Real-Business-Cycle Models and the Forecastable Movements in Output, Hours, and Consumption

Rather than studying total (unconditional) fluctuations, the authors focus on the forecastable component of movements in output, consumption, and hours, following Beveridge and Nelson’s (1981) definition of a series’ cyclical component as the gap between its current value and its expected value in the indefinite future (net of mean growth) – “the amount by which the series can be expected to decline” (Introduction). They argue this choice matters because it isolates a statistic about which standard single-shock RBC models make a sharp, testable prediction, and because a dating of the cycle based on these forecastable movements “coincides empirically with other familiar definitions,” matching NBER troughs closely (Section I): output is found to be expected to grow fastest exactly at NBER-dated troughs.

At the 12-quarter horizon – the horizon at which predictable output movements are largest – the standard deviation of expected output changes exceeds 3.2%, and the variance of these predictable movements “equals over half of the variance of total movements in output over this horizon” (Section I). This establishes that forecastable movements are not a minor statistical curiosity but a central part of observed output variation, which the authors use as their yardstick for judging the RBC model’s performance.

The data show that forecastable changes in output are “highly correlated” with forecastable changes in consumption, investment, and hours: at the 12-quarter horizon the correlation of expected output changes with expected consumption changes is about 0.79, with expected hours changes about 0.98, and with expected investment changes high as well, while the correlation with expected productivity changes is low (and in fact slightly negative at some horizons), “much lower than the overall correlation between these two series” (Section I, Tables 3-4). Regression-based elasticities confirm the pattern: expected hours growth responds “nearly one for one” to expected output growth, expected investment growth is highly elastic, but expected consumption growth has an elasticity below 0.6 relative to expected output growth at long horizons (and lower still at short horizons) – a finding the authors note is itself inconsistent with the simple permanent-income hypothesis, which would predict an elasticity of zero.

In the standard growth model, all predictable movements arise from the gap between the current capital stock and its steady-state level: when capital is below its new steady state following a positive technology shock, the model implies the real interest rate is temporarily high, which induces households to postpone both consumption and leisure – so consumption is expected to rise over time while hours are expected to fall, meaning the model’s regression coefficient of expected hours on expected output is predicted to be negative, the opposite sign from the positive relationship found in the data (Section III, comparing Tables 4 and 6). The model also predicts the regression coefficient of expected consumption on expected output should exceed 2, implying predictable consumption movements should be more variable than predictable output movements, whereas the data show a coefficient “significantly smaller than 1.”

The model’s standard-calibration prediction for the variance of 12-month-ahead forecastable output movements is “about 1 percent of the actual variance of forecastable movements in output,” i.e., the data show forecastable output variance roughly one hundred times larger than the model implies (Abstract; Introduction), a finding the authors relate to similar critiques by Watson (1993) and by Cogley and Nason (1995), the latter showing RBC model variants cannot match the observed serial correlation of output growth.

Raising labor’s income share to 0.7 and the labor-supply elasticity to infinity (the Hansen-Wright “indivisible labor” calibration) makes hours and output rise and fall together, reversing the wrong sign on hours, and even implies (more realistically) that output growth is largest after negative rather than positive technology shocks – but this fix “still implies that expected-hours growth should be negatively correlated with expected-consumption growth,” so that expected-output growth ends up negatively associated with expected-consumption growth, the opposite sign from the data (Section IV, Table 7). Alternatively, sharply lowering the intertemporal elasticity of substitution and the labor-supply elasticity (σ=4, capital share 0.36, εHW=0.2) makes hours and consumption rise together as the data show, and even gets the consumption/output elasticity below 1 as in the data – but this calibration “worsen[s] significantly the model’s ability to match the moments… usually stressed in the RBC literature”: predicted hours volatility falls to about 3% of output volatility (versus much higher values in the data), predicted consumption volatility now exceeds output volatility, and the model implies a strong negative overall correlation between hours and output – the opposite of the robustly positive correlation long emphasized in RBC calibration exercises.

The authors state the core problem plainly: because all predictable movements in the model derive from the capital stock’s gap relative to its steady state, and a capital shortfall simultaneously implies high rates of return (pushing consumption to rise over time) and – under meaningful intertemporal substitution – a decline in current leisure (hours to fall over time), “consumption and hours are expected to move in opposite directions” whenever intertemporal substitution is strong enough to matter, so “the regression coefficient of consumption on output and the regression coefficient of hours on output should have opposite signs,” whereas the data show both coefficients are positive (Section III). Every parameter adjustment the authors try either preserves this opposite-sign problem or trades it for a different, equally serious failure elsewhere in the model’s predictions.

The authors report (summarizing their companion paper, Rotemberg and Woodford 1994) that introducing additional, purely transitory disturbances does not solve the comovement problem “regardless of the nature or magnitude of the disturbances contemplated, as long as these additional disturbances are sufficiently transitory”; any fix would require the added disturbances to exhibit significant persistence, which would then itself constitute an extra propagation mechanism beyond the basic growth model. They also note that empirical studies of the diffusion of individual productivity-enhancing inventions (citing Mansfield 1968) suggest genuine technological improvements diffuse slowly and should display positive serial correlation, but show elsewhere that forecastable productivity growth of this kind “still leads to forecastable movements in hours that are of negligible amplitude relative to those reported here.”

The authors suggest the standard growth model may need to be augmented with additional sources of dynamics – inventory dynamics, slow adjustment of the work force as in labor-hoarding models, or slow adjustment of nominal wages and/or prices as in overlapping-nominal-contract or price-adjustment-cost models – and single out this last class, nominal-rigidity models, as “at least from an intuitive point of view” capable of explaining their principal findings, since a contraction in aggregate demand under sticky prices or wages would be expected to reduce output, consumption, and hours together, exactly the positive comovement pattern found in the data (Section V, Conclusions). They are explicit, however, that “the issue of whether a model of this type can explain our quantitative findings remains a topic for future research” – a conjecture, not a demonstrated result.