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Optimal Stratified Sampling for Probability-Based Online Panels
September 2025
Working Paper Number:
CES-25-69
Online probability-based panels have emerged as a cost-efficient means of conducting surveys in the 21st century. While there have been various recent advancements in sampling techniques for online panels, several critical aspects of sampling theory for online panels are lacking. Much of current sampling theory from the middle of the 20th century, when response rates were high, and online panels did not exist. This paper presents a mathematical model of stratified sampling for online panels that takes into account historical response rates and survey costs. Through some simplifying assumptions, the model shows that the optimal sample allocation for online panels can largely resemble the solution for a cross-sectional survey. To apply the model, I use the Census Household Panel to show how this method could improve the average precision of key estimates. Holding fielding costs constant, the new sample rates improve the average precision of estimates between 1.47 and 17.25 percent, depending on the importance weight given to an overall population mean compared to mean estimates for racial and ethnic subgroups.
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Manufacturing Dispersion: How Data Cleaning Choices Affect Measured Misallocation and Productivity Growth in the Annual Survey of Manufactures
September 2025
Working Paper Number:
CES-25-67
Measurement of dispersion of productivity levels and productivity growth rates across businesses is a key input for answering a variety of important economic questions, such as understanding the allocation of economic inputs across businesses and over time. While item nonresponse is a readily quantifiable issue, we show there is also misreporting by respondents in the Annual Survey of Manufactures (ASM). Aware of these measurement issues, the Census Bureau edits and imputes survey responses before tabulation and dissemination. However, edit and imputation methods that are suitable for publishing aggregate totals may not be suitable for estimating other measures from the microdata. We show that the methods used dramatically affect estimates of productivity dispersion, allocative efficiency, and aggregate productivity growth. Using a Bayesian approach for editing and imputation, we model the joint distributions of all variables needed to estimate these measures, and we quantify the degree of uncertainty in the estimates due to imputations for faulty or missing data.
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Earnings Measurement Error, Nonresponse and Administrative Mismatch in the CPS
July 2025
Working Paper Number:
CES-25-48
Using the Current Population Survey Annual Social and Economic Supplement matched to Social Security Administration Detailed Earnings Records, we link observations across consecutive years to investigate a relationship between item nonresponse and measurement error in the earnings questions. Linking individuals across consecutive years allows us to observe switching from response to nonresponse and vice versa. We estimate OLS, IV, and finite mixture models that allow for various assumptions separately for men and women. We find that those who respond in both years of the survey exhibit less measurement error than those who respond in one year. Our findings suggest a trade-off between survey response and data quality that should be considered by survey designers, data collectors, and data users.
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Accounting for Trade Patterns
February 2024
Working Paper Number:
CES-24-07
We develop a quantitative framework for decomposing trade patterns. We derive price indexes that determine comparative advantage and the aggregate cost of living. If firms and products are imperfect substitutes, we show that these price indexes depend on variety, average appeal (including quality), and the dispersion of appeal-adjusted prices. We show that they are only weakly related to standard empirical measures of average prices. We find that 40 percent of the cross-section variation in comparative advantage, and 90 percent of the time-series variation, is accounted for by variety and average appeal, with less than 10 percent attributed to average prices.
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Has toughness of local competition declined?
May 2022
Working Paper Number:
CES-22-13
Recent evidence on rm-level markups and concentration raises a concern that market
competition has declined in the U.S. over the last few decades. Since measuring competition is difficult, methodologies used to arrive at these findings have merits but also raise technical concerns which question the validity of these results. Given the significance of documenting how competition has changed, I contribute to this literature by studying a different measure of competition. Specifically, I estimate the toughness of local competition over time. To derive this estimate, I use a generalized monopolistic competition model with variable markups. This model generates insights that allows me to measure competition as the sensitivity of weighted-average markup to changes in the number of competitors using directly observable variables. Compared to firm-level markups estimation, this method relaxes the need to estimate production functions. I then use confidential Census data to estimate toughness of local competition from 1997 to 2016, which shows that local competition has decreased in non-tradable industries on average in the U.S. during this time period.
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Misallocation or Mismeasurement?
