The short answer
—
of a single exercise's price move is explained by quota, macro and observable behaviour combined.
At the fortnight, COE is close to a random walk. The read-the-auction commentary genre is describing noise.
—
of explained variation over two-year windows is the quota supply cycle.
Supply doesn't move individual auctions. It moves the cycle — and the cycle is what people actually remember.
—
is what dealer-behaviour proxies retain at two years, against — at two weeks — on the conservative spec.
Behaviour is small at every horizon once momentum — the previous window's own move — is counted separately. It is not why COE cost $122k in 2023.
If you are actually buying a car
The rest of this page is about why the premium moves. This part is about what the same data says if you are the one paying it. Three widely-repeated timing strategies are tested below — two of them do not survive contact with the record, which is worth more than another chart.
What it actually costs you
Three things people believe about timing
The cost of waiting
"Wait for it to come down" is a bet, not a plan. Here is the range of what the premium has actually done over each waiting period, across the whole record — 10th percentile, median, 90th percentile.
Read the outer columns, not the middle one. Over six months Category A has ranged from roughly a fifth cheaper to a third dearer. The median is near zero, so waiting has no consistent edge in either direction — it just widens the range of outcomes.
None of this is advice. These are historical patterns in official LTA results, not predictions. The strongest finding on this whole page is that a single exercise's move is essentially unforecastable, which is itself a reason to distrust anyone — including this page — who claims to know where the premium goes next.
What the car actually costs you
A listing quotes one number — "depreciation $X/year" — and it is the answer to a question you probably are not asking. It assumes you hold the car the full ten years. Get out earlier and your real cost per year is higher, sometimes much higher, because the rebate you get back does not shrink smoothly. It steps.
This will not tell you what your car is worth. Resale price depends on the model, the mileage, the colour and the mood of the market, and nothing here can know any of that. What it computes is the floor LTA guarantees in writing: the PARF rebate plus the unused COE. That is the part that is knowable, so it is the only part quoted.
Cost per year, by when you get out
Every exit year, in full
Arithmetic, not advice. These are LTA's published formulas applied to the numbers you typed. The rebate is a floor, not a valuation — if you sell to a dealer rather than scrap the car you may get more, and what you get above the floor is exactly the part nobody can promise you. Rebates also assume the car was never laid up and is deregistered within ten years; past ten there is no PARF at all.
1 · The raw relationship
Premium against quota, every bidding exercise since 2002. The inverse relationship is not subtle — which is exactly why the interesting question is how much, not whether.
2 · The decomposition
Share of explained variation attributable to each channel, at horizons from one exercise to two years. Shares are exact Shapley values — averaged over all orderings of the four blocks, so the answer doesn't depend on which variable you happen to enter first.
3 · How much does quota actually matter?
Long-run elasticity of the premium with respect to quota, in levels. Read: a sustained 10% cut in quota is associated with this much higher premium. Both series are persistent, so this is a long-run association, not an experiment.
Category E (Open) is the most elastic. That fits: it is the fungible, marginal category, disproportionately taken by dealers, so it absorbs pressure first.
4 · Where the supply cycle comes from
Quota is not a free parameter — it tracks deregistrations. A COE lasts ten years, so today's scrappage should echo registrations a decade ago. Testing that honestly requires removing the contemporaneous replacement channel first: households deregister and re-register in the same month, which swamps the echo.
Method, and what this can't tell you
Does the answer survive the judgement calls?
Two choices could plausibly drive the headline: the $1,000 premium floor, and whether to use the longer spliced sample at all. Here is the same figure — share of explained variation at each horizon — under all three cuts. If the conclusion only held in one column, it would not be a conclusion.
What was done
Quota is split into a mechanical component (the part predicted by the deregistration cycle) and a policy component (the residual — LTA discretion: injections, cut-backs, the 2013 phase-in, the recent smoothing). Those, plus a macro block, a momentum block and a behaviour block, are decomposed by exact Shapley value on R². Momentum is the prior window's own price change — the lagged dependent variable — and is kept out of the economic blocks, because a block holding the dependent variable's own history is not comparable with one that does not. Inference uses Newey-West standard errors; overlapping windows at horizon h use 1.5h lags.
Four honest limits
- Two sources, spliced — and checked. The machine-readable LTA bidding dataset starts 2010-01. SingStat table M651121 carries the same LTA fields back to 2002. They overlap for — cells from 2010 onward, and they agree — exactly (largest disagreement: —). That is why the splice is trusted. The panel starts 2002-04, not 2002-02, because the Open Bidding System only replaced closed bidding in April 2002 — earlier rounds are a different price-formation mechanism.
- Behaviour is bracketed, not identified. Same-exercise bid pressure is jointly determined with the premium — high expected prices attract bids, and bids set the price. So two specifications are reported: a conservative floor using only pre-window state, and an upper bound that lets contemporaneous bid pressure count as behaviour. The truth is inside the bracket. Neither number is a causal estimate of "what dealers do".
- The supply split only works for cars. The deregistration cycle explains — of log quota for Category B and — for Category A, but only about 15% for motorcycles (D) and 38% for goods vehicles (C). Headline figures are Categories A, B and E only. For C and D the mechanical/policy split is not meaningful and is not claimed.
- A floor had to be imposed, and one control thrown out. Extending to 2002 brings in real clearing-at-the-floor events — Category A settled at $2 in November 2008, when 1,852 bids chased a quota of 1,851. Those prints are genuine, but unfloored they carry 93% of squared log-variation and would drive everything, so logs use a premium floored at $1,000. The robustness table above shows this does not change the conclusion. Separately, Singapore's all-items CPI includes private road transport — which embeds the COE premium itself — so using it means partly regressing COE on COE. It was carrying about 90% of the macro block. It was replaced with MAS Core Inflation, which excludes private road transport by construction.
What it is not
This is variance accounting, not causal inference. Shapley shares answer "how much of the movement co-moves with each channel", which is the question people usually mean — but a share is not an effect, and none of these channels was randomly assigned. The elasticities are long-run associations between two persistent series. Nothing here is a forecast, and nothing here is advice about when to bid.
Sources
Every number on this page is generated by the analysis pipeline from the sources
above. None is hand-entered. Rebuild: ingest.py → panel.py → horizon.py →
validate.py → export.py.