Economics: Price Level, Inflation, and Index Calculations

Price Level

A summary measure of the average price of a representative basket of goods and services in the economy, reported as an index relative to a base year.

Purchasing Power of Money

Purchasing Power = 1 ÷ Price Level (after you put both on compatible scales).

Effect of Rising Price Level on Purchasing Power

It falls—mechanically and inversely.

Inflation

Prices rising.

Deflation

Prices falling.

Disinflation

Inflation rate is falling (prices still rise, just more slowly).

Index Value of 130

The basket is 30% more expensive than in the base year.

Effect of Changing Base Year on Inflation Rates

No. Rebasing rescales levels but leaves growth rates unchanged.

CPI

Prices faced by consumers for a defined consumption basket; it's oriented to household out-of-pocket spending.

Preference for PCEPI over CPI

PCEPI has broader coverage, chain weights that update over time, and integrates with national accounts—useful for coherent macro policy.

GDP Deflator's Scope

Prices of all domestically produced final goods and services (includes investment and government purchases, excludes imports).

Comparison of CPI and GDP Deflator

Not cleanly—CPI is consumer-focused; the deflator covers all domestic final output.

Index for Cost-of-Living Adjustments

Typically CPI, because it aligns with household out-of-pocket costs.

Index to Deflate Nominal GDP to Real GDP

The GDP deflator.

Substitution Bias in Fixed-Weight Indices

When relative prices change, consumers substitute toward cheaper goods; fixed weights miss this, tending to overstate inflation.

Chain-Weighting

It updates weights over time (e.g., chain Fisher or chain Laspeyres/Paasche blends), better capturing shifting expenditure patterns.

Hedonic Adjustment

A method to isolate pure price changes from quality differences in products (e.g., better camera in a phone) by modeling value of attributes.

PCE Inflation vs. CPI

Broader coverage, different weights (including third-party medical payments), and chain methods typically imply slightly lower measured inflation.

Imports in GDP Deflator

No. They are not domestically produced; import price changes affect consumers but not the deflator directly.

Core Inflation

These components are volatile; core aims to track underlying, persistent inflation pressure.

Simple Inflation Formula

(P1−P0)/P0.

Continuously-Compounded Annual Rate (CCAR)

When intervals differ in length or when you want clean annualization: π=[ln(Pt)−ln(Pj)]/n, where n is years.

Year-over-Year (YoY) Inflation Calculation

(206−200)/200=0.03=3.0%.

Monthly increase of 0.6%

Annualized simple rate is approximately 7.44%.

CCAR for index rise from 100 to 105 over two years

Calculated as ln(105/100)/2 which is approximately 2.44% per year.

CCAR for index move from 110 to 112 in three months

Calculated as ln(112/110)/(3/12) which is approximately 7.21% per year.

Net change for two months: −0.3% then +0.2%

Result is approximately −0.1006% (about −0.10%).

Rebasing an index

Divide every value by the index in the new base year, then multiply by 100.

2025 purchasing power relative to 2000 when rebased index is 160

Calculated as 100/160 which equals 62.5% of 2000's purchasing power.

Labeling base years when comparing indices

Without a common base, index levels aren't directly comparable.

Approximate real wage growth with nominal wage up 4% and CPI up 3%

Roughly 1%. Exact calculation gives approximately 0.97%.

Real rate when nominal interest is 5% and expected inflation is 3%

Calculated as (1.05/1.03)−1 which is approximately 1.94%.

Difference in revisions between CPI and PCE

PCE revises with national accounts; CPI revisions are more limited.

Why inflation may not equal cost of living for every household

Households have different baskets and weights; aggregate index can't match each household's consumption patterns.

Disinflation and purchasing power

Disinflation slows the loss of purchasing power; purchasing power rises only if the price level falls or nominal income outpaces inflation.

Producer Price Index (PPI) as a consumer cost measure

PPI tracks prices received by domestic producers; it's not a direct consumer out-of-pocket measure.

Log differences for growth decomposition

They are additive over time and across components, making analysis cleaner.

Comparing headline CPI to core PCE without disclosure

Risks misinterpretation due to different scopes and exclusions.

Fastest way to convert nominal series to real terms

Divide by the relevant price index, e.g., Real = Nominal ÷ (Deflator/100).

GDP deflator excluding import prices

The deflator covers domestic production; CPI covers consumer purchases, including imports.

Better tool for international price level comparisons than raw CPI levels

Purchasing Power Parity (PPP) or harmonized indices designed for cross-country comparability.

Definition of rebasing

Rebasing resets the index's reference period to 100 by rescaling every observation relative to the new base period.

Annualized simple rate from a monthly increase of 0.6%

Approximately 7.44%.

CCAR calculation for index changes

ln(new index/old index)/number of years.

Net change calculation for consecutive percentage changes

Multiply the factors: (1 + first change) * (1 + second change).