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Journal Article•DOI•

Reconciling Jaimovich–Rebello preferences, habit in consumption and labor supply

Tom Holden1, Paul Levine1, Jonathan Swarbrick2•
University of Surrey1, Bank of Canada2
25 Apr 2018-Economics Letters (Elsevier)-Vol. 168, pp 132-137
TL;DR: In this paper, a form of a utility function of consumption with habit and leisure that is compatible with long-run balanced growth, hits a steady state observed target for hours worked, and is consistent with micro-econometric evidence for the inter-temporal elasticity of substitution and the Frisch elasticity was studied.
Abstract: This note studies a form of a utility function of consumption with habit and leisure that (a) is compatible with long-run balanced growth, (b) hits a steady state observed target for hours worked and (c) is consistent with micro-econometric ev- idence for the inter-temporal elasticity of substitution and the Frisch elasticity of labor supply. Employing Jaimovich-Rebello preferences our results highlight a con- straint on the preference parameter needed to target the steady-state Frisch elastic- ity. This leads to a lower bound for the latter that cannot be reconciled empirically with external habit, but the introduction of a labor wedge solves the problem. We also propose a dynamic Frisch inverse elasticity measure and examine its business cycle properties.

Summary (2 min read)

Jump to: [1 Introduction] – [2 The Frisch Elasticity of Labor Supply] – [3 The Household Problem] – [3.4 Numeral Illustration] – [4 A Resolution: Generalized JR Utility and Labor Wedge] and [5 Conclusions]

1 Introduction

  • In particular, RBC-DSGE models in which a consumer’s utility level not only depends on her consumption level but also how that level compares to a standard set either by her own past consumption levels (internal habit-formation) or the levels of those in her peerage (catching-up with the Joneses’ or external habit) are now ubiquitous in the literature.
  • At the same time to achieve co-movement of output, hours, consumption and investment modellers turn to preferences proposed by Jaimovich and Rebello (2008) (henceforth JR) that control short-run wealth effects.

2 The Frisch Elasticity of Labor Supply

  • Bilbiie (2011) shows that the constantmarginal-utility inverse elasticity of labor supply is given by δ = ULCH UL ( ULC UCC − ULL ULC ) and it is straightforward to show that g′′ >.
  • Microeconomic and macroeconomic estimates of the Frisch elasticity differ significantly, the former typically ranging from 0 to 0.5 and the latter from 2 to 4 (Peterman, 2016).
  • Estimations of the elasticity of labor supply found using microeconomic data depend on factors such as gender, age, marital status and dependants.
  • Reichling and Whalen (2017) give a thorough review of the estimates found in the literature based on microeconomic data, finding that estimates typically range from 0 to over 1.

3 The Household Problem

  • Households choose between work and leisure and therefore how much labor they supply.
  • They also own the capital stock which is rented to firms at a rental rate rKt and choose an optimal investment path.
  • The single-period utility is given by JR preferences (3) and (4).
  • Tt where All variables are expressed in real terms relative to the price of output.

3.4 Numeral Illustration

  • The authors can now assess the empirical plausibility of JR preferences with habit in consumption.
  • From their numerical results for the lower bound δJR(ψ), this rules out external habit if the authors are to choose JR preferences that allow for only weak wealth effects (γ very small).
  • But even without habit, or with internal habit, it is difficult to reconcile the extreme choice of γ almost zero with a Frisch elasticity within this empirical range.

4 A Resolution: Generalized JR Utility and Labor Wedge

  • Again for a given H this pins down % given the remaining parameters.
  • The second modification is to introduce a labor wedge into the household problem (as in Shimer (2009).
  • Figure 1 shows that a combination of their generalized JR utility and an empirically supported wedge, the authors can calibrate parameters to achieve the desired empirical value for δJR.

