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| The authors estimate a mixed effects model and observe changes in the levels of error as priors vary. | The authors estimate a mixed effects model and observe changes in the levels of error as priors vary. "The advantage of the MLMM framework is that it shows with full generality how to accommodate two or more matched observations of earnings on the same job, how to vary the prior assumptions about which measure is 'true' systematically, and how to use external audit information, if available, to update the posterior distribution over which value is 'true'." |
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| Building off of [[MeasurementErrorModels|Fuller]], the authors specify a measurement ''Y,,t,,'' in terms of a true value ''y,,t,,'' and uncorrelated measurement error ''u,,t,,''. The reliability ratio is characterized by: | Building off of [[MeasurementErrorModels|Fuller]] and [[EvidenceOnTheValidityOfCrossSectionalAndLongitudinalLaborMarketData|Bound et al]], the authors specify a measurement ''Y,,t,,'' in terms of a true value ''y,,t,,'' and uncorrelated measurement error ''u,,t,,''. The reliability ratio is characterized by: |
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| When a variable is a function of the true value (like ''A,,t,, = βy,,t,, + ε,,t,,'') but is regressed on the measurement (like ''A,,t,, = βY,,t,, + ε,,t,, = βˆ(y,,t,, + u,,t,,) + ε,,t,,''), then the estimated coefficient is biased. | When a variable is a function of the true value (like ''A,,t,, = βy,,t,, + ε,,t,,'') but is regressed on the measurement (like ''A,,t,, = βY,,t,, = βˆ(y,,t,, + u,,t,,)''), then the estimated coefficient is biased to zero. |
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| TODO: re-review notes about MLMM and how it compares to Bayesian statistics, then continue reading from chapter 3 |
Estimating Measurement Error in Annual Job Earnings: A Comparison of Survey and Administrative Data
Estimating Measurement Error in Annual Job Earnings: A Comparison of Survey and Administrative Data (DOI: https://doi.org/10.1162/REST_a_00352) was written by John M. Abowd and Martha H. Stinson. It was published in the Review of Economics and Statistics (2013). (My copy was actually published in the 2012 Social, Economic, and Housing Statistics Division (SEHCD) working papers series.)
Errors are typically measured with reference to some external, true-er data source. This is a prior.
The authors estimate a mixed effects model and observe changes in the levels of error as priors vary. "The advantage of the MLMM framework is that it shows with full generality how to accommodate two or more matched observations of earnings on the same job, how to vary the prior assumptions about which measure is 'true' systematically, and how to use external audit information, if available, to update the posterior distribution over which value is 'true'."
Job-level annual earnings are collected from 5 SIPP panels and from the SSA Detailed Earnings Record (DER) (which itself is sourced from IRS W-2 forms). (The authors use confidential, unanonymized data.) Matching of these two sources evaluates the error of employee vs. employer report of earnings.
Building off of Fuller and Bound et al, the authors specify a measurement Yt in terms of a true value yt and uncorrelated measurement error ut. The reliability ratio is characterized by:
When a variable is a function of the true value (like At = βyt + εt) but is regressed on the measurement (like At = βYt = βˆ(yt + ut)), then the estimated coefficient is biased to zero.
TODO: re-review notes about MLMM and how it compares to Bayesian statistics, then continue reading from chapter 3