Proxy (statistics)

Variable used in place of another variable

In statistics, a proxy or proxy variable is a variable that is not in itself directly relevant, but that serves in place of an unobservable or immeasurable variable.[1] In order for a variable to be a good proxy, it must have a close correlation, not necessarily linear, with the variable of interest. This correlation might be either positive or negative.

Proxy variable must relate to an unobserved variable, must correlate with disturbance, and must not correlate with regressors once the disturbance is controlled for.

## Examples

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In social sciences, proxy measurements are often required to stand in for variables that cannot be directly measured. This process of standing in is also known as operationalization. Per-capita gross domestic product (GDP) is often used as a proxy for measures of standard of living or quality of life. Montgomery et al. examine several proxies used, and point out limitations with each, stating "In poor countries, no single empirical measure can be expected to display all of the facets of the concept of income. Our judgment is that consumption per adult is the best measure among those collected in cross-sectional surveys."[2]

Frost lists several examples of proxy variables:[3]

Proxy variable  | Unobserved variable

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Tree ring width | Historical climate
GDP per capita | Quality of life
Body mass index | Body fat percentage
Years of education | Intelligence
Grade Point Average
Height growth | Hormone levels

## See also

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* Instrumental variable
* Latent variable
* Operationalization
* Proxy (climate)

## References

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1. ^ Upton, G., Cook, I. (2002) Oxford Dictionary of Statistics. OUP ISBN 978-0-19-954145-4
2. ^ Mark R. Montgomery, Michele Gragnolati, Kathleen Burke, and Edmundo Paredes, Measuring Living Standards with Proxy Variables, Demography, Vol. 37 No. 2, pp. 155-174 (2000). (retrieved 9 Nov. 2015)
3. ^ Jim Frost, Proxy Variables: The Good Twin of Confounding Variables, 22 September 2011 (retrieved 9 Nov. 2015)

* Toutenburg, Helge; Götz Trenkler (1992). "Proxy variables and mean square error dominance in linear regression". Journal of Quantitative Economics. 8: 433–442.
* Stahlecker, Peter; Götz Trenkler (1993). "Some further results on the use of proxy variables in prediction". The Review of Economics and Statistics. 75 (4). The MIT Press: 707–711\. doi:10.2307/2110026. JSTOR 2110026.
* Trenkler, Götz; Peter Stahlecker (1996). "Dropping variables versus use of proxy variables in linear regression". Journal of Statistical Planning and Inference. 50 (1). NORTH-HOLLAND: 65–75\. doi:10.1016/0378-3758(95)00045-3.

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