Bernanke & Gertler (1989) - Agency Costs, Net Worth, & Business Fluctuations

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1 Bernanke & Gertler (1989) - Agency Costs, Net Worth, & Business Fluctuations Robert Kirkby UC3M November 2010

2 The Idea Motivation Condition of firm & household often suggested as a determinant of macroeconomic activity, eg. Miskin (1978) & Bernanke (1983) argue that the weakness of borrowers balance sheets contributed to the severity of Great Depression Eckstein & Sinai (1986) put firm balance sheets at the center of their analysis of cyclical dynamics. Numerous studies have connected balance sheet conditions with household & firm spending decisions.

3 The Idea Agency Costs Introduce imperfect information into an RBC framework. Assume an information assymetry between entrepreneurs who organise and manage physical investment and the savers from whom they borrow. Specifically, assume a costly state verification problem (Townsend, 1979, 1988). This makes the Modigliani-Miller theorem inapplicable, opening up possibility of interaction between real and financial (ie. balance sheet) factors

4 The Model The Model Use an RBC model, extended to a two-period OLG framework. Each individual lives two periods, can earn labour income only in the first, and so must save to finance the consumption in the second. Saving can be done either in inventories or capital. Two goods produced, output good and capital. Capital good production is the one suffering from information asymmetries.

5 The Model The Agents Countable infinity of agents in each generation. Fraction η of agents in each generation are entrepreneurs. Rest are lenders. ω U[0, 1]; indexes productivity of the entrepreneurs (low ω = low cost)

6 The Model The Goods Two goods: Capital good & Output good Output good can be consumed, invested as capital, or stored as inventory. One unit of output stored in period t yields r units in period t+1 (r is gross rate of return). Capital fully depreciates each period (this is for expositional reasons only).

7 The Model Output production Production function for per-capita output is (assume that labour supply is fixed): y t = θ t f (k t ),f (0) > 0, θ t iid, E( θ ) ) = θ k t capital per head θ t agg. productivity shock

8 The Model Capital production Each entrepreneur has a project they can invest in. It requires an input of x(ω) (x is inc in ω). Any project undertaken in t, yields an amount of capital in t+1 given by κ i κ i is an iid discrete random variable taking values i = 1,..., n, κ j > κ k, j > k The probability of outcome κ j is π j, and the expected outcome is κ. Note that ω does not affect outcome, only required inputs. This is a simple way of motivating an upward-sloping supply curve.

9 The Model Asymmetric Information Project outcome is costlessly observable to the entrepreneur who operates it. Any other agent must pay an audit cost, γ units of capital, which makes project outcome visible to all agents. We assume that there is no other way to determine the outcome (eg. by looking at agents consumption). We assume random auditing is feasible (lenders can precommit to audit with some probability). Chronologically; Project outcomes are realized, announcements are made (of realized κ i ), and auditing takes place before the current period value of θ t.

10 The Model Capital production cont. Investment project outcomes are mutually independent so at aggregate level there is no uncertainty about the level of capital produced. So, k t+1 = (κ h t γ)i t h t fraction of projects initiated in t that are audited i t number of investment projects undertaken in t per-capita We also assume θf (0)κ > rx(0) + γ θf (κη) < rx(1) Which guarantees that some but not all entrepreneurs will always invest.

11 The Model Labour Supply & Prefs Labour Supply= 1 = ηl e + (1 η)l L, L e labour endowment of lenders & entrepreneurs Lenders Prefs: U(z y t ) + βe t (z o t+1 ) Follow Sappington (1983) in assuming risk-neutrality of consumption when old. This allows to concentrate on role of agents wealth in mitigating agency costs, rather than on issues of risk-sharing. Entrep. Prefs: E t (z o t+1 ) The assumptions that entrepreneurs & lenders have different prefs, & in particular, that entreprenteurs do not consume when young are inessential.

12 The Model Wages & Savings Wage w t ; so entrepreneurs have per-capita incomes of w t L e (lenders have w t L). Entrepreneurs do not consume when young, so avg. entrepreneurial savigns, S e t, is S e t = w t L e Solving lenders problem for optimal cons. when young as fn of r, z y (r), avg. saving by lenders is S t = w t L z y (r) Main importance of these to equations is to esablish a link between wages (marg. productivities) & savings.

