Economic and Financial Models

Tensor Bridge Invest AB uses advanced economic and financial models to assess investment value and risk. Our models employ cutting-edge techniques from the fields of Economics, Mathematics, and Artificial Intelligence (AI) to analyze a wide range of economic, financial, and value creation activities. These models are unique to our company and draw on original research, offering a level of insight that is not typically found in the academic or financial sectors.

In traditional simulations, an economic or financial theory is expressed in mathematical form as a model with unknown parameters. During the model identification phase, the values for all parameters are determined from theory, experience, or experimental work. Economic models are difficult to validate as controlled experiments are challenging and economic situations depend on multiple variable factors.

Validating a model against economic reality has at least two primary goals: to show that (1) the model can be used for faithful prediction, and (2) the model can be used to present a reasonable explanation of some economic reality in accordance with economic theory.

At Central Banks or at a policy/forward guidance level, the Projection Narrative has the highest priority. Structural models such as DSGE models are used to study the behavior of macroeconomic variables as a response to policy interventions. DSGE models capture the underlying relationships between economic variables and contain many microeconomic models, meaning that the number of parameters to identify is very large. Bayesian methods, Hidden Markov Models with Metropolis-Hastings samplers, importance sampling, etc., are used to identify these parameters. Central Banks appreciate the narrative and the possibility to exchange experiences when using DSGE models familiar to a larger community.

During validation there is often a difference between theoretical predictions and actual data observed in the real world. This difference is captured by an error term added to the equations of the model. The error term might indicate that the model is not good enough, there is noise in data, the data is not appropriate for the model, an unexpected shock occurred, there is an innovation process, or there are other unknown factors. Mathematical characterizations of the error term are used to identify its nature. Even with a significant error, it is possible to improve the theory and the model until the error term vanishes. This usually means adding new features to the model, increasing the number of parameters to be identified and increasing the complexity of the projection narrative. Model patching might however increase the size of the error term instead of reducing it, leading to erroneous results known in economics as the Simultaneous Equation Bias. Causality plays an important role here, and different concepts of statistical causality (Granger causality) and dynamic causality have been developed.

As known from Dynamic Systems theory, aggregated models might have emergent properties which could be different from the properties of individual components. The Sonnenschein-Mantel-Debreu (SMD) theorem is an instance of this property pointing e.g. to the difference between aggregated market demand curves at system and microfoundations levels.

Another category of models is the Semi-Structured Models (SSM), which are used by some Central Banks and the ECB. These models incorporate underlying relationships that may originate from experts or other models. While there are many implementations of SSM with varying levels of performance, they are generally appreciated for their ability to integrate relevant sub-models and enable richer policy analysis. However, SSM may not provide as accurate predictions as DSGE models. Matching models to each other and to the data can be a challenging task. For instance, it may require adjusting sample time granularity among models or using mixed data sampling regressions (MIDAS).

Alternatively, predictions can be made directly from data without using a formal economic model. These parameter-free methods are familiar in AI, but the economics and finance community has preferred historically vector autoregressive methods (VAR) or Bayesian VAR (BVAR). These models use a linear combination of a number of lags of the available time series to make predictions. These models are mainly used for reference predictions.

To address these and some other modeling challenges, Tensor Bridge Invest uses mathematical optimizations over a larger space of model structures with an AI search based on statistical attention mechanism. The result is a model structure which matches optimally the experimental data. While traditional error terms are euclidian distances, having abstract model structures in the search space requires more advance distance measures, usually a tensor distance. With this approach, the projection narrative is no longer a text devised by an economist, but the time evolution is an orbit generated mathematically in the phase space of the model. These orbits can be classified and translated. The orbits are also included in the error terms and used for search and optimization.

In summary, there are various types of models used in economics and finance, each with its strengths and limitations. While highly structured models like DSGE provide accurate predictions, they may not fit the data well. Semi-structured models like SSM allow for richer policy analysis but may not be as precise as DSGE models. Parameter-free models can provide a quick and easy way to make predictions, but they may lack the theoretical rigor of structured models. Selecting an optimized model structure overcomes possible misalignments between data and models and gives a narrative which is less subjective and with increased relevance for investment purposes.