The Investment Acceleration Principle Revisited by means of a Neural Network

Guido Fioretti

cs.NEOct 2, 2026

The Investment Acceleration Principle Revisited by means of a Neural Network

Authors: Guido Fioretti

Organizations: Universität Stuttgart Institute for Theoretical Physics and Synergetics Stuttgart, Germany · International Centre for Economic Research Turin, Italy

Abstract

The investment acceleration principle is a heuristic for modelling investment time series out of consumption time series. The model presented herein develops a disaggregated accelerator equation whose coefficients are the weights of a Kohonen neural net that represents firms' decision-making. According to this model, investments take place when managers recognise emerging technological patterns. Furthermore, a technique borrowed from the theory of self-organising systems is used in order to disentangle innovation-driven investments from plant-replication investments.

Figures & tables

Figure 1: Decision-making by a firm in the final goods sector. The Kohonen neuron consists of a summator of inputs $\Delta c_{i}$ and $\Delta\mathbf{e}$ with weights $a_{i}$ and $b_{i}$ , respectively. Both sets of weights are influenced by a feed-back $\phi$ and a feed-forward $\gamma$ , respectively. Left of the neuron, a first differences operator $\Delta$ performs the discrete-time derivative of the demand for final goods $\mathbf{c}$ and state-of-affairs in technology $\mathbf{e}$ , respectively. Right of the neuron, a summator performs the discrete-time integration of investments $\Delta\mathbf{k}$ , yielding capital stock $\mathbf{k}$ .

Figure 2: Decision-making by a firm in the capital goods sector. The Kohonen neuron consists of a summator of inputs $\Delta k_{i}$ with weights $d_{i}$ . These weights are influenced by a feed-back $\phi$ and a feed-forward $\gamma$ , respectively. Left of the neuron, a first differences operator $\Delta$ performs the discrete-time derivative of the demand for capital goods $\mathbf{k}$ . Right of the neuron, a summator performs the discrete-time integration of demand for labour $\Delta\mathbf{l^{\prime\prime}}$ , yielding employment $\mathbf{l^{\prime\prime}}$ .

Figure 3: The structure of information flows within a productive system. Each neuron represents decision-making by one firm. The left layer represents firms in the final goods sector, the right layer represents firms in the capital goods sector, respectively. A double feed-back arises through the labour market.

Figure 4: A sequence of a hundred vectors $\mathbf{e}$ from $t=1$ to $t=100$ , horizontal sections at $\mathbf{e}=\mathbf{0}$ . Black areas denote regions where $\mathbf{e}>\mathbf{0}$ , white areas denote regions where $\mathbf{e}\leq\mathbf{0}$ . The sinusoid spans 100 goods with 5 periods of 20 goods each, its amplitude increasing from $A_{min}=0$ at $t=1$ to $A_{max}=2$ at $t=100$ . Upon it, a normal distribution centred around zero adds noise with variance decreasing from $\sigma^{2}_{max}=1$ at $t=1$ to $\sigma^{2}_{min}=0$ at $t=100$ . In order to simplify the image only one out of four goods and one out of four time periods have been shown, resulting in a $25\times 25$ grid.

Figure 5: Investments by each single firm. Each curve represents a different $\Delta k_{i}$ for $i=1,2,\ldots 100$ during one single simulation. In order to depict zero values of investments on the logarithmic scale, a one has been added to all values.

Figure 6: Aggregate investments produced by ten different simulations (dashed lines) and their average (thick line). In order to depict zero values of investments on the logarithmic scale, a one has been added to all curves.

Figure 7: Variation of matrices $\mathbf{A}$ , $\mathbf{B}$ , $\mathbf{D}$ illustrated by indicators $\alpha$ , $\beta$ , $\delta$ , respectively. Indicators $\alpha$ , $\beta$ , $\delta$ are defined as the sum of the absolute variations of all elements of $\mathbf{A}$ , $\mathbf{B}$ , $\mathbf{D}$ , respectively. The graph illustrates the average of ten simulations.

Figure 8: Aggregate investments calculated by assuming that information vectors $\Delta\mathbf{c}$ and $\Delta\mathbf{k}$ vary with infinite speed. The figure illustrates ten single runs (dashed lines) as well as their average (thick solid line).

Figure 9: Variation of matrices $\mathbf{A}$ , $\mathbf{B}$ , $\mathbf{D}$ illustrated by indicators $\alpha$ , $\beta$ , $\delta$ , respectively. Indicators $\alpha$ , $\beta$ , $\delta$ are defined as the sum of the absolute variations of all elements of $\mathbf{A}$ , $\mathbf{B}$ , $\mathbf{D}$ , respectively. The graph illustrate the averages of ten simulations.

Figure 10: Aggregate investments according to the original model (thin line) and aggregate investments according to the two-regimes model (thick line). Both curves depict the average of ten simulation runs.

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Abstract

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