13 Equilibrium Perfect Information Case, gamma = 0 For ω ω, entrepreneurs make investment. ˆq, the relative price of capital, and k are constant over time. Investment is fixed. So production of the output good fluctuates in proportion to the (serially uncorrelated) productivity shock. Consumption is positively serially correlated with output. We will consider this as the benchmark case.

14 Equilibrium with Asymmetric Information Optimal Financial Contract Look at optimal contract for entrepreneur who needs to borrow (x(ω) > S e ). If entrepreneur announces κ 2 there will be no auditing (n = 2) If S e is sufficiently large that, ˆqκ 1 r(x(ω) S e ), then agent is fully collateralized and there is no moral hazard problem. If S e is not this large, then we are in the incomplete collateralized case, & there will be positive agency costs. Can solve for optimal auditing probability p. Note that when there is incomplete collateralization, cˆ ic S = αr > r, that is, return to inside funds is higher than return e to outside funds (as lower agency cost).

15 Equilibrium with Asymmetric Information Optimal Financial Contract Agents problem is maxπ 1 (pc a + (1 p)c 1 ) + π 2 c 2 s.t π 1 [ˆqκ 1 p(c a + ˆqγ) (1 p)c 1 ] + π 2 [ˆqκ 2 c 2 ] r(x S e ) Outside Option (r) c 2 (1 p)(ˆq(κ 2 κ 1 ) + c 1 ) Incentive Compatibility c 1, c a 0 Limited Liability 0 p 1

16 Equilibrium with Asymmetric Information Entrepreneurial Investment Decision Now consider whether investor will want to use his savings, and the effects of audit costs on his choice. Defining ω & ω by: ˆqκ rx(ω) ˆqπ 1 γ = 0 ˆqκ rx( ω) = 0 We distinguish 3 types of entrepreneur; Good, ω ω; positive net exp. return on projects is always positive (even if audit with prob. 1) Fair, ω ω ω; exp. returns will be positive or negative depending on auditing level Poor, ω ω; returns are negative even with zero auditing

17 Equilibrium with Asymmetric Information Again, for any ω, define full collateralization level of entrepreneurial savings, S (ω) to be S (ω) = x(ω) (ˆq/r)κ 1 And, for fair entrepreneurs, defining S (ω) as the saving level that makes investment have the same rate of return as storage. We get that, all good entrepreneurs invest, all poor do not, and a fraction of the fair do. Only the good will be audited (as they use a lottery on the fair so the fraction that does invest all ends up fully-collateralized)

18 Equilibrium with Asymmetric Information Within-Period Equilibrium Let p(ω) be probability of audit for good type, and g(ω) the fraction of fair type who invest. Total capital formation (per capita), taking k t given, is then k t+1 = [κω ω 0 π 1γp(ω)dω]η + [κ ω ω g(ω)dω]η This gives k t + 1 as a function of ˆq t+1. The demand function is the same as for the perfect information case.

19 Macro-Implications of Model Statics Compartive Statics k is lower with γ > 0 than benchmark full information case, gamma = 0. An increase in current incomve (either higher inherited k t or higher θ t ) will increase entrepreneurial savings, S e, lowering agency costs, and thereby increasing k t+1. Debt-deflation: raise L & lower L e. The motivation for this exercise is to model unindexed debt contracts & unexpected deflation redistributing wealth from the debtor class to the creditor class. Decreasign L e, lowers S e, increasing agency costs and thus leads to lower investment k t+1.

20 Macro-Implications of Model Dynamics Aggregate Dynamics Consider a productivity shock. In the informationally constraint region, a (temporary) rise in θ stimulates investment by increasing net worth. The expansion persists because the rise in the future capital stock makes investment in the subsequent period higher than it would otherwise be. The intuition; In good times, when profits are high & balance sheets are healthy, it is easier for firms to obtain outside funds. This stimulates investment & propagates the good times. Vice-versa for bad shock/times.

21 Macro-Implications of Model Dynamics This is the finacial accelerator effect; income has a sort of accelerator effect on investment. Note that countercyclical agency costs are crucial to the story. A redistributional shock (ie. the debt-deflation case described earlier) will instigate a similar sort of dynamics. Thus, balance sheet considerations may initiate, as well as propagate, cyclical fluctations.

22 Macro-Implications of Model Dynamics Conclusions The existence of countercyclical agency costs that cause any deviations from first-best outcomes associated with the necessity of external finance will generate an accelerator effect, in which financial (balance sheet) effects increase the size of business fluctuations. They also mean that financial shocks can have real effects.