Numerical Analysis of the Disequilibrium Monetary Growth Model: Secular Stagnation, Slow Convergence, and Cyclical Fluctuations

Ogawa, Shogo and Sasaki, Hiroaki (2020): Numerical Analysis of the Disequilibrium Monetary Growth Model: Secular Stagnation, Slow Convergence, and Cyclical Fluctuations.

Abstract

This study presents a monetary disequilibrium growth model and conducts numerical simulations to investigate how dynamic paths are affected by the initial conditions and the parameters of expectation formation. The main results are as follows. First, dynamic properties such as stable convergence and cyclical fluctuations depend on the type of expectation formation rather than on the initial regimes. Stable convergence takes an excessively long time when expectation formation is too rational and cyclical fluctuations appear when it is too adaptive. Second, when the economy converges to the steady state (i.e., the Walrasian equilibrium), persistent Keynesian unemployment is likely to appear along the dynamic path. Third, the dynamics of inflation expectation that contain the price dynamics in the feedback loop might play an important role in convergence to the steady state.

• Item Type: MPRA Paper
• Language: English
• Keywords: Disequilibrium macroeconomics; Non-Walrasian analysis; Economic growth; Simulation
• Subjects: E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E12 - Keynes ; Keynesian ; Post-Keynesian; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E17 - Forecasting and Simulation: Models and Applications; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E40 - General; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O42 - Monetary Growth Models

References

Asada, T., Chen, P., Chiarella, C., and Flaschel, P. 2006. Keynesian Dynamics and the Wage-Price Spiral: A Baseline Disequilibrium Model. Journal of Macroeconomics, 28(1):90–130.

Backhouse, R. E. and Boianovsky, M. (2012). Transforming Modern Macroeconomics: Exploring Disequilibrium Microfoundations, 1956–2003. Cambridge University Press, Cambridge.

Barro, R. J. and Grossman, H. I. (1971). A General Disequilibrium Model of Income and Employment. American Economic Review, 61(1):82–93.

Bénassy, J.-P. (1975). Neo-Keynesian Disequilibrium Theory in a Monetary Economy. The Review of Economic Studies, 42(4):503–523.

Benigno, G. and Fornaro, L. (2018). Stagnation Traps. Review of Economic Studies, 85(3):1425–1470.

Böhm, V. (1978). Disequilibrium Dynamics in a Simple Macroeconomic Model. Journal of Economic Theory, 17(2):179–199.

Calvo, M., Montijano, J. I., and Rández, L. (2016). Algorithm 968: DISODE45: A Matlab Runge-Kutta Solver for Piecewise Smooth IVPs of Filippov Type. ACM Transactions on Mathematical Software, 43(3):1–14.

Chiarella, C. and Flaschel, P. (1996). Real and Monetary Cycles in Models of Keynes- Wicksell Type. Journal of Economic Behavior and Organization, 30(3):327–351.

Chiarella, C. and Flaschel, P. (2000a). High Order Disequilibrium Growth Dynamics: Theoretical Aspects and Numerical Features. Journal of Economic Dynamics and Control, 24(5-7):935–963.

Chiarella, C. and Flaschel, P. (2000b). The Dynamics of Keynesian Monetary Growth: Macro Foundations. Cambridge University Press, Cambridge.

Chiarella, C., Flaschel, P., and Franke, R. 2005. Foundations for a Disequilibrium Theory of the Business Cycle: Qualitative Analysis and Quantitative Assessment. Cambridge University Press, Cambridge.

Chiarella, C., Flaschel, P., Groh, G., Semmler, W. 2000. Disequilibrium, Growth and Labor Market Dynamics. Springer Verlag, Berlin.

Christiano, L. J., Eichenbaum, M. S., and Evans, C. L. (2005). Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy. Journal of Political Economy, 113(1):1–45.

Clower, R. W. (1965). The Keynesian Counterrevolution: A Theoretical Appraisal. The Theory of Interest Rates, 103:125.

Dupor, B., Li, J., and Li, R. (2019). Sticky Wages, Private Consumption, and Fiscal Multipliers. Journal of Macroeconomics, 62:103–157.

Eggertsson, G. B. and Krugman, P. R. (2012). Debt, Deleveraging, and the Liquidity Trap: A Fisher-Minsky-Koo Approach. Quarterly Journal of Economics, 127(3):1469– 1513.

Eggertsson, G. B., Mehrotra, N. R., and Robbins, J. A. (2019). A Model of Secular Stagnation: Theory and Quantitative Evaluation. American Economic Journal: Macroeconomics, 11(1):1–48.

Filippov, A. F. (1988). Differential Equations with Discontinuous Righthand Sides: Control Systems. Kluwer Academic Publishers, Norwell, MA.

