Many models of capital market imperfections reach the conclusion that ﬁnancing an investment project is cheaper with ‘internal’ than with ‘external’ funds. (Internal funds are those that the ﬁrm owns, for example, in its bank account; external funds are obtained from outsiders like banks or new investors). For a lucid exposition of an example of models of this kind, see the discussion of ﬁnancial market imperfections in Romer (2011).

Such models tend to be highly specialized, with entrepreneurs who miraculously receive exogenously speciﬁed endowments of ‘internal’ cash and who make a one- (or at most two-) period investment decision. This is a striking contrast with the generality of the canonical $ϙ$ model of investment in which optimizing ﬁrms make investment decisions that take into account inﬁnite future paths of adjustment costs, marginal products of capital, taxes, and all other features of the environment.

But models with imperfect capital markets are always very clear on who receives what cash, when, and why. In contrast, the power of the $ϙ$ model comes at a high cost: The model has no implications whatsoever for the ﬁrm’s decisions about when and how to make payments to shareholders and lenders.

1 Modigliani-Miller

To see this, consider the benchmark discrete-time framework qModel without taxes or depreciation, and (as in that handout) assume that the ﬁrm issues or repurchases shares to maintain a number of shares $st$ outstanding equal to the size of the physical capital stock (so $st = kt$ in every period). Suppose we assume that the ﬁrm has a ‘dividend policy’: In every period, it pays to each shareholder a dividend equal to the ﬂow of revenues per share.

In this case, the value of all the ﬁrm’s shares $st$ (the equity value of the ﬁrm) will be

(Notice that because the ﬁrm always has $st = kt,$ the value of the ﬁrm’s shares deﬁned here $ˆet(st)$ is identical to the value of the ﬁrm’s capital $et(kt)$ deﬁned in qModel.)

Now suppose the ﬁrm decides to deviate, just a little bit, from this dividend policy. It issues an extra share in period $t$ , which (assuming capital markets are eﬃcient) raises an amount of money equal to the share price $λt$ ; it invests the proceeds in the riskless asset, earning return $R$ , then pays out the resulting cash to shareholders in the next period. However, we assume that the ﬁrm continues to maximize its value. This modiﬁes the inﬁnite sum to:

but since by assumption $− 1 β = R$ this expression reduces to the original expression.

The point can be extended to show that the ﬁrm can raise an arbitrary amount of money in one period, paying it back in another, or vice versa, without having any eﬀect on its value or its optimal investment plans.

This is an example of the famous theorem by Modigliani and Miller (1958), who showed that under perfect capital markets the value of the ﬁrm is identical whether its investment is ﬁnanced by equity, debt, or any combination of the two.

It is precisely to get around this result that models of imperfect capital markets were invented, since from the beginning many economists did not believe that the result is a plausible description of reality (including, I believe, Modigliani and Miller). Indeed, the existence (and high salaries) of corporate ﬁnancial oﬃcers constitute a proof that the proposition is not true – if it were true, CFOs would have no eﬀect on the value of the ﬁrm, and could all be ﬁred (thus saving the ﬁrm their salaries!). What remains true, however, is that models of investment that relax the assumption of perfect capital markets are much more diﬃcult to work with – and harder to extract implications from – than models that assume capital markets are perfect.

A testable result that generally emerges from models of capital market imperfections, however, is that the amount of a ﬁrm’s investment depends on the amount of cash the ﬁrm has on hand, with which it can ﬁnance that investment.

2 Testing for the Failure of Modigliani-Miller

qModel shows that the $ϙ$ model can be manipulated (abstracting from depreciation, taxes, and other complications) to yield an implication for investment dynamics of approximately the following kind:

The simplest class of imperfect capital markets models is one in which the ﬁrm is constrained to pay dividends to shareholders equal to whatever is its ﬂow of cash after subtracting oﬀ expenses. But the rate of return that the ﬁrm must pay for external funds exceeds the return it can earn on internal funds. Without going into details, the rough implication of this is that an empirical model of the ﬁrm’s investment choices should augment (3) with a measure of the funds the ﬁrm has in its hands at the time the investment decision is made:

A large literature spurred by the seminal paper of Fazzari, Hubbard, and Petersen (1988) estimates equations like this, and virtually always ﬁnds a statistically signiﬁcant estimate of $ψ2$ , interpreted as indicating the importance of ‘cash ﬂow’ for investment decisions. But there are many criticisms of this literature, and the importance of imperfections in capital markets remains a lively area of debate. My own view is that the most persuasive evidence of large deviations from the benchmark of the MM theorem is the fact that the ﬁnancial services industry (including corporate CFOs) absorbs a very substantial amount of resources every year. Why would such a large industry exist if the informational problems were easy to solve? It wouldn’t - especially in the internet era, where it would be a trivial matter to match up borrowers and lenders in the absence of informational and enforcement diﬃculties.

References

Fazzari, Stephen, R. Glenn Hubbard, and Bruce C. Petersen (1988): “Financing Constraints and Corporate Investment,” Brookings Papers on Economic Activity, 1988(1), 141–206.

Modigliani, Franco, and Merton H. Miller (1958): “The Cost of Capital, Corporation Finance, and the Theory of Investment,” American Economic Review, 48(3), 261–297.

Romer, David (2011): Advanced Macroeconomics. McGraw-Hill/Irwin, fourth edn.