PPI Introduces Hedonic Price Estimation for Integrated Microcircuits Indexes

Effective with the release of Producer Price Index (PPI) data for January 2018 on February 15, 2018, the Bureau of Labor Statistics began using hedonic modeling to estimate quality adjusted prices for desktop microprocessor items within the PPI indexes for integrated microcircuits:

• PCU3344133344131 — PCU3344133344131, Semiconductors and related device manufacturing: Integrated microcircuits, including semiconductor networks, microprocessors, and MOS memories
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• WPU11783911 — Machinery and equipment: Integrated microcircuits

Desktop 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
• Threads
• 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 the desktop microprocessor items in the integrated microcircuits indexes. The basic regression formula is shown in Equation 1, and the results for January 2018 are shown in Table 1.

Equation 1

Log Price_it = Α₀ + Δd_Τ+1 (Log X_2i) + Β₃ (Log X_3i) … Β_k (Log X_ki) + Μ_it

Where:

• Log Price_it  is the Log price of the ith model in period t

• Α₀  is the intercept

• Log X_i  are the logged variables representing product characteristics

• Δ is the time dummy coefficient

• Β₂ … Β_k  are the regression/slope coefficients

• Μ_it  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. The PassMark benchmark is also included in the model.²

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 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 desktop microprocessors for January 2018

Variables	17Q4-18Q1
Quarter Dummy	0.007
	(0.0605)
log PassMark	0.1574
	(0.1292)
log Cores	0.6613(*)
	(0.1176)
log Threads	0.5243(*)
	(0.1047)
Observations	81
Adjusted R2	0.9114
Inflation	0.0071
Footnotes: (*) Significant at the 5 percent level. Standard errors are in parentheses.

Using the procedure described above, in addition to the time dummy and performance benchmark variables, two variables were selected. The model estimates a price change of 0.71 percent for desktop microprocessors.

PPI plans to re-estimate the hedonic desktop 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.

Learn more about the use of hedonic models in the PPI »

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 that gauges the performance of microprocessors.

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Last Modified Date: February 20, 2018