Maxim Gusev and Dimitri Kroujiline
Macroeconomic models rarely make explicit how people actually interact. When this is explicitly specified, the link between the micro and macro properties of models becomes much richer. Can methods from statistical mechanics and dynamical systems describe these interactions and give insights into macroeconomic instability? Our research project looks at how financial models of interaction can be extended to macroeconomics.
Real world decision making involves both independent thinking and the exchange of ideas with others. By taking into account our interactions with others, we may be better able to capture some sources of instability (see an overview by Lux, 2009). For example, interactions may lead small disturbances to have much larger consequences for the economy. An example of this sort of amplification was of course the sub-prime crisis leading to the Global Financial Crisis.
To explore how some simple interactions between agents can create instability, we wish to extend the model of Gusev et al. (2015) of the stock market to the macroeconomy. This stock market model has two types of agents who interact by exchanging opinions: investors who trade based on their expectations and analysts who form expectations by interpreting financial news and channel these expectations to investors. This specification of how agents interact creates, on a macro level, a nonlinear dynamical system that links news, expectation and price together. The form of this linkage can create a feedback mechanism whereby news events influence investor expectations, which affects investment decisions that cause price changes; then, price changes themselves draw media attention and trigger further news releases – which becomes a source of instability.
But how realistic is this? Kroujiline et al. (2016) show that this stock market model replicates actual past prices within reasonable tolerance. It can also predict returns with a precision sufficient for designing a trading strategy. Kroujiline et al. (2018) attached it to a reduced-form economic model (Blanchard, 1981) to suggest an endogenous mechanism of business cycles.
The observation that firms’ investment spending decisions involve the expectation of return on investment and the information (news) underlying these expectations (e.g. about the economy’s growth) invokes similarity to the stock market modeling described above, making it relevant to the real economy.
The basic modeling framework is as follows. Output grows as a function of investment. The amount of investment depends on the expected return on investment. Hence, the dynamics of expectations must enter the modeling problem, and we treat these expectations, similar to Gusev et al. (2015), as depending on interactions across the economy and news about economic development.
The real economy and the stock market become mutually linked in two ways. First, there are borrowing constraints on capital deployment (determined as a function of firms’ valuations). Second, economic growth modulates the news flow relevant to the stock market (because the volume of positive news increases where the economy expands and decreases where it contracts). The figure below sets out a schematic view of the model.
The specification of the macroeconomy will rely on traditional macroeconomics. The micro-level interaction which feeds into the macro-level equations will use ideas from statistical mechanics. Studying the derived equations will utilize methods developed in dynamical systems analysis.
We are particularly interested in applying this model to study business cycles and regime transitions with the objective to better understand the mechanisms behind these phenomena. We also hope to identify the empirical characteristics of these mechanisms in the actual market and economic behaviors. This may enable us to apply the model to determine the economy’s position within a business cycle, design leading indicators of regime changes or offer scenarios for economic development given its initial state.
Blanchard, O. 1981. Output, the stock market, and interest rates. American Economic Review, 71, 132-143.
Gusev, M., Kroujiline, D., Govorkov, B., Sharov, S. V., Ushanov D., Zhilyaev, M. 2015. Predictable markets? A news-driven model of the stock market. Algorithmic Finance, 4, 5-51.
Kroujiline, D., Gusev, M., Ushanov, D., Sharov, S. V., Govorkov, B. 2018. An endogenous mechanism of business cycles. Working paper.
Kroujiline, D., Gusev, M., Ushanov, D., Sharov, S. V., Govorkov, B. 2016. Forecasting stock market returns over multiple time horizons. Quantitative Finance, 16, 1695-1712.
Lux, T. 2009. Stochastic behavioral asset-pricing models and the stylized facts. In: Handbook of Financial Markets: Dynamics and Evolution, North-Holland (pp. 161-216).