5 Conclusions

  • This note has reviewed a utility function commonly used in RBC-DSGE models that is nonseparable in habit-adjusted consumption and leisure, compatible with balanced growth and elim- 7 inates counterfactual wealth effects highlighted by Jaimovich and Rebello (2008).
  • The authors main contributions are first, Theorems 1 and 2 that highlight a constraint on the preference parameter ψ needed to target the Frisch elasticity.
  • This leads to a lower bound for the latter that cannot be reconciled empirically with external habit.
  • Even with internal or no habit, the range of possible values of the Frisch elasticity lie outside empirical results unless the authors allow for a modest wealth effect.

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Abstract: Recent evidence suggests that credit booms and asset price bubbles may undermine economic growth even as they occur, regardless of whether a crisis follows, by crowding out investment in more productive, R&D-intensive industries. This paper incorporates Schumpeterian endogenous growth into a DSGE model with credit-constrained entrepreneurs to show how shocks affecting firms’ access to credit can generate boom-bust cycles featuring large fluctuations in land prices, consumption, and investment. During the expansion, rising land prices tend to crowd out capital and (especially) R&D investment: over the medium term, this results in a slowdown in the rate of creation of new (innovative) firms. Moreover, higher initial loan-to-value ratios tend to be associated with larger macroeconomic fluctuations. A counter-cyclical LTV ratio targeting credit growth has relevant stabilization effects but brings about small gains in terms of long-run consumption levels, and thus of welfare.

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TL;DR: In this paper, the authors used Jaimovich-Rebel preferences with internal habits in consumption and showed that asset prices are superior when the first channel is strong and the second channel is weak.
Abstract: This paper studies how i¬‚exible labour decisions ai¬€ect asset pricing in a Real Business Cycle model. It uses Jaimovich-Rebelo preferences with internal habits in consumption and distinguishes between two income effect channels (i) the ‘habit income ei¬€ect’ channel and (ii) the ‘separability income ei¬€ect’ channel. I i¬ nd that asset prices are superior when the i¬ rst channel is strong and the second is weak, this is the case of using GHH preferences with internal habits in consumption.

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Cites background from "Reconciling Jaimovich–Rebello prefe..."

  • ...JR preferences with habits are studied in Schmitt-Groh and Uribe (2012) in the context of news shocks and business cycles, and more recently by Holden et al. (2017) in the context of reconciling these preferences with estimates of the Frisch elasticity of labour supply....

    [...]

References
More filters
Journal Article•DOI•
Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy

[...]

Lawrence J. Christiano, Martin Eichenbaum, Charles L. Evans1•
Federal Reserve System1
01 Feb 2005-Journal of Political Economy
TL;DR: In this article, the authors present a model embodying moderate amounts of nominal rigidities that accounts for the observed inertia in inflation and persistence in output, and the key features of their model are those that prevent a sharp rise in marginal costs after an expansionary shock to monetary policy.
Abstract: We present a model embodying moderate amounts of nominal rigidities that accounts for the observed inertia in inflation and persistence in output. The key features of our model are those that prevent a sharp rise in marginal costs after an expansionary shock to monetary policy. Of these features, the most important are staggered wage contracts that have an average duration of three quarters and variable capital utilization.

4,250 citations

Posted Content•
Investment, Capacity Utilization and the Real Business Cycle

[...]

Jeremy Greenwood, Zvi Hercowitz
01 Jan 1986-The American Economic Review
TL;DR: In this article, the authors adopt the Keynesian view that direct shocks to investment are important for business fluctuations, but incorporate them in a neo-classical framework where the rate of capital expenditure is fixed.
Abstract: The present paper adopts the Keynesian view that direct shocks to investment are important for business fluctuations, but incorporates them in a neo-classical framework where the rate of capital ut ...

2,208 citations

Additional excerpts

  • ...Two special cases are worth noting: KPR (γ = 1) : δF (ψ, 1) = ψ + (1 + ψ)%H1+ψ(2σ − 1) σ(1− %H1+ψ) , GHH (γ = 0) : δF (ψ, 0) = ψ, where KPR preferences are those proposed by King et al. (1988), and GHH preferences are those proposed by Greenwood et al. (1988)....

    [...]

