and opportunities for continued growth. It opens with an editorial overview; continues with thematic chapters on a variety of topics linked by a common concern with investment; and concludes with country studies of Malaysia, Indonesia, India, China, Thailand and the Philippines. The seventeen contributing authors are economists either in regional academic institutions or at the Manila-based Asian Development Bank. The book's central concern is, in the editors' words, developing middle-income Asian countries maintain their economic dynamism and navigate through deep economic crises against the backdrop of continuing global uncertainty and instability (p. 3). The focus is on macroeconomic dimensions, notably in managing the inevitable slowdown from earlier decades of rapid growth and dealing with the effects of external economic challenges, like the GFC, that threaten to push domestic savings, investment and financial development off their desired paths. The primary contribution is to help us understand better how investment, the wellspring of economic growth, is affected by global shocks in a set of economies with imperfect markets, policies and institutions. Authors of the thematic chapters deploy a wide variety of methods and data. Chapter 2 by Emmanuel De Dios and Geoffrey Ducanes, entitled Institutions and Governance, deploys a linear regression model with a 164-country data set to investigate the influence of institutions on change in investment/GDP ratios from 1991-95 until 2002-06. They conclude that and institutional factors do exert an influence on investment in Asia and that they form part of the explanation of the observed investment behaviour in the region. Similarly, Chapter 3, by Douglas Brooks and Eugenia Go, sets up a Solow-type aggregate growth model and then proposes a large array of infrastructure investment proxies to be included as additional explanatory variables, in estimates based on a panel of 123 countries over the period 1971-2005. They report (among other things) that investments in telecomms, road and air transport systems and energy consumption all support economic growth. However, this chapter reports neither data nor econometric results, so it is impossible to evaluate the authors' claims. More generally, the use of global data sets and generic models in both these chapters makes it a priori difficult to identify phenomena specific to developing Asia. In other thematic chapters, Kyoji Fukao (Chapter 4) sets up a dynamic macro growth model and uses it to evaluate the likely impacts of an exogenous drop in productivity growth on capital accumulation and other indicators of economic structure and performance. Charles Horioka and Akiko Terada-Hagiwara (Chapter 5) and Shin-ichi Fukuda (Chapter 6) present careful examinations of Asian (rather than global) cross-country data to explore, respectively, the role of demographic trends as drivers of household savings rates, and the contribution of financial development to investment growth. Diane Desierto (Chapter 7) presents a textual analysis of ASEAN investment treaties. The six country chapters document responses to the 1997-98 Asian Financial Crisis (AFC) and GFC, taking a more narrative approach. Chapters on China (by Siow Yue Chia) and Thailand (Bhanupong Nhidiprabha) are both very nice examples of near-term macroeconomic history. As with the earlier chapters, a concern with investment (or, in some cases, the lack of it) is common to nearly all the country chapters. Several make the point that domestic investment rates were quick to decline, yet slow to recover during the 2000s for reasons that went well beyond the AFC itself to deeper weaknesses, notably the lack of complementary infrastructure or governance institutions. …

Proportional economic growth under conditions of limited natural resources

The paper is devoted to economic growth models in which the dynamics of production factors satisfy proportionality conditions. One of the main production factors in the problem of optimizing the productivity of natural resources is the current level of resource consumption, which is characterized by a sharp increase in the prices of resources compared with the price of capital. Investments in production factors play the role of control parameters in the model and are used to maintain proportional economic development. To solve the problem, we propose a two-level optimization structure. At the lower level, proportions are adapted to the changing economic environment according to the optimization mechanism of the production level under fixed cost constraints. At the upper level, the problem of optimal control of investments for an aggregate economic growth model is solved by means of the Pontryagin maximum principle. The application of optimal proportional constructions leads to a system of nonlinear differential equations, whose steady states can be considered as equilibrium states of the economy. We prove that the steady state is not stable, and the system tends to collapse (the production level declines to zero) if the initial point does not coincide with the steady state. We study qualitative properties of the trajectories generated by the proportional development dynamics and indicate the regions of production growth and decay. The parameters of the model are identified by econometric methods on the basis of China’s economic data.

