A central bank that promises low inflation, then quietly delivers a little more, can buy a brief burst of output. But everyone anticipates the temptation, so the promise is not believed and the economy just ends up with higher inflation and no extra output. This page works through that trap — rules versus discretion — and the fix that reshaped modern monetary policy: an independent central bank tied to a public inflation target, the topic that most often brings intermediate students to an economics tutor in Toronto.
1 · Rules versus discretion, and time inconsistency
Under discretion, policymakers re-optimise each period, doing what looks best right now. Under a rule, they commit in advance and stick to it. The surprise is that the rule can beat discretion even when the policymaker is competent and well-meaning.
The reason is time inconsistency (Kydland and Prescott). A policy optimal when announced can stop being optimal to keep once expectations are locked in. Announce low inflation, let firms set wages on that basis, and you are tempted to inflate a little to push output up. People anticipate this and build it into their expectations — so you never get the surprise, only the higher inflation. The problem is not bad intentions. It is the inability to commit.
2 · Inflation targeting, and why it anchors expectations
Inflation targeting is the institutional answer, with three moving parts: a public numerical target (commonly 2%, often a band such as 1–3% around it); instrument independence, so the bank sets its tools — above all the short-term interest rate — free of political direction; and accountability, publishing forecasts and explaining any miss. The target is the commitment device; independence is what makes it credible.
This anchors expectations: if the public believes the target, expected inflation settles there, and the temptation term that drives the bias (you derive it below) collapses. Independence earns the credibility, by removing the incentive to spring surprises for a boom or to erode the real value of debt.
Goal versus instrument independence. Instrument independence means the bank chooses its tools to hit a target that elected officials set; goal independence means it sets the target itself. Most regimes grant the first but keep the goal with government, leaving the objective and its accountability with elected representatives.
3 · The Bank of Canada, and the evidence on independence
The framework is not a blackboard abstraction. The Bank of Canada adopted formal inflation targets in 1991, immediately after New Zealand’s 1990 pioneer move — a joint target set with the federal government, pursued with operational independence and refined every few years since. It became a template others studied.
What does the cross-country record show? Broadly, economies whose central banks are more insulated from political control have tended to run lower, more stable average inflation with no systematic output cost — the pattern that made independence the consensus design. Read it with care: independence is hard to measure, and a society that dislikes inflation may both grant it and keep inflation low, so the causation is debated — the direction is well established, the size is not.
Worked example — the temptation to inflate
A central bank faces the expectations-augmented Phillips constraint y − yₙ = α(π − πᵉ) with α = 1, where πᵉ is expected inflation. Its loss is L = ½(y − y*)² + (β⁄2)(π − π*)², with target π* = 2 and weight β = 1. The key assumption: an output goal κ = 2 points above natural, so y* = yₙ + 2.
Step 1 — The setup. In gaps, y − y* = α(π − πᵉ) − κ. The public sets πᵉ first; the bank then chooses π.
Step 2 — The commitment benchmark. The bank commits to π = π* = 2 and is believed, so πᵉ = 2. No surprise, output sits at natural, and L = ½(−2)² + 0 = 2.
Step 3 — The temptation. Let the bank re-optimise with expectations fixed at πᵉ = 2. Minimising L gives the first-order condition α[α(π − πᵉ) − κ] + β(π − π*) = 0, so π = 3 — above the promise. Output rises 1 point and the loss falls to ½(−1)² + ½(1)² = 1. Cheating looks great.
Step 4 — The public is not fooled. Households know the incentive, so they will not sit at πᵉ = 2 while the bank plans 3. In equilibrium expectations are correct: πᵉ = π.
Step 5 — Discretion, and its cost. Impose πᵉ = π. The surprise term vanishes, leaving π − π* = ακ⁄β, so π = 2 + (1)(2)⁄1 = 4 — the inflation bias is ακ⁄β = 2 points. Output is back at natural, where commitment left it, but inflation is 4, so L = ½(−2)² + ½(2)² = 4, double the commitment loss.
Step 6 — Interpret. Line the three losses up: cheating 1, commitment 2, discretion 4. The bank would love to cheat, but because it cannot commit not to, the public pre-empts it and everyone lands at the worst. The bias buys no lasting output — it is pure cost. The cure is a credible commitment: an independent bank bound to a public target.
Can you derive the inflation bias — ακ⁄β — and explain why it buys no lasting output? Lining up the three losses (cheating 1, commitment 2, discretion 4) and showing why no-commitment lands on the worst is exactly what monetary-policy questions reward. A one-on-one economics tutor works the Barro–Gordon derivation with you until credibility is something you derive, not recite. Book a trial session.
Practice
Q1. A more inflation-averse governor raises the weight to β = 2 (α = 1, κ = 2, π* = 2). Find the bias and discretionary inflation.
Q2. Instead the bank is content with the natural rate, so κ = 0 (α = 1, β = 1). Find the bias and inflation, and compare discretion with commitment.
Q3. A supply shock raises the Phillips slope to α = 2 (κ = 2, β = 1). Find the bias and discretionary inflation.
Answers. Q1: bias = ακ⁄β = 1×2⁄2 = 1 point, so π = 3% — the “conservative” central banker inflates less. Q2: bias = 1×0⁄1 = 0, so π = 2%, the target itself; discretion and commitment coincide, at zero loss. Q3: bias = 2×2⁄1 = 4 points, so π = 6%.
Key takeaways
- Time inconsistency drives the bias. A policy optimal when announced is not optimal to keep once expectations are set; that gap, not incompetence, produces excess inflation that buys no lasting output — output returns to natural, so it is pure deadweight.
- The bias is ακ⁄β. It grows with the output ambition κ and the Phillips slope α, shrinks with inflation aversion β, and vanishes at κ = 0 — the temptation, not discretion, is the source.
- Inflation targeting is a commitment device. A public target plus instrument independence anchors πᵉ, collapsing the bias toward zero.
- You need both halves. Independence removes the incentive to surprise; the target pins expectations. One without the other does not anchor.
Why Toronto students choose our economics tutoring
- Models derived, not memorised: sessions build the Barro–Gordon result from the loss function and the Phillips constraint, so you can reproduce the bias under exam pressure instead of quoting it.
- The distinctions examiners test, drilled: rules versus discretion, goal versus instrument independence, credibility versus control — the lines that separate a first from a 2:1.
- One-on-one and matched to your course: a tutor works from your own notation and past papers, whether your module follows Romer, Carlin and Soskice, or Blanchard.
FAQ
Q: What is the time-inconsistency problem in one sentence?
A: A plan that is best when you announce it — low inflation — stops being best once expectations are locked in, because you are then tempted to spring a surprise. So it is never believed.
Q: Why does an independent central bank tend to get lower inflation?
A: Independence removes the temptation to engineer surprises for a boom or to erode government debt. With that gone and a public target, expectations settle at the target and the bias collapses.
Q: Goal independence or instrument independence — what’s the difference?
A: Instrument independence is choosing the tools to hit a target set by government; goal independence is setting the target too. Most regimes grant the first only.
Q: Why a band rather than a single number?
A: Inflation cannot be steered exactly, and shocks push it around. A band — 1–3% around a 2% midpoint — marks which deviations are tolerated and which demand a response.
Q: Isn’t this just the Taylor rule?
A: No. The Taylor rule sets the interest rate from inflation and the output gap — the how. Inflation targeting is the commitment framework the rule operates inside — the why.
Book an economics tutor in Toronto or online
Monetary policy rewards students who can derive the inflation bias, not just name it — the loss function, the Phillips constraint, and the credibility argument behind modern central banking. 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 the right tutor this week.
