Animal spirits in an open economy: an interaction-based approach to the business cycle

Tae-Seok Jang

doi:10.1515/bejm-2016-0141

Published by De Gruyter December 12, 2019

Animal spirits in an open economy: an interaction-based approach to the business cycle

Tae-Seok Jang

From the journal The B.E. Journal of Macroeconomics

https://doi.org/10.1515/bejm-2016-0141

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Abstract

This paper examines the effects of boundedly rational expectation on the business cycle in a two-country New Keynesian model. Forecast heuristics in a closed-economy, De Grauwe’s (2011) model, is extended, and the effects of heterogeneous agents are incorporated in an open economy. In particular, the expectation formation process is constrained by waves of optimists and pessimists – the so-called “animal spirits.” As a result, the model is able to explain group behavior based on forecast performance, which has significant effects on output and inflation dynamics in the two countries. The simulation results suggest that heterogeneity in group behavior and nominal rigidities, as well as a moderate degree of international trade, amplify spillover effects on international business cycles leading to high cross-correlations in output and inflation.

Keywords: animal spirits; business cycle; boundedly rational; New Keynesian; two-country

JEL Classification: C63; E32; F41

Acknowledgement

A preliminary version of this paper was presented at the Econophysics Colloquium 2015 in Prague and the 11th Dynare Conference in Brussels. I would like to thank all the participants for their active involvement in the conferences. In particular, I am grateful for the helpful comments provided by anonymous referees. All remaining errors are mine.

Appendix: Two-country model in canonical form

This section describes in detail the setup of the two-country model. The complete derivation of deep parameters can be found in the literature on standard two-country New Keynesian models (Galí and Monacelli 2005; Da Silveira 2006; Jang and Okano 2015).

xt=Et(xt+1)−ω4+1(ω2+1−α)σ{rt−Et(πt+1)}+α+ω2ω2+1−α{Et(xt+1∗)−xt∗};πt=βEt(πt+1)−βασω4+1{Et(xt+1)−Et(xt+1∗)}+ασ(1+β)+κHςω4+1xt−σ[α(1+β)−κHω2]ω4+1xt∗−ασω4+1{xt−1−xt−1∗}+κHrt;rt=ϕrrt−1+(1−ϕr)(ϕππt+ϕxxt);xt∗=Et(xt+1∗)−ω4+1(ω2+1−α)σ{rt∗−Et(πt+1∗)}+α+ω2ω2+1−α{Et(xt+1)−xt};πt∗=βEt(πt+1∗)−βασω4+1{Et(xt+1∗)−Et(xt+1)}+ασ(1+β)+κFςω4+1xt∗−σ[α(1+β)−κFω2]ω4+1xt−ασω4+1{xt−1∗−xt−1}+κFrt∗;rt∗=ϕr∗rt−1∗+(1−ϕr∗)(ϕπ∗πt∗+ϕx∗xt∗),

where ω0=2(1−α)(ση−1), ω2=2α(1−α)(ση−1) and ω4=4α(1−α)(ση−1). ς, κ_H, and κ_F are defined as (ω2+1)σ+(ω4+1)φ, (1−θH)(1−θHβ)θH, and (1−θF)(1−θFβ)θF, respectively.

Table 5:

Calibrated values for animal spirits in a two-country model.

Parameters	Description	Value
σ	Risk aversion	1.0
η	Elasticity of substitution between goods	2.0
φ	Labor disutility	20.0
θ_H	Calvo lotteries in country ℋ’s price	0.9
θ_F	Calvo lotteries in country ℱ’s price	0.75
ϕ_π	Taylor rule inflation in country ℋ	1.75
ϕ_y	Taylor rule output growth in country ℋ	0.75
ϕ_r	Interest rate smoothing in country ℋ	0.5
ϕπ∗	Taylor rule inflation in country ℱ	1.25
ϕy∗	Taylor rule output growth in country ℱ	1.0
ϕr∗	Interest rate smoothing in country ℱ	0.5

The discount factor β is set to 0.99. The effect of trade openness on the model is examined using simulations (α = 0.1, 0.9).

Table 5 shows the calibrated values for deep parameters in the model. Concerning price stickiness, Smets and Wouters (2003) estimate the Calvo price in the Euro Area. In their studies, they use the time period 1980:Q2–1999:Q4, and estimate the price indexation parameter as 0.908. This is roughly 2.5 years in quarterly magnitude (11−0.908≈10). In their subsequent study, Smets and Wouters (2007) use a US data set for the period 1984:Q4–2004:Q4 (“Great Moderation”), and found that the estimated Calvo price is 0.73. This corresponds to roughly 1 year in quarterly magnitude (i.e. 11−0.73≈4). Hence, the parameters values used in the paper can be considered to be the case for the Euro Area (country ℋ ’ price) and the US economy (country ℱ ’ price), respectively.

The parameters are connected to the model coefficients in canonical form as follows:

{κH=(1−θH)⋅(1−θH⋅β)/θH;κF=(1−θF)⋅(1−θF⋅β)/θF;ω2=2⋅α⋅(1−α)⋅(σ⋅η−1);ω4=4⋅α⋅(1−α)⋅(σ⋅η−1);ς=(ω2+1)⋅σ+(ω4+1)⋅φ;

{a1=(ω4+1)/{(ω2+1−α)⋅σ};a2=(α+ω2)/(ω2+1−α);b1=(β⋅α⋅σ)/(ω4+1);b2={α⋅σ⋅(1+β)+κH⋅ς}/(ω4+1);b3=σ⋅{α⋅(1+β)−κH⋅ω2}/(ω4+1);b4=(α⋅σ)/(ω4+1);b2∗={α⋅σ⋅(1+β)+κF⋅ς}/(ω4+1);b3∗=σ⋅{α⋅(1+β)−κF⋅ω2}/(ω4+1).

Note that trade openness influences the coefficients of the IS relations and the Phillips curves. One of the key parameters is an index of openness, α, which corresponds to the share of domestic consumption allocated to imported goods. For example, a high degree of trade openness (α ↑) can make the demand and supply schedule shift to the right (or the left) (a1, a2, b1, b2, b3, b4, b2∗, b3∗ ↑).

z~t is used to denote the state vector of [ xt πt rt xt∗ πt∗ rt∗ ]′. The structural model of a symmetric open economy can be rewritten in canonical form:

(14)A~⋅E~tz~t+1+B~⋅z~t+C~⋅z~t−1=0,

where:

A~=[1a10a200−b1β0b100000000a2001a10b100−b1β0000000],B~=[−10−a1−a200b2−10−b300(1−c1)⋅c3(1−c1)⋅c2−1000−a200−10−a∗−b3∗00b2∗−10000(1−c1∗)⋅c3∗(1−c1∗)⋅c2∗−1],C~=[000000−b400b40000c1000000000b400−b40000000c1∗].

The method of undetermined coefficients and iterative methods can be used to solve the system of equations. This solution indicates the equilibrium values of the observable variables in the system.

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Published Online: 2019-12-12

Animal spirits in an open economy: an interaction-based approach to the business cycle

Abstract

Acknowledgement

Appendix: Two-country model in canonical form

References

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