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 trained inside the estimated economy sits +0.768 points above the FOMC's realized decisions on average over the record, and that distance is learned from the record: frozen at 2015:Q4, the same construction sits +0.235 above the FOMC on average thereafter.
The economy's agents
Whether the agents' expectation of inflation is the model's own forecast, an anchor, a discounted forecast, or a level updated from experience. The record chooses the model's forecast: 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 comparison 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 held-out draws, and its distance from the FOMC is read against what the record had taught it by the decision date.
One rail for each learner, in the order of the boxes above. A mark is filled where the section belongs to the learner and hollow where the learner passes through it. Each section ends on the question the next one answers. Every value is the paper's printed number.
1IntroductionThe economy's agentsThe econometricianThe correctionThe policymaker
The question: what optimal policy is when the model it is optimal against must be learned from the record. Learning enters at four levels, each measured on real-time data for the United States, and the four findings of the paper are read at one calibration, the book's loss.
On what record is each learner measured?
2The Real-Time Record
Every observation at a decision point is one the FOMC could have seen. A store of 30 series gives 146 decision points from 1990:Q1 through 2026:Q2; the estimation window runs from 1996:Q1 through 2026:Q2, 122 quarters and 836 observation rows, with 36 quarters at the floor in two spells.
What is optimal policy, and who learns what?
3Optimal Policy, Rules, and LearnersThe economy's agentsThe econometricianThe correctionThe policymaker
The book's quadratic loss, equation (1). Two distinctions carry the paper: an optimal path against an optimal rule, and the four senses in which something is learned. In the book's experiment from the 2014:Q4 state, the IFB rule lifts off in 2015:Q1, the DM1 path in 2016:Q1, and the learned rule in 2016:Q2, at losses of 14.44, 9.95, and 10.64.
Equation (1), the loss; Figure 1, the four learners; Figure 2, the book's experiment on the learned rule.
In what economy is the rule learned?
4The World ModelThe econometrician
An IS block, a hybrid Phillips block, and a policy slot with a floor, equations (2) through (4), with model-consistent expectations. The likelihood does not fix the scale of the policy block, which a convention fixes at an inflation response of 3. The likelihood has many basins: of 44 starts, the deepest, 0.1445 per row, is reached by two warm starts and by none of the 40 random starts. The estimate of record carries a weight of 0.946 on expected inflation and a Phillips slope of 0.0596. The staff forecasts better than the model on every line; the ratio of four-quarter inflation errors is 1.32.
Equations (2) through (4), the blocks; Figure 3, the profile and the optima; Table 1, the estimate of record; Table 2, the model against the staff.
The model's agents hold model-consistent expectations. Does the record select that?
5The Expectations Block Against Three FamiliesThe economy's agents
The anchored, cognitive-discounting, and learned-anchor families each estimate at 1.000, the model-consistent value. Holding the parameter at 0.8 costs 39.8 units of log-likelihood for the anchored family and 110.9 for cognitive discounting. The long-run survey follows a constant-gain learner's anchor at a gain of 0.030, yet the weight on the model-consistent expectation stays at 1.000: the survey learns, and the agents in the macro rows do not lean on it.
Table 3, the families; Figure 4, the likelihood profiles; Figure 5, the survey and the learned anchor.
What do the blocks leave in the residuals, and is it signal?
6Residual Components and a Floor-Aware NullThe correction
A floor spell puts structure into the filtered shocks even at the true parameters, so a comparison without a floor reads that structure as signal. Against a comparison that carries a floor, the Phillips component carries no signal; the IS component's excess, 0.239, lies above the comparison's bound of 0.145. The components are not part of the agent's training environment.
In which environment is the rule trained, and how is one rule selected?
7The Policy AgentThe correctionThe policymaker
An inertial rule of four coefficients, trained from the 118 real-time starts under draws from the estimate's uncertainty. Over 100 draws the agent of record beats the book rule on 100, by 4.24 on average; the agent trained with the components beats it on 43, by 0.41. The rule of record is the best checkpoint of a search over eight training streams over 2,000 steps, stream 8 at step 450; the validation ranking of the streams says little about their test ranking, so the coefficients are read as one point on a ridge of rules.
Figure 6, the performance profile; Figure 7, the search over training streams.
Where does the rule stand against the FOMC's decisions?
8The Optimal Policy and the FOMCThe econometricianThe policymaker
The central result. Over all 118 quarters the agent of record sits +0.768 points above the realized funds rate on average, with the realized rate below the agent's band on 88 quarters; over the first floor spell the difference is +0.03. The distance is learned from the record: the same construction frozen at 2015:Q4 sits +0.235 above the FOMC on average thereafter, against +1.297 for the agent of record, because the frozen estimate's Phillips slope, 0.0172, is a third of the full sample's; the slope that puts the optimal rate above the FOMC's is identified by the inflation of 2021–2023, and the rolling real-time agent stays within +0.02 of the FOMC until the record contains it. 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.
Figure 8, the agent of record against the FOMC; Figure 9, the frozen agent; Tables 4 through 8.
Do these readings depend on the loss weights, the training stream, or the construction?
9Sensitivity and LimitationsThe economy's agentsThe econometricianThe correctionThe policymaker
Under four variants of the loss weights the full-record mean difference runs from +0.614 through +0.902, every variant within 0.15 points of the record's +0.768; across five searches at the weights of record it runs from +0.733 through +0.789. The limitations that bound the reading are stated in Section 9, among them the structure left in the IS residual, the convention for the policy block's scale, and the selection among training streams.
Table 9, the loss weights; Table 10, the training streams.
What, then, is optimal policy when the economy must be learned?
10ConclusionThe economy's agentsThe econometricianThe correctionThe policymaker
Optimal policy is not a single path but a rule whose optimality is conditional on four learners, each measured; what it says about the FOMC is a property of that conditional object and depends on what the record had taught the construction by the decision date. The conclusion closes on what would change the reading.
Appendix A, the oracle conditions O1 through O18.