Chapter 21 The financial accelerator in a quantitative business cycle framework

The authors open by noting that both the canonical real business cycle model and the textbook Keynesian IS-LM model “share one strong implication”: absent effects on the real interest-rate term structure, “conditions in financial and credit markets do not affect the real economy” – an implicit adoption of Modigliani-Miller (1958) irrelevance (Section 1, p. 1343). Against this, they invoke “a long-standing alternative tradition… beginning with Fisher and Keynes,” citing Fisher’s (1933) attribution of the Great Depression’s severity partly to debt-deflation, and note that “when credit markets are characterized by asymmetric information and agency problems, the Modigliani-Miller irrelevance theorem no longer applies” (Section 1, pp. 1343-1345). The chapter’s “principal objective… is to show that credit-market imperfections can be incorporated into standard macroeconomic models in a relatively straightforward yet rigorous way” (Section 1, p. 1345).

Following Townsend (1979), lenders can only observe an individual borrower’s privately known realized return on capital by paying a fixed auditing cost, set proportional to the realized gross payoff, μωR^k_{t+1}Q_tK^j_{t+1} (Section 3, p. 1350). The resulting optimal contract resembles standard risky debt: the entrepreneur repays a fixed contractual amount if the idiosyncratic shock ω^j exceeds a threshold ω̄^j, and defaults (triggering costly auditing) otherwise. Because the lender must break even in expectation at the safe rate, this generates equation (3.5) linking the threshold ω̄^j to the entrepreneur’s leverage; the interior-optimum condition on the hazard rate (eq. 3.1) ensures that as leverage rises the expected return to the lender first rises, then falls – pinning down an equilibrium (non-rationed) contract in which higher leverage (lower net worth relative to capital) raises the required premium.

Equation (3.8), Q_tK^j_{t+1}=Ψ(s_t)N^j_{t+1} with Ψ(1)=1 and Ψ’(·)>0, “describes the critical link between capital expenditures by the firm and financial conditions, as measured by the wedge between the expected return to capital and the safe rate, s_t, and by entrepreneurial net worth” (Section 3.3, pp. 1353-1354). Equivalently (eq. 3.9), E{R^k_{t+1}}=s(N^j/Q_tK^j_{t+1})R_{t+1} with s’(·)<0: the external finance premium depends inversely on the share of a firm’s investment financed by its own net worth. The chapter illustrates this with a calibrated numerical example (Figure 1): a firm able to finance up to K=4.6 units of capital from net worth alone faces the risk-free cost of funds, but the cost-of-funds curve turns upward beyond that, and a 15% increase in net worth shifts this curve so the firm’s optimal capital stock (where marginal cost meets a flat expected-return curve two points above the risk-free rate) expands.

Because entrepreneurs are risk-neutral and households are risk-averse, “the entrepreneur is willing to bear all the aggregate risk,” offering the lender a state-contingent non-default payment that guarantees an expected return equal to the riskless rate no matter how the aggregate return to capital, R^k_{t+1}, is realized (Section 3.2, pp. 1351-1352). The practical implication is that “the existence of aggregate uncertainty effectively ties the risky loan rate… to macroeconomic conditions” – a lower-than-expected aggregate return to capital raises the default threshold and hence the loan rate, so “the model implies, reasonably, that default probabilities and default premia rise when the aggregate return to capital is lower than expected” (Section 3.2, p. 1352).

Embedding the CSV contract in general equilibrium closes the loop described in Section 1: a shock that raises asset prices and profits raises entrepreneurial net worth, which (via QK=Ψ(s)N) lowers the required external finance premium and stimulates further investment and asset-price appreciation, which raises net worth again – “a kind of multiplier effect” that the simulation results (Section 5.2.1) describe explicitly: “the unanticipated decline in the funds rate stimulates the demand for capital, which in turn raises investment and the price of capital. The unanticipated increase in asset prices raises net worth, forcing down the external finance premium, which in turn further stimulates investment” (p. 1370).

Three additions: (1) Calvo-style price stickiness and money, “using modeling devices familiar from New Keynesian research, which allows us to study the effects of monetary policy in an economy with credit-market frictions”; (2) decision lags in investment, which “enables the model to generate both hump-shaped output dynamics and a lead-lag relationship between asset prices and investment, as is consistent with the data”; and (3) heterogeneity among firms, “to capture the real-world fact that borrowers have differential access to capital markets” (Section 1, p. 1346).

Simulating an unanticipated 25-basis-point (annualized) decline in the nominal interest rate, “with the financial accelerator included, the initial response of output to a given monetary impulse is about 50% greater, and the effect on investment is nearly twice as great” than in the baseline model with the external finance premium held fixed at steady state; further, “relative to trend, output and investment in the model with credit-market imperfections after four quarters are about where they are in baseline model after only two quarters” (Section 5.2.1, pp. 1370-1371). The external finance premium itself, “passive in the baseline model (by assumption),” “declines sharply in the complete model, slowly reverting to trend” – this slow reversion is identified as “the additional source of dynamics” behind the greater persistence (p. 1371).

A five-variable VAR (real GDP, the GDP deflator, a commodity price index, the federal funds rate, and two credit-spread variables) shows that after a negative funds-rate innovation, “output declines after about two quarters, and the price level declines after about six quarters… [and] each of the spread variables rises fairly quickly, leading the downturn in output” (Section 5.2.1, p. 1370). The authors note “the response of the spread in the model economy matches the VAR evidence reasonably well,” and separately that the prime-rate spread’s impulse response is about twice as large as the commercial-paper spread’s – “consistent with our model’s implication that lower-quality borrowers experience larger spread movements in response to business cycle shocks” (p. 1370, fn. 27).

In a two-sector version with investment delays and differential access to external finance, “investment by firms with relatively poor access to external credit markets rises by nearly three times as much as the investment of firms with better access to credit” following an expansionary monetary shock – an “excess sensitivity” result the authors describe as “consistent with evidence reported by Gertler and Gilchrist (1994), Kashyap, Lamont and Stein (1994), Oliner and Rudebusch (1994), Morgan (1998), and others” (Section 5.2.3, p. 1375). The authors explicitly contrast this with Fisher (1996), who “obtains an ambiguous result,” attributing the difference to their own model’s endogenous net worth: “in Fisher’s model… borrowers’ equity positions are exogenously fixed and are unaffected by changes in policy” (p. 1375). Aggregate output effects are similar across sectors even though investment differs sharply, which the authors suggest could change if inventories or borrowing-financed inputs were added.

Four directions are named (Section 7, p. 1380): incorporating a nontrivial role for banks (by giving financial intermediaries their own net-worth-dependent financing frictions); moving from real to nominal debt contracts, “to evaluate whether the redistributions among debtors and creditors associated with unanticipated changes in the price level are of quantitative significance” and to assess deflation risk; extending to an open economy to study how currency crises transmit financial distress; and extending credit-market frictions beyond investment to consumption, inventories, and housing. These are explicit scope conditions: the published model’s credit frictions apply only to entrepreneurial investment financed with real (not nominal) debt in a closed economy with no separate banking-sector friction, and the authors flag each of these as a simplification rather than a finding.