Output does not grow in a straight line. It climbs over the decades, but around that path it booms and slumps in an irregular rhythm — the business cycle. This page splits output into a growth trend and the fluctuations around it, then works through the theory that treats those fluctuations as the economy’s efficient response to real shocks. It is the topic that most often brings intermediate students to an economics tutor in Warwick.
1 · What a business cycle is
A business cycle is a recurrent fluctuation in aggregate output around its long-run trend. Two words carry the weight.
Recurrent, not periodic. Expansions and recessions repeat, but not on a fixed clock — a cycle is not a sine wave with a set wavelength. Some run for years, some are short and sharp, and no calendar predicts the next turn.
Around a trend. Growth theory studies the trend itself — why the path rises decade after decade. Business-cycle theory studies the wiggles around it, and you need the trend defined before “a boom” or “a slump” means anything.
So the first task is bookkeeping. Write log output as two parts:
yₜ = τₜ + cₜ
with yₜ 100 times the log of real output, τₜ the trend, and cₜ the cyclical component. Work in logs because a log difference is a percentage: cₜ is then the percentage deviation of output from trend — the output gap.
Fit a straight line in logs — a constant growth rate — and the residual yₜ − τₜ is the cycle. That is what the diagram shows: output wiggling around its trend line above, the residual alone below. (Whether that trend is deterministic or stochastic is a stationarity question tested elsewhere; here the split is bookkeeping, not a test.)
2 · The stylised facts
Before any theory come the stylised facts — regularities any model must reproduce. State them as directions, not magnitudes.
- Consumption is smoother than output. Households dislike volatile consumption, saving in booms and drawing down in slumps to damp the swings they feel.
- Investment is far more volatile than output. Firms bunch big, postponable projects into good times and cancel them in bad.
- Employment is procyclical. Hours and headcount rise in expansions and fall in recessions, moving with output, not against it.
These are the targets: a theory earns its keep by generating them from something deeper.
3 · Real business cycle theory
Real business cycle (RBC) theory gives one answer, and a bold one. The impulse is real: swings in productivity — the rate at which inputs become output. A wave of technological progress, a better production method, a supply disruption — each shifts total factor productivity up or down.
Propagation runs through choices made over time. When productivity is temporarily high, the real wage is high, so you work more now and rest later — intertemporal substitution of labour — which is why employment moves with output. The windfall is mostly saved and invested, spreading the shock forward and making investment swing more than consumption. The stylised facts drop out of optimising behaviour.
Then the striking claim: in the baseline RBC model, the cycle is the efficient response to real shocks. Nothing is broken in a recession — productivity is genuinely lower, so producing less is the right call. There is no output gap to close and no stabilisation role for policy. That is the model’s claim, at full strength.
It is the mirror image of the demand-side view, in which recessions are shortfalls of spending for policy to fill — the IS–LM model, taught in full on its own page; here, only the foil.
4 · The critique, and where the field landed
The critique is fair. Three objections recur:
- Negative technology shocks are hard to picture. A boom from new technology is easy; a recession as society forgetting how to produce is not.
- The labour-supply elasticity is too big. To swing hours as much as the data show, the model needs a Frisch elasticity larger than most microeconometric estimates of individual labour supply.
- Money looks non-neutral. Monetary policy moves real output in the data; a model built on real shocks alone has no room for that.
So the field landed between the camps. Modern New Keynesian models keep the RBC method — optimising agents, an economy solved forward — and add sticky prices, so demand and policy matter again. Today’s mainstream is that synthesis, not either parent alone.
Worked example — a temporary technology shock
Take the simplest production relation that shows the mechanism. Hold capital fixed and let labour vary, so Y = A × L, with A total factor productivity and L hours. In logs, y = a + l.
Step 1 — the base. Normalise to one: A = 1, L = 1, so Y = 1.
Step 2 — the wage. With Y = A × L, the marginal product of labour is A, so the real wage is w = A = 1, and households supply L = 1 at it.
Step 3 — confirm output. Y = 1 × 1 = 1 — the economy at trend.
Step 4 — the shock. Productivity rises 2 percent: A → 1.02. Because the wage equals A, the real wage rises 2 percent too.
