Real Credit Cycles

Mon, 01 Jan 0001 00:00:00 +0000

This paper incorporates diagnostic expectations — beliefs that overweight the representativeness of recent data, formalized as $E_t^\theta(A_{t+1}) = E_t(A_{t+1}) + \theta[E_t(A_{t+1}) - E_{t-1}(A_{t+1})]$ with θ > 0 — into a workhorse real business cycle model with heterogeneous firms and risky defaultable debt, to assess whether non-rational belief overreaction can account for boom-bust credit cycles without requiring large fundamental shocks. The diagnosticity parameter θ is structurally estimated via simulated method of moments, targeting moments including forecast-error predictability from the IBES manager guidance database, and yields θ ≈ 0.991, consistent with prior estimates from financial analysts and professional forecasters. The estimated DE model generates several untargeted results that the rational-expectations (RE) benchmark cannot: countercyclical credit spreads, predictable firm-level bond returns, and investment fragility in good times — specifically, a one-standard-deviation negative TFP shock causes a much larger investment decline when the previous period had good TFP news than in normal times. The model also shows that the 2008-09 spread increase can be generated by mere disappointment of overoptimistic beliefs, not requiring a large negative TFP shock. These findings establish diagnostic expectations as a parsimonious and empirically disciplined mechanism for producing financial reversals in business cycle models.

Summary of a published paper based on the NBER working paper full text (w28416), AI-assisted, pending human review. See the linked original for the authoritative claims and full conditions.

Layer 1: Overview

Bordalo, Gennaioli, Shleifer, and Terry modify a standard heterogeneous-firm RBC model with risky defaultable debt by a single behavioral parameter — the diagnosticity θ governing belief overreaction to TFP news — to assess whether non-rational beliefs can quantitatively account for boom-bust credit cycles. The model departs from the rational expectations (RE) benchmark only in that firms and lenders form expectations diagnostically: after good TFP news, agents become excessively optimistic about future TFP, causing too much investment and debt issuance; when TFP growth disappoints relative to those optimistic expectations (even without an outright TFP decline), agents sharply revise down their beliefs, causing credit spreads to spike and investment to collapse. The diagnosticity parameter θ ≈ 0.991 is estimated by structural SMM targeting 16 moments — including 3 moments from IBES manager guidance data directly measuring the predictability of forecast errors — and is consistent with independent estimates from analyst forecasts (θ ≈ 0.9, Bordalo et al. 2019), professional macroeconomic forecasters (θ ≈ 0.5, Bordalo et al. 2020), and bond-price-implied beliefs (θ = 1.0, D’Arienzo 2020). The paper shows that the estimated DE model, unlike the RE benchmark, delivers countercyclical spreads, predictable firm-level bond returns, investment nonlinearity (fragility in good times), and an account of the 2008-09 spread episode requiring only a modest TFP disappointment.

In depth

Q1. What are diagnostic expectations, and how does the single parameter θ govern their departure from rational expectations?

Diagnostic expectations (DE) are beliefs that overweight outcomes that are representative of recent news relative to their true base rate, formalized as $E_t^\theta(A_{t+1}) = E_t(A_{t+1}) + \theta[E_t(A_{t+1}) - E_{t-1}(A_{t+1})]$, where $\theta \geq 0$ is the diagnosticity parameter: when $\theta = 0$ beliefs are rational, and when $\theta > 0$ agents exaggerate the persistence of current news shocks. The mechanism is grounded in the psychology of selective recall: good news makes good future outcomes top-of-mind and thus overweighted. In the context of an AR(1) TFP process, DE agents effectively behave as if TFP follows an ARMA(1,1) with an additional moving-average term that boosts the perceived response to current shocks. The parameter θ has a clean measurement interpretation: θ ≈ 1 means that for every unit of incoming news, agents’ beliefs overshoot by approximately one additional unit (forecast errors are roughly equal in magnitude to the news that generated them). DE are forward-looking (unlike adaptive expectations) and hence not mechanically subject to the Lucas critique, since agents’ beliefs respond to news in a structured way.

Q2. How is θ identified and estimated, and what disciplines the model’s departure from rationality?

The diagnosticity parameter θ is identified from three moments that directly exploit the predictability of future forecast errors from current firm-level investment and debt issuance growth — moments that are positive under DE and exactly zero under RE — drawn from the IBES manager guidance database covering 1999-2018. The key identification equation is: $\text{cov}(\Delta \text{Forecast Error}{t+1}, \Delta x_t) = a\pi a_x \rho \theta (1+\theta)$ where $x$ is investment or debt, positive if and only if θ > 0. In the data, a one-standard-deviation increase in the firm’s investment rate predicts approximately 10 percentage points stronger disappointment in next-year earnings, and a one-standard-deviation increase in debt issuance predicts about 5 percentage points stronger disappointment — robust to within-firm estimation that controls for heterogeneity in optimism across firms. The estimated θ ≈ 0.991 (s.e. 0.074) is precisely estimated and falls well within the range [0.5, 1.5] implied by independent estimates from other datasets. The RE model (constrained to θ = 0) cannot generate any comovement between future forecast error growth and current firm fundamentals, offering a falsifiable restriction that the data reject.

Q3. What is the investment fragility finding, and why can the RE model not replicate it?

