Entrepreneurship, Frictions and Wealth

Transcription

1 Entrepreneurship, Frictions and Wealth Marco Cagetti University of Virginia 1 Mariacristina De Nardi Federal Reserve Bank of Chicago, NBER, and University of Minnesota

2 Previous work: Potential and existing entrepreneurs face borrowing constraints. Entrepreneurship is key to understand wealth inequality. 2

3 Entrepreneurs and borrowing constraints entrepreneurial choice depends on own assets and received bequests entrepreneur s portfolio undiversified collateral 3

4 Entrepreneurs and wealth inequality wealth more concentrated than labor earnings and income small fraction of entrepreneurs hold large share of total wealth (they also have higher saving rates) 4

5 5 Top % Whole population % total net worth held Active Bz. owners % hhs in given perc SE % hhs in given perc SE and Bz. owners % hhs in given perc

6 What we do: Construct a quantitative model consistent with observed data. Evaluate model along dimensions not matched by construction. 6 Study effects of borrowing constraints on aggregates and wealth inequality.

7 Preview of results Model accounts very well for wealth distributions of entrepreneurs and workers Model generates entry into entrepreneurship consistent with Hurst and Lusardi s estimates 7 Model generates entrepreneurial returns consistent with those in SCF data

8 More stringent borrowing constraints less inequality but also less investment Voluntary bequests important for wealth concentration

9 Demographics households: overlapping generations (possibly) with altruism. Two stages of life: young and old, stochastic aging 1 π y =pr of aging 1 π o =pr of dying 8

10 Demographics: OLG with stochastic aging 1 model period = 1 year Trick to keep computations manageable with short time periods Dynasty 1 Dynasty 2 Person 1 + Person Young Old Young Old Young... π y 1 π y π o 1 π o Old Young Old Young Old Young 9

11 Household s preferences Period utility: CRRA in consumption c 1 σ 1 σ Discount the future at rate β. Potentially altruistic toward own descendants (η). 10

12 Technology entrepreneurial sector: (1 δ)k + θk ν 0 < ν < 1 non-entrepreneurial sector: Cobb-Douglas tech employs all workers and the rest of the capital 11

13 Time line of decisions Young Assets Abilities Worker Entrepreneur Young Old retiree Young Old entrepreneur t t Retire Old entrepreneur Assets Ability Old retiree Assets Entrepreneur Old retiree Die Young Old entrepreneur Die Young Old retiree Die Young

14 Households observe (y,θ) choose (w,e) for the period workers earn y 13 entrepreneurs invest k

15 Credit market constraints imperfectly enforceable contracts: can borrow (k a), be worker, keep fk, creditors seize (1 f)k value (investing and repaying) value (keeping f k) and being worker 14 e can borrow at r, invest k, worker can save at r

16 Young s problem { } V (a, y, θ) = max V e (a, y, θ), V w (a, y, θ) 15

17 Young entrepreneur s problem V e (a, y, θ) = max c,k,a { u(c) + βπ y EV (a, y, θ ) + β(1 π y )EW(a, θ ) a = (1 δ)k + θk ν (1 + r)(k a) c V e (a, y, θ) V w (f k, y, θ) } 16 a 0 k 0

18 Young worker s problem V w (a, y, θ) = max c,a { u(c) + βπ y EV (a, y, θ ) + β(1 π y )W r (a ) a = (1 + r)a + w g y c a 0 } 17

19 Old entrepreneur s problem { } W(a, θ) = max W e (a, θ), W r (a) { W e (a, θ) = max u(c) + βπ o EW(a, θ )+ c,k,a ηβ(1 π o )EV (a, y, θ } ) a = (1 δ)k + θk ν (1 + r)(k a) c W e (a, θ) W r (f k) 18 a 0 k 0

