Core Import Price Inflation in the United States

Abstract

The cross-section distribution of U.S. import prices exhibits some of the fat-tailed characteristics that are well documented for the cross-section distribution of U.S. consumer prices. This suggests that limited-influence estimators of core import price inflation might outperform headline or traditional measures of core import price inflation. We examine whether limited influence estimators of core import price inflation help forecast overall import price inflation. They do not. However, limited influence estimators of core import price inflation do seem to have some predictive power for headline consumer price inflation in the medium term.

Appendix: Computing Trimmed Mean Import Price Inflation

Each month’s trimmed mean import price inflation rate is calculated using the following steps.

• 1. Compute the monthly percent change (without annualization) in each component import price index.

• 2. Sort the percent changes in price from smallest to largest, and sort the relative importance weights for each component along with the price changes. The ordered inflation rates and weights are denoted, respectively, π _i and w _i, i = 1, 2, 3....,n.

• 3. Form the cumulative sum of the sorted relative importance weights for each ordered price change i. For example, the cumulative weight associated with π ₄,the fourth-ranked price change, equals w ₁ + w ₂ + w ₃ + w _4.

• 4. Exclude those percent changes in price for which the cumulative weight is either equal or more than α, the percent you would like to trim to compute a (α)-trimmed mean inflation, i.e. let $i_{t} (\alpha) = \min \left\{ I:\sum\limits_{i=1}^{I}w_{i,t} \geq\alpha\right\}$ for α ∈ [0, 100]

• 5. A trimmed mean import price inflation (α, β) that drops α % of the weight from the left tail of each month’s distribution and β % of the weight from the right tail of each month’s distribution is computed as $\pi_{i}^{(\alpha,\beta)}=\frac{1}{100-\alpha-\beta} \sum\limits_{i=i_{t} (\alpha)}^{i_{t}(100-\beta)}w_{i,t}\pi_{i,t}$ for each date t

  Below is an example of the computation of trimmed mean inflation measures. The table lists sample inflation data for six import price components for month t.

  	Import price components
  	A	B	C	D	E	F
  m/m % import price inflation ordered from smallest to largest	1.25	1.80	2.50	3.20	3.60	4.50
  Corresponding weights in import price index	0.05	0.04	0.25	0.38	0.18	0.10
  Cumulative weights	0.05	0.09	0.34	0.72	0.90	1.00

  To compute a trimmed mean inflation that truncates 10 % on each side, start by eliminating price changes whose cumulative weights fall outside the 0.1 and 0.9 range, i.e. only consider the price changes that are in the center of the price distribution after trimming 10 % from both left and right tail of the distribution. Product A, with the smallest price change and with a weight of 0.05 is eliminated. Product B is also eliminated because its cumulative weight is within than the 0.1 needed to be trimmed. Products C, D and E are retained as their cumulative weights fall within the 0.1 and 0.9 range. Product F is eliminated as its weight is exactly 0.1, the percent to be trimmed from the right tail of the import price distribution.

  The new weighted average is computed using price changes of products C, D, and E i.e. (2.50 × 0.25) + (3.20 × 0.38) + (3.60 × 0.18) = 2.489. This average is normalized by dividing by the sum of the remaining weights (0.25 + 0.38 + 0.18) = 0.81

  Therefore, the weighted average (a 10 % trimmed mean measure) for month t is $\frac{2.489}{0.81}=3.07$