REAL-TIME QUARTERLY SIGNAL-PLUS-NOISE MODEL FOR ESTIMATING "TRUE" GDP
Bibliographic record
Abstract
Gross domestic product (GDP) cannot be sampled directly, for example, like employment or unemployment rates, but must be computed using other, related, sampled data. The Bureau of Economic Analysis (BEA) computes quarterly estimates of U.S. GDP and releases them to the public shortly after the end of each quarter. BEA releases three initial estimates, termed advance, preliminary, and respectively, one, two, and three months after the end of a quarter. Every July, BEA makes further benchmark revisions to the previous year's estimates. Finally, BEA revises estimates comprehensively, following censuses or changes in definitions or estimating methods, to maintain consistency in historical time series. In other words, GDP estimates are never final, i.e., the revisions never attain values of GDP. In this paper, we model the three initial estimates of GDP as a quarterly, trivariate, signal-plus-noise (S+N) process, specifically, as a univariate, AR(2), signal process of GDP plus a trivariate, AR(1), noise process of estimation errors. The S+N model implies a trivariate ARMA(3,2) reduced-form process of the estimates. We show that the S+N model is identified under weak parametric assumptions. We obtain maximum likelihood estimates (MLE) of a simplified scalar version of the model, using the initial estimates of real GDP from the first quarter of 1978 to the first quarter of 1999 (78:1-99:1). We use the estimated model to compute quarterly model-based estimates of true real GDP and compare the estimates to recent, comprehensively revised, estimates of real GDP for the same period. In the literature, Young (1987, 1993) explained properties of initial GDP estimates. Academics (e.g., Mankiw and Shapiro, 1986; Mork, 1987) studied whether GDP revisions are best characterized as optimal forecast errors or as measurement errors. Other academics and Federal Reserve researchers
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".