# Producer Price Index

Producer price index (PPI) is a measure of average prices received by producers of domestically produced goods and services. It is calculated by dividing the current prices received by the sellers of a representative basket of goods by their prices in some base year multiplied by 100.

Government agencies such as US Bureau of Labor Statistics, collect data for a range of goods and services at different data points and create different variants of the producer price indices. BLS creates more than 10,000 producer price indices for individual goods and services which cover virtually all industries. They are summarized into three different structures: (a) index of final and intermediate demand, (b) index of commodity prices and (b) index of net output of industries and their products based on the NAICS industry classification.

## PPI vs CPI

Producer Price Index summarizes price level from the perspective of sellers while the Consumer Price Index (CPI) summarizes prices from the perspective of buyers. PPI is considered a good economic indicator because it provides early information about consumer demand and consumption. This is because prices received by producers are an indication of the demand that exist at retail level.

Despite the PPI’s ability to foretell the consumer demand and spending level, there are reasons that may cause PPI and CPI to diverge. First, PPI excludes imports while CPI includes imports. Further, PPI includes prices regardless whether they are paid for the consumers or not while CPI includes only such prices which are paid by the consumer directly.

## Formula

PPI equals the ratio of current price of the representative basket divided by the base price of the basket:

$$PPI=\frac{current\ price\ of\ basket}{base\ price\ of\ basket}$$

The basket can be defined based on the relative weights at the current time or the base year or even some other year.

The PPI formula that weighs goods in proportion of their quantities in the base year is called the Laspeyres index and is the most common definition used:

$$PPI\ (Laspeyres)=\frac{\sum{q_0\times p_t}}{\sum{q_0\times p_0}}\times100$$

An index in which the prices are weighted based on current year quantities is called the Paasche index and its formula is:

$$PPI\ (Paasche)=\frac{\sum{q_t\times p_t}}{\sum{q_t\times p_0}}\times100$$

Where q0 is the quantity in the base period, qt is the quantity in current period, pt is the current price of the product and p0 is the price of the product in the base year, the year when the index started or the year which was set as a new reference. The reference currently used by BLS is 1982.

Another formula, called the Fisher formula/index, calculates PPI as the geometric mean of the Laspeyres and Paasche indices:

$$PPI\ (Fisher)\\=\sqrt{Laspeyres\ Index\times Paasche\ Index}\\=\sqrt{\frac{\sum{q_0\times p_t}}{\sum{q_0\times p_0}}\times100\times\ \frac{\sum{q_t\times p_t}}{\sum{q_t\times p_0}}\times100}$$

BLS uses the modified Laspeyres formula to calculate PPI.

## Example

Calculate the PPI values for 2017 given the following data using the Laspeyres, Paasche and Fisher formulas:

Quantity in 2007 Quantity in 2017 Price in 2007 Price in 2017
20 18 10 12
40 43 15 17
25 26 20 25

2007 is the base year.

The Laspeyres formula uses the quantities in base year to work out PPI:

$$PPI\ (Laspeyres)\\=\frac{20\times12+40\times17+25\times25}{20\times10+40\times15+25\times20}\times100\\=118.85$$

The Paasche formula uses the quantities in the most recent year:

$$PPI\ (Paasche)\\=\frac{18\times12+43\times17+26\times25}{18\times10+43\times15+26\times20}\times100\\=118.74$$

The Fisher formula is the weighted average of the above indices:

$$PPI\ (Fisher)\\=\sqrt{118.85\times118.74}\\=118.79$$