Instrumented Principal Component Analysis

33 Pages Posted: 9 Jun 2017 Last revised: 11 Jun 2017

See all articles by Bryan T. Kelly

Bryan T. Kelly

Yale SOM; AQR Capital Management, LLC; National Bureau of Economic Research (NBER)

Seth Pruitt

Arizona State University (ASU) - Finance Department

Yinan Su

Johns Hopkins University - Carey Business School

Date Written: June 9, 2017


We propose a method of factor estimation for a data panel Y by using the data tensor Z to parameterize loadings --- Instrumented Principal Component Analysis. IPCA allows us to identify a model wherein factor loadings vary over both panel dimensions, which is an implication of various economic theories. Our benchmark estimator is computed virtually instantaneously using the singular value decomposition --- we show the consistency and asymptotic distribution for resulting estimates. An application to international macroeconomics suggests that a nation's import share, gross capital formation share, and overall level of GDP drive its relationship to a global growth factor, whereas population density does not.

Keywords: factor model, principal components, tensor, asymptotic theory, international macroeconomics, dynamic loading

JEL Classification: F44, C55

Suggested Citation

Kelly, Bryan T. and Pruitt, Seth and Su, Yinan, Instrumented Principal Component Analysis (June 9, 2017). Available at SSRN: or

Bryan T. Kelly

Yale SOM ( email )

135 Prospect Street
P.O. Box 208200
New Haven, CT 06520-8200
United States

AQR Capital Management, LLC ( email )

Greenwich, CT
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Seth Pruitt (Contact Author)

Arizona State University (ASU) - Finance Department ( email )

W. P. Carey School of Business
PO Box 873906
Tempe, AZ 85287-3906
United States

Yinan Su

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

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