Insurance and Opportunities: The Welfare Implications of Rising Wage Dispersion Jonathan Heathcote (Georgetown University) Kjetil Storesletten (University of Oslo) Gianluca Violante (New York University) Money and Banking Workshop, University of Chicago, March 14 2006 Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 1/30
Motivation • Welfare analysis in heterogeneous agents models with incomplete insurance against idiosyncratic risk is central to macroeconomics Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 2/30
Motivation • Welfare analysis in heterogeneous agents models with incomplete insurance against idiosyncratic risk is central to macroeconomics • Examples: welfare effects of a... 1. change in the amount of risk ( technology ) ◮ Attanasio-Davis (1996), Blundell-Preston (1998), Krueger-Perri (2003), Heathcote-Storesletten-Violante (2005) Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 2/30
Motivation • Welfare analysis in heterogeneous agents models with incomplete insurance against idiosyncratic risk is central to macroeconomics • Examples: welfare effects of a... 1. change in the amount of risk ( technology ) ◮ Attanasio-Davis (1996), Blundell-Preston (1998), Krueger-Perri (2003), Heathcote-Storesletten-Violante (2005) 2. change in the insurability of risk ( markets ) ◮ Levine-Zame (2002), Kubler-Schmedders (2001) Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 2/30
Motivation • Welfare analysis in heterogeneous agents models with incomplete insurance against idiosyncratic risk is central to macroeconomics • Examples: welfare effects of a... 1. change in the amount of risk ( technology ) ◮ Attanasio-Davis (1996), Blundell-Preston (1998), Krueger-Perri (2003), Heathcote-Storesletten-Violante (2005) 2. change in the insurability of risk ( markets ) ◮ Levine-Zame (2002), Kubler-Schmedders (2001) 3. change in redistributive policies ( government ) ◮ Long list... related to welfare costs of business cycles (Lucas, 2003) Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 2/30
Contributions 1. Tractable framework delivering transparent mapping between primitives of economy (preferences, risk, insurance market structure) and welfare expressions Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 3/30
Contributions 1. Tractable framework delivering transparent mapping between primitives of economy (preferences, risk, insurance market structure) and welfare expressions 2. Role of flexible labor supply: insurance vs. opportunities Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 3/30
Contributions 1. Tractable framework delivering transparent mapping between primitives of economy (preferences, risk, insurance market structure) and welfare expressions 2. Role of flexible labor supply: insurance vs. opportunities 3. Alternative representation of welfare effects based on changes in observable cross-sectional moments Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 3/30
Outline of the Talk 1. Baseline economy with Cobb-Douglas preferences and simple statistical representation of individual risk • Equilibrium allocations • Welfare expressions for 3 thought experiments • Alternative representation for welfare effects 2. Some illustrative calculations 3. Extension to richer process for individual risk • Tractability preserved by no-bond-trade equilibrium (Constantinides-Duffie, 1996) 4. Separable preferences Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 4/30
The Economy • Demographics and preferences : Continuum of agents with time-separable preferences ∞ t (1 − h t ) 1 − η ) 1 − θ − 1 β t ( c η � E 0 1 − θ t =0 Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 5/30
The Economy • Demographics and preferences : Continuum of agents with time-separable preferences ∞ t (1 − h t ) 1 − η ) 1 − θ − 1 β t ( c η � E 0 1 − θ t =0 • Endowments : initial wealth is zero for all agents and assets are in zero net supply Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 5/30
The Economy • Demographics and preferences : Continuum of agents with time-separable preferences ∞ t (1 − h t ) 1 − η ) 1 − θ − 1 β t ( c η � E 0 1 − θ t =0 • Endowments : initial wealth is zero for all agents and assets are in zero net supply • Technology : linear in aggregate hours weighted by efficiency-units of labor Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 5/30
