Nominal Rigidities and the Phillips Curve

Why don’t prices change every second, like stock prices? If you’ve ever noticed that the price of a cup of coffee stays the same for months, you’ve already spotted a big puzzle in macroeconomics. This chapter explores why prices adjust slowly, how that stickiness shapes inflation, and the modern Phillips curve that ties it all together.

The Big Picture#

A central bank that wants to keep inflation low and stable needs to understand how the real economy and prices are linked. The Phillips curve—the idea that inflation tends to rise when the economy is running hot and fall when it is weak—gives us that link. But first we must answer a deeper question: why don’t firms instantly change their prices whenever costs or demand shift? The answer lies in nominal rigidities, the frictions that make prices sticky. By the end of this chapter, you’ll see how tiny costs of changing prices, the way firms schedule their price reviews, and the slow spread of information all combine to produce the inflation patterns we observe.

Why Prices Are Sticky: Evidence and Menu Costs#

Look closely at the prices around you. A grocery store might leave the price of milk unchanged for a few months, then raise it by a few cents. A hairdresser posts a new price list maybe once a year. Studies that track individual prices across thousands of products find that a typical price lasts between four months and a year before it changes. That is a long time when you think about how often costs—wages, raw materials, energy—bounce around. This sluggishness is what economists call nominal rigidity: the dollar price of a good does not adjust smoothly to keep supply and demand in balance.

Why would a firm wait so long? The simplest answer is the menu cost. Imagine you run a restaurant. Changing prices means printing new menus, updating the website, maybe even explaining to annoyed customers why the burger now costs more. Those costs are small, but they are real. You won’t reprint menus every morning just because the price of beef nudged up by a penny. You wait until the gap between your current price and the price you would like to charge becomes large enough to justify the hassle.

This story, however, hides a deeper insight. Even tiny menu costs can make prices a lot stickier than is good for the economy. The reason: when a firm lowers its price a little, the benefit to society—more output, more jobs—is much bigger than the extra profit the firm gets. Most of the gain goes to customers and other businesses. So a firm weighs its own gain from changing the price against the menu cost, but it ignores the wider benefits to everyone else. As a result, prices stay fixed longer than they should for the economy as a whole. This is what we mean by socially inefficient price adjustment: the economy would be better off if prices moved more often, but no single firm has a strong enough reason to go first. It is a classic coordination problem.

Menu cost: Any cost a firm incurs when it changes its listed price—printing, advertising, managerial time, or even customer irritation.

Nominal rigidity: The tendency of a price (or wage) set in money terms to resist change, even when economic conditions shift.

📝 Section Recap: Micro data show prices change roughly every 4–12 months. Even small menu costs can cause sticky prices because firms ignore the large social benefits of price adjustment, leading to an inefficiently slow response to economic shocks.

How Firms Set Prices: Time‑Dependent and State‑Dependent Models#

To build a workable theory of inflation, we need a model of how firms decide when to adjust prices. Two broad families of models have been developed: time‑dependent pricing and state‑dependent pricing.

Time‑Dependent Pricing: The Calvo Model#

The most widely used framework in macroeconomics is the Calvo model. It is beautifully simple. Imagine that each period—say, each quarter—every firm faces a random draw. With probability , the firm gets a “green light” and can set its price to whatever it wants. With probability , it gets a “red light” and must keep its old price (though later we may add an automatic adjustment rule). The chance of getting a green light does not depend on how long the firm has waited or how far its current price is from what it would ideally charge. It is purely a roll of the dice.

This assumption makes the model very easy to work with. Because the probability is constant, the average length of time a price stays in place is periods. If , for example, prices last four quarters on average—roughly matching the micro evidence.

When a firm does win the right to reset, it chooses a price that maximises its expected profits over the time its price might remain stuck. It looks ahead, weighing the fact that the price it sets today may still be in place several quarters later. This forward‑looking behaviour is at the heart of the New Keynesian Phillips curve we’ll derive shortly.

Calvo pricing: A time‑dependent model in which a firm can adjust its price with a fixed probability each period, independent of how long it has been since the last adjustment.

State‑Dependent Pricing: The Golosov–Lucas Model#

An alternative approach says firms do not simply roll dice; they adjust when the state of their business demands it. In the Golosov–Lucas model, each firm faces a menu cost that it must pay every time it changes its price. The firm watches the gap between its actual price and the price that would be best if it could adjust freely. When the gap grows large enough—when the profit loss from keeping the old price outweighs the menu cost—the firm pays the cost and resets. Between adjustments, the price stays fixed.

The result is an (S,s) policy: there is a band within which the firm does nothing. The firm lets its price drift relative to the ideal until it hits an upper or lower trigger, then it jumps back to a target. At any moment, many firms are inside their bands, so overall prices still move slowly. But large shocks can push many firms to the edge of their bands at once, causing a wave of price changes. This state‑dependent behaviour captures the idea that price stickiness is not a fixed mechanical delay; it responds to how big the shocks are.

Golosov–Lucas model: A state‑dependent pricing model where firms incur a fixed menu cost to change prices and adjust only when the gap between the current and desired price becomes large enough.

📝 Section Recap: Time‑dependent models like Calvo assume a random chance to adjust, making them simple and tractable. State‑dependent models like Golosov–Lucas tie the decision to the economic state, producing richer dynamics where the frequency of price changes varies with the size of shocks.

The New Keynesian Phillips Curve#

We can now build the modern Phillips curve from the Calvo model. The result is the New Keynesian Phillips curve (NKPC), a central equation in monetary policy analysis.

