nach oben

Erschienen in:

2017 | OriginalPaper | Buchkapitel

4. Sunspot Fluctuations in Two-Sector Models with Variable Income Effects

verfasst von : Frédéric Dufourt, Kazuo Nishimura, Carine Nourry, Alain Venditti

Erschienen in: Sunspots and Non-Linear Dynamics

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We analyze a version of the Benhabib and Farmer (1996) two-sector model with sector-specific externalities in which we consider a class of utility functions inspired from the one considered in Jaimovich and Rebelo (2009) which is flexible enough to encompass varying degrees of income effect. First, we show that local indeterminacy and sunspot fluctuations occur in 2-sector models under plausible configurations regarding all structural parameters—in particular regarding the intensity of income effects. Second, we prove that there even exist some configurations for which local indeterminacy arises under any degree of income effect. More precisely, for any given size of income effect, we show that there is a non-empty range of values for the Frisch elasticity of labor and the elasticity of intertemporal substitution in consumption such that indeterminacy occurs. This contrasts with the results obtained in one-sector models in both Nishimura et al. (2009), in which it is shown that indeterminacy cannot occur under either GHH and KPR preferences, and in Jaimovich (2008) in which local indeterminacy only arises for intermediary income effects.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel From Sunspots to Black Holes: Singular Dynamics in Macroeconomic Models

Nächstes Kapitel From Self-Fulfilling Mistakes to Behavioral Learning Equilibria

Nur mit Berechtigung zugänglich

Nishimura and Venditti (2010) show that local indeterminacy can occur under both GHH and KPR preferences—the latter displaying positive income effect—but there is no clear picture of the impact of the income effect on the occurrence of sunspot fluctuations.

We do not consider externalities in the consumption good sector as they do not play any crucial role in the existence of multiple equilibria.

It is important to note that when \(\gamma \ne 0\), this utility function may not be concave. This characteristic is well-known for the KPR specification with \(\gamma =1\) for which additional restrictions on \(\sigma \) and \(\chi \) are required to guarantee concavity (see for instance Hintermaier 2003). However, in order to avoid technical and cumbersome assumptions, we will only focus with Lemma 1 below on the conditions for local concavity properties around the steady state. Precise general conditions for global concavity can be provided upon request.

When there is no possible confusion, the time index (t) is not mentioned.

See Appendix “Proof of Lemma 1”.

We will show in this case that there exists a Hopf bifurcation leading to the existence of periodic cycles.

For example, Basu and Fernald (1997) obtain a point estimate for the degree of IRS in the durable manufacturing sector in the US economy of 0.33, with standard deviation 0.11.

It can be shown indeed that \(\underline{\Theta }(\gamma )\) is an increasing function of \(\gamma \) while \(\underline{\chi }(\gamma )\) is a decreasing function.

See Prescott and Wallenius (2011) for a discussion of the factors that make the wage elasticity of aggregate labor supply significantly differ from the corresponding elasticity at the micro level.

See Benhabib and Farmer (1994).

Recall however that his utility formulation contains an additional state variable \(X_{t}\) which may play a significant role for these result.

See Jaimovich (2008), Nishimura et al. (2009).

See also Guo and Harrison (2010), Nishimura and Venditti (2010).

See Khan and Tsoukalas (2011), Schmitt-Grohé and Uribe (2012).

Basu, S., & Fernald, J. (1997). Returns to scale in US production: Estimates and implications. Journal of Political Economy, 105, 249–283.CrossRef

Benhabib, J., & Farmer, R. (1994). Indeterminacy and increasing returns. Journal of Economic Theory, 63, 19–41.CrossRef

Benhabib, J., & Farmer, R. (1996). Indeterminacy and sector specific externalities. Journal of Monetary Economics, 37, 397–419.CrossRef

Campbell, J. (1999). Asset prices, consumption and the business cycle. In J. B. Taylor & M. Woodford (Eds.), Handbook of macroeconomics (pp. 1231–1303). Amsterdam: North-Holland.

Chetty, R., Guren, A., Manoli, D., & Weber, A. (2012). Does indivisible labor explain the difference between micro and macro elasticities? A meta-analysis of extensive margin elasticities. NBER Working Paper No. 16729.

Dufourt, F., Nishimura, K., & Venditti, A. (2015). Indeterminacy and sunspots in two-sector RBC models with generalized no-income-effect preferences. Journal of Economic Theory, 157, 1056–1080.CrossRef

Grandmont, J. -M. (2008). Nonlinear difference equations, bifurcations and chaos: An introduction. Research in Economics, 62, 122–177.

Greenwood, J., Hercovitz, Z., & Huffman, G. (1988). Investment, capacity utilization and the real business cycle. American Economic Review, 78, 402–417.

Guo, J. T., & Harrison, S. (2010). Indeterminacy with no-income effect preferences and sector-specific externalities. Journal of Economic Theory, 145, 287–300.CrossRef

Hintermaier, T. (2001). Lower bounds on externalities in sunspot models. Working Paper EUI.

Hintermaier, T. (2003). On the minimum degree of returns to scale in sunspot models of business cycles. Journal of Economic Theory, 110, 400–409.CrossRef

Jaimovich, N. (2008). Income effects and indeterminacy in a calibrated one-sector growth model. Journal of Economic Theory, 143, 610–623.CrossRef

Jaimovich, N., & Rebelo, S. (2009). Can news about the future drive the business cycles? American Economic Review, 99, 1097–1118.CrossRef

Khan, H., & Tsoukalas, J. (2011). Investment shocks and the comovement problem. Journal of Economic Dynamics and Control, 35, 115–130.CrossRef

King, R., Plosser, C., & Rebelo, S. (1988). Production, growth and business cycles. Journal of Monetary Economics, 21, 191–232.CrossRef

Kocherlakota, N. (1996). The equity premium: It’s still a puzzle. Journal of Economic Literature, 36, 42–71.

Mulligan, C. (2002). Capital interest and aggregate intertemporal substitution. NBER Working Paper 9373.

Nishimura, K., & Venditti, A. (2010). Indeterminacy and expectation-driven fluctuations with non-separable preferences. Mathematical Social Sciences, 60, 46–56.CrossRef

Nishimura, K., Nourry, C., & Venditti, A. (2009). Indeterminacy in aggregate models with small externalities: An interplay between preferences and technology. Journal of Nonlinear and Convex Analysis, 10(2), 279–298.

Prescott, E., & Wallenius, J. (2011). Aggregate labor supply (p. 457). Research Department Staff Report: Federal Reserve Bank of Minneapolis.

Rogerson, R., & Wallenius, J. (2009). Micro and macro elasticities in a life cycle model with taxes. Journal of Economic Theory, 144, 2277–2292.CrossRef

Schmitt-Grohé, S., & Uribe, M. (2012). What’s news in business cycles. Econometrica, 80, 2733–2764.CrossRef

Vissing-Jorgensen, A., & Attanasio, O. (2003). Stock-market participation, intertemporal substitution and risk aversion. American Economic Review Papers and Proceedings, 93, 383–391.CrossRef

Titel: Sunspot Fluctuations in Two-Sector Models with Variable Income Effects
verfasst von: Frédéric Dufourt
Kazuo Nishimura
Carine Nourry
Alain Venditti
Verlag: Springer International Publishing
Buch: Sunspots and Non-Linear Dynamics
Print ISBN: 978-3-319-44074-3

Electronic ISBN: 978-3-319-44076-7

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-44076-7_4