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Producer Price Indexes

## PPI Introduces Hedonic Price Estimation for Notebook Microprocessors

Effective with the release of Producer Price Index (PPI) data for July 2018 on August 9, 2018, the Bureau of Labor Statistics began using hedonic modeling to estimate quality adjusted prices for notebook microprocessor items within the PPI indexes for integrated microcircuits:

Notebook microprocessors are subject to rapid technological change. This makes it difficult to perform quality adjustment, which requires distinguishing price changes arising from changes in microprocessor quality from price changes resulting from other factors. The following characteristics are the main measures of quality for microprocessors. PPI collects information pertaining to these measures from publicly available sources:

• Cores
• Base frequency
• Turbo frequency
• Cache1
• Thermal design power (TDP)
• Integrated graphics

Beginning with this release, PPI is using a two-period time dummy hedonic model to measure quality-adjusted price change for notebook microprocessor items in the integrated microcircuits indexes. The basic regression formula is shown in Equation 1, and the results for July 2018 are shown in Table 1.

### Equation 1

Log Priceit = Α0 + ΔdΤ+1 + Β2 (Log X2i) + Β3 (Log X3i) + … + Βk (Log Xki) + Μit

Where:
• Log Priceit  is the Log price of the ith product in period t
• Α0  is the intercept
• Log Xi  are the logged variables representing product characteristics
• dΤ+1 is the indicator for period two
• Δ is the time dummy coefficient
• Β2 … Βk  are the regression/slope coefficients
• Μit  is the residual or error term

The two periods in the model are adjacent quarters. The time dummy coefficient gives an estimate of price change between the two quarters when the variables representing product characteristics have been controlled for. The product characteristics that may be included in the model are those listed above. Cache is divided by the number of cores in the microprocessor. The PassMark2 benchmark is also included in the model.

The choice of regressors affects the time dummy coefficient estimate. PPI turned to statistical learning to evaluate objectively the performance of different model specifications. Specifically, PPI used repeated cross-validation to calculate the mean squared error (MSE) for different model specifications. The MSE is calculated by using a model to predict the prices of observations and then finding the differences between the predictions and the actual prices. PPI selected the model with the lowest MSE because the lower the MSE, the better predictive performance of the model. Please note that PPI constrained the PassMark variable to be in the model because performance benchmarks can capture improvements in microprocessors that are not captured by the other characteristics.

Table 1. PPI hedonic model regression results for notebook microprocessors
for July 2018
Variables18Q2-
18Q3

Quarter Dummy

-0.0317
(0.0422)

log PassMark

-0.6657
(0.4535)

log Cores

0.489 (*)
(0.1831)

0.6483 (*)
(0.193)

log Base Frequency

1.1247 (*)
(0.1725)

log Turbo Frequency

0.9737 (*)
(0.5103)

log (Cache/Cores)

0.4778 (*)
(0.185)

log TDP

-0.4427 (*)
(0.1214)

log Graphics

0.234(*)
(0.0945)

Observations

43

0.9254

Inflation

-0.0312

Footnotes:
(*) Significant at the 5 percent level.
Standard errors in parentheses.

Using the procedure described above, in addition to the time dummy and performance benchmark variables, seven variables were selected. The model estimates a price change of -3.12 percent for notebook microprocessors.

PPI plans to re-estimate the hedonic notebook microprocessors model quarterly. Each time the model is re-estimated, the specification selection method for variable selection will be used. This may cause the model specification to change from quarter to quarter.

For further information on PPI data for integrated microcircuits, contact Steven Sawyer at sawyer.steven@bls.gov or (202) 691-7845.

## Footnotes

1 Cache is divided by the number of cores in the microprocessor.

2 PassMark is a company that has developed a suite of software to gauge the performance of a microprocessor.