Abstract
This study provides a heterogeneous agent-based microfoundation to the concept of “liquidity trap” with a binary choice model, in which an economic agent stochastically changes her decisions. The transition rates from one state to the other vary, depending on the degree of diversity in expectations. Applying this model to the money/bond choice, this study seeks to derive the money demand function proposed by Keynes and analyze how the heterogeneity of expectations affects it. The model demonstrates that money holding becomes relatively advantageous as the proportion of money holders increases and that such a situation could bring about multiple equilibria. Through comparative statics, this study finds that the heterogeneity of expectations plays a crucial role for existence of multiple equilibria. Demonstrating that a financial crisis is a leap from one equilibrium to the other, the model helps to explain the recent crisis and offers practical implications for monetary policies. In particular, in analyzing the influences of heterogeneous expectations on the economy, this study uncovered an interesting fact that unconventional monetary policies work better than conventional ones in fighting against crises induced by a flight to liquidity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
We need the boundary condition for \(n=0\) and \(n=N\),
$$\begin{aligned} \frac{dP_t(0)}{dt}= & {} P_t(1)w_{1,0}-P_t(0)w_{0,1},\\ \frac{dP_t(N)}{dt}= & {} P_t(N-1)w_{N-1,N}-P_t(N)w_{N,N-1}. \end{aligned}$$When N is large, we can use Stirling formula,
$$\begin{aligned} N! \approx \sqrt{2\pi N} \Bigl ( \frac{N}{e} \Bigr ) ^N, \end{aligned}$$and then we obtain
$$\begin{aligned} \ln {N\atopwithdelims ()n} =NH\left( \frac{n}{N}\right) + O\left( \frac{1}{N}\right) . \end{aligned}$$A good example of the entropy effect is the existence of air at high altitudes. If particles of air were influenced only by gravitational force, air would not exist at any point above a certain height. However, air in fact exists at high altitudes although it is very thin. This is because not only gravity but also the entropy effect affects particles in air.
The average of the capital gain is assumed to be zero without loss of generality. Note that the adoption of the logistic distribution is not crucial for the results. It is possible to assume the normal distribution if we are willing to deal with two parameters in our analysis. See also footnote 6.
If normal distribution \(N(\mu ,\sigma ^2)\) is assumed at (9), the LHS of (12) should be
$$\begin{aligned} -\ln \frac{\eta _1}{\eta _2}=\ln \frac{{\varPhi }\bigl ( \frac{r+\mu }{\sigma } \bigr )}{1-{\varPhi }\bigl ( \frac{r+\mu }{\sigma } \bigr )}, \end{aligned}$$where \({\varPhi }\) shows the cumulative distribution function of the standard normal distribution. Since this is a monotonically decreasing function in r and \(\sigma \), we will obtain essentially the same results even if we use the normal distribution rather than the logistic distribution.
This definition is from Aoki (1996, Ch. 5). It can be interpreted as Marshallian externalities in microeconomics.
I thank the referee for providing helpful comment on this point.
Let us denote \(f(x)=N\ln \frac{1-x}{x} +\frac{\alpha }{\gamma }x\) and set \(x_0\) and \(x_1 \ (x_0 < x_1)\) for two real solutions of \(x^2-x+\frac{N\gamma }{\alpha }=0\). The condition for existence of multiple equilibria is \(f(x_0) \le \frac{r}{\gamma }-N\ln \frac{1-\lambda }{\lambda } \le f(x_1)\).
Keynes (1937) notes:
Because, partly on reasonable and partly on instinctive grounds, our desire to hold Money as a store of wealth is a barometer of the degree of our distrust of our own calculations and conventions concerning the future. Even tho this feeling about Money is itself conventional or instinctive, it operates, so to speak, at a deeper level of our motivation. It takes charge at the moments when the higher, more precarious conventions have weakened. The possession of actual money lulls our disquietude; and the premium which we require to make us part with money is the measure of the degree of our disquietude.
Aoki et al. (2005) analyze theoretically by using binary choice model and explain long stagnation by rising the degree of uncertainty.
References
Allen F, Carletti E (2008) Mark-to-market accounting and liquidity pricing. J Account Econ 45:358–378
Aoki M (1996) New approaches to macroeconomic modeling. Cambridge University Press, Cambridge
Aoki M (1998) Simple model of asymmetrical business cycles: interactive dynamics of a large number of agents with discrete choices. Macroecon Dyn 2:427–442
Aoki M, Yoshikawa H (2006) Uncertainty, policy ineffectiveness, and long stagnation of the macroeconomy. Jpn World Econ 18:261–272
Aoki M, Yoshikawa H, Shimizu T (2005) The long stagnation and monetary policy in Japan: a theoretical explanation. In: Semmler W (ed) Monetary policy and unemployment: the US, Euro-area and Japan. Routledge, Abingdon, pp 133–165
Blanchard O, Kiyotaki N (1987) Monopolistic competition and the effects of aggregate demand. Am Econ Rev 77:647–666
Branch WA, McGough B (2009) A new keynesian model with heterogeneous expectations. J Econ Dyn Control 33:1036–1051
Brunnermeier M, Crocket A, Goodhart C, Hellwig M, Persaud AD, Shin HS (2009) The fundamental principles of financial regulation. Geneva Report on World Economy, vol 11
Cooper R, John A (1988) Coordinating coordination failures in keynesian models. Q J Econ 103:441–463
Diamond DW, Dybvig PH (1983) Bank runs, deposit insurance, and liquidity. J Polit Econ 91:401–419
Diamond DW, Rajan RG (2011) Fear of fire sales, illiquidity seeking, and credit freezes. J Polit Econ 126:557–591
Diamond PA (1982) Aggregate-demand management in search equilibrium. J Polit Econ 90:881–894
Hart O (1982) A model of imperfect competition with keynesian features. Q J Econ 97:109–138
Keynes JM (1936) The general theory of employment, interest, and money. Macmillan, London
Keynes JM (1937) The general theory of employment. Q J Econ 51:209–223
Morris S, Shin HS (2000) Rethinking multiple equilibria in macroeconomic modeling. NBER Macroecon Annu 15:139–161
Oda N, Ueda K (2007) The effects of the bank of japan’s interest rate commitment and quantitative monetary easing on the yield curve: A macro-finance approach. Jpn Econ Rev 58:303–328
Scharfstein D, Stein JC (1990) Herd behavior and investment. Am Econ Rev 80:465–479
Shin HS (2005) Commentary: has financial development made the world riskier? In: Proceedings of the Federal Reserve Bank of Kansas City Symposium at Jackson Hole, pp 381–386
Shin HS (2008) Risk and liquidity in a system context. J Financ Intermed 17:315–329
Taylor JB (1993) Discretion versus policy rules in practice. In: Carnegie-Rochester conference series on public policy, vol 39, pp 195–214
Tobin J (1958) Liquidity preference as behavior towards risk. Rev Econ Stud 26:65–86
Author information
Authors and Affiliations
Corresponding author
Additional information
I thank Katsuhito Iwai, Yukiko Muraoka, Yoshikiyo Sakai, Hideki Takayasu, Misako Takayasu, Tsutomu Watanabe, and Hiroshi Yoshikawa for their insightful comments and suggestions. All remaining errors are mine.
Rights and permissions
About this article
Cite this article
Shimizu, T. Heterogeneity of expectations and financial crises: a stochastic dynamic approach. J Econ Interact Coord 12, 539–560 (2017). https://doi.org/10.1007/s11403-016-0175-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11403-016-0175-y