The objection stated at full strength
Central banks already run the correct system, and it is not continuous. Eight times a year — the Federal Open Market Committee's schedule, matched closely by the European Central Bank and the Bank of England's Monetary Policy Committee — a staff team reruns a full macroeconomic model: FRB/US, the ECB's New Area-Wide Model, dozens of satellite equations for inflation, output gaps, credit conditions. This is a rebuild in the strict sense. It is expensive, it is scheduled, and between rebuilds the forecast simply ages. That is the batch discipline, and it has a hard economic argument behind it, not merely institutional inertia.
Forecasting works because we concentrate the expensive judgement into one room, one week, with every input reconciled at once. Streaming that judgement across the quarter does not make it cheaper. It makes it undisciplined — twenty small updates instead of one coherent one, each pulling the policy rate in a slightly different direction, none of them subjected to the committee's scrutiny.
This is the amortised-complexity case turned against continuous intake, and it deserves to be taken at face value before any concession is offered.
Why batch has the arithmetic on its side
Robert Tarjan's 1985 paper gave the batch defence its proper form, even though it was written for data structures, not monetary policy. Amortised analysis prices a rebuild by spreading it across the whole interval it covers. If a full model rerun costs, say, four hundred economist-hours and covers a six-week inter-meeting interval, the amortised cost per day is small. Continuous nowcasting — updating a policy-relevant estimate every time a data point lands — pays overhead on every arrival: retail sales, weekly claims, PMI flash readings, breakeven inflation extracted from swaps. Each update is small, but the sum of small updates, weighted by the staff time needed to interpret rather than merely ingest them, can exceed the cost of one disciplined rebuild by a wide margin. This is not a rhetorical point. Reconciling twenty streams continuously requires standing infrastructure — a nowcasting desk, real-time seasonal adjustment, a data engineer keeping series revisions aligned — that a quarterly round does not need at all. Batch is often cheaper in total. An economist who says so is not being complacent; they are reading the same ledger Tarjan taught engineers to read.
Where the arithmetic stops covering the cost
The gap in the batch defence is that amortised bounds are bounds on total work, not on the timing of when the belief is correct. The FOMC sets a rate on the data available at the meeting. Payrolls come out revised, sometimes sharply — the U.S. Bureau of Labor Statistics' benchmark revision to March 2024 payrolls cut the level by roughly 800,000 jobs, discovered a full year after the fact. GDP first estimates in the UK are routinely revised by several tenths of a percentage point once fuller survey and VAT data arrive. None of that revision cost appears in the rebuild's amortised total, because amortisation counts total computation, not the staleness of the number a committee acted on. Staleness is a latency cost, paid by whoever sets the rate, and it does not net out against the batch's cheaper constant factor. This is exactly the reasoning that pushes engineers to deamortise garbage collection in systems where a multi-second pause is unacceptable even though it does strictly more total work. A central bank tightening into a labour market that turns out, eighteen months later, to have already been softening is the monetary equivalent of that stop-the-world pause: the total accounting was fine: the moment was wrong.
So both things are true at once, and the honest position holds them together rather than picking a side. Batch minimises total computation. Streaming minimises the staleness of what the committee is looking at when it moves the rate. Central banks already know this, which is why nearly every one of them runs a continuous nowcasting layer — the Federal Reserve Bank of Atlanta's GDPNow, the New York Fed's staff nowcast, the Bank of England's weekly activity indicators built from card-spending and job-posting data — alongside the scheduled model rerun. The nowcast does not replace the round. It amortises the intake per arrival so that by the time the round happens, the batch calculation starts from a belief state that has already absorbed the week's data, rather than from a corpus frozen since the last meeting.
The concession: potential functions need forgetting, and forgetting is a policy choice
The second objection is the one that survives fully, and it matters more in central banking than almost anywhere else. An amortised guarantee needs a bounded potential function — some finite ledger of credit the cheap operations bank up to pay for the occasional expensive one. Continuous intake of price indices, labour flows, credit aggregates and market expectations has no natural bound on that ledger. Every observation adds to the belief state: a revision to last month's CPI print does not just update one number, it can force a re-estimation of the seasonal factors underneath the whole series, and that recomputation grows with the length of history held. A nowcast that never forgets accumulates provenance chains — which vintage of which series produced which estimate — that grow without limit. This is not a hypothetical: real-time databases of vintage macro data, such as the Philadelphia Fed's Real-Time Data Set, exist precisely because analysts discovered that "the CPI figure" is not one number but a sequence of numbers, each superseding the last, and keeping track of which one a decision used is itself a storage problem that grows with the archive.
There is no engineering trick that removes this. What removes it is a forgetting policy: discounting older vintages, coarsening provenance from full audit trails to hashes and summary flags after some retention window, treating a benchmark revision as a regime break rather than folding it silently into a continuous series. Every such policy throws away something a future inquiry might have wanted — precisely the trade-off archives and telemetry systems argue about under names like retention schedules and rollup granularity. Central banks make this choice already, informally, when staff decide how many vintages of a series to carry in the nowcast versus how many to leave to the historical database. Conceding this fully changes nothing about the domain's fundamental billing scheme; it only says that the per-arrival price is not free, and that keeping it bounded is a design decision, not a windfall.
Reflexivity: the adversarial case central banking cannot avoid
There is a version of the adversarial objection specific to this domain, sharper than hash-flooding a web server. Market expectations are not a passive stream. They are generated partly in response to what the central bank is expected to do, and once policy nowcasting becomes visible — a published weekly indicator, a well-known model like GDPNow — market participants price against it. Breakeven inflation extracted from swaps can start to reflect expectations of the central bank's reaction to breakeven inflation, a loop with no independent ground truth. This is the amortised-complexity worry about adversarial input sequences, restated as reflexivity: the stream itself changes shape because it knows it is being read.
Provenance is the answer available, and it is only partial. A belief state that records which stream produced an estimate — survey-based inflation expectations, market-implied breakeven, a model-based nowcast — can be revised locally when one source is discovered to be reflexive or manipulated, rather than forcing a full rebuild of the policy stance. The 2022 UK gilt market episode showed the opposite failure: a shock in one narrow segment (LDI-driven pension fund selling) briefly read as a broad market judgement on fiscal policy, because the provenance separating "one leveraged corner of the market" from "aggregate market expectations" was not sharp enough for real-time decision-making. Separating streams by source is a trust problem, and it sits downstream of intake, not inside it.
The claim that survives
Central banking already runs the layered system the amortised argument predicts: a periodic rebuild (the forecast round) for coherence, and continuous per-arrival maintenance (the nowcast) to bound staleness between rebuilds, with a growing, deliberately incomplete effort to bound the potential function through vintage discipline and provenance. Batch remains cheaper in aggregate computation; that is not in dispute. What is in dispute, and resolved in favour of continuous intake, is the claim that total computation is the only cost a policy institution has to price. Staleness is a cost too, and it is charged to whoever raises or holds the rate on a number that gets revised the following spring.