# Phillips Curve Calculator

By applying the **Phillips curve calculator**, you can study the **relationship between inflation and other Phillips curve model variables**. Since the Phillips curve went through considerable development due to the continuous development of macroeconomic theories, we included the following **three versions of the Philips curve** in the Phillips curve equation calculator :

**Traditional**Phillips curve;**New classical**Phillips curve; and**New Keynesian**Phillips curve (NKPC).

Each of these options reflects a different theoretical economic background. Read further and learn the **Phillips curve definition** and the *difference between the short-run and long-run Phillips curve* in economics. We also show you the *short-run Phillips curve graph* and explain what the *expectations augmented Phillips curve* is.

## What is Phillips curve?

The concept of the Phillips curve comes from a famous 1958 paper by the New Zealand–born economist A. **William Phillips**. Studying the historical data for Britain, he found that **when the unemployment rate was high**, the **wage rate was falling**, and when the unemployment rate was low, the wage rate was rising.

Other economists soon found a similar **relationship between the unemployment rate and inflation** in other industrialized economies. The conclusion became clear: there is a **negative short-run relationship between the unemployment rate and the inflation rate**, which can be plotted as a **short-run Phillips curve**.

This **short-term trade-off between unemployment and inflation** is represented in the below **short-run Phillips curve graph**: lower unemployment leads to higher inflation, and vice versa.

## What is the traditional Phillips curve?

The **initial form of Phillips curve, à la Phillips,** describes the empirical phenomena where the **unemployment rate drives the growth rate of money wages**. Therefore, this basic Phillips curve shows the relationship between money wages and the unemployment rate.

The **traditional Phillips curve** is the simplest one we included in the Phillips curve calculator, and is its original form outlined by Phillips himself.

This Phillips curve equation says that **the rate of growth of the money wage rate** depends on the trend rate of growth of money wages and **the unemployment rate**. This can be written in the following form:

where:

- The operator $g$ -
*The percentage rate of growth*of the variable that follows; - $W$ -
*Money wage rate*representing the total money wage costs per production employee including benefits and payroll taxes; - $W^T$ -
*Trend rate of growth of money wages*; and - $f(U)$ -
*Unemployment rate*in a given function.

In other words, periods of above-average inflation tend to be associated with above-trend economic activity (i.e. higher than expected GDP growth rate), for example, as measured by a relatively low unemployment rate.

## The New Classical Phillips curve equation

Parallel with the progression of economic theories, economists became more interested in finding **theoretical foundation for the Phillips curve equation**. It led to the appearance of the **New Classical Phillips curve**, which is **derived from a classical economic model** following simple economic principles.

More precisely, it is the *Lucas aggregate supply function* augmented by the concept of the *natural rate of unemployment* (or NAIRU) and the *Okun's law* which drives to the final form of the New Classical Phillips curve that we use in the Phillips curve calculator:

where:

- $b$ - Positive constant;
- $U$ - Unemployment rate;
- $U_n$ - Natural rate of unemployment, or NAIRU; and
- $v$ - Unexpected exogenous supply shocks.

## The New Keynesian Phillips curve model (NKPC) in the Phillips curve calculator

The **New Keynesian Phillips curve (NKPC)**, firstly introduced in 1995, constitutes one of the key building blocks for the *New Keynesian general equilibrium model*. Due to the high complexity of the model and the limited space here, we'll introduce only its main features and parameters. If you'd like a deeper insight into this topic, feel free to take a look at the article titled The New Keynesian Phillips Curve: Lessons

From Single-Equation Econometric Estimation. You can also use our Phillips curve calculator without fully understanding the math behind it!

The **NKPC** is a structural **model of inflation dynamics** where one of the key driving factors is *price stickiness*, the parameter that **governs the passthrough of marginal costs into inflation**. In other words, the NKPC model takes into consideration the fact that firms do not update the prices of their products constantly and uniformly; instead, they keep their prices fixed over a specific interval. Therefore, prices do not reflect the actual condition of the economy immediately. The average price duration provides a measure for the degree of price stickiness. The higher the parameter (*the stickier the prices*), the more limited the transition of marginal costs into inflation, making the *Phillips curve flatter*.

The Phillips curve equation calculator uses the following sets of equations to describe the New Keynesian Phillips curve model:

where:

- $\pi_{t+1}$ - Inflation rate at period $t+1$;
- $Eₜ{πₜ₊₁}$ - Inflation expectation at period $t$;
- $\tilde{y}_t$ - Output gap: the difference between the actual output and its potential level at period $t$;
- $\beta$ - Households’ discount factor (the default value of 0.99 implies a steady state real return on financial assets of about 4 percent);
- $\theta$ - Price stickiness: this parameter represents the average time over which prices are kept fixed (the default value of 0.75 implies an average price duration of four quarters);
- $\sigma$ - Utility of consumption: intertemporal elasticity of substitution;
- $\varphi$ - Disutility of labor: the inverse labor supply elasticity (the default value of 5 implies a Frisch elasticity of labor supply of 0.2);
- $\alpha$ - Labor supply elasticity;
- $\epsilon$ - Demand elasticity: a measure of the change in the quantity of a product purchased in relation to a change in its price (the default value of 9 implies a steady state markup value of a 12.5 percent);
- $\bar y_t$ - Potential output: a hypothetical level of output associated with flexible prices in the economy at period $t$; and
- $y_t$ - Actual output or GDP at period $t$.

## FAQ

### What is the Phillips curve definition?

The **Phillips curve represents the inverse relationship between inflation and unemployment**.

In its modern form, it is a relationship between inflation, cyclical unemployment, expected inflation, and supply shocks, derived from the short-run aggregate supply curve.

### What is the difference between NAIRU and natural rate of unemployment?

The **natural rate of unemployment corresponds to the number of unemployed people due to structural issues** in the labor market caused by **new technology or lack of skills required** to gain employment.

**NAIRU** (*non-accelerating inflation rate of unemployment*) is the particular **level of unemployment associated with** an economic condition resulting in **stable inflation**.

### Does Phillips curve take inflation into account?

While multiple versions of the Phillips curve exist, they all have one common point: they **all take inflation into account**.

However, they might not include inflation in the same way during the calculation procedure.

### What is the difference between the short-run and long-run Philips curves?

The Phillips curve shows the relationship between inflation and unemployment. While **inflation and unemployment are inversely related in the short run**, there is **no trade-off in the long run**.

### What are the possible Philipps curves in economics?

There are three common forms of Phillips curves in economics:

**Traditional**Phillips curve, which is the original form where unemployment rate drives the growth rate of money wages;**New classical**Phillips curve, which follows economic principles based on the classical theoretical model; and**New Keynesian**Phillips curve (NKPC), which is the key building block for the most advanced New Keynesian general equilibrium models.