Flaschel, P. (1999). On the Dominance of the Keynesian Regime in Disequilibrium Growth Theory: a Note. Journal of Economics, 70(1):79–89.

Flaschel, P., Gong, G., and Semmler, W. 2001. A Keynesian Macroeconometric Framework for the Analysis of Monetary Policy Rules. Journal of Economic Behavior and Organization, 46(1):101–136.

Gelain, P., Iskrev, N., J. Lansing, K., and Mendicino, C. (2019). Inflation Dynamics and Adaptive Expectations in an Estimated DSGE Model. Journal of Macroeconomics, 59(December 2018):258–277.

Guardia, M., Seara, T. M. and Teixeira, M. A. (2011). Generic Bifurcations of Low Codimension of planar Filippov Systems. Journal of Differential Equations, 250(4):1967–2023.

Hayashi, F. (1982). Tobin’s Marginal q and Average q: A Neoclassical Interpretation. Econometrica, 50(1):213.

Henry, C. (1972). Differential Equations with Discontinuous Right-hand Side for Planning Procedures. Journal of Economic Theory, 4(3):545–551.

Ito, T. (1979). A Filippov Solution of a System of Differential Equations with Discontinuous Right-Hand Sides. Economics Letters, 4(4):349–354.

Keynes, J. M. (1936). The General Theory of Employment, Interest and Money. Macmillan, New York.

Krugman, P. R. (1998). It’s Baaack: Japan’s Slump and the Return of the Liquidity Trap. Brookings Papers on Economic Activity, (2):137–205.

Kuznetsov, Y. U. A., Rinaldi, S., and Gragnani, A. (2003). One-Parameter Bifurcations in Planar Filippov Systems. International Journal of Bifurcation and Chaos, 13(8):2157-2188.

Leijonhufvud, A. (1967). Keynes and the Keynesians: A Suggested Interpretation. American Economic Review, 57(2):401–410.

Leijonhufvud, A. (1973). Effective Demand Failures. The Swedenish Economic Journal, 75(1):27–48.

Malinvaud, E. (1977). The Theory of Unemployment Reconsidered. Basil Blackwell, Oxford.

Malinvaud, E. (1980). Profitability and Unemployment. Cambridge University Press, Cambridge.

Nakayama, K. and Oshima, I. (1999). On Formation of Inflation Expectations (Infure Kitai ni tsuite). Bank of Japan Working Paper Series. (In Japanese)

Neary, J. P. and Stiglitz, J. E. (1983). Towards A Reconstruction of Keynesian Economics: Expectations and Constrained Equilibria. Quarterly Journal of Economics, 98(2):199–228.

Ogawa, S. (2020). Monetary Growth with Disequilibrium: A Non-Walrasian Baseline Model. MPRA Paper, 101236.

Palley, T. I. (2019). The Fallacy of the Natural Rate of Interest and Zero Lower Bound Economics: Why Negative Interest Rates may not Remedy Keynesian Unemployment. Review of Keynesian Economics, 7(2):151–170.

Piiroinen, P. T. and Kuznetsov, Y. A. (2008). An Event-Driven Method to Simulate Filippov Systems with Accurate Computing of Sliding Motions. ACM Transactions on Mathematical Software, 34(3):13.

Sargent, T. J. (1987). Macroeconomic Theory. Academic Press, Inc, London, 2nd edition.

Sargent, T. J. and Wallace, N. (1973). The Stability of Models of Money and Growth with Perfect Foresight. Econometrica, 41(6):1043–1048.

Schoder, C. (2017). Are Dynamic Stochastic Disequilibrium Models Keynesian or Neoclassical? Structural Change and Economic Dynamics, 40:46–63.

Schoder, C. (2020). A Keynesian Dynamic Stochastic Disequilibrium Model for Business Cycle Analysis. Economic Modelling, 86(June 2019):117–132.

Smets, F. and Wouters, R. (2003). An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area. Journal of the European Economic Association, 1(5):1123–1175.

Stiglitz, J. E. (2018). Where Modern Macroeconomics Went Wrong. Oxford Review of Economic Policy, 34(1-2):70–106.

Summers, L. H. (2014). U.S. Economic Prospects: Secular Stagnation, Hysteresis, and the Zero Lower Bound. Business Economics, 49(2):65–73.

Summers, L. H. (2015). Demand Side Secular Stagnation. American Economic Review, 105(5):60–65.

Weddepohl, C. and Yildirim, M. (1993). Fixed Price Equilibria in an Overlapping Generations Model with Investment. Journal of Economics, 57(1):37–68.

Yoshikawa, H. (1980). On the “q” Theory of Investment. The American Economic Review, 70(4):739–743.