The rate of unemployment when the economy is in equilibrium.
The baseline inflation rate anticipated by the public.
Responsiveness of inflation to the unemployment gap (typically 0.1 to 1.0).
Unemployment Gap
0.00%
Inflation Impact
0.00%
Estimated Inflation Rate
0.00%
function calculateInflation() {
// Get input values
var u = parseFloat(document.getElementById('currentUnemployment').value);
var un = parseFloat(document.getElementById('naturalRate').value);
var pieE = parseFloat(document.getElementById('expectedInflation').value);
var beta = parseFloat(document.getElementById('slopeBeta').value);
// Validation
if (isNaN(u) || isNaN(un) || isNaN(pieE) || isNaN(beta)) {
alert("Please enter valid numbers for all fields.");
return;
}
// Logic based on Short-Run Phillips Curve: Inflation = Expected Inflation – Beta(Unemployment – Natural Rate)
// Formula: π = πe – β(u – un)
var unemploymentGap = u – un;
var inflationImpact = beta * unemploymentGap; // How much inflation is reduced/increased by the gap
var estimatedInflation = pieE – inflationImpact;
// Display results
var resultBox = document.getElementById('resultBox');
resultBox.style.display = 'block';
// Format and set text
document.getElementById('resGap').innerHTML = unemploymentGap.toFixed(2) + "%";
document.getElementById('resImpact').innerHTML = (inflationImpact > 0 ? "-" : "+") + Math.abs(inflationImpact).toFixed(2) + "%";
var inflEl = document.getElementById('resInflation');
inflEl.innerHTML = estimatedInflation.toFixed(2) + "%";
// Color coding for visual feedback
if (estimatedInflation > pieE) {
inflEl.className = 'result-value positive-val';
} else if (estimatedInflation < pieE) {
inflEl.className = 'result-value negative-val';
} else {
inflEl.className = 'result-value';
}
// Explanation text
var explanationText = "";
if (u un) {
explanationText = "Because the current unemployment rate (" + u + "%) is higher than the natural rate (" + un + "%), there is slack in the economy, putting downward pressure on inflation.";
} else {
explanationText = "The economy is at full employment. Inflation remains at the expected rate.";
}
document.getElementById('resExplanation').innerHTML = explanationText;
}
Understanding the Relationship Between Inflation and Unemployment
Calculating the inflation rate from the unemployment rate relies on an economic model known as the Phillips Curve. This macroeconomic concept suggests an inverse relationship between rates of unemployment and corresponding rates of inflation. When unemployment is low, inflation tends to rise, and when unemployment is high, inflation tends to fall.
The Short-Run Phillips Curve Formula
This calculator uses the standard expectations-augmented Phillips Curve equation to estimate the current inflation rate. The mathematical formula is defined as:
π = πₑ – β(u – uₙ)
Where:
π (Pi): The Estimated Inflation Rate.
πₑ (Pi expected): The Expected Inflation Rate (often based on recent history or central bank targets).
β (Beta): The slope coefficient, representing how sensitive inflation is to changes in unemployment.
u: The Current Unemployment Rate.
uₙ: The Natural Rate of Unemployment (NAIRU).
Definitions of Key Inputs
To use the calculator effectively, it helps to understand the economic variables involved:
Current Unemployment Rate: The percentage of the labor force that is jobless and actively looking for work.
Natural Rate of Unemployment (NAIRU): This is the specific level of unemployment that is evident in an economy that does not cause inflation to rise up. It represents the "full employment" level, accounting for structural and frictional unemployment. In the US, this is often estimated between 4% and 5%.
Expected Inflation Rate: Inflation expectations are crucial because workers and firms set wages and prices based on what they think inflation will be in the future.
Slope Parameter (Beta): This variable determines the magnitude of the trade-off. A steeper slope (higher Beta) means that a small drop in unemployment leads to a large spike in inflation.
How the Calculation Works
The logic follows the concept of the Unemployment Gap. The gap is the difference between the actual unemployment rate and the natural rate (u – uₙ).
Negative Gap (Overheating Economy): If current unemployment (e.g., 3%) is lower than the natural rate (e.g., 4.5%), the gap is negative (-1.5%). The formula subtracts a negative number, effectively adding to the expected inflation. This indicates that labor markets are tight, forcing wages and prices up.
Positive Gap (Slack Economy): If current unemployment (e.g., 6%) is higher than the natural rate (e.g., 4.5%), the gap is positive (1.5%). The formula subtracts this value from expected inflation. This indicates low demand and downward pressure on prices.
In this scenario, because unemployment is lower than the natural rate, the estimated inflation rises to 2.5%, exceeding the expected rate of 2.0%.
Limitations of the Model
While the Phillips Curve is a fundamental tool in macroeconomics, it is not without flaws. The relationship can break down due to Supply Shocks (like a sudden increase in oil prices), which can cause Stagflation—a situation where both inflation and unemployment are high simultaneously. Additionally, in the long run, the Phillips Curve is generally considered to be vertical, meaning unemployment essentially returns to its natural rate regardless of inflation levels.