Factor-Hoarding and the Propagation of Business-Cycle Shocks

The authors’ starting point is that “standard Real Business Cycle models do not embody quantitatively important propagation mechanisms,” so they must rely on implausibly large, volatile exogenous technology shocks to match observed output fluctuations. Citing Cochrane (1994) and others on the difficulty of finding quantitatively large aggregate shocks to the postwar U.S. economy, the authors motivate their search for a propagation mechanism that would let smaller technology shocks still generate realistic output volatility, rather than assuming shocks large enough to do the job unaided.

Factor hoarding is modeled as firms choosing a capital utilization rate U_t below full capacity in equilibrium, so that “they can immediately increase the effective stock of capital in response to shocks that raise the marginal product of capital” rather than waiting a period (or longer, with time-to-build) to add new capital. Output depends on effective capital services (U_t times the physical stock K_t) and effective hours (effort W_t times hours N_t); the depreciation rate rises with utilization, so utilization trades off current output against future capital. The model nests three cases: if utilization is fixed, it collapses to the “labor hoarding model” of Burnside, Eichenbaum and Rebelo (1993); if neither effort nor utilization is chosen contingently on current shocks, it is “observationally equivalent to the standard RBC indivisible labor model” used as the paper’s “benchmark model” (following Christiano and Eichenbaum 1992); allowing both margins gives the paper’s own “factor hoarding model.”

The authors exploit the model’s own equilibrium first-order conditions to back out time series for utilization and effort from observable aggregates (output, capital, hours, consumption) and a subset of estimated structural parameters, rather than using existing capacity-utilization data, which they note is “sector specific and subject to substantial measurement error.” The utilization series derived this way “tracks the analog time series published by the Federal Reserve… quite closely,” which the authors offer as an informal check on the procedure, while cautioning that the Fed’s own series “is subject to substantial measurement error” and covers only manufacturing.

Because the conventionally computed Solow residual uses measured hours and the official (fixed-depreciation) capital stock, the paper shows it decomposes into the true technology shock X_t and a separate “factor hoarding component” driven by utilization and effort, so “shocks which cause capital utilization or labor effort to vary over time drive a wedge between actual technology shocks and the Solow residual.” This wedge is shown to be persistent in the model’s impulse responses: after a technology shock, the Solow residual overshoots and then approaches its new steady-state growth path only slowly as utilization reverts, so “naive Solow residual accounting… clearly overstates the volatility of technology shocks” – and, after a pure demand (government-spending) shock with no technology shock at all, the Solow residual still rises before decaying, which the authors note could lead an analyst to wrongly infer a sequence of technology shocks.

The model is estimated by a Generalized Method of Moments (GMM) procedure following Christiano and Eichenbaum (1992) on quarterly U.S. data covering 1955:3-1984:1, using Hansen’s (1984) household-hours series along with national accounts data on consumption, government purchases, investment and the capital stock. Because the estimator is exactly identified, several structural parameters have closed-form sample-moment interpretations (e.g., the point estimate of the expected depreciation rate equals the sample average of the official depreciation rate implied by investment and capital data); the authors separately test a battery of non-targeted moments (relative volatilities, autocorrelations, cross-correlations) using Wald statistics, rather than treating the GMM-targeted moments themselves as a test of the model.

The point estimates imply that capital utilization is highly volatile relative to the physical capital stock – the standard deviation of the growth rate of effective capital services is “roughly 4.5 times higher than the standard deviation of the growth rate of the stock of physical capital” – and that correcting for factor hoarding “leads to a 58% reduction in the variance of the innovation to technology shocks” relative to the benchmark model, “most of this reduction… attributable to cyclical movements in the capital utilization rate.” Isolating labor hoarding alone (fixing utilization at its steady-state value) leads to only a 21% reduction in that variance, so the authors conclude capital utilization “plays a larger role than labor hoarding in reducing the estimated volatility of technology shocks.”

