When a Shock Makes the Future Worth Planning
This chapter follows the price-setting firm as its economic state changes and asks when another period of explicit planning becomes worth buying. The focus is the relationship among shock size, shock persistence, and the firm’s longer-run inflation reference point. Understanding that relationship lets us predict when the model selects a longer horizon, why the choice can become asymmetric, and where the model’s simple stop rule ceases to be a global answer.
The state that makes an extra period matter
The firm’s choice begins with a simple comparison. It has already chosen a price using a planning horizon of k periods. It can keep that price, or it can evaluate the consequences of one more period and re-solve the pricing problem. The extra period is valuable only if it changes the price enough to improve expected profits. The current state of the economy determines how likely that is.
A small, short-lived disturbance may have little effect on the price that will be appropriate over the relevant future. The firm’s continuation value can absorb the difference. A large disturbance is different: it can move demand, costs, or the desired relative price far enough that a plan based on a shorter window becomes noticeably inadequate. Persistence matters for the same reason. If the shock is expected to disappear quickly, distant consequences are discounted both by time and by the shock’s fading. If it persists, the price chosen today remains exposed to a changed environment for longer.
In the Federal Reserve model, the analytical object that captures this effect is the change in the firm’s desired reset price when the horizon moves from k to k+1. The marginal benefit of extending the horizon is proportional to the square of that change. The square is useful for intuition: the sign of the price adjustment tells us which way the firm wants to move, but the value of doing more analysis depends on how far the current plan is from the better-informed one.
In the cleanest case, the only relevant disturbance is aggregate demand, it is stationary, and the firm’s trend-inflation reference is at its steady state. The desired-price change shrinks as the horizon grows because future demand effects are discounted and the disturbance becomes less influential farther out. The marginal benefit of each additional period therefore declines geometrically. A firm confronted with a small demand gap stops early; one facing a larger gap continues farther before the incremental benefit falls below the cost.
This is a threshold rule, not a claim that all firms with the same shock choose the same literal number of quarters in the real world. The threshold is a model result under a specified cost schedule and shock process. It says that the selected horizon is weakly increasing in the absolute size of the demand disturbance in the simplified case. A positive and a negative disturbance of equal size create equal planning incentives there because each produces a mismatch of the same magnitude between the short-horizon and expanded-horizon prices.
Persistence changes the thresholds even when the current shock is the same size. A more persistent demand process gives future consequences greater weight. The firm is not merely reacting to the level of demand today; it is asking how many future periods are likely to inherit the disturbance. That is why the paper’s result is about planning distance, not just price flexibility. A firm can face a large current movement but rationally plan less far if the movement is expected to reverse quickly, while a smaller but persistent movement can justify more explicit analysis.
Consider two otherwise identical firms facing the same current demand gap. If one expects the gap to decay rapidly, the future price path soon returns toward the continuation value, so extending the explicit calculation may barely alter the reset price. If the other expects the gap to persist, the price selected today will be evaluated against a sequence of future states that remain displaced. The second firm has more to gain from calculating another period, even though the initial observation is identical. In this sense, persistence raises the economic exposure of the current decision, and exposure raises the return to planning.
The threshold is also relative to the cost schedule. A larger incremental cognitive cost moves the stop point inward: more states will be treated with the continuation value because the benefit of re-solving must clear a higher bar. A smaller cost lets the firm continue farther, approaching the long-planning limit. The model therefore separates two reasons for a short horizon—future consequences may be unimportant, or explicit analysis may be expensive—and the observed horizon alone cannot distinguish them.
The same logic applies to a supply or markup disturbance. In the model, the coefficients governing demand and supply effects are tied to their respective persistence. A firm extends its horizon when the additional future state would materially alter its desired price. The relevant input is therefore not “demand” in isolation, but the state-dependent gap between the price implied by a short plan and the price implied by incorporating the next contingency.
The transition from one horizon to the next can be represented as follows:
The economic state behind every comparison includes more than the current shock. It includes how persistent the disturbance is expected to be and where the firm’s longer-run beliefs currently sit. That last element becomes important once the continuation value learns from realized inflation.
The states in the diagram are decision states, not stages that every firm must pass through on a common calendar. A firm can stop at horizon zero, or it can extend several times before setting its price. “Horizon 2 and beyond” represents the repeated comparison, not a claim that all later periods have the same value. At each step the firm reassesses whether the next period would materially change the price. The trigger is always the net value of the next extension, while the state variables determine how large that value is.
This also clarifies what the stopping threshold is not. It is not a cutoff in the inflation rate beyond which firms become more rational, and it is not a regulatory or managerial rule that can be read directly from a survey response. It is a boundary in a model’s value comparison. Crossing it means that, given the assumed cost and shock processes, the next explicit calculation is worth doing. That interpretation will matter when the reference point begins to move.
From a clean threshold to a moving reference point
The no-learning result is symmetric because the firm is comparing the current state with a fixed reference. Once the continuation value contains a trend-inflation component, the relevant mismatch is no longer just the demand gap. It is the demand disturbance relative to the inflationary reference implied by the firm’s longer-run belief. A current condition can therefore look more or less exceptional depending on what the firm has come to regard as normal.