The DE model generates a strong nonlinearity in investment: the same one-standard-deviation negative TFP shock causes a much larger investment decline when it follows a period of good TFP news (good times) than when it follows average or bad news; the RE model produces essentially no such nonlinearity, with investment responses roughly flat across initial conditions. The mechanism is as follows: after a positive TFP shock, firms and lenders become overoptimistic, driving high investment and low credit spreads. The aggregate investment response to the subsequent negative shock is therefore large — overoptimism has boosted the capital stock and the debt level beyond what fundamentals warrant, so the negative shock both lowers true productivity and triggers a sharp correction in beliefs. Under RE, agents correctly anticipate mean reversion of TFP and do not overbuild, so the same negative shock hits a less-leveraged economy and generates a smaller correction. This fragility-in-good-times mechanism is consistent with empirical evidence from Bachmann et al. (2013), Winberry (2017), and Bloom et al. (2018) that investment is more sensitive to shocks during booms.

Q4. How does the DE model account for countercyclical spreads, and why does the RE model predict the wrong sign?

Under DE, credit spreads are countercyclical because lenders become excessively optimistic about future TFP in good times, driving down perceived default risk and hence spreads below their rational counterpart; when optimism wanes, spreads spike beyond what fundamental deterioration alone would warrant. Under RE with constant required returns (as modeled), the supply of capital tracks fundamentals; in good times with high TFP, default risk is genuinely lower, so spreads fall — a qualitatively correct prediction. But the RE model also generates a positive correlation between spreads and investment in the cross-section of firms, while the data show a strong negative correlation (Column 10 of Table 5: Corr(Investment, Spread) = -0.057 in data, -0.054 in DE model, +0.083 in RE model). The DE mechanism driving this: overoptimistic lenders simultaneously over-supply credit (reducing spreads) and firms over-invest, creating the negative comovement. The paper links this formally to the concept of “financial shocks” in Jermann and Quadrini (2012) and Gilchrist and Zakrajšek (2012): in the DE framework, waning optimism produces inward shifts in the supply of capital that appear as exogenous financial shocks in reduced-form analyses.

Q5. How does the model account for the 2008-09 spread episode, and what shock size is required?

The DE model generates a spread increase consistent in magnitude with the 2008-09 episode from a modest moderation in TFP growth — not an outright TFP decline, but merely disappointment relative to the optimistic expectations formed during the preceding boom — while the RE model requires a large negative TFP shock of implausible size. During 2005-2007, a sequence of positive TFP shocks made firms and lenders excessively optimistic; when TFP growth merely slowed in 2007-08 (below the high level agents had been projecting), their beliefs corrected sharply, spreading up and investment down. In the DE model, the deceleration of TFP growth is sufficient to produce spread increases matching the observed magnitude during 2008-09, along with quantitatively consistent declines in aggregate investment, credit, and earnings forecast revisions. The RE model cannot match this because rational agents, correctly anticipating mean reversion, would not have built up the overoptimistic base to correct from.

Q6. How do the microeconomic boom-bust predictions of the model perform out-of-sample?

The model-simulated data replicate the firm-level boom-bust cycles documented in the paper’s Section 2: current overoptimism (proxied by high investment or debt issuance) predicts next-year spread increases, lower realized bond returns, and subsequent investment declines, with magnitudes that quantitatively match the data regressions; the RE model generates none of these predicted cycles. Specifically, in model-simulated firm-level regressions: higher current investment predicts 1-year-ahead spread increases; current spread increases predict negative future bond returns (the diagnostic model implies bonds are overpriced during booms, consistent with predictable low returns); and current high investment predicts future investment declines (mean reversion amplified by DE correction). All three predictions are also confirmed in the data and at the sectoral level, providing multiple out-of-sample validation tests. The diagnosticity parameter θ = 1 estimated from forecast errors simultaneously fits these untargeted dynamics.

Key Concepts

diagnostic expectations : beliefs that overweight outcomes representative of recent news, with the single deparature parameter θ ≥ 0 governing the degree of overreaction; in the AR(1) TFP context, agents act as if TFP follows an ARMA(1,1) with over-weighted current shocks; estimated at θ ≈ 1 from firm-level forecast error data, consistent with independent estimates from multiple other datasets.

fragility in good times : the paper’s key qualitative finding that the investment response to a given negative TFP shock is much larger when the shock follows a period of positive TFP news; arises because DE agents have built up excessive optimism, inflated capital stocks, and stretched leverage during the boom, making the correction larger; absent in the RE model.

diagnosticity parameter (θ) : the single behavioral parameter governing the degree to which agents overweight representative recent outcomes; θ = 0 is rational expectations; θ ≈ 1 is the structural SMM estimate, implying that forecast errors are roughly as large as the news that generated them; identified from the covariance between future forecast-error growth and current investment/debt changes.

financial shocks as waning optimism : the paper’s interpretation of “financial shocks” — inward shifts in the supply of capital generating spread spikes — as the endogenous waning of previously excessive diagnostic optimism, rather than exogenous disturbances to lender preferences or required returns; provides microfoundations for the Jermann-Quadrini and Gilchrist-Zakrajšek empirical findings.

countercyclical credit spreads : the empirical regularity that credit spreads fall in good times and rise in bad times, a moment the DE model matches (through overoptimistic lenders compressing spreads in booms) but the RE model with constant required returns fails to match in the cross-section (predicting a positive correlation between investment and spreads).

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