Step 5 — resolve. With Frisch elasticity η = 0.5, hours rise by 0.5 × 2% = 1 percent: L → 1.01. Output is Y = 1.02 × 1.01 = 1.0302 — a rise of about 3 percent (2 from productivity, 1 from hours).
Step 6 — interpret. A 2 percent shock produced a 3 percent boom: output moves more than productivity because hours move with it — the amplification. And the shock persists — with AR(1) persistence 0.7, next period productivity is still 1.4 percent above normal — so the boom fades gradually. That is why the cycle drifts in runs, a boom followed by more boom. In the baseline model the whole path is efficient: you worked more because it was genuinely worth more.
Given log output and a trend, could you isolate the cycle — and defend the real-business-cycle claim that a recession is an efficient response to a real shock, then say where its critics land? Splitting output into trend and cycle and building the RBC mechanism from the production function up, rather than naming the theory, is exactly what business-cycle questions reward. A one-on-one economics tutor works the decomposition and the amplification with you until the model and its critique are arguments you make, not lines you memorise. Book a trial session.
Practice
Q1. Log output follows the trend τₜ = 100 + 0.5t. In period t = 16 you measure 109.5. (a) The trend level? (b) The cyclical component? (c) Above or below trend?
Q2. A technology shock raises productivity 1.5 percent, with Y = A × L and Frisch elasticity η = 0.4. (a) By how much do hours rise? (b) By how much does output rise?
Q3. The cycle follows cₜ = 0.7 cₜ₋₁ + εₜ. This period c = +2.0 and next period’s shock is ε = −0.5. (a) Next period’s cycle? (b) Still above trend?
Answers. Q1: (a) τ = 100 + 0.5 × 16 = 108. (b) c = 109.5 − 108 = +1.5. (c) Above, by 1.5 percent. Q2: (a) 0.4 × 1.5% = 0.6%. (b) 1.5% + 0.6% = 2.1%. Q3: (a) c′ = 0.7 × 2.0 − 0.5 = +0.9. (b) Yes — still positive, so still above trend; the boom persists.
Key takeaways
- Recurrent, not periodic. Fluctuations around trend repeat without a fixed wavelength — no calendar times the next turn.
- Decompose in logs. Log output = trend + cycle, so the cyclical component is the percentage deviation from trend.
- RBC turns the stylised facts into optimising behaviour. Technology shocks are the impulse; intertemporal labour substitution and saving the propagation; the cycle is efficient in the baseline.
- The synthesis won. New Keynesian models keep RBC’s method and add sticky prices, restoring a role for demand and policy.
Why Warwick students choose our economics tutoring
- Models built, not memorised: sessions derive the trend–cycle decomposition and the RBC impulse from the production function up, so you reconstruct them under exam pressure rather than quote them.
- Both sides argued fairly: the efficiency claim and its critique, RBC against the New Keynesian synthesis — the debates examiners reward even-handed answers on.
- Matched to your module: a tutor works one-on-one from your own notation and past papers, whether your course follows Williamson, Carlin and Soskice, or Blanchard.
FAQ
Q: What is the difference between a business cycle and economic growth?
A: Growth is the long-run rise in the trend; the cycle is the fluctuations around it — one is the path, the other the deviations.
Q: Why do economists work with log output?
A: In logs, the gap between two values is a percentage, so the cyclical component is the percentage deviation from trend — the output gap.
Q: What does “real” mean in real business cycle theory?
A: The shocks are real, not monetary — productivity and technology, not the money supply. The baseline model makes cycles with no nominal forces at all.
Q: Does RBC theory really say recessions are efficient?
A: In its baseline form, yes: if productivity is genuinely lower, producing less is optimal, so there is no gap for policy to close. That claim is what the critique targets.
Q: Is real business cycle theory still used?
A: Its method is everywhere — New Keynesian models are the RBC framework plus sticky prices, so RBC is the entry point to almost all current macro modelling.
Book an economics tutor in Warwick or Coventry
Business cycles reward students who can do both halves: split output into trend and cycle, and argue the RBC model and its critique on their merits. One-on-one sessions build that fluency on your own past papers. Tell us your course and exam date, and we will match you with a tutor this week.