Suppose a firm that resets its price in period chooses . It wants to set a price that stays close, on average, to the nominal marginal cost of production over the life of that price. Because the firm discounts future profits by a factor and knows that its price will survive to period with probability , the optimal reset price satisfies (in log‑linearised form around a zero‑inflation steady state):

where is real marginal cost at time and is the aggregate price level. The firm cares about future nominal marginal cost (real marginal cost plus the price level) because that determines the profit margin.

The aggregate price level today is a mixture of the prices that were reset today and the prices that remain from the past. With a fraction of firms resetting, the price level evolves as:

Subtracting from both sides gives inflation . After working through the math, we obtain the NKPC:

where is a positive parameter that captures the sensitivity of inflation to real marginal cost. The smaller (i.e., the more frequently prices adjust), the larger , and the more inflation responds to current cost pressures.

Often, we link real marginal cost to the output gap—the difference between actual output and its natural (flexible‑price) level. Using , we get the more familiar form:

The striking feature of this Phillips curve is that inflation today depends on expected future inflation and the current output gap. There is no direct role for past inflation. This pure forward‑looking nature implies that a credible central bank could, in theory, bring down inflation without any output cost—if it could instantly shift expectations. Real‑world inflation, however, tends to keep moving in the same direction for a while, a fact we will address shortly.

New Keynesian Phillips curve: A relationship derived from optimising firms with sticky prices, stating that current inflation is driven by expected future inflation and a measure of real economic activity (such as the output gap or real marginal cost).

📝 Section Recap: The NKPC emerges from Calvo pricing: firms that can adjust set prices looking forward, so inflation depends on expected future inflation and current marginal cost. The slope is larger when prices adjust more frequently.

Sticky Information and the Phillips Curve#

The NKPC assumes that firms always keep their information up to date and form smart forecasts. But what if information itself updates slowly? The sticky information Phillips curve (SIPC) gives another way to think about it.

In this model, prices are flexible—firms can change them at any time—but they base their decisions on outdated information. Each period, only a fraction of firms update their knowledge about the economy; the rest continue to set prices using forecasts they made in the past. For example, a firm that last updated its information in period sets its price equal to what it thought back then the optimal price would be: .

Aggregating across firms, inflation in the SIPC depends on the output gap and on past expectations of current inflation. The resulting equation is:

where is the fraction of firms that update information each period. The big contrast with the NKPC is that inflation takes time to react to shocks, because many firms are still acting on old forecasts. This model naturally produces the delayed, hump‑shaped responses to monetary policy that we often see in the data, without needing to add backward‑looking behaviour artificially.

Sticky information: The idea that information about macroeconomic conditions spreads slowly through the population of price‑setters, so many firms set prices based on outdated forecasts.

📝 Section Recap: When information spreads slowly, even flexible prices can produce sluggish inflation. The sticky information Phillips curve explains delayed reactions to policy because many firms rely on old forecasts.

Why Inflation Is Persistent: Habits and Indexation#

The baseline NKPC has a problem: it says inflation should jump immediately when expectations change. If a central bank tightens policy today, inflation should fall right away, as long as expectations adjust. Yet real‑world inflation is persistent—it tends to keep moving in the same direction for several quarters. Two popular extensions fix this.

Habit Formation#

When households have consumption habits, their well‑being depends not only on how much they consume today, but also on how that compares with yesterday’s consumption. This makes them reluctant to change consumption quickly. Because firms’ real marginal cost depends on the path of consumption, habit formation makes those costs adjust slowly. So when a shock hits, marginal cost changes only gradually, and through the NKPC, inflation does too. In effect, the output gap term in the Phillips curve picks up a backward‑looking piece, giving inflation inertia without changing the forward‑looking basis of price setting.

Price Indexation#

A more direct route to persistence is to change the Calvo model so that firms that cannot reoptimise do not simply keep their price fixed; instead, they automatically tie it to past inflation. For example, a firm that last reset its price six months ago might increase it by the inflation rate that prevailed over that period. This price indexation means that even when a firm is stuck with an old price, that price still creeps up with the general trend.

When we add indexation to the Calvo model, the Phillips curve becomes a hybrid NKPC:

where captures the degree of indexation to past inflation. Now inflation depends on its own past as well as its expected future. This simple modification brings the model much closer to the data, where inflation tends to be slow and persistent.

Habit formation: The idea that people care about consumption relative to their own past consumption, making spending and therefore marginal cost adjust gradually.

Price indexation: A rule by which firms that cannot reoptimise their price automatically increase it by a fraction of past inflation, building inertia directly into the price level.

📝 Section Recap: Pure forward‑looking models lack inflation persistence. Habit formation makes marginal cost sluggish, while price indexation gives the Phillips curve an explicit backward‑looking term, producing the hybrid NKPC that matches the observed inertia in inflation.

Summary#

We started with a simple observation: prices don’t change every day. That stickiness, caused by menu costs and slow information flow, is the foundation of the Phillips curve. The Calvo model gave us a clean framework where only a random group of firms can adjust each period, leading to the New Keynesian Phillips curve. In that curve, inflation depends on expected future inflation and current economic slack. Other views, like state‑dependent pricing and sticky information, add more depth and help explain why inflation takes time to react to shocks. Finally, adding habits and indexation builds in the persistence we see in the data, giving us a hybrid Phillips curve that looks both forward and backward. Understanding these mechanisms is key to grasping how central banks steer the economy.