Real and financial interacting markets: A behavioral macro-model

Abstract

a b s t r a c tIn the present paper we propose a model in which the real side of the economy, described via a Keynesian good market approach, interacts with the stock market with heterogeneous speculators, i.e., optimistic and pessimistic fundamentalists, that respectively overestimate and underestimate the reference value due to a belief bias. Agents may switch between optimism and pessimism according to which behavior is more profitable. To the best of our knowledge, this is the first contribution considering both real and financial interacting markets and an evolutionary selection process for which an analytical study is performed. Indeed, employing analytical and numerical tools, we detect the mechanisms and the channels through which the stability of the isolated real and financial sectors leads to instability for the two interacting markets. In order to perform such analysis, we introduce the "interaction degree approach", which allows us to study the complete three-dimensional system by decomposing it into two subsystems, i.e., the isolated financial and real markets, easier to analyze, that are then linked through a parameter describing the interaction degree between the two markets. We derive the stability conditions both for the isolated markets and for the whole system with interacting markets. Next, we show how to apply the interaction degree approach to our model. Among the various scenarios we are led to analyze, the most interesting one is that in which the isolated markets are stable, but their interaction is destabilizing. We choose such setting to give an economic interpretation of the model and to explain the rationale for the emergence of boom and bust cycles. Finally, we add stochastic noises to the optimists and pessimists demands and show how the model is able to reproduce the stylized facts for the real output data in the US.

Agents' beliefs and economic regimes polarization in interacting markets

“…From Proposition 1, it is possible to have either one or three steady states, whose existence is triggered by sufficiently large values of β and b. Steady state S * , in which Y * reduces to the same steady state of the Samuelson model when ω = 0, is in agreement with those found in [4,21,23], so that all the comments therein apply to S * , as well.…”

“…In order to discipline the evolution of the agents' share employing a certain speculative rule, we assume that a fraction of optimistic agents can switch from period to period to the other behavior, and vice versa. In the present model, differently from [23] and similarly to [5], such an evolutionary process is governed by the squared forecasting error evaluated on the last realization of the fundamental value and of the stock price, namely…”

“…In particular, we want to understand what kinds of dynamics occur when S * becomes unstable, as well as to investigate the possible scenarios arising with the emergence of S L and S H . Secondly, we want to study the qualitative properties of the time series when exogenous non-deterministic effects are taken into account, that is, considering a stochastically perturbed version of the model, in agreement with [4,11,23]. In continuity with Section 3, we focus on the effect of the degree of interaction ω and of the intensity of choice β.…”

“…In order to investigate these aspects, building on the approach pursued in the above mentioned contributions, we analyze an economy made by two, possibly interdependent, subsystems, namely a real and a financial sector. The real sector essentially recalls the economy presented in [4] and [24], in which a multiplier-accelerator model with a bounded investment function is studied, and it is coupled with a stock market populated by optimistic and pessimistic fundamentalists, modeled by following the approach in [23]. In so doing, we shall focus our attention on the degree of interaction between markets, which positively depends on the parameter ω ∈ [0, 1], as well as we shall take into account the role of agents' beliefs, represented by a symmetric optimistic/pessimistic bias b > 0, and their willingness to switch toward the best performing strategy while operating in the stock market, described by the so-called intensity of choice β > 0 (see e.g.…”

Heterogeneity and the (de)stabilizing role of rationality

“…Function (4.2) indeed satisfies the requirements on σ specified in Section 2. We remark that a similar approach has been used in [32,33] in microeconomic frameworks, and in [34][35][36] in macroeconomic settings. We notice that for (4.2) we have Performing a simulation of (4.1) for the parameters choice c R = 0.1063, c N = 0.1 and k = 0.5, we find the unconditionally stable scenario, in which all the oligopoly configurations ω = 1/10, 2/10, .…”