Chaotic dynamics in a cash-in-advance economy

Abstract:In this paper, we study the occurrence of local indeterminacy in two-sector monetary economies. In order to capture the credit market imperfections and the liquidity services of money, we consider a general MIUF model with two alternative timings in monetary payments: the Cash-In-Advance timing, in which the cash available to buy goods is money in the consumers' hands after they leave the bond market but before they enter the goods market, and the Cash-After-the-Market timing, in which agents hold money for transactions after leaving the goods market. We consider three standard specifications of preferences: the additively separable formulation, the Greenwood-Hercovitz-Huffman (GHH) [18] formulation and the King-Plosser-Rebelo (KPR) [21] formulation. First, we show that for all the three types of preferences, local indeterminacy easily arises under the CIA timing with a low enough interest rate elasticity of money demand. Second, we show that with the CAM timing, determinacy always holds under separable preferences, but local indeterminacy can arise in the case of GHH and KPR preferences. We thus prove that compared to aggregate models, two-sector models provide new rooms for local indeterminacy when non-separable standard preferences are considered.

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“…Let b be the capital intensity difference across sectors as defined by (24). We know from Benhabib and Nishimura [5] that…”

Section: The Characteristic Polynomialmentioning

confidence: 99%

Multiple equilibria in two-sector monetary economies: An interplay between preferences and the timing for money

Bosi¹,

Nishimura²,

Venditti³

2010

Journal of Mathematical Economics

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“…To be more concrete, consider the standard CIA model of [7] as analyzed in [4] [5,6] and [11]. As shown in [4], an equilibrium in this model corresponds to a sequence {x 1 The inherent utility associated with an equilibrium…”

Section: (B) ⊆ Y Where B ∈ B(x) Is Given By λ(B)/λ(x)mentioning

confidence: 99%

“…See [11] or [4] for more details. Let M t be the money supply at time t. The government controls the money supply using a money growth rule:…”

Section: (B) ⊆ Y Where B ∈ B(x) Is Given By λ(B)/λ(x)mentioning

confidence: 99%

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Uniform measures on inverse limit spaces

Stockman

2009

Applicable Analysis

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Abstract. Motivated by problems from dynamic economic models, we consider the problem of defining a uniform measure on inverse limit spaces. Let f : X → X where X is a compact metric space and f is continuous, onto and piecewise one-to-one and Y := lim ←− (X, f ). Then starting with a measure µ 1 on the Borel sets B(X), we recursively construct a sequence of probabil-and n ∈ N. This sequence of probability measures is then uniquely extended to a probability measure on the inverse limit space Y . If µ 1 is a uniform measure, we argue that the measure induced on the inverse limit space by the recursively constructed sequence of measures is a uniform measure. As such, the measure has uses in economic theory for policy evaluation and in dynamical systems in providing an ambient measure (when Lebesgue measure is not available) with which to define an SRB measure or a metric attractor for the shift map on the inverse limit space.

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“…4 Complicated motion in money-in-the-utility models with nonseparable utility function and separable utility function are considered by Matsuyama [21] and Fukuda [15], respectively. Michener and Ravikumar [24] and Chen and Li [7] show that chaos can occur in a LucasStokey type monetary model where consumers consume cash goods and credit goods. Auray et al [2] introduce habit persistence as a way to generate complex dynamics in a cash-in-advance (CIA) economy and find that chaotic dynamics can emerge for reasonable degrees of habit.…”

mentioning

confidence: 99%