# Monetary rules in a two-sector endogenous growth model

- 56 Downloads

## Abstract

We study the balanced growth paths and their stability features of a monetary two-sector endogenous growth model with physical capital and human capital accumulation. The demand of money is motivated on the ground of a fractional cash-in-advance constraint on consumption expenditures and on those in the investment in physical capital. We consider, in sequence, two monetary rules implemented by the Central Bank. First, we assume that the latter pegs the money growth rate and then the nominal interest rate according to a Taylor feedback rule. When the Central Bank pegs the money growth rate, there emerges a unique balanced growth path which turns out to be indeterminate for a low amplitude of the liquidity constraint and/or for a low enough intertemporal elasticity of substitution in consumption even under the hypothesis that the cash-in-advance constraint applies uniquely on consumption expenditures. On the other hand, when the monetary policy is implemented according to a Taylor feedback rule, an unintended *liquidity trap* equilibrium may coexist with multiple interior Taylor equilibria. If, on the one hand, the *liquidity trap* equilibrium is bound to be locally determinate; on the other hand, the Taylor interior equilibrium may become locally indeterminate provided the cash-in-advance constraint applies also on the investment in physical capital good and under a physical capital intensive human capital good. A global analysis is performed in which we show that the Taylor equilibrium and the *liquidity trap* one are connected through a heteroclinic orbit.

## Keywords

Cash-in-advance Endogenous growth Indeterminacy Monetary policy Two-sector## JEL Classification

