Financial Intermediation, Loanable funds and the Real Sector Bengt Holmstrom and Jean Tirole Quarterly Journal of Economics, 1997
Vol. 112, No. 3 pp 663-691 A Presentation by Twinemanzi Tumubweinee
In this paper Holmstrom and Tirole (1997) construct a simple principal-agent equilibrium model that attempts to replicate some of stylized facts on loanable funds and the role of capital constraints in explaining them. New to their model is the provision for both firm and financial intermediary financial structures. Below are some of the stylized facts their model attempts to replicate;
Firms with substantial net worth can rely on cheaper less information intensive financing channels.
Highly leveraged firms demand more information intensive finance
Reduce monitoring capital, and capital poor firms are the first to suffer.
Credit crunches increase the spread between intermediated and market debt
Holmstrom and Tirole(1997) note that if there capital squeezes for both intermediaries and firms, then the sign of the change in the interest rate spread depends on the change in the relative amounts of capital.
The assumptions of the model though simplifying to allow for tractability are;
Three types of agents; firms, intermediaries and investors.
Two time periods with returns being realized only at time t=2.
All parties are risk neutral and are protected by limited liability.
Different firms have different initial endowments A ( cash for ease of analysis)
Distribution of A across firms follows a CDF G(A)
The Real Sector (Firms or Entrepreneurs);
In the aggregate the total capital outlay by firms is given by
The firm is undertaking a project at time t=1 with cost I > 0, so the initial funding requirement is I – A if A < I.
In the absence of incentives or monitoring, entrepreneurs or firm owners can deliberately reduce the project’s chance of success to allowing them some private benefit .
The open market ROR on investment capital is , a good project is then viable if
The private benefits, representing the private opportunity costs to managing the project diligently are ordered and the level of effort e to generate or is the same.
The Financial Sector:
The first assumption is that monitoring prevents B, so the private benefit is reduced to b, with cost. Secondly all projects financed by intermediaries are perfectly correlated (an extreme case). And lastly each intermediary’s capital is sufficiently large vis-à-vis the scale of the project.
Assumed to be uninformed relative to the intermediaries, and they demand an expected ROR that is exogenous, implying infinite opportunities on the open market capable of generating. Furthermore is assumed to be an increasing supply function. Lastly firms cannot monitor other firms and excess cash in firms earns.
Direct Financing (the two party contract)
Investors supply I –A, with I being of fixed scale. If the project fails neither party gets anything. The distribution of returns is
For the firm to prefer diligence then
the minimum return to the firm must be ,and
is the maximum pledgeable income to investors. The opportunity cost of funds supplied by investors is , so a necessary and sufficient condition for direct finance is (2)
Rearrange (2) and define (3)
It’s easily seen that only firms with can invest using direct finance. To ensure that , use Eqn (3) to show that the total surplus from a project has got to be less than the share due to a firm to ensure diligence.
Indirect Finance Scenario:
If Rm is the return due to the intermediaries, and their monitoring eliminates B then
Rm + Ru + Rf = R , (5)
and the firm’s incentive constraint is modified to . For the intermediary to monitor, with a cost and ensure a positive return, the following must hold with strict inequality (6)
The maximum pledgeable expected income to investors is
Using Eqn (7) we get the minimum contribution an intermediary can make to a project that it monitors is
Since uninformed investment is, then a sufficient and necessary condition for a firm to be financed with uninformed capital is ( cf. to Eqn (2)) is
, and in the spirit of Eqn (3) to access uninformed funding (10)
Applying partial derivatives of Eqn (10) w.r.t and , its clear that is increasing in both parameters, implying it’s difficult to get financing when they increase. Note that if , then the price of monitoring is high, there will be no demand for monitoring and will have to come down but will still hold. Assume there exists a minimum acceptable , such that .
Then its value is given by (11)
To ensure a social benefit from monitoring must hold with the sufficient condition being; (use Eqns (10) and (3))
The firm, gets direct finance.
