The four learners and the finding
What the paper finds
Optimal policy against a model that must be learned from the record is a rule whose optimality is conditional on four learners, each measured on real-time data for the United States; the rule sits above the FOMC's decisions on average, and the distance is learned from the record.
The four learners
Learning enters at four levels: the economy's agents, the econometrician, a correction, and the policymaker.
The economy's agents
The question is whether the agents' expectation of inflation is the model's own forecast, an anchor, a discounted forecast, or a level updated from experience. On the record, three families of departures each estimate at the model-consistent value.
The econometrician
The blocks of the world model are learned from the real-time record by a likelihood filter. The record fixes the Phillips slope and the weight on expected inflation; it does not fix the scale of the policy block, which a convention does.
The correction
Nonparametric components on the residuals learn what the blocks miss. Against a null that carries a floor spell, the Phillips component carries no signal, and the IS component does; neither enters the environment the rule is trained in.
The policymaker
The rule is learned by reinforcement inside the estimated economy, so what the first three learners get wrong is the fourth learner's opportunity. The rule is selected on a held-out validation set, and its distance from the FOMC is read against what the record had taught it by the decision date.
The record, the loss, and the world model
The Real-Time Record (Section 2)
Every observation the model sees at a decision point is one the FOMC could have seen.
Optimal Policy, Rules, and Learners (Section 3)
Equation (1) is the book's loss with its sum taken from one quarter ahead, where the book's runs from the current quarter; the book's optimal policy minimizes it, and the learned rule is trained on it.
π⁴ is four-quarter inflation, π* the target, y the output gap, and i the policy rate; the weights α and β are one and γ one half.
The book's experiment on the learned rule (Section 3.1)
From the book's 2014:Q4 state, the IFB rule lifts off in 2015:Q1, the DM1 path in 2016:Q1, and the learned rule in 2016:Q2.
The World Model (Section 4)
The blocks are learned from the record by a likelihood filter; the estimate of record is the deepest basin of the multi-start search, re-polished under a widened box.
The staff forecasts better than the model of record on every line of the paper's Table 2.
Expectations and residual components
The Expectations Block Against Three Families (Section 5)
The anchored, cognitive-discounting, and learned-anchor families each estimate at the model-consistent value.
Residual Components and a Floor-Aware Null (Section 6)
Against the floor-aware null, the IS component's excess lies above the null's 95th percentile, and the Phillips component carries no signal.
The learned rule
The Policy Agent (Section 7)
The optimal rule under the book's loss is an inertial rule of four coefficients, trained inside the estimated economy and selected from a search over eight training streams.
The optimal policy and the FOMC
The agent of record against the FOMC (Section 8.1)
Across every environment since 1997 the agent of record sits +0.768 points above the FOMC's realized rate on average, the realized rate below the agent's band on 88 of 118 quarters, with the first floor spell the exception, where the agent holds the floor as the FOMC did.
- The realized funds rate
- The agent of record
- The agent's band, 10th through 90th percentiles over 20 draws of the estimated blocks
Table 4 of the paper gives the mean differences by period.
The frozen and rolling agents, and counterfactual outcomes
The agent frozen at the end of the first floor spell (Section 8.2)
Frozen at 2015:Q4, the construction stays close to the FOMC; the rolling real-time agent, its blocks re-estimated and its rule re-trained at each decision point from 2006:Q1, opens its distance as the record takes in the inflation of 2021–2023.
- The realized funds rate
- The agent of record
- The rolling real-time agent
- The agent frozen at 2015:Q4
The full sample's Phillips slope is 3.5 times the frozen estimate's slope of 0.0172.
Counterfactual outcomes (Section 8.3)
With the record's own shocks, four-quarter inflation over 2021–2023 averages 2.25 under the agent of record and 4.42 under the frozen agent, against the realized 4.29.
The book loss over the record falls from 989.3 to 261.6 under the agent of record.
Sensitivity, limitations, and the conclusion
Sensitivity and Limitations (Section 9)
Under the four variants of the loss weights and across five searches at the weights of record, every full-record mean difference lies within 0.16 points of the record's +0.768.
Eight limitations bound the reading, among them the structure the IS residual carries beyond the floor-aware null, the convention that fixes the policy block's scale, and the selection among training streams.
Conclusion (Section 10)
What would change the reading is an expectations construction that varies across regimes, a loss with the history dependence of the FOMC's 2020 framework, a scale of the policy block the record pins rather than a convention fixes, and a selection among training streams that its own test set confirms.
What the values are
Charts, definitions, and data
The charts draw the realized funds rate and the paths the paper computes.
- The first chart draws two of the three rates of the paper's Figure 8, the realized rate and the agent of record's, with the agent's band; Figure 8 also carries the book rule's rate.
- From 2016:Q1 the second chart draws the paths of Figure 9: the realized rate, the frozen agent, the rolling agent, and the agent of record; Figure 9 also shades the range of the rolling agent's eight checkpoints' rates.
- Before 2016:Q1 the second chart's realized rate and agent of record are the paths of Figure 8, and the rolling agent's rates are those computed in Section 8.2, which prints their mean difference from the FOMC over 2006:Q1–2015:Q4, +0.02.
- A mean difference is the mean, over decision quarters, of a prescribed rate less the realized federal funds rate, in percentage points; a loss is in the units of the loss of equation (1), and the book loss over the record is its quarterly term summed over the record's quarters (Table 8).
- Sources: ALFRED, RTDSM, SPF, HLW, and Federal Reserve Board vintages as accessed 5 September 2026; author's calculations.
- The real-time record, its series, and their vintages are set out in Section 2 of the paper.