Journal Article•DOI•
Production, growth and business cycles: I. The basic neoclassical model

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Robert G. King1, Charles I. Plosser1, Sergio Rebelo1•
University of Rochester1
01 Mar 1988-Journal of Monetary Economics
TL;DR: In this paper, the authors present the neoclassical model of capital accumulation augmented by choice of labor supply as the basic framework of modern real business cycle analysis and explore the implications of the basic model for perfect foresight capital accumulation and for economic fluctuations initiated by impulses to technology.
Abstract: This paper presents the neoclassical model of capital accumulation augmented by choice of labor supply as the basic framework of modern real business cycle analysis. Preferences and production possibilities are restricted so that the economy displays steady state growth. Then we explore the implications of the basic model for perfect foresight capital accumulation and for economic fluctuations initiated by impulses to technology. We argue that the neoclassical approach holds considerable promise for enhancing our understanding of fluctuations. Nevertheless, the basic model does have some important shortcomings. In particular, substantial persistence in technology shocks is required if the model economy is to exhibit periods of economic activity that persistently deviate from a deterministic trend.

1,945 citations

Journal Article•DOI•
Saving and Growth with Habit Formation

[...]

Christopher D. Carroll1, Jody Overland, David N. Weil2•
Johns Hopkins University1, Brown University2
01 Jun 2000-The American Economic Review
TL;DR: The authors show that if utility depends partly on how consumption compares to a "habit stock" determined by past consumption, an otherwise-standard growth model can imply that increases in growth can cause increased saving.
Abstract: Saving and growth are strongly positively correlated across countries. Recent empirical evidence suggests that this correlation holds largely because high growth leads to high saving, not the other way around. This evidence is difficult to reconcile with standard growth models, since forward-looking consumers with standard utility should save less in a fast-growing economy because they know they will be richer in the future than they are today. We show that if utility depends partly on how consumption compares to a ‘habit stock’ determined by past consumption, an otherwise-standard growth model can imply that increases in growth can cause increased saving

603 citations

Journal Article•DOI•
Labor Supply and Taxes: A Survey

[...]

Michael Keane
01 Dec 2011-Journal of Economic Literature
TL;DR: In this paper, the authors survey the male and female labor supply literatures, focusing on implications for effects of wages and taxes, and conclude that two factors drive many of the differences in results across studies.
Abstract: I survey the male and female labor supply literatures, focusing on implications for effects of wages and taxes. For males, I describe and contrast results from three basic types of model: static models (especially those that account for nonlinear taxes), life-cycle models with savings, and life-cycle models with both savings and human capital. For women, more important distinctions are whether models include fixed costs of work, and whether they treat demographics like fertility and marriage (and human capital) as exogenous or endogenous. The literature is characterized by considerable controversy over the responsiveness of labor supply to changes in wages and taxes. At least for males, it is fair to say that most economists believe labor supply elasticities are small. But a sizeable minority of studies that I examine obtain large values. Hence, there is no clear consensus on this point. In fact, a simple average of Hicks elasticities across all the studies I examine is 0.30. Several simulation studies have shown that such a value is large enough to generate large welfare costs of income taxation. For males, I conclude that two factors drive many of the differences in results across studies. One factor is use of direct vs. ratio wage measures, with studies that use the former tending to find larger elasticties. Another factor is the failure of most studies to account for human capital returns to work experience. I argue that this may lead to downward bias in elasticity estimates. In a model that includes human capital, I show how even modest elasticities - as conventionally measured - can be consistent with large welfare costs of taxation.

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Frequently Asked Questions (1)
Q1. What are the contributions in "Reconciling jaimovich-rebello preferences, habit in consumption and labor supply" ?

This note studies two forms of a utility function of consumption with habit and leisure that are ( a ) compatible with long-run balanced growth, ( b ) hit a steady state observed target for hours worked and ( c ) are consistent with micro-econometric evidence for the inter-temporal elasticity of substitution and the Frisch elasticity of labor supply. In Theorem 3 the authors propose a generalized JR utility function that in conjunction with a labor wedge solves the problem.