20 Old retiree s problem W r (a) = max c,a { u(c) + βπ o EW r (a ) + ηβ(1 π o )EV (a, y, θ ) a = (1 + r)a + p c a 0 } 19

21 Equilibrium Prices, decision rules and distribution m over x s.t. decision rules solve hh s problem capital and labor mkts clear prices equal marginal products 20 m is invariant distribution

22 Fixed Parameter Value σ 1.5 δ.06 α.33 A 1 π y.98 π o.91 P y + p 40% average yearly income η

23 Calibrated Parameter Value β.852 θ [0, 0.55] P θ see text ν.88 f 75% Match following moments: capital to GDP ratio frac. of entr. in pop. frac. of entr. becoming workers in each period frac. of workers becoming entr. in each period 22 median net worth of entr./median net worth. workers fraction of people with zero wealth

24 Evaluate model along: overall wealth distribution entrepreneurs wealth distribution Hurst and Lusardi s key regression results 23 Private equity returns

25 Perc. wealth in the top K/Y Wealth Perc. Gini entr. 1% 5% 20% 40% U.S. data % Baseline with entrepreneurs %

26 Distribution of wealth, model with entrepreneurs Fraction of people Fraction of people Positive wealth, in thousands of dollars Positive wealth, in thousands of dollars 25 Population Entrepreneurs Dash-dot line: data; Solid line: baseline model.

27 Saving rate for highest-ability workers. Solid: high entr. ability; dash-dot: no entr. ability Saving rate Wealth, in thousands of dollars

28 Probability of entering entrepreneurship as function of own wealth (as Hurst and Lusardi). 7 7 Probability of entrepreneurial entry Probability of entrepreneurial entry Wealth, in thousands of dollars Benchmark Wealth, in thousands of dollars Small fraction of non-entrepreneurial self-employed

29 Median rate of return (income divided by business net worth). SCF data, capital income only: 3% SCF data, total income: 40% Model, total income: 47% Model, total income, 10% underreporting: 40% 28 Model, total income, 20% underreporting: 35%.

30 Capital- Percentage wealth in the top output Wealth Perc. ratio Gini entr. 1% 5% 20% 40% U.S. data % Baseline with entrepreneurs % More stringent borrowing constraints: f = % No altruism: η = 0, only involuntary bequests % η = 0, recalibrated β %

31 Maximum investment. Solid line: baseline; dash-dot line: more restrictive BC Maximum investment Own assets, in thousands of dollars

32 U.S. wealth and earnings distributions Percentage held by the top 1% 5% 20% 40% 80% Wealth Gross earnings

33 SCF questions: 1. Do you work for someone else, are you selfemployed, or what? 2. Do you (and your family living here) own or share ownership in any privately-held businesses, farms, professional practices or partnerships? Do you (or anyone in your family living here) have an active management role in any of these businesses?

34 33 % in pop. Share tot. wealth Bz. owners or SE All bz. owners Active bz. owners All SE SE bz. owners

35 34 median mean Whole population Business owners or SE All business owners Bus owners but not active mgmt Business owners not SE All self-employed SE (active) business owners SE and not business owners

36 35 Top % Whole population % total net worth held Bz. owners or SE % hhs in given perc All Bz. owners % hhs in given perc Active Bz. owners % hhs in given perc SE % hhs in given perc SE and Bz. owners % hhs in given perc

37 Related Literature entrepreneurial choice Gentry and Hubbard, Evans and Jovanovic, Quadrini wealth accumulation Diaz-Gimenez et at., Quadrini and Rios-Rull, Castañed et al., De Nardi 36 optimal contracts Albuquerque and Hopenhayn, Monge

38 Algorithm fix ˆk( ) = k max, solve val. fns check endogenous b.c. if not satisfied, update ˆk( ) 37 iterate until ˆk( ) satisfies end. b.c.

39 iterate until capital markets clear

40 Distribution of wealth, model without entrepreneurs. Dash-dot: data; Solid: model. Fraction of people Positive wealth, in thousands of dollars

41 Firm size distribution, baseline model with entrepreneurs. Fraction of firms Firm size, in thousands of dollars