The Seasonal Cycle and the Business Cycle

The paper’s starting point is that “almost all recent research on macroeconomic fluctuations has worked with seasonally adjusted or annual data,” typified by Sims’s (1974) treatment of seasonal components as “errors in variables” to be purged as “seasonal noise”; Barsky and Miron instead treat seasonal fluctuations “as worthy of study in their own right” (Introduction), reviving an older NBER tradition exemplified by Kuznets (1933) in which both seasonal and business-cycle frequencies were objects of study. Rather than assume seasonal and business-cycle fluctuations follow different models, they ask how similar the two actually are.

They model each detrended quarterly series as the sum of deterministic seasonal dummy coefficients and a stationary moving-average stochastic component (Section II, eq. 1-2), estimating the dummy coefficients by OLS with Hansen-Hodrick/Newey-West standard errors, and detrend using both a unit-root ARIMA specification and the Hodrick-Prescott (1980) filter so that results are not an artifact of the detrending choice. They emphasize deterministic (not just stochastic) seasonality because, empirically, deterministic dummies “go a long way toward accounting for the variation in the data,” and because recurring causes such as “holidays, school calendars, the weather” produce seasonal peaks and troughs “in the same season year after year” (Section II) – a pattern a purely stochastic seasonal model cannot capture, since it implies the unconditional first- and fourth-quarter means of a series are equal.

For real GNP, deterministic seasonal fluctuations account for more than 85% of the variance of the log growth rate and more than 55% of (Hodrick-Prescott) percentage deviations from trend, with the standard deviation of the seasonal component in GNP growth estimated at 5.06% against a 1.91% standard error of the regression (Table 1); output is, on average, 8.08% lower in the first-quarter trough than in the preceding fourth-quarter peak (Section III.A). Seasonality of this magnitude is present in nearly every GNP component and in employment and the money stock, but seasonal movements in real and nominal price variables are “noticeably smaller”: the standard deviation of the seasonal component of price growth is only 0.21% (versus 5.06% for output), and seasonal dummies explain just 3.1% of price variation; there is no detectable deterministic seasonality in nominal interest rates.

Output growth is strongly positive in the second and fourth quarters, strongly negative in the first quarter, and mildly negative in the third quarter (Table 2a); in deviation-from-trend terms output is well below trend in the first quarter and well above trend in the fourth (Table 2b), and this pattern recurs “across the board” in nearly every component of economic activity (Section III.B). The authors attribute the pattern primarily to Christmas (driving the fourth-quarter surge in durables and non-durables consumption) and to weather (driving second- and third-quarter strength in structures investment), with the fourth-quarter-to-first-quarter decline reflecting “both the end of the Christmas season and the comparatively poor weather in the first quarter.”

Yes: the authors identify “the most basic feature of the business cycle,” per Lucas’s (1977) “now famous article” – that output movements across broadly defined sectors move together – and show this comovement also holds at seasonal frequencies, with the seasonal cycle “more pronounced than the business cycle for most quantity variables” (Section IV.A). They note this is a priori surprising: it is not obvious why weather alone should be strong enough to drive nearly every sector of a modern, largely non-agricultural economy, and standard neoclassical models with concave production functions and no seasonality in technology or preferences would predict output produced “nearly evenly throughout the year.”

The authors find that production tracks sales closely at seasonal frequencies with “minimal at best” production-smoothing, corroborating Miron and Zeldes’s (1988) finding that seasonal production in 2-digit manufacturing matches shipments almost exactly (Section IV.B), and they argue this evidence against production smoothing is “perhaps even more striking” than the analogous business-cycle evidence, because seasonal demand fluctuations are anticipated and transitory – precisely the fluctuations inventory models predict firms should smooth most easily. They offer two competing interpretations: a static one in which a Christmas-driven demand (taste) shift identifies a highly elastic aggregate supply curve, given that price does not rise much even as quantity surges; and a “calendar-year” planning story in which flat marginal cost (due to idle labor/excess capacity) makes the timing of physical production nearly indeterminate.