Standards, learning, and growth inBritain, 1901–2009

This article considers the model of voluntary, consensus based standardization as developed through theBritishStandardsInstitution (BSI) and its contribution to learning and productivity growth. It discusses the significant role played by professional engineers in the model's introduction, its extension at home, and its imitation overseas. It is argued that by 1931 theBSIcatalogue of standards represented a considerable stock of codified knowledge whose growth reflected underlying aggregate technological opportunities, assisting in their transformation into technological advance. To help validate this claim, a measure of the size of theBSIcatalogue of standards is incorporated into an econometric model of aggregate productivity growth in Britain. Findings show that the growth of the standards catalogue is associated with a substantial proportion of labour productivity growth over the period 1931–2009. Estimates relating to the short‐run dynamics involved are consistent with the idea that there are causal linkages running from standards to growth. When interpreting these findings, it is argued that the overall weight of historical evidence points to standardization—coordinated through theBSI—as providing an important path of learning for the British economy over the period considered.

Structural change, aggregate demand and employment dynamics in the OECD, 1970–2010

The paper combines Baumol's model of structural change with a model of aggregate demand growth in the Keynesian–Kaleckian tradition to predict the dynamics of aggregate employment. The model for the demand regime is estimated with – and Baumol's model for the productivity regime is calibrated on – OECD data. The trajectory for employment predicted by the combination of the two models tracks the actual employment dynamics in the OECD over the period 1970–2010 remarkably well.

Structural change, aggregate demand and employment dynamics in the OECD, 1970 - 2010

Abstract The paper combines Baumol's model of structural change with a model of aggregate demand growth in the Keynesian–Kaleckian tradition to predict the dynamics of aggregate employment. The model for the demand regime is estimated with – and Baumol's model for the productivity regime is calibrated on – OECD data. The trajectory for employment predicted by the combination of the two models tracks the actual employment dynamics in the OECD over the period 1970–2010 remarkably well.

English

In this paper authors have demonstrated the possibility of using aggregative growth model to search conditions of synthesis required composition AgxPb1−xS1−δ thin films. According to simulation results concentration areas of forming supersaturated solid solution components with a maximum of Ag2S up to 12,8 mol.% have established. The experiment confirmed the adequacy of the model for the PbS–Ag2S system.

Change of scaling and appearance of scale-free size distribution in aggregation kinetics by additive rules

The idealized general model of aggregate growth is considered on the basis of the simple additive rules that correspond to a one-step aggregation process. The two idealized cases were analytically investigated and simulated by the Monte Carlo method in the Desktop Grid distributed computing environment to analyze “pile-up” and “wall” cluster distributions in different aggregation scenarios. Several aspects of aggregation kinetics (change of scaling, change of size distribution type, and appearance of scale-free size distribution) driven by the “zero cluster size” boundary condition were determined by the analysis of evolving cumulative distribution functions. The “pile-up” case with a minimum active surface (singularity) could imitate piling up aggregations of dislocations, and the case with a maximum active surface could imitate arrangements of dislocations in walls. The change of scaling law (for pile-ups and walls) and availability of scale-free distributions (for walls) were analytically shown and confirmed by scaling, fitting, moment, and bootstrapping analyses of simulated probability density and cumulative distribution functions. The initial “singular” symmetric distribution of pile-ups evolves by the “infinite” diffusive scaling law and later it is replaced by the other “semi-infinite” diffusive scaling law with asymmetric distribution of pile-ups. In contrast, the initial “singular” symmetric distributions of walls initially evolve by the diffusive scaling law and later it is replaced by the other ballistic (linear) scaling law with scale-free exponential distributions without distinctive peaks. The conclusion was made as to possible applications of such an approach for scaling, fitting, moment, and bootstrapping analyses of distributions in simulated and experimental data.

Heterogeneous expectations and debt in a growth model for a small open economy

We extend an aggregative growth model for a small open economy by developing a framework in which boundedly rational agents raise credit in proportion to their expected income. Moreover, these agents are heterogeneous in the sense that they switch between an extrapolative and a regressive forecasting rule with respect to perceived market circumstances. Using a mixture of analytical and numerical tools, we attempt to describe the characteristics of our model’s dynamical system. Our results then suggest that self-fulfilling short-run expectations do not only have important consequences for fluctuations in economic activity but are also a source of simple endogenous dynamics.