The unit-root demand case makes this especially clear. The model combines the demand disturbance with the trend-inflation term into a single state: the distance between current demand pressure and the firm’s trend-adjusted reference point. When that distance is small, a short-horizon price is already close to the price chosen with more information about the future. The marginal benefit of looking farther ahead is low. When the distance is large, the short plan omits consequences that matter, and the firm has more reason to extend its horizon.
This is a different kind of state dependence from simply saying that “high inflation makes firms more attentive.” The model does not make the level of inflation a universal trigger. It asks whether the current disturbance is sufficiently far from the belief-based reference point that another period of planning would change the desired price. The same observed demand movement can therefore produce different horizon choices at different points in the belief cycle.
A moving reference point can also break the symmetry between positive and negative disturbances. Suppose trend inflation is positive and demand is stationary. A positive demand disturbance may be partly consistent with the firm’s existing inflationary reference. It does not move the desired price as far away from what the continuation value already represents. A negative disturbance of the same absolute size may instead pull current conditions away from that reference. The marginal value of extending the horizon can consequently be larger for the negative disturbance.
The reference point is not an extra shock layered on top of demand. It changes the benchmark used to judge whether the next period is consequential. If firms have learned to expect a higher trend of inflation, a positive current pressure may look less like a departure from normal and more like a continuation of what they already anticipate. A negative pressure can then create the larger mismatch, even though its absolute size is the same. The model’s asymmetry is thus about the interaction between a current disturbance and accumulated beliefs.
This asymmetry belongs to the model’s planning decision. It should not be confused with the separate empirical finding that Italian firms pass input-cost increases through to prices more strongly than decreases. Both involve unequal responses, but their sources differ. In the model, the asymmetry arises because a moving trend belief changes the reference point against which demand is evaluated. In the survey evidence, the asymmetry is estimated in the pass-through from positive and negative input-price surprises and is discussed through mechanisms such as pricing power, adjustment incentives, and financial constraints.
Learning is what allows the reference point to move. After the firm observes the state and makes its pricing decision, it forms a new estimate of the continuation value associated with the horizon it actually selected. It then averages this experience with its previous continuation value. A larger weight on recent experience makes the reference adapt more quickly; a smaller weight preserves more of the accumulated past. In the model, this update appears as a trend-inflation state that is an exponentially weighted average of realized inflation.
The consequence is a feedback across dates. A persistent shock can raise current inflation. Higher realized inflation changes the firm’s longer-run reference. A later shock is then evaluated against that updated reference rather than against the original steady state. The reference can make a subsequent disturbance look less exceptional in one direction and more exceptional in another. Planning distance is therefore not only a response to the current shock; it is also shaped by the history of inflation that the firm carries into the decision.
The threshold logic remains useful, but its interpretation must be precise. In the simplified cases, the marginal benefit of extending the horizon is weakly decreasing with k. If the benefit has fallen below the incremental cost at one horizon, it will not become worthwhile at a later one. The first stop is then the unique selected global solution, subject to the model’s tie-breaking convention. The firm can decide sequentially without surveying every possible horizon.
That monotonicity need not survive when several disturbances enter at once. Consider a positive demand disturbance and a negative supply disturbance with different persistence. At a short horizon, the two components may offset one another in the change between the k-horizon and k+1-horizon prices. The marginal benefit of extending the plan can initially be small. If the supply component fades more quickly than the demand component, the offset can disappear at a longer horizon, making the next extension valuable again.
The timing of the offset is the crucial detail. At the first comparison, the firm sees a combined future in which one force partly cancels the other. At a later comparison, the faster-fading force has contributed less, while the persistent force still affects the price that will be in place. The value of another period can therefore be low, then higher, without any change in the firm’s cognitive cost. A one-dimensional rule based only on the size of the current disturbance would miss this interaction.
In that situation, the first crossing of benefit and cost is not necessarily the horizon a firm would choose after a costly global search over all possible lengths. The model deliberately does not replace the sequential rule with such a search. A global comparison would require the firm to evaluate many candidate horizons, which is itself an additional cognitive burden. The one-stage rule is consequently interpreted as a bounded-rational or myopic planning procedure in the general case. It remains well defined, but it no longer carries the stronger claim of global optimality.
This distinction matters for reading the model’s predictions. A longer horizon is not always the result of a larger shock in a simple one-dimensional sense. It can reflect a large mismatch, a persistent component that has not yet faded, or the way multiple shocks combine at different horizons. Conversely, a firm may stop early even in a volatile environment if the current combination of disturbances leaves its short-horizon price close to its expanded-horizon price.
It also explains why “more planning” should not be treated as a synonym for “better outcomes.” A longer horizon can improve the firm’s private pricing decision by incorporating consequences that a short plan omits, but it also raises the sensitivity of the price to the shocks being projected. At the aggregate level, that can increase inflation volatility rather than reduce it. The model is describing an adaptation to a more consequential future, not promising that the adaptation makes the economy calmer.
The durable conclusion is therefore a conditional one. The value of looking ahead rises when future contingencies can materially change today’s price, and that value depends on the size and persistence of shocks relative to learned beliefs. In the clean cases, this produces transparent thresholds. With learning, it produces a moving and potentially asymmetric reference point. With multiple disturbances, it can make the sequential decision intentionally myopic. The horizon is a state variable, not a fixed personality trait of the firm. The next question is what happens to inflation once that state variable changes the way firms load current shocks into their prices.