This study reveals endogenous instability in the financial market based on the dynamic interaction between endogenous investment behavior and debt in a nonlinear framework, by using a nonlinear model predictive control (NMPC) approach. It is found that when the debt ratio is below a critical threshold, increased debt has a positive effect on investment. On the other hand, when the debt ratio is above that threshold, growing financial stress and greater debt become a drag on investment, leading to an economic downturn and an outbreak of financial crisis. The paper provides theoretical support for Minsky’s financial instability hypothesis.
The traditional Keynesian macroeconomic theory considers the financial sector only as the intermediary for investment and cannot fully explain economic instability induced by a complex financial system [
[
A vast literature on the relationship between the financial sector and the real sector has emerged since the 2007-09 global economic recession. Much of the recent research emphasizes the role of asset prices and asset- volatility in downward destabilization, such as [
While the financial instability hypothesis puts investment in a core position, the aforementioned studies take investment as an exogenous control variable, which leads to the intractability of investment dynamics. Since investment accounts for a large proportion of national income in China, it is important to track the dynamic evolutionary path of investment. In this paper, to capture the dynamics between investment and debt, we extend the models of [
Our model is mostly related to [
subject to:
where Kt is the capital stock, It the aggregate investment,
In order to determine the rate of investment, following [
Equation (8) indicates the investment ratio in terms of output as being dependent on profits and debt. It allows the rate of investment to be endogenously determined which is consistent with the financial instability hypothesis. The production function is provided in Equation (6).
The above system is conventionally solved by a dynamic programming (DP) approach. However, DP is subject to the curse of dimensionality since the computation time increases exponentially with the dimension of the state variables. A remedy to this problem is to use the nonlinear model predictive control (NMPC), which is an attractive alternative to the DP approach, because it only computes single (approximate) optimal trajectories and not the optimal value function for all possible initial states ([
As shown in
Endogenously unstable financial markets have attracted much attention since the outbreak of the global financial crisis in 2007. To better model the dynamic mechanism of the financial instability hypothesis initially put forth by [
economy is being exposed to shocks in credit spread. In particular, our model incorporates investment as one of endogenous constraints. By using a nonlinear model predictive control approach, we have examined how financial instability is created endogenously. The model established in this paper can be used to capture the core of the financial instability hypothesis and demonstrate financial endogenous instability. Our theoretical model implies that unfavorable credit spreads and high leverage ratios play an important role for the recession of the investment and financial instability. In the presence of large credit spreads and high leveraging, increasing leveraging can induce instabilities and the meltdown of investment. In terms of policy implications, our results strongly suggest that excessive leverage is one of the important reasons leading to declining investment at present in China, and so deleveraging can be currently a wise strategy in China. For future research, one may conduct empirical test to verify the theory developed in this paper.
We would like to thank Cong Qin, Mandy Cheung and Junjie Guo for able research assistant. The financial support from the National Natural Science Foundation of China (71201174), the Natural Science Foundation of Guangdong Province, China (S2013010015019) and Fundamental Research Funds for the Central Universities (1209022) are gratefully acknowledged.