Optimal Monetary Policy When the Economy Must Be Learned

The question is 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 policymaker's findings are read at the book's loss weights, which Section 9 states are not estimated.

On what record is each learner measured?

Every observation the model sees 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?

Equation (1) is the book's loss with its sum taken from one quarter ahead, where the book's runs from the current quarter. 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?

The world model is 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 more than one basin: 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 of Table 2; the model's root-mean-square error in four-quarter inflation is 1.32 times the staff's.

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?

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 behaves as a learner's anchor, the learned anchor's gain estimated at 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?

A floor spell puts structure into the filtered shocks at the true parameters, and a component fitted to the shocks reads that structure as signal against a null without a floor. Against the floor-aware null, the Phillips component carries no signal, and the IS component carries structure beyond it. The components are not part of the agent's training environment.

In which environment is the rule trained, and how is one rule selected?

The rule is 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 of 2,000 steps each, stream 8 at step 450. The streams' validation ranking says little about their test ranking. The rules at the checkpoints differ by more than their losses, 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?

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. Frozen at 2015:Q4, the same construction sits +0.235 above the FOMC on average thereafter, against +1.297 for the agent of record. The frozen agent sits nearer the FOMC because the record through 2015:Q4 does not identify the steeper Phillips slope that the inflation of 2021–2023 identifies: the full sample's slope is 3.5 times the frozen estimate's slope of 0.0172. The rolling real-time agent's mean difference is +0.02 over 2006:Q1–2015:Q4 and +0.48 over 2016–2020, and it rises to +2.15 once its record includes 2021. 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, the rolling agent, and the agent of record; Table 4, the agent of record against the FOMC by period; Table 5, the agent, the book rule, and three published rules; Table 6, the frozen estimate beside the estimate of record; Table 7, the frozen and rolling agents; Table 8, the counterfactual outcomes.

Do these readings depend on the loss weights, the training stream, or the construction?

Under four variants of the loss weights the full-record mean difference runs from +0.614 through +0.902, every variant within 0.16 points of the record's +0.768; across five searches at the weights of record it runs from +0.733 through +0.789. Eight limitations bound the reading.

Table 9, the loss weights; Table 10, the training streams.

What, then, is optimal policy when the economy must be learned?

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. 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.

Appendix A, the oracle conditions O1 through O18.