Output Dynamics in Real-Business-Cycle Models

Questions & answers

Q1. What two stylized facts about U.S. output dynamics does the paper use to evaluate RBC models?

Drawing on an extensive prior empirical literature (Nelson and Plosser 1982; Watson 1986; Campbell and Mankiw 1987; Cochrane 1988; Blanchard and Quah 1989; Hamilton 1989; King et al. 1991; Cochrane 1994), the authors document that (1) GNP growth is positively autocorrelated over short horizons (1-2 quarters) with weak and possibly insignificant negative autocorrelation at longer horizons, and (2) GNP has “an important trend-reverting component” whose transitory impulse-response function is hump-shaped (Abstract; Section I). Using quarterly real per capita GNP growth, 1954:1-1988:4, they find statistically significant positive autocorrelations at lags 1 and 2, and a spectral density for output growth with “a broad peak ranging from approximately 2.33 to 7 years per cycle, with maximum power at roughly 3.2 years per cycle” – confirming that a substantial share of output growth’s variance occurs at conventional business-cycle frequencies.

Q2. How do the authors decompose output into permanent and transitory components, and what do they find?

Following Blanchard and Quah (1989), the authors use a structural VAR (with output growth and the unemployment rate, substituting per capita production for RBC-model comparability) to decompose GNP into a permanent component driven by one shock and a transitory component driven by a second, orthogonal shock (Section I.B). In the actual data, the permanent response to its shock “rises gradually and reaches a plateau after about six years,” while the transitory response shows output rising for a few quarters before returning to trend – and “a substantial portion of the variation in output growth is due to transitory fluctuations,” which is the empirical basis for calling the trend-reverting component “important.”

Q3. How does the paper test RBC models against these facts, and what is the “test of the Adelmans” analogy?

The authors’ approach “is similar to the ’test of the Adelmans’”: they simulate 1,000 artificial samples from each calibrated RBC model, compute the same autocorrelation and impulse-response statistics used on actual U.S. data for each simulated sample, and see what fraction of simulated samples produce results resembling the data (Introduction). This is formally a specification test of a given RBC model (via a generalized Q statistic comparing sample and simulated autocorrelation functions) but can also, in the authors’ words, be read as “an informal guide to model reformulation.”

Q4. How do baseline RBC models (with no adjustment costs or lags) perform, and why do they fail?

Testing baseline models from King, Plosser, and Rebelo (1988b), Hansen (1989), Greenwood, Hercowitz, and Huffman (1988), Christiano and Eichenbaum (1992), Benhabib, Rogerson, and Wright (1991), and Braun (1994), the authors find “all models are rejected at roughly the 1-percent level or better” on the autocorrelation dimension (Table 1), and, for the models that generate an impulse-response decomposition, the transitory response is rejected even more decisively (e.g., a Q-statistic of 449.3 with a p-value of 0.000 for the Christiano-Eichenbaum model’s transitory impulse response). The underlying diagnosis is that because the models’ output-growth dynamics are “close to being white noise” – the model-generated autocorrelations lie near zero at every lag, missing the data’s positive dependence at lags 1 and 2 – the model’s permanent component inherits the dynamics of the (random-walk) technology shock almost unchanged, and the transitory component inherits the dynamics of the (AR(1)) government-spending shock almost unchanged: “propagation mechanisms damp but do not alter [the shocks’] dynamics,” so that “output dynamics are essentially the same as impulse dynamics,” i.e., the model has a weak internal propagation mechanism.

Q5. Can augmenting the shock processes themselves (“external sources of dynamics”) rescue the baseline model’s fit?

The authors test three external fixes – temporal aggregation (output following a weekly random walk, aggregated to quarters), serially correlated (ARIMA(1,1,0)) technology-shock increments, and higher-order autoregressive (AR(2)) government-spending shocks – and find mixed, partial success (Table 2): temporal aggregation improves the match on the permanent impulse response but still fails badly on the transitory impulse response (Q-statistic 803.7, p=0.000), while AR(2) government-spending shocks “perform best overall” among the alternatives tested, passing the autocorrelation test (p=0.705) and performing much better, though still imperfectly, on both impulse responses. This section’s implicit conclusion is that fixing the problem by assuming more serially correlated shocks works better than relying on the model’s own internal propagation – precisely the opposite of what RBC theory’s advocates originally hoped to demonstrate.

Q6. Do gestation lags or capital adjustment costs improve the model’s ability to generate output dynamics?

Testing a time-to-build model (with a three-quarter gestation/installation lag, following Rouwenhorst 1991) and a Q-theoretic model with quadratic capital-adjustment costs, the authors find both are still rejected on autocorrelation (Table 3; p=0.008 for both) and the adjustment-cost model is rejected decisively on its transitory impulse response (p=0.000), concluding that “gestation lags and quadratic adjustment costs do not generate serial correlation or business-cycle periodicity in output growth” (Section III) because the resulting change in the flow of new capital is small relative to the existing capital stock, leaving the propagation mechanism too weak to matter.

Q7. What do labor-adjustment-cost and labor-hoarding models get right, and what do they still get wrong?

Testing a labor-hoarding model (Burnside, Eichenbaum, and Rebelo-type, in which firms choose labor force size before observing the current state) and an adjustment-cost model penalizing rapid changes in both capital and employment, the authors find these models “endogenously generate positive autocorrelation” in output growth matching the data’s qualitative pattern – the labor-hoarding model is not rejected on autocorrelation at conventional levels (p=0.049, borderline) and the adjustment-cost model passes comfortably (p=0.326) (Section IV, Table 4). However, “neither model generates an important trend-reverting component”: both are rejected at the 1-3% level on matching the magnitude of the transitory impulse response, meaning that to generate a transitory component of the right qualitative shape at all, these models require implausibly large transitory shocks – a partial success (getting the autocorrelation sign and rough shape right) alongside a continued quantitative failure (getting the size of the trend-reverting component right).

Q8. What is the paper’s overall conclusion about real-business-cycle models’ propagation mechanisms?

The authors conclude that “existing RBC models must rely heavily on exogenous factors to replicate both stylized facts,” since “many RBC models have weak internal propagation mechanisms and must rely on impulse dynamics,” and that even the partially successful labor-adjustment-cost models, while getting the autocorrelation pattern right, “need implausibly large transitory shocks to match the large transitory impulse response found in the data” (Abstract; Conclusion). They frame this as a surprising result relative to the expectations of 1970s-early-1980s business-cycle theorists, who had hoped that mechanisms like capital accumulation and adjustment costs could turn serially uncorrelated shocks into serially correlated, business-cycle-like output movements on their own; the paper’s clear message is that current RBC models’ internal propagation mechanisms do not accomplish this, and that “RBC theorists should devote further attention to modeling internal sources of propagation.”