Voksmodellen

Voksmodellen, or growth model, is a term used in Norwegian and Danish to refer to mathematical or statistical models that describe how a quantity grows over time. Such models are used across disciplines, including economics, biology, and demography, to analyze long‑term dynamics and forecasting.

In economics, voksmodellen describes how an economy grows over the long run, typically by mapping outputs to inputs such as capital and labor and to technology. A classic example is the Solow growth model, which includes a production function, capital accumulation with depreciation, and exogenous technological progress. Endogenous growth models, such as Romer’s, attempt to explain technological progress from within the model through investment in knowledge and ideas.

In ecology and demography, growth models describe populations or biomass as they increase or fluctuate. The exponential and logistic models are common, with logistic growth incorporating a carrying capacity that slows growth as population density rises. More complex models may include age structure, density dependence, and interactions with resources or predators.

Typical components of a voksmodell are variables representing state factors (capital stock, population, technology), parameters (growth rate, investment rate, depreciation), and a mathematical rule that updates the state over time, either continuously or in discrete steps. Models are calibrated with data and used for scenario analysis and policy assessment.

Limitations include simplifying assumptions, sensitivity to parameter choices, and the omission of shocks and structural breaks. Model validity depends on context, data quality, and the appropriateness of the growth mechanism being represented.

See also: Solow model, endogenous growth theory, logistic growth model, Gompertz function.