Ben Bernanke, together with Mark Gertler, has advocated to study the importance of financial factors in economic allocations. In particular, the misallocations created by asymmetric information. In their American Economic Review (1989) paper (https://lnkd.in/gF3r6zq7) titled Agency Costs, Net Worth and Business Fluctuations, they introduced the financial accelerator mechanism through which small shocks get amplified due to financial market imperfections.

Here I present a simplified model to illustrate this financial accelerator mechanism.

Consider a world with Agency Costs in which the portion of net worth owned by entrepreneurs (nw_t) has a positive effect on the value of capital (q_t):

(1) q_{t} = p*nw_{t} + ϵd_{t}

where ϵd_t is an exogenous shock to capital prices.

p > 0 would be a manifestation of agency costs (or financial frictions) in that the distribution of net worth across lenders and borrowers affects asset prices. The idea is that higher net worth in the hands of entrepreneurs makes it easier for them to access a loan with which to buy capital, so that higher levels of net worth act like a demand channel on asset prices. In a world without credit market imperfections we would have p = 0.

The entrepreneur accumulates net worth to mitigate the agency problems involved in direct lending. The agency problem arises from a Costly State Verification (CSV) problem in the entrepreneur’s production technology. The entrepreneur takes one unit of input and creates ω_t units of capital, where the unit-mean random variable ω_t is privately observed by the entrepreneur but can be verified by the lender only by paying a cost. This CSV problem makes equity finance problematic, so that the optimal contract is given by a risky debt contract with a promised repayment of rp_t.

Entrepreneurial net worth accumulates with the profit flow from the investment project according to:

(2) nw_{t} = κ(q_{t} – rp_{t}) + nw_{t}-1 + rp_{t} + ϵn_{t}

where κ > 1 denotes leverage (the ratio of project size to net worth) and ϵn_t is an exogenous shock to net worth.

Eqs. (1) and (2) are a simultaneous system in net worth and the price of capital. We can solve for the two endogenous variables, nw_t and q_t, as a function of the pre-determined and exogenous variables:

(3) nw_{t} = [1 / (1 – pκ)] * ((κ – 1)rp_{t} + nw_t-1 + ϵn_{t} + κ*ϵd_{t})

(4) q_{t} = [1 / (1 – pκ)] * (p((κ – 1)rp_{t} + nw_{t}-1 + ϵn_{t}) + ϵd_{t}))

where [1 / (1 – pκ)] in (3) and (4) is the “multiplier” arising from two endogenous variables with positive feedback. This then implies that exogenous shocks are “multiplied” or “financially accelerated”. The multiplier is larger, as financial frictions, captured by p, are larger, and as leverage, κ, is also larger.

Under a standard parametrization as Bernanke, Gertler and Gilchrist, with p = 0.45 and κ = 2, we have [1 / (1 – pκ)] = 10, this means shocks are multiplied 10 times.