The Economy • Demographics and preferences : Continuum of agents with time-separable preferences ∞ t (1 − h t ) 1 − η ) 1 − θ − 1 β t ( c η � E 0 1 − θ t =0 • Endowments : initial wealth is zero for all agents and assets are in zero net supply • Technology : linear in aggregate hours weighted by efficiency-units of labor • Labor market : competitive, hourly wages equal individual labor productivities Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 5/30
Individual Productivity Shocks • Two orthogonal log-Normally distributed components log w = α + ε t � − v α � � − v ε � α ∼ N 2 , v α , ε t ∼ N 2 , v ε i.i.d. • Hence: � − v � log w ( α, ε t ) = ( α + ε t ) ∼ N 2 , v , with E [ w ] = 1 • We model α as a permanent individual effect and ε t as i.i.d. shock (Gottschalk-Moffitt, 1994) Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 6/30
Asset Market Structure • Three distinct structures: 1. Autarky: no financial instruments Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 7/30
Asset Market Structure • Three distinct structures: 1. Autarky: no financial instruments 2. Complete markets: complete insurance against either component of the wage shock ◮ Trade opens before the realization of α Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 7/30
Asset Market Structure • Three distinct structures: 1. Autarky: no financial instruments 2. Complete markets: complete insurance against either component of the wage shock ◮ Trade opens before the realization of α 3. Incomplete markets: no insurance against the permanent component of wages, complete insurance against transitory shocks ◮ Trade opens after the realization of α Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 7/30
Incomplete-Markets Economy: Interpretations • Households literally have access to insurance against some shocks, but not others ◮ Cochrane (1991), Altonji-Hayashi-Kotlikoff (1991), Guiso-Pistaferri-Schivardi (2005) Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 8/30
Incomplete-Markets Economy: Interpretations • Households literally have access to insurance against some shocks, but not others ◮ Cochrane (1991), Altonji-Hayashi-Kotlikoff (1991), Guiso-Pistaferri-Schivardi (2005) • Ex-post complete markets with ex-ante heterogeneous agents ◮ Cunha-Heckman-Navarro (2005) Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 8/30
Incomplete-Markets Economy: Interpretations • Households literally have access to insurance against some shocks, but not others ◮ Cochrane (1991), Altonji-Hayashi-Kotlikoff (1991), Guiso-Pistaferri-Schivardi (2005) • Ex-post complete markets with ex-ante heterogeneous agents ◮ Cunha-Heckman-Navarro (2005) • Economy with a non-contingent bond (i.e., “Bewley economy") where precautionary saving and borrowing allow smoothing shocks that aren’t too persistent ◮ Numerical comparison of two economies → good approximation Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 8/30
Properties of Cobb-Douglas Preferences u ( c, h ) = ( c η (1 − h ) 1 − η ) 1 − θ − 1 1 − θ Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 9/30
Properties of Cobb-Douglas Preferences u ( c, h ) = ( c η (1 − h ) 1 − η ) 1 − θ − 1 1 − θ • Coefficient of relative risk aversion: ¯ γ ≡ 1 − η + ηθ Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 9/30
Properties of Cobb-Douglas Preferences u ( c, h ) = ( c η (1 − h ) 1 − η ) 1 − θ − 1 1 − θ • Coefficient of relative risk aversion: ¯ γ ≡ 1 − η + ηθ • Frisch labor supply elasticity: φ ≡ λ 1 − h h ◮ where λ ≡ 1 − η + ηθ is the Frisch elasticity of leisure θ ◮ Non-stochastic Frisch labor supply elasticity: φ = λ · 1 − η ¯ > 1 − η η Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 9/30
Properties of Cobb-Douglas Preferences u ( c, h ) = ( c η (1 − h ) 1 − η ) 1 − θ − 1 1 − θ • Coefficient of relative risk aversion: ¯ γ ≡ 1 − η + ηθ • Frisch labor supply elasticity: φ ≡ λ 1 − h h ◮ where λ ≡ 1 − η + ηθ is the Frisch elasticity of leisure θ ◮ Non-stochastic Frisch labor supply elasticity: φ = λ · 1 − η ¯ > 1 − η η • ( c, 1 − h ) substitutes when θ > 1( λ < 1) Heathcote-Storesletten-Violante, ”Insurance and Opportunities” – p. 9/30
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