Replication
Reproduce or improve this
An invitation to independently implement, verify and improve the research, using explicit sources, frozen numerical inputs and a complete downstream specification.
1. The question and the identity
What explains the level and history of the UK five-year, five-year forward gilt rate, and how much of its real compensation is shared with foreign markets?
The global reference is a fixed, equal-weight US, German and Australian real-compensation benchmark. A separate US/Australia version extends the history to 2005. Foreign expected real rates are also reported, without counting them twice in this identity.
2. What replication means here
No code is published. A replication is an independent implementation from the sources and specification, using the replicator’s own tools or AI model. The first exercise is to reproduce the recorded calculations from the same numerical inputs. A second is to change the data or economic assumptions and explain the resulting difference.
A different result is useful when its cause can be traced. A discrepancy remains unresolved until it is attributed; agreement on the market inputs alone does not establish that a model difference is legitimate rather than an implementation error.
3. Exact sources, identifiers and vintages
The source inventory distinguishes the publisher’s series, original file hashes, retrieval time, reference date and vintage. An unknown timestamp is recorded as unknown. The Bank of England’s real-curve archive is available from its yield-curve page, but it is not a separate direct input to this downstream calculation: UK real-related forwards are nominal minus the inherited CPIH-equivalent series.
Machine-readable source inventory (JSON) · Readable source inventory (Markdown)
Read the complete source map and series identifiers
This inventory describes the 17 September 2026 checkpoint, with market observations no later than 31 July 2026. Direct decomposition inputs are separated from sources used only in the inherited CPIH conversion.
sources.json lists exact URLs, filenames, series identifiers, original SHA-256 hashes and retrieval metadata. Unknown dates remain unknown. Provider pages may now serve revised vintages.
| Source | Official link | Exact selection | Retrieval and vintage |
|---|---|---|---|
| BoE nominal | Yield curves | glcnominalddata.zip; full spot worksheet, exact 5/10-year columns. Annual continuous percentages. |
15 September 2026, 15:27 UTC. Latest-vintage fitted curves; observation publication times unknown. |
| BoE implied inflation | Daily archive | Exact 5/10 implied-inflation spot nodes. RPI is read from this curve, not independently recalculated from nominal and real archives. | Fresh comparison retrieved 15 September 2026, 16:00 UTC. CPIH retains its inherited public vintage and correction. |
| BoE real curve | Official collection | Separately published family, not a direct downstream input. UK adjusted real is nominal minus frozen CPIH-equivalent compensation. | No separate real-archive retrieval or vintage is claimed here. |
| ONS MM23 | RPI CHAW, CPIH L522, formula CPTJ | Indices CHAW/L522; annual rates CZBH/L55O; formula CPTJ; reconciliation CPTE, CPTG, CPTH, CTUY, CPTI, CPTK, CPTF. Upstream conversion only. | 19 August 2026 release through July; retrieved 10 September. Individual timestamps and hashes in JSON. |
| HMT forecasts | Database | 84 rounds, February 2005 to May 2026. Published Independent average, terminal calendar year = round year +4. Annual-average Bank Rate/repo and CPI. PDF M3/M4 and June 2026 panel; source row/page per observation. | Retrieved 17 September 2026. Earlier archived PDFs; later retrospective database. Seven month-end date proxies in the specification. |
| BoE MPS | Market Participants Survey | 27 releases, March 2023 to June 2026. Seven-bin probabilities for annual CPI inflation averaged over years 5-10; exact sheet/cell per row. | Workbooks retrieved 15 September 2026. Publication dates and fieldwork windows retained. |
| Fed TIPS | TIPS curve | feds200805.csv: Date, TIPSY05, TIPSY10, continuous zero yields. Coupon-equivalent TIPS5F5 excluded. |
Retrieved 15 September 2026, 16:00 UTC; HTTP modification 8 September. Revisable provider estimates. |
| German Finance Agency | Inflation-linked securities | ISIN factsheets, embedded Price histories: real clean prices around noon Frankfurt. Terms from index-ratio workbook headers. Individual ISIN URLs/hashes in JSON. | Retrieved 17 September 2026. Data through 31 July. Exact dated constituents and endpoint schedules bundled. |
| RBA / AOFM linkers | RBA tables, AOFM bonds | F16 security real yields/terms: 1992-2008, 2009-13 and current. Actual RDP 2018-02 supplement observations fill supported missing dates. TI identifiers retained; ISIN crosswalk unverified. | Current CSV retrieved 17 September 2026, 15:31 UTC. Some archive retrieval times absent; byte capture verified that day. Supplement retrieved 15 September. |