The authors find labor productivity “if anything even more procyclical” at seasonal than at business-cycle frequencies, with the estimated gain from hours growth to output growth running from about one to one-and-a-half (Section IV.C), and they argue the seasonal evidence favors a labor-hoarding explanation over a pure technology-shock explanation of the Kydland-Prescott/Prescott (1986) real-business-cycle type, since most jobs are year-round (the fourth-quarter productivity surge is attributable to Christmas-driven durable goods sales “not accompanied by much increase in hours of work”) even as they acknowledge seasonal shifts in technological opportunities (e.g., weather effects on the first-to-second-quarter recovery) likely play some role too.

Nominal money (M1) and real output are highly correlated at seasonal frequencies – a regression of the seasonal pattern in output growth on the seasonal pattern in money growth yields a coefficient of 2.84 (standard error .38), and the coherence of the two series’ stochastic seasonal components runs around 0.8 at both seasonal and business-cycle frequencies (Section IV.D) – comparable in strength to the classic Friedman-Schwartz (1963) business-cycle correlation, though the amplitude of the seasonal in money is about a quarter that of output’s, versus about half at business-cycle frequencies. Because seasonal money and output movements are largely anticipated, the authors argue the correlation cannot reflect the Lucas (1972, 1973, 1977) misperceptions mechanism, under which only unanticipated money should move output; it more plausibly reflects an endogenous, accommodative response of the money stock (via King and Plosser’s 1984 and Tobin’s 1970 reverse-causation channel) to Christmas-driven increases in real spending and money demand. Applying “the principle of parsimony” that Friedman and Schwartz (1963b) themselves invoked to argue that one mechanism should explain both major and minor cycles, the authors suggest – while noting they are “of two minds on this issue,” and citing Minsky’s (1963) rebuttal that major and minor cycles may simply have different causes – that the same endogenous-money mechanism evident at seasonal frequencies plausibly also explains much of the money-output correlation at business-cycle frequencies.

Prices are “sticky” at seasonal as well as business-cycle frequencies: the seasonal standard deviation in prices (0.17) is roughly 1/30th that in output (5.06), and even non-seasonal price variation is smaller than output’s, though less dramatically (Section IV.E). They show a simple durable-goods arbitrage argument (a la Roll 1972) does not by itself rule out seasonal price movements once a nominal-return asset exists (Fisher 1930); instead they attribute the near-constancy of seasonal prices and nominal interest rates mainly to an accommodative money supply that lets the quantity of money adjust to clear the money market without price or interest-rate movements, with secondary roles for countercyclical markup behavior (Stiglitz 1984; Bils 1987) and Rotemberg and Summers’s (1988) model in which retailers avoid “peak-load pricing” near Christmas because it would alienate customers.

Because Christmas timing is exogenous and known with certainty, while ordinary business-cycle impulses are not directly observed, the authors argue the seasonal cycle offers “an identifying restriction of a sort unavailable for the ordinary business cycle”: one can be confident the fourth-quarter demand surge is a real, anticipated taste shift rather than a monetary shock, since “one would hardly wish to maintain that a capricious Paul Volcker conducts monetary experiments at the seasonal frequencies” (Section IV.D). This lets them infer that the accompanying money growth is a response to, not a cause of, the output surge – an inference about causal direction that is normally much harder to establish using unanticipated business-cycle shocks alone.

The authors’ conclusion is explicit that the similarity “should be challenging to researchers aiming at a deeper understanding of macroeconomic fluctuations,” and, paraphrasing Lucas (1977), that it “suggests the possibility of a unified explanation” of both seasonal and business cycles (Section V). They advance, as “a strong potential inference” rather than a proven result, the idea that the stylized facts of the conventional business cycle – failure of production smoothing, procyclical productivity, money-output comovement, and sticky prices relative to quantities – may reflect propagation mechanisms that are not fundamentally different for anticipated versus unanticipated disturbances, even though the two cycles’ underlying impulses (anticipated Christmas/weather versus unanticipated shocks) differ in nature.