The paper’s own propagation statistic – the ratio of output’s standard deviation with all internal margins responding to a standard deviation with those margins held at their non-stochastic steady-state values, denoted σ_ỹ/σ_ŷ – is 1.47 in the factor hoarding model (a 47% amplification of the shock’s direct effect) versus only about 1.05 in the benchmark model and 1.01 in the labor-hoarding-only model. Table 3’s formal test cannot reject, even at the 25% significance level, that either the benchmark or the factor-hoarding model’s implied output volatility matches the U.S. data; the paper’s point is that the two models reach a similar fit to output volatility by very different routes – “what distinguishes the models is not whether but how they account for the volatility of output.”

In response to a 1% technology shock, output in the factor-hoarding model rises by 1.078% on impact and then continues climbing to 1.51% one period later before slowly decaying, whereas in the benchmark model output rises by 1.043% on impact and then declines monotonically toward its new steady-state path. The authors trace this hump to the dynamics of effort and utilization: effort jumps by 0.29% on impact and immediately reverts (reflecting the assumption that hours are costlessly adjustable only within the shift already chosen), while utilization rises by 0.7% on impact and keeps climbing to 0.96% the following period before slowly declining – so effective labor and capital inputs together display a hump-shaped path that output, as their function, inherits. Hours worked show a parallel but more muted pattern (0.59% on impact in the benchmark model versus a delayed 0.8% rise the period after the shock in the factor-hoarding model, since hours cannot respond within the impact period by construction).

No: on the standard business-cycle moments emphasized in the RBC literature – the volatility of consumption, investment and hours relative to output, and of hours relative to average labor productivity – “both models do very well,” and the paper cannot reject, even at the 15% significance level, that either model’s implied moments equal their data counterparts. The authors also show the factor-hoarding model does not produce an implausibly smooth consumption path despite its stronger propagation: consumption reaches 75% of the way to its new post-shock steady-state growth path within 4 quarters in the factor-hoarding model, versus 15 quarters in the benchmark model – i.e., the extra output generated by higher utilization and effort in the shock’s aftermath is partly used to let consumption catch up faster, not just to prolong the adjustment.

The authors report that “the actual growth rate of U.S. output displays positive persistence” – the first two autocorrelation coefficients of output growth are positive and significant – which the benchmark model cannot replicate (it implies all autocorrelations are negative), whereas for the factor-hoarding model “the joint hypothesis that the first two autocorrelation coefficients… are the same as those in the data cannot be rejected at conventional significance levels.” The same hump-shaped propagation generates a matching result for the spectrum of output growth: the benchmark model’s spectrum of output growth is “almost identical” to the (white-noise) spectrum of the technology shock itself, with no peak at business-cycle frequencies, while the factor-hoarding model “induces a significant spectral peak in output growth at business cycle frequencies” even though the underlying technology shock has no such peak. The authors note both models correctly reproduce the (different) autocorrelation pattern of the Solow residual, so the factor-hoarding model’s gain on output growth is not purchased by sacrificing fit to the Solow residual’s own time-series properties.

Using the same second-order VAR specification as Rotemberg and Woodford (1994), the factor-hoarding model “does considerably better” than the benchmark at generating variation in the forecastable component of output growth at various horizons, and it “fully accounts for” the correlations between that forecastable component and both current output growth and the growth rate of average productivity – correlations the benchmark model gets the wrong sign on. The authors are explicit about a remaining shortfall, however: “neither model fully accounts for the magnitude of the correlation [between output and its own forecastable component] found at short horizons,” though the factor-hoarding model comes closer than the benchmark; the paper reads this residual gap as evidence that “additional sources of shocks to agents’ environments and propagation mechanisms” beyond factor hoarding are still needed.

The authors describe their single, economy-wide utilization margin as “a minimal perturbation of the standard RBC model” chosen for comparability with existing work, explicitly acknowledging this “is purchased at the cost of descriptive realism” relative to the richer, multi-margin adjustment documented at the plant level by Bresnahan and Ramey (1993) (e.g., shutting an auto plant down for a week, or adding/dropping a shift). They conjecture that an aggregate utilization rate built up from such richer micro-level margins “would also respond positively to technology shocks,” so they expect their qualitative conclusions to be robust to how utilization is modeled in detail, but they state plainly that “the robustness of our quantitative results remains very much an open issue to be addressed in future research” – i.e., the paper’s magnitudes (the 58% variance reduction, the 1.47 propagation ratio) are tied to this specific, stylized utilization margin.