E32 E52 O41 O42## Notes

## References

- Barro, R.: Government spending in a simple model of endogenous growth. J. Polit. Econ.
**98**, 103–125 (1990)CrossRefGoogle Scholar - Baxter, M.: Are consumer durables important for business cycles? Rev. Econ. Stat.
**78**, 147–155 (1996)CrossRefGoogle Scholar - Benhabib, J., Schmitt-Grohé, S., Uribe, M.: The perils of Taylor rules. J. Econ. Theory
**96**, 40–69 (2001)CrossRefGoogle Scholar - Bich, P., Drugeon, J.P., Morhaim, L.: On temporal aggregators and dynamic programming. Econ. Theory
**66**, 787–817 (2018). https://doi.org/10.1007/s00199-017-1045-0 CrossRefGoogle Scholar - Bond, E.W., Wang, P., Yip, C.K.: A general two-sector model of endogenous growth with human and physical capital: balanced growth and transitional dynamics. J. Econ. Theory
**68**, 149–173 (1996)CrossRefGoogle Scholar - Benhabib, J., Nishimura, K.: Competitive equilibrium cycles. J. Econ. Theory
**35**, 284–306 (1985)CrossRefGoogle Scholar - Bosi, S., Magris, F.: Indeterminacy and endogenous fluctuations with arbitrary small liquidity constraint. Res. Econ.
**57**, 39–51 (2003)CrossRefGoogle Scholar - Bosi, S., Magris, F., Venditti, A.: Multiple equilibria in a cash-in-advance two-sector economy. Int. J. Econ. Theory
**1**, 131–149 (2005a)CrossRefGoogle Scholar - Bosi, S., Cazzavillan, G., Magris, F.: Plausibility of indeterminacy and complex dynamics. Annales d’Economie et de Statistique
**78**, 103–115 (2005b)CrossRefGoogle Scholar - Brito, P., Venditti, A.: Local and global indeterminacy in two-sector models of endogenous growth. J. Math. Econ.
**46**, 893–911 (2010)CrossRefGoogle Scholar - Clarida, R., Gali, J., Gertler, M.: Monetary policy in practice: some international evidence. Eur. Econ. Rev.
**42**, 1033–1067 (1998)CrossRefGoogle Scholar - Drugeon, J.P.: On the emergence of competitive equilibrium growth cycles. Econ. Theory
**52**, 397–427 (2013). https://doi.org/10.1007/s00199-011-0631-9 CrossRefGoogle Scholar - Drugeon, J.P., Ha-Huy, T., Nguyen, T.D.H.: On maximin dynamic programming and the rate of discount. Econ. Theory (2018). https://doi.org/10.1007/s00199-018-1166-0
- Grandmont, J.-M.: Nonlinear difference equations, bifurcations and chaos: an introduction. Res. Econ.
**62**, 122–177 (2008)CrossRefGoogle Scholar - Grandmont, J.-M., Pintus, P., de Vilder, R.: Capital-labor substitution and competitive nonlinear endogenous business cycles. J. Econ. Theory
**80**, 14–59 (1998)CrossRefGoogle Scholar - Gruber, J.: A tax-based estimate of the elasticity of intertemporal substitution. Q. J. Finance
**3**, 1–20 (2013)CrossRefGoogle Scholar - Hahn, F., Solow, R.: A Critical Essay on Modern Macroeconomic Theory. Basil Blackwell, Oxford (1995)Google Scholar
- Hori, T., Mizutani, N., Uchino, T.: Endogenous structural change, aggregate balanced growth, and optimality. Econ. Theory
**65**, 125–153 (2018). https://doi.org/10.1007/s00199-016-1012-1 CrossRefGoogle Scholar - Huang, K.X.D., Meng, Q., Xue, J.: Money growth targeting and indeterminacy in small open economies. Econ. Theory
**66**, 1–37 (2018). https://doi.org/10.1007/s00199-018-1132-x CrossRefGoogle Scholar - Jones, R.W.: The structure of simple general equilibrium models. J. Polit. Econ.
**73**, 557–572 (1965)CrossRefGoogle Scholar - Kuznetsov, Y.: Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, vol. 112. Springer, Berlin (1965)Google Scholar
- Le Riche, A., Magris, F., Parent, A.: Liquidity trap and stability of Taylor rules. Math. Soc. Sci.
**88**, 16–27 (2017)CrossRefGoogle Scholar - Le Van, C., Pham, N.S.: Intertemporal equilibrium with financial asset and physical capital. Econ. Theory
**62**, 155–199 (2017). https://doi.org/10.1007/s00199-015-0881-z CrossRefGoogle Scholar - Leeper, E.M.: Equilibria under ’Active’ and ’Passive’ monetary and fiscal policies. J. Monet. Econ.
**27**, 129–147 (1991)CrossRefGoogle Scholar - Lucas, R.E.: Interest rates and currency prices in a two-country world. J. Monet. Econ.
**10**, 335–359 (1982)CrossRefGoogle Scholar - Lucas, R.E., Stokey, N.L.: Optimal fiscal and monetary policy in an economy without capital. J. Monet. Econ.
**12**, 55–93 (1983)CrossRefGoogle Scholar - Menuet, M., Minea, A., Villieu, P.: Deficit, monetization, and economic growth: a case for multiplicity and indeterminacy. Econ. Theory
**65**, 819–853 (2018). https://doi.org/10.1007/s00199-017-1040-5 CrossRefGoogle Scholar - Mino, K.: Long-run effects of monetary expansion in a two-sector model of endogenous growth. J. Macroecon.
**19**, 635–655 (1997)CrossRefGoogle Scholar - Mino, K., Nishimura, K., Shimomura, K., Wang, P.: Equilibrium dynamics in discrete-time endogenous growth models with social constant returns. Econ. Theory
**34**, 1–23 (2008). https://doi.org/10.1007/s00199-007-0211-1 CrossRefGoogle Scholar - Mulligan, C.: Capital interest and aggregate intertemporal substitution. NBER Working Paper 9373 (2002)Google Scholar
- Romer, P.M.: Increasing returns and long-run growth. J. Polit. Econ.
**94**, 1002–1037 (1986)CrossRefGoogle Scholar - Schmitt-Grohé, S., Uribe, M.: Price-level determinacy and monetary policy under a balanced-budget requirement. J. Monet. Econ.
**45**, 211–246 (2000)CrossRefGoogle Scholar - Sorger, G.: Cycles and chaos in the one-sector growth model with elastic labor supply. Econ. Theory
**65**, 55–77 (2018). https://doi.org/10.1007/s00199-016-1005-0 CrossRefGoogle Scholar - Svensson, L.E.O.: Money and asset prices in a cash-in-advance economy. J. Polit. Econ.
**5**, 919–944 (1985)Google Scholar - Takahashi, H.: Optimal balanced growth in a general multi-sector endogenous growth model with constant returns. Econ. Theory
**37**, 31–49 (2008). https://doi.org/10.1007/s00199-007-0287-7 CrossRefGoogle Scholar - Takahashi, H., Mashiyama, K., Sakagami, R.: Does the capital intensity matter? Evidence from the postwar Japanese economy and other OECD countries. Macroecon. Dyn.
**16**, 103–116 (2012)CrossRefGoogle Scholar - Vissing-Jorgensen, A., Attanasio, O.: Stock-market participation, intertemporal substitution and risk aversion. Am. Econ. Rev. Pap. Proc.
**93**, 383–391 (2003)CrossRefGoogle Scholar - Woodford, M.: Interest Rate and Prices: Foundation of a Theory of Monetary Policy. Princeton University Press, Princeton (2003)Google Scholar