Authors: Martín Almuzara, Gabriele Fiorentini, and Enrique Sentana
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Staff Reports
Aggregate Output Measurements: A Common Trend Approach
Number 962
March 2021
March 2021
JEL classification: C32, E01
We analyze a model for N different measurements of a persistent latent time series when measurement errors are mean-reverting, which implies a common trend among measurements. We study the consequences of overdifferencing, finding potentially large biases in maximum likelihood estimators of the dynamics parameters and reductions in the precision of smoothed estimates of the latent variable, especially for multiperiod objects such as quinquennial growth rates. We also develop an R2 measure of common trend observability that determines the severity of misspecification. Finally, we apply our framework to U.S. quarterly data on GDP and GDI, obtaining an improved aggregate output measure.
Author Disclosure Statement(s)
Martín Almuzara
The author declares that he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
Gabriele Fiorentini
The author declares that he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
Enrique Sentana
The author declares that he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
The author declares that he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
Gabriele Fiorentini
The author declares that he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
Enrique Sentana
The author declares that he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
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