February 2020
Working Paper Number:
CES-20-07
The ratio of revenue to inputs differs greatly across plants within countries such as the U.S. and India. Such gaps may reflect misallocation which hinders aggregate productivity. But differences in measured average products need not reflect differences in true marginal products. We propose a way to estimate the gaps in true marginal products in the presence of measurement error. Our method exploits how revenue growth is less sensitive to input growth when a plant's average products are overstated by measurement error. For Indian manufacturing from 1985'2013, our correction lowers potential gains from reallocation by 20%. For the U.S. the effect is even more dramatic, reducing potential gains by 60% and eliminating 2/3 of a severe downward trend in allocative efficiency over 1978'2013.
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Missing Growth from Creative Destruction
April 2018
Working Paper Number:
CES-18-18
Statistical agencies typically impute inflation for disappearing products based on surviving products, which may result in overstated inflation and understated growth. Using U.S. Census data, we apply two ways of assessing the magnitude of 'missing growth' for private nonfarm businesses from 1983'2013. The first approach exploits information on the market share of surviving plants. The second approach applies indirect inference to firm-level data. We find: (i) missing growth from imputation is substantial ' at least 0.6 percentage points per year; and (ii) most of the missing growth is due to creative destruction (as opposed to new varieties).
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Aggregating From Micro to Macro Patterns of Trade
February 2018
Working Paper Number:
CES-18-10
We develop a new framework for aggregating from micro to macro patterns of trade. We derive price indexes that determine comparative advantage across countries and sectors and the aggregate cost of living. If firms and products are imperfect substitutes, we show that these price indexes depend on variety, average demand/quality and the dispersion of demand/quality-adjusted prices, and are only weakly related to standard empirical measures of average prices, thereby providing insight for elasticity puzzles. Of the cross-section (time-series) variation in comparative advantage, 50 (90) percent is accounted for by variety and average demand/quality, with average prices contributing less than 10 percent.
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Total Error and Variability Measures with Integrated Disclosure Limitation for Quarterly Workforce Indicators and LEHD Origin Destination Employment Statistics in On The Map
January 2017
Working Paper Number:
CES-17-71
We report results from the rst comprehensive total quality evaluation of five major indicators in the U.S. Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) Program Quarterly Workforce Indicators (QWI): total employment, beginning-of-quarter employment, full-quarter employment, total payroll, and average monthly earnings of full-quarter employees. Beginning-of-quarter employment is also the main tabulation variable in the LEHD Origin-Destination Employment Statistics (LODES) workplace reports as displayed in OnTheMap (OTM). The evaluation is conducted by generating multiple threads of the edit and imputation models used in the LEHD Infrastructure File System. These threads conform to the Rubin (1987) multiple imputation model, with each thread or implicate being the output of formal probability models that address coverage, edit, and imputation errors. Design-based sampling variability and nite population corrections are also included in the evaluation. We derive special formulas for the Rubin total variability and its components that are consistent with the disclosure avoidance system used for QWI and LODES/OTM workplace reports. These formulas allow us to publish the complete set of detailed total quality measures for QWI and LODES. The analysis reveals that the five publication variables under study are estimated very accurately for tabulations involving at least 10 jobs. Tabulations involving three to nine jobs have quality in the range generally deemed acceptable. Tabulations involving zero, one or two jobs, which are generally suppressed in the QWI and synthesized in LODES, have substantial total variability but their publication in LODES allows the formation of larger custom aggregations, which will in general have the accuracy estimated for tabulations in the QWI based on a similar number of workers.
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Ranking Firms Using Revealed Preference
January 2017
Working Paper Number:
CES-17-61
This paper estimates workers' preferences for firms by studying the structure of employer-toemployer transitions in U.S. administrative data. The paper uses a tool from numerical linear algebra to measure the central tendency of worker flows, which is closely related to the ranking of firms revealed by workers' choices. There is evidence for compensating differential when workers systematically move to lower-paying firms in a way that cannot be accounted for by layoffs or
differences in recruiting intensity. The estimates suggest that compensating differentials account
for over half of the firm component of the variance of earnings.
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