| NYFed Primary Dealers | Archive | 114 longer-run policy forecasts, June 2012 to July 2026. Median dealer modal forecast/longer-run estimate from original pre-meeting releases. Fieldwork-end dating. | Frozen acquisition 17 September 2026; individual original-file metadata in JSON. Most results-publication dates unverified. |
| Philadelphia SPF | SPF | CPI05YF05 observed mean, 84 rounds August 2005 to May 2026. Calendar-deferred annual CPI average; response-deadline dates. |
Retrieved 15 September 2026. Calendar-defined horizon differs from rolling interval. |
| ECB SMA | Survey of Monetary Analysts | 42 CSV rounds: measure=MEDIAN, date_descr=long run, area=U2; DFR/ESTR units I, HIC units Y. Per-round keys supplied. |
Retrieved 17 September 2026. Submission-deadline updates; publication dates separate. |
| RBA J1 | CSV | JSVNNIREMN / JSVNNIREMED: neutral-rate mean/median. JSVIEXPMN / JSVIEXPMED: next-5-10-year inflation mean/median. |
Retrieved 17 September 2026; snapshot update 28 August. Use rounds through May. Reference-month ends proxy historical release dates. |
| HLW neutral rates | NYFed r-star | Real-time workbook, sheet 2026Q1: US r-star (K), euro-area r-star (M); one-sided 2023 COVID-adjusted model. Real annual percentages. |
Retrieved 17 September 2026. Reference vintage scheduled 1 June 2026. Later revised history is a sensitivity. |
| RBA macro models | 26 March 2026 speech | Data sheet, Graph 3, columns H/I/J: three identically labelled Semi structural nominal-neutral variants. Exact columns used; unique variant names unavailable. | Published 26 March 2026; retrieved 17 September, 15:50 UTC. Retrospective quarters through December 2025. |
| FRED reform control | T5YIFR | Upstream CPIH policy control alongside T5YIE/T10YIE. Public HTML date/value extract; converted with log(1+rate). Not the downstream US real curve. | Retrieved 10 September 2026, 10:38:51 UTC. Direct CSV attempts failed; captured-table provenance explicit. |
Frozen numerical inputs
The download inventory identifies each numerical file, byte size, SHA-256 and original source hash. It distinguishes byte copies from selections and deterministic term/schedule exports. The specification explains their use.
The pack includes selected numerical extracts, author calculations, dated security membership, endpoint cash flows and reference outputs. It excludes executable code and complete provider HTML, PDF, XLS/XLSX and ZIP documents. Original provider hashes allow comparison if the same vintage is obtained independently.
CPIH replication boundary
Use cpih_equivalent_frozen_daily.csv as the standalone market input. The matched market table supplies all three conversion variants on the exact downstream grid. Rebuilding the ONS statistical wedge and policy add-back is a separate research exercise.
Metadata and rights
Some Australian archive retrieval timestamps were not retained. Byte-capture verification times are shown separately and are not substituted for retrieval dates. Historical release dates and original-vintage availability are incomplete. Australian TI identifiers lack a verified ISIN crosswalk. The RBA workbook identifies exact H/I/J columns without distinct variant names.
Original text, charts and research outputs by Russ Oxley are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). Third-party inputs remain subject to their publishers’ terms; this licence does not relicense third-party documents or databases. Read the licence. Original provider documents are not bundled.
4. Frozen inputs, outputs and hashes
Start with the numerical replication pack. It contains the market-forward and CPIH input histories, dated survey observations, foreign bond terms and support schedules, macro anchors, scenario definitions and selected numerical comparison outputs. Provider source documents and executable code are excluded. The manifest records SHA-256 hashes so a replicator can check that the input bytes agree.
The daily CPIH-equivalent conversion is an explicit input boundary. Everything downstream is specified here. Independently reconstructing the ONS index-gap and reform-discount conversion is a separate research exercise; agreement on downstream results does not validate that upstream conversion.
Some inherited source files extend beyond July 2026. Only observations through 31 July 2026 are admitted to the published histories. No later market observations enter the charts.
The download catalogue provides individual files and derived outputs; the chart book links each image to its data.
5. The specification pack
The full methods specification brings together quote conversions, exact filter likelihood and optimiser rules, cash-flow construction, maturity support, source timing, scenario fields and aggregation. The seven older HMT date proxies and all 27 MPS bin definitions are listed explicitly. The source files preserve numerical precision; display rounding does not feed back into the calculations.
