Business Cycle Fluctuations in US Macroeconomic Time Series

The authors adopt a bandpass-filtering approach (a finite approximation to the ideal Baxter-King-type filter) to isolate business-cycle frequencies, specifically fluctuations with periods between 6 quarters and 8 years, and use the resulting cyclical component of real GDP as the benchmark series against which every other series’ comovement, leads, and lags are measured (Introduction). They show that bandpass-filtered cyclical GDP is “more tightly centered around zero” than a simple linearly detrended series and that it highlights the major postwar recessions (1973-75, the early 1980s, 1990-91) clearly, while noting that the classical (NBER, absolute-decline) dating and the growth-cycle (deviation-from-trend) dating can diverge – some slowdowns, such as 1967 and 1986, register as “growth recessions” under the latter without being NBER-dated recessions.

Sectoral employment in manufacturing and construction is “strongly procyclical,” with contract and construction employment “more than twice as volatile” as the cyclical component of real GDP and manufacturing employment “about 50% more volatile,” while services, trade, and transportation employment are procyclical but less volatile, and government employment shows “negligible cyclical movement” (Comovement). Consumption, investment, inventories, and imports are procyclical, with durable consumption especially so; exports are less strongly procyclical, leaving the trade balance mildly countercyclical on net; and business inventories’ cyclical swings are large enough to mechanically account for “roughly one-quarter of the cyclical standard deviation of GDP.” Total employment and hours lag GDP by about a quarter, while capacity utilization is roughly coincident with the cycle.

The authors find that price levels are “often countercyclical,” tending to lead the cycle by a few quarters, while inflation rates tend to be procyclical and lag the cycle (Comovement) – a distinction between the level and the rate of change in prices that recurs throughout the chapter’s later discussion of the Phillips curve.

Short-term nominal interest rates (3-month Treasury bills, the federal funds rate) and especially the term-structure spread between long and short rates are found to be leading indicators of output, with an historically observed tendency for an inverted yield curve to precede declines in activity, and the long-short spread showing considerable predictive content for real GDP at one- and four-quarter horizons (Leading and Lagging Indicators). The commercial-paper/Treasury-bill spread, a risk-premium measure, is countercyclical and leads output by about a year; housing starts, building permits, new orders, and help-wanted/vacancy measures also show useful leading-indicator properties. By contrast, monetary aggregates “had predictive power in bivariate relations, but their relationships are unstable over time”: the contemporaneous cross-correlation of nominal M2 and real GDP was about 0.6 in 1959-1979 and fell to about -0.1 in 1980-1996, and a formal stability (QLR) test rejects the constancy of the yield-curve forecasting relationship at the 1% level, with an estimated break around 1972.

The authors distinguish (i) a level relationship between the unemployment rate and the inflation rate, (ii) a relationship between unemployment and changes in (or unanticipated) inflation, and (iii) a structural relationship describing contemporaneous price adjustment to demand shocks, and find that the level relationship “shows no stable negative relationship” over the full sample, shifting across subperiods, while the unemployment/change-in-inflation relationship shows “a clear negative relation” (The Phillips Curve). At business-cycle frequencies, the correlation between bandpass-filtered cyclical unemployment and cyclical inflation is about -0.6, with subperiod estimates ranging from -0.4 to -0.65, and this correlation is robust enough that adding four lags of unemployment to a univariate autoregression for inflation raises the in-sample R-squared by about 0.18 (one quarter ahead) up to about 0.28 (four quarters ahead).

NAIRU estimates across several specifications cluster “in the roughly 5-7% range” but carry wide 95% confidence intervals – for example, a constant-NAIRU specification using CPI inflation gives a point estimate near 6.1% with a confidence interval of roughly 4.9% to 7.7% (The Phillips Curve, Table 4), leading the authors to characterize the NAIRU as “moderately stable but…imprecisely measured” – a level-based concept that remains far less reliable than the more robust cyclical correlation between changes in inflation and unemployment.

Narrow money and nominal M2 show predictive content for output in simple bivariate relationships, but the authors stress this content “is unstable” and “weakened when controlling for interest rates and other aggregates,” with QLR stability tests rejecting constancy for many monetary specifications (Money, Credit, and the Business Cycle). On longer-run relationships, dynamic-OLS estimates of long-run money demand put the income elasticity at about 0.87 and the interest-rate semielasticity at about -0.094, and the authors note that, unlike the unstable short-run/cyclical monetary relationships, the long-run money-demand relationship itself behaves as a stable cointegrating relationship, with residuals from it mean-reverting over periods of decades.

They report that interest-rate spreads are substantially less persistent than individual interest-rate levels – the largest estimated autoregressive root is about 0.84 for the 10-year Treasury rate and about 0.76 for the 90-day bill, but only about 0.22 for the spread between them (Money, Credit, and the Business Cycle, Table 6) – consistent with spreads being a more cyclically informative, mean-reverting signal than the levels of the underlying rates themselves. More broadly, the chapter treats such long-run relationships (money demand, the term structure, and the long-run expenditure shares of consumption, investment, and government in GNP) as useful benchmarks precisely because they are more stable than many of the shorter-run comovement and predictive relationships documented earlier in the chapter.

The authors’ own summary groups their findings into: (1) business-cycle fluctuations are “an enduring feature of the U.S. economy,” with widespread, systematic comovement across many series; (2) quantities (employment, hours, consumption, investment, inventories) comove strongly and with small, fairly stable leads/lags, while prices show the more complex, level-versus-rate-of-change pattern described above; (3) the Phillips-curve relationship is most robust in its cyclical (change-based) form, with a reasonably stable negative correlation and genuine marginal predictive content for inflation, even though NAIRU-type level estimates remain imprecise; (4) monetary and credit variables have real but time-unstable bivariate predictive power, reduced once other variables are controlled for; and (5) long-run relationships (money demand, spreads, balanced-growth expenditure shares) are comparatively persistent and provide more durable benchmarks than the shorter-run cyclical relationships (Conclusion). The chapter frames all of these regularities – stable and unstable alike – as the empirical benchmarks any structural macroeconomic model of the business cycle should be checked against.