Abstract
We extend an aggregative growth model for a small open economy by developing a framework in which boundedly rational agents raise credit in proportion to their expected income. Moreover, these agents are heterogeneous in the sense that they switch between an extrapolative and a regressive forecasting rule with respect to perceived market circumstances. Using a mixture of analytical and numerical tools, we attempt to describe the characteristics of our model’s dynamical system. Our results then suggest that self-fulfilling short-run expectations do not only have important consequences for fluctuations in economic activity but are also a source of simple endogenous dynamics.
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Notes
Please note the time structure of our model. All decisions regarding credit and savings are made at the beginning of each period, while income is generated afterwards. Thus, credit decisions have to rely on expectations of the income which will be earned in the current period. Unfortunately, these expectations are hard to observe such that the empirical evidence of the proposed relationship is rare at best. For example, Bacchetta and Gerlach (1997) find a high positive correlation between consumption and credit growth, indicating that credit may adjust to (desired) consumption which, in turn, relates to expected (future) income. Alternatively and favoured by the authors, credit constraints may also be reflected in consumption.
It is worth noting that there exists no consensus on how to incorporate heterogeneous beliefs in a macroeconomic framework. However, Anufriev et al. (2008) argue that the most natural way to embed heterogeneous expectations in a linear macroeconomic framework which has no underlying microfoundation is to use a simple weighted average of the individual expectations.
Of course, \(\overline{y}=0\) also defines a steady-state solution of our nonlinear system. But since this trivial solution is not particularly meaningful from an economic point of view, we will omit it in the further discussion.
Clearly, these results may change if we allow the risk-free interest rate to become unrealistically high and to exceed \(r>1\). In this case, condition (24) may also be violated for certain parameter combinations. However, since this theoretical case is too detached from reality we will omit it in the further examination.
More precisely, (25) is not a necessary and sufficient condition for a Neimark–Sacker bifurcation to occur, that is, violation of (25) just implies a loss of stability but does not necessarily imply the birth of a Neimark–Sacker bifurcation, the existence of which still has to be proven. However, the exact mathematical proof is tricky at best and may not be accomplished easily. For that reason, a majority in the economic literature tends to accept condition (25) as being both necessary and sufficient if the existence of the predicted bifurcation is numerically confirmed.
That is to say, \(\sigma =0\) indicates that the system is in equilibrium.
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Wegener, M. Heterogeneous expectations and debt in a growth model for a small open economy. Decisions Econ Finan 37, 125–136 (2014). https://doi.org/10.1007/s10203-013-0142-1
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DOI: https://doi.org/10.1007/s10203-013-0142-1