Machine-readable specification (JSON) · Readable specification (Markdown)
The scenario dictionary separates 41 global alternatives from 21 UK inflation cases. The latter are four HMT methods plus three MPS tail conventions, crossed with three market conversions, then embedded in three fixed foreign families. They are not 63 independent estimates of a single causal model. Scenario ranges measure sensitivity to those declared choices.
6. Replication targets
Same-input numerical reproduction requires the same date selection, conventions and full-series values, not merely a similar endpoint. The tolerances below are engineering comparison thresholds, not confidence intervals. Values here are rounded; the JSON supplies unrounded targets.
| Tier | Targets on 31 July 2026 | Comparison rule |
|---|---|---|
| A · Measurement and accounting | UK nominal 564.923050391 bp; market inflation 300.316638 bp; adjusted real 264.606412391 bp. RPI and CPIH-equivalent compensation coincide at this date. | Same frozen bytes and rules: absolute tolerance 0.000001 bp, plus exact dates/support. Check the full identity. |
| B · Same inputs and specification | UK expected nominal 316.583654954 bp; inflation 208.339724274 bp; real 108.243930680 bp; inflation compensation 91.9769137261 bp. Macro global/local 188.704816464 / −32.3423347526 bp; survey 193.387491224 / −37.0250095127 bp. | Absolute tolerance 0.01 bp for solver-dependent full-series calculations. Report fitted parameters and every convention. |
| C · Findings and extensions | Reference rise since 30 December 2019: global real +282.6 bp, expected real +125.4 bp, inflation compensation +32.6 bp, UK-relative +12.8 bp, expected inflation +0.5 bp. Quarter trends are on the Results page. | Same-method comparisons should reproduce these numbers. With improved data or methods, report agreement or disagreement; no required sign or scenario range is a pass band. |
Unrounded replication targets and rules (JSON) · Quarterly findings.
7. What better data could change
- Traded forwards: RPI swaps and nominal swap forwards could quantify differences from fitted government-bond curves.
- A wider real benchmark: France could provide another euro-area curve; Italy, Japan, Sweden, New Zealand and Canada are candidates subject to historical maturity support and data access.
- Long-horizon expectations: licensed forecasts, such as Consensus Economics, could test the HMT terminal-year mapping directly.
- Term-structure estimates: an independently specified term-premium model could crosscheck the real-compensation split.
- Real-time vintages: historical ONS and HLW releases would allow an available-at-the-time reconstruction.
Dataset contributions are welcome. Where access and licensing permit, the intention is to rerun the published specification, credit the contributor and publish the differences as a new checkpoint. Shared data can be hosted where their licence permits.
8. The weakest links and open problems
- The HMT terminal-year forecast is around four years ahead; its use for years 5–10 is an economic assumption. The varying HMT–MPS gap is reported on the Results page.
- The CPIH conversion is synthetic and retrospective. A changing CPIH/CPI expectation gap or instrument effect can change the inflation-compensation trend.
- The three-market benchmark is narrow. Germany’s sparse curve makes interpolation material; changing weights or the UK loading can reverse the UK-relative component’s sign.
- Australian security identifiers are retained as the RBA TI codes. An independently verified ISIN crosswalk and bond-specific historical base-index series were not assembled; the numerical construction uses index-normalised cash flows.
- Historical surveys and macro estimates differ in horizon, respondent group, statistic and vintage. They are imperfect expected-policy anchors.
- Internal AI checks do not replace independent reimplementation. The component histories do not identify causal shares for AI investment, fiscal credibility, Brexit or monetary-policy credibility.
9. Report a replication or improvement
Email russ.oxley@avroxasset.com with your name, model and version, data and vintages, implementation choices, numerical comparisons and a clear account of where results diverge. Include a link to shareable material and any redistribution restrictions.
The Replications page will curate attempts, findings and corrections. Working notes describe the internal AI checks behind this checkpoint.
10. Reuse and citation
Original text, charts and research outputs: CC BY 4.0. Third-party inputs remain subject to their publishers’ terms.
Suggested citation: Oxley, Russ (2026), “What is driving UK long-term interest rates?”, Modern Tontines Macroeconomic Research, published 18 September 2026, research checkpoint 17 September 2026, market data through 31 July 2026. https://moderntontinesmacro.netlify.app.