Financial Accelerator - A Simple Theoretical Framework

A Simple Theoretical Framework

There are various ways of rationalizing a financial accelerator theoretically. One way is focusing on principal-agent problems in credit markets, as adopted by the influential works of Bernanke, Gertler and Gilchrist (1996) or Kiyotaki and Moore (1997).

The principal-agent view of credit markets refers to the costs (agency costs) associated with borrowing and lending due to imperfect and asymmetric information between lenders (principals) and borrowers (agents). Principals cannot access the information on investment opportunities (project returns), characteristics (creditworthiness) or actions (risk taking behavior) of the agents costlessly. These agency costs characterize three conditions that give rise to a financial accelerator:

1. External finance (debt) is more costly than internal finance (equity) unless it is fully collateralized, by which agency costs disappear as a result of guaranteed full repayment.
2. The premium on external finance increases with the amount of finance required but given a fixed amount of finance required, premium inversely varies with the borrower’s net worth, which signals ability to repay.
3. A fall in borrower’s net worth reduces the base for internal finance and raises the need for external finance at the same time raising the cost of it.

Thus, to the extent that net worth is affected by a negative (positive) shock, the effect of the initial shock is amplified due to decreased (increased) investment and production activities as a result of the credit crunch (boom).

The following model simply illustrates the ideas above:

Consider a firm, which possesses liquid assets such as cash holdings (C) and illiquid but collateralizable assets such as land (A). In order to produce output (Y) the firm uses inputs (X), but suppose that the firm needs to borrow (B) in order to finance input costs. Suppose for simplicity that the interest rate is zero. Suppose also that A can be sold with a price of P per unit after the production, and the price of X is normalized to 1. Thus, the amount of X that can be purchased is equal to the cash holdings plus the borrowing

X = C + B.

Suppose now that it is costly for the lender to seize firm’s output Y in case of default; however, ownership of the land A can be transferred to the lender if borrower defaults. Thus, land can serve as collateral. In this case, funds available to firm will be limited by the collateral value of the illiquid asset A, which is given by

B ≤ P A

This borrowing constraint induces a feasibility constraint for the purchase of X

X ≤ C + P A.

Thus, spending on the input is limited by the net worth of the firm. If firm’s net worth is less than the desired amount of X, the borrowing constraint will bind and firm’s input will be limited, which also limits its output.

As can be seen from the feasibility constraint, borrower’s net worth can be shrunk by a decline in the initial cash holdings C or asset prices P. Thus, an adverse shock to a firm’s net worth (say an initial decline in the asset prices) deteriorates its balance sheet through limiting its borrowing and triggers a series of falling asset prices, falling net worth, deteriorating balance sheets, falling borrowing (thus investment) and falling output. Decreased economic activity feeds back to a fall in asset demand and asset prices further, causing a vicious cycle.