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Producer Price Indexes

## PPI Modifies Hedonic Quality Adjustment for Microprocessors

Effective with the release of Producer Price Index (PPI) data for January 2024 on February 16th, 2024, the Bureau of Labor Statistics began adding a bias adjustment term to the hedonic estimation of quality adjusted prices for desktop, notebook, and server microprocessors within the PPI indexes for integrated microcircuits:

Hedonics, like the time dummy models used to estimate prices for PPI desktop, notebook, and server microprocessor items, that implicitly use predicted price levels that are exponentiated predictions of log prices, require a bias adjustment term. Specifically, the need for a bias adjustment term occurs when prices in levels are converted to logs, price relatives are calculated, and the results are exponentiated back to levels. The results are typically different than if price relatives are formed directly from prices in levels.

In order to mitigate this issue, the PPI is introducing a bias adjustment term into the calculation formula utilized to estimate quality adjusted prices for microprocessors. The calculations associated with this change are noted below:

The time dummy hedonic model is shown in equation 1.

Equation 1

Log Priceit=A0+∆dT+1+B2 (Log X2i)+B3 (Log X3i)+⋯+Bki (Log Xki)+Mit

• Log Priceit is the Log price of the ith product in period t
• A0 is the intercept
• Log Xi are the logged variables representing product characteristics
• dT+1 is the indicator for period 2
• Δ is the time dummy coefficient
• B2⋯Bk are the regression/slope coefficients
• Mit is the residual or error term

The first step to calculate the bias adjustment term is to take the mean of the summation of exponentiated residuals.

Equation 2

τt=Nt-1ΣNti=1eMit

Nt is the number of products in a time period. The bias adjustment term is given by equation 3.

Equation 3

τ2⁄τ1

Previously, the microprocessors models estimate quality adjusted price change with equation 4.

Equation 4

(eΔ—1)

With the addition of the bias adjustment term, the microprocessors models estimate quality adjusted price change with equation 5.

Equation 5

(eΔ✱τ2⁄τ1)—1

For further information on the use of hedonics for quality adjustment in the PPI, contact Steven Sawyer at sawyer.steven@bls.gov or (202) 691-7845.