Endogenous employment and incomplete markets

Transcription

1 Endogenous employment and incomplete markets Andres Zambrano Universidad de los Andes June 2, 2014

2 Motivation Self-insurance models with incomplete markets generate negatively skewed wealth distributions But observed wealth distribution is positively skewed Density Assets Survey of Consumer Finances 2010

3 There is evidence of non-market mechanisms to smooth consumption (Cochrane, 1991) This paper explores effort and human capital as non-market mechanisms to alleviate idiosyncratic risk Education increases lifetime earnings: Higher earnings Less incidence and duration of unemployment Effort is used to increase probability of employment, as in search models

4 Questions and Preview of Results How do market and non-market mechanisms interact? What are their consequences for long run unemployment and wealth distribution? Since education is acquired by richer households, it creates long run tension towards more inequality But effort has an inverse relationship with wealth, which generates a short run effect towards less inequality Useful to think on optimal combination of unemployment insurance and subsidies to education

5 Model Preview Heterogeneous agents with incomplete markets but endogenous transitions Risk-free bond to partially insure Effort (flow) and human capital (stock) increase prob of employment Focus on stationary equilibrium and wealth distribution

6 Environment Exchange economy with mass one of agents who face idiosyncratic risk. Two commodities: perishable consumption good c and asset holdings a. Each agent receives stochastic endowment s t in each period: s L < s H (unemployed, employed) Effort e increases probability of good state next period Efficiency of effort determined by having college degree or not: h H or h L Pr (s t+1 = s H s t, h) = P (e t ; s t, h) increasing in all arguments and concave in e

7 Environment continued... Individuals discount future at rate β Agent dies with probability 1 δ and is replaced by a newborn Newly born agent inherits wealth and decides whether to get college degree or not at cost φ. Agents are altruistic: maximize lifetime utility of household.

8 Agent s problem represented in recursive formulation as { [ ( v (a, s, h; q) = max u (c) e + βδes c,e,a v a, s, h; q ) e, s, h ] +β (1 δ) v 0 ( a ; q )} subject to c + qa s + a, and a a min where v 0 (a ; q) = max {v (a, s L, h L ; q) ; v (a φ, s L, h H ; q)}

9 Lemma Effort is a decreasing function of assets Intuition When unemployed, richer individuals can rely on assets and wait to be lucky next period Very poor agents cannot longer rely on debt, must exert lots of effort Lemma Education will be acquired by rich-enough households Intuition: Marginal return of assets is relatively higher when poor

10 Lemma In equilibrium βδ < q Intuition: Stochastic discount factor is a supermartingale, to assure finite consumption and asset holdings we need βδ < q Assets holdings increase (decrease) when facing a good (bad) state An endogenous upper bound arises

11 Equilibrium Definition Stationary equilibrium is defined by c (a, s, h; q), e (a, s, h; q), a (a, s, h; q); price q; and λ (a, s, h; q), such that Policy and value functions solve the agent s problem Markets clear: 1 a s h c (a, s, h; q) λ (a, s, h; q) da = a s h sλ (a, s, h; q) da 2 a s h a (a, s, h; q) λ (a, s, h; q) da = 0 Stationary distribution λ (a, s, h; q) induced by policy functions and endogenous Markov chain P (e (a, s, h; q) ; s, h)

12 Numerical Exercise Utility function takes form u (c) = c1 σ 1 σ and Prescott, 1985) with σ = 1.5 (Mehra Rest of parameters calculated according to periods of 8.5 weeks (Huggett, 1993) s H = 1, s L = 0.1, β = 0.993, δ = φ = 4 Average cost of public college (College Board 2011) a min = 5 (Aiyagari, 1994) P ( e; s i, h j ) = 1 exp s i h j e where h H = 11.9, h L = 10

13 Transition probabilities Probability of being employed Effort Unemployed No College Employed No College Unemployed College Employed College

14 Results Optimal policy rule for assets 5 4 Future assets Assets Unemployed No College Employed No College Unemployed College Employed College 45 0

15 Optimal policy for probability of being employed Probability of being employed Assets Unemployed No College Employed No College Unemployed College Employed College Evidence: Unemployment duration rises with holdings of short-term liquid assets (Algan et al.; 2003)

16 Results Baseline calibration: φ = 4 Statistic φ = 4 Real Interest rate 4.36% Percentage with college 29.68% 29% Total Unemployment 7.88% 7.6% Unemployed with college 6.91% 4.9% Unemployed no college 8.29% 9.5%

17 Stationary Wealth Distribution is now right skewed φ= Density Assets Intuition: Agents prefer to diversify between market and non-market mechanisms

18 Conditional stationary distribution of assets Density Unemployed No College Unemployed College Employed NoCollege Employed College Density Assets (a) Estimated density x College No college (b) SCF 2010 More dispersed and less skewed for college graduates College educated create fat tail

19 Concluding remarks Effort and assets are inverse related and only rich enough agents invest in education Consumption smoothing by diversifying between riskless asset and non-market mechanisms Wealth distribution skewed to the right, closer to observed one Distribution of wealth for college graduates is more dispersed and less skewed Useful to think on potential consequences of raising college fees and/or decreasing unemployment insurance

20 Extensions Optimal government policies: Government has budget to split between unemployment insurance and subsidies for college What is the optimal combination of such policies? Matching: Include aggregate firm to generate probabilities from microfundamentals Too many college graduates reduces employment probabilities: GE effect Harder: Optimal fiscal policy when transition probabilities are endogenous (persistence)

21 Related literature Heterogenous agents and incomplete markets: Huggett (1993), Aiyagari (1994) Optimal unemployment insurance: Hopenhayn and Nicolini (1997), Wang and Williamson (2002) Endogenous employment and search: Algan et al. (2003), Lentz and Tranaes (2005)