Census Bureau’s Own Calculating Methods for Advanced Retail Sales Makes March 2021’s Supposed Jump of 9.8% Highly Unreliable

by Aegidius25


The U.S. Census Bureau conducts the Advance Monthly Sales for Retail and Food Services Survey (MARTS) to produce early national estimates of total and month-to-month change in sales for retail and food service establishments located in the United States. A retail establishment is one that sells merchandise to the general public (final consumers). The estimates from MARTS are released approximately ten business days after the end of the reference month and are revised one month later by estimates from the Monthly Retail Trade and Food Services Survey (MRTS). Estimates are summarized by industry classification based on the North American Industry Classification System (NAICS).

Sampling Frame

Companies or Employer Identification Numbers (EINs) selected in the Monthly Retail Trade Survey (MRTS).

Sample Design

The MARTS is a sample of approximately 5,500 units (companies and EINs) selected from the MRTS sample of about 13,000 units. The MARTS units are stratified by somewhat broader industry categories and substratified by monthly sales as measured in the Monthly Retail Trade Survey. There are 36 primary strata defined by industry and three to twelve size substrata for each primary stratum. Sample sizes are calculated to meet hypothetical reliability constraints on estimated monthly sales totals for specified industries. Sample selection is done independently within each size stratum using a systematic probability-proportional-to-size procedure where the size used is the MRTS sampling weight. Sampling weights range from 1 to 1,000. No births are added to the MARTS sample. Instead, we redesign and reselect the sample for MARTS approximately every 2½ to 3 years.

Data Collection

Data are collected by mail, facsimile, or telephone from approximately 5,500 employer firms. Collection units may be companies, parts of companies (defined by Employer Identification Numbers (EINs) or divisions of diversified companies), or single unit establishments (also defined by EINs). We request data for activity taking place during the calendar month. Followup is conducted by telephone beginning on the third business day after the reference month. Data collection is completed by the sixth business day following the end of the reference month. Response to the survey is voluntary. Nonresponding firms are accounted for via the estimation method. Data from nearly 1.8 million firms without paid employees, or nonemployers, are represented in the published estimates through the estimation procedure.

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Estimation and sampling variance

Advance sales estimates for the most detailed industries are computed using a type of ratio estimator known as the link-relative estimator. For each detailed industry, we compute a ratio of current-to-previous month weighted sales using data from units for which we have obtained usable responses for both the current and previous month. For each detailed industry, the advance total sales estimates for the current month is computed by multiplying this ratio by the preliminary sales estimate for the previous month (derived from the larger MRTS) at the appropriate industry level. Total estimates for broader industries are computed as the sum of the detailed industry estimates. Note that the preliminary sales estimate used in this computation includes data for nonemployers; therefore, nonemployers are represented in the published MARTS estimates. The link relative estimate is used because imputation is not performed for most nonrespondents in MARTS. For a limited number of nonresponding companies that have influential effects on the estimates, sales may be estimated based on historical performance of that company. The link-relative estimator differs from the usual ratio estimator because it does not estimate monthly totals prior to estimating the month-to-month change. Variances are estimated using the method of random groups and are used to determine if measured changes are statistically significant.


Estimates are benchmarked to annual survey estimates via the estimation method.

Seasonal Adjustment

Estimates are adjusted for seasonal variation and holiday and trading-day differences using the Census Bureau’s X-13ARIMA-SEATS program using the X-11 filter-based adjustment procedure.

Important uses of results

Retail sales are one of the primary measures of consumer demand for both durable and non-durable goods. They are used as inputs for estimating personal consumption expenditures.

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Reliability of Estimates

Because the estimates are based on a sample survey, they contain sampling error and nonsampling error.

Sampling error is the difference between the estimate and the result that would be obtained from a complete enumeration of the sampling frame conducted under the same survey conditions. This error occurs because only a subset of the entire sampling frame is measured in a sample survey. Standard errors and coefficients of variation (CV) are estimated measures of sampling variation.

The margin of sampling error gives a range about the estimate which is a 90 percent confidence interval. If, for example, the percent change estimate is +1.2 percent and its estimated standard error is 0.9 percent, then the margin of sampling error is ±1.753 x 0.9 percent or ±1.6 percent, and the 90 percent confidence interval is −0.4 percent to +2.8 percent. If the interval contains 0, then one does not have sufficient evidence to conclude at the 90 percent confidence level that the change is different from zero and therefore the change is not statistically significant. Estimated changes are statistically significant unless otherwise noted. For a monthly total, the median estimated coefficient of variation is given. The resulting confidence interval is the estimated value ±1.753 x CV x (the estimated monthly total). The Census Bureau recommends that individuals using MARTS estimates incorporate this information into their analyses, as sampling error could affect the conclusions drawn from the estimates.

Nonsampling error encompasses all other factors that contribute to the total error of a sample survey estimate. This type of error can occur because of nonresponse, insufficient coverage of the universe of retail businesses, mistakes in the recording and coding of data, and other errors of collection, response, coverage, or processing. Although nonsampling error is not measured directly, the Census Bureau employs quality control procedures throughout the process to minimize this type of error.



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