Yoel Izsak

Monica Moleres

Bureau of Labor Statistics

November 2, 2021

Imputation Methods for Missing Prices in the PPI Survey

‹#› — U.S. Bureau of Labor Statistics • bls.gov

PPI at BLS

The Producer Price Index (PPI) program measures the average change over time in the selling prices received by domestic producers for their output. The prices included in the PPI are from the first commercial transaction for most products and some services.

Data collection consists of a voluntary survey for probability selected production companies in over 500 different industries

Survey Units report monthly, data is considered missing if we do not receive an item’s price for a month

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Industry and Cell Structure

Current Method: Cell Mean Imputation

Cell Indexes: the index for lowest level grouping of items in each industry

Each Cell Index is aggregated up the tree structure (seen below) to compute the industry index

Tree Structure

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Cell Mean Imputation

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Missing Data Mechanisms

Missing at Random (MAR): Missing Price related to Observed Variable

Missing Not at Random (MNAR): Missing Price related to Price

Missing Completely at Random (MCAR): Missing Price related to No Variable

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5

Imputation Methods

Random Forest  (RF)	

		-> mice(data, m = 20, method = "rf")

Amelia (AMELIA)

		-> amelia(data, m = 5, p2s = 1, idvars = c("ITEM"), noms = c("REGION", 				"MAJORPRODUCER"), bounds = bounds, empri = .01*nrow(data))

MICE Predictive Mean Matching (MICE)

		-> mice(data, m = 5, method = "pmm")

MI Predictive Mean Matching (MI) 

		-> mi(data, n.iter = 20, n.chains = 10, max.minutes = 20)

MICE Classification and Regression Trees (CART)

		-> mice(data, m = 5, method = "cart")

‹#› — U.S. Bureau of Labor Statistics • bls.gov

Simulated Data Sets

Take all of the items with reported prices to use as the control dataset – approximately 60% of the data

Simulate prices with 40% missing data, simulated missing using variables found to influence if a price is missing

Run imputation methods on the simulated datasets, then compare to the control dataset later

Metric of precision: Root Mean Square Error of the industry index

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Variable Selection Process

Step 1. Exclude variables with no possible way of predicting price, also duplicate variables

Example: Street Address, Company Name have no relation to Price Change

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Step 2. Certain variables are not feasible to use in specific software packages, due to run time	

Example: Over 500 current product codes, some software packages crashed

Variable Selection Process

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Step 3: Which combination of variables produces the lowest RMSE compared to the control data

Compare index estimates from imputed datasets to those produced by the control dataset

Variable Selection Process

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Variable Comparison

Variables

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‹#› — U.S. Bureau of Labor Statistics • bls.gov

Improve upon Cell Mean

Overall, there was not enough evidence to suggest that switching imputation methods would be beneficial for our data

Problems: 

1. No minimum threshold for calculating cell mean. With only 1 reported price in a cell, all other items will exactly follow that single price

2. If we have no good prices for a month, aggregate (higher level) index cells are used, and this works poorly

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‹#› — U.S. Bureau of Labor Statistics • bls.gov

Possible Solutions

Problems: 

1. No minimum threshold for calculating cell mean. With only 1 reported price in a cell, all other items will exactly follow that single price

Institute a minimum threshold such as number of reported prices or percentage of reported weight 

2. If we have no good prices for a month, aggregate (higher level) index cells are used, and this works poorly

Instead, use Random Forest to impute prices for that cell

‹#› — U.S. Bureau of Labor Statistics • bls.gov

CMRF: 

Step 1: Add in 2 reported price minimum and increase the percent reported weight threshold to 25% reported weight. 

Step 2: If conditions fail, use Random Forest

Proposed Initial Solution

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Further Exploration

Do we need both the reported price number minimum and reported percentage weight minimum? 

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Decided to drop reported price minimum down to one, two good prices only affect an additional 6% of cells

Change in Criteria

‹#› — U.S. Bureau of Labor Statistics • bls.gov

Current Recommendation

Cell Mean Random Forest:

Step 1: Instate a minimum 20-25% reported item weight threshold 

Step 2: If threshold is not met, use Random Forest to impute prices

So far we have run these processes on industry indexes, commodity index results in the works

‹#› — U.S. Bureau of Labor Statistics • bls.gov

References and Further Reading

1. Missing Data Mechanisms

https://www.theanalysisfactor.com/missing-data-mechanism/

2. PPI Concepts and Methods 

https://www.bls.gov/opub/hom/pdf/ppi-20111028.pdf

3. Missing Data, Imputation, and Regression Trees

http://pages.stat.wisc.edu/~loh/treeprogs/guide/LZZZ20.pdf

4. Imputation of Missing Data

https://stefvanbuuren.name/fimd/sec-problem.html

‹#› — U.S. Bureau of Labor Statistics • bls.gov

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