The firms won’t get funding and is thus unable to invest
These firms can invest but with a mixture of informed and uniformed financing and require monitoring. Size of the intermediary’s stake in the firm is a certification signal as to its ex-post behavior, and it determines how much the capital the uninformed investors will commit. This is the “free riders” aspect to intermediated finance.
Equilibrium in the Credit Market:
The aggregate demand for informed capital is
Note that and , it follows that
For a given, there’s a unique that clears the market for informed credit. However the sign for is ambiguous since its also dependant on the distribution .
Eqn (13) holds for exogenous. Assuming the endogeneity of being fully described by some inelastic supply, then the demand for uninformed capital is given by
And note that , using Liebnitz Rule. For the uninformed market to clear we need , the equilibrium in both credit markets is then
Taking I as fixed, Holmstrom and Tirole apply comparative statics to the supply of capital using three forms of capital constriction: a “credit crunch”, a “collateral squeeze” and a “savings squeeze”.
Proposition 1: Either or will go up during a capital squeeze, but NEVER both. And in a fixed investment model, the equilibrium is unique.
, and. Given , and initial endowment denoted, then a firm maximizes
Subject to the following constraints;
By dividing through all constraints by , and normalizing, to see that firms with different levels of assets use the same optimal policy scaled by their assets.
Substituting (i) and (iii) – (vii) into (ii) gives
is the amount of firm’s own capital needed to make a unit size of investment.
A firm can NEVER lever its own capital, i.e.
In equilibrium and, must be such so that a firm can never invest without limit.
From Eqn (16) and its constraints, the firm’s objective function in unconstrained form is reduced to
The term in brackets is the net value of leverage to the firm, if monitoring is valuable then its positive, representing the excess of IRR over the market return which the Holmstrom and Tirole refer to as the “incentive effect”.
Equilibrium in capital market with variable Investment:
Since firms choose the same optimal policy per unit of own capital, the equilibrium is then easily computed by aggregating across firms;
(NB: Use Eqns (22a) – (22c), by applying partial derivatives w.r.t and.)
Market equilibrium is the same whether investors invest directly or indirectly in firms. They only care about the contingent interest held by the intermediary (informed investor) in the project.
Assume a continuous set of possible bad projects with differing levels of private benefit, i.e. it’s a continuous variable. Monitoring intensity of, eliminates projects with private benefit greater than. Since the monitoring cost is a function of the fixed return , [see Eqn (6)], in the fixed investment case, firms for whom Eqn (10) holds with strict inequality are able to replace the more expensive intermediary capital with the cheaper uniformed capital. Note increasing , implies lower Rm and a lower C for a fixed Ifrom the definition of R. A lower C, implies a lower from Eqn (9) . The shortfall in intermediary capital is them replaced with cheaper uninformed capital since. Intensity of monitoring is positively related to, and a higher C, implies a higher. With variable investment, all monitoring is at the same intensity since b is independent of, see Eqns (16)-(20). Note that in this case, from Eqns (17)-(19) the firm ideally chooses, the own assets per unit of private benefit. An increase in, leads to an increase in b, assuming an exogenous ,implying scarcity of informed capital leads to less intensive monitoring.
Fifth result: With endogenous monitoring, aggregate investment (see Eqn 22) also depends on the relative amounts of firm and intermediary capital.
Furthermore assume continuous investment, decreasing returns to scale and gross firm profit satisfying the Inada conditions. The firm’s net utility is expected net profit less extra opportunity cost of intermediary capital given by
using constraints (iii), (v) from Eqn (16) and , similar to the derivation of (17) and (18), we will have given by;
In this case, incentive compatibility for the firm requires. Recall U(I) is maximized at some I*, sofirms with are credit constrained. The shape of R(I) determines the impact of reduced intermediary capital on firms with more assets.
Sixth Result: Lower leverage reduces sensitivity to a rise in. Lower marginal returns make large firms more sensitive to a rise in.
Holmstrom, Bengt., Tirole, Jean.,1997. Financial Intermediation, Loanable Funds and the Real Sector. Quarterly Journal of Economics, 112, pp 663-691