Instrumented Principal Component Analysis

71 Pages Posted: 9 Jun 2017 Last revised: 28 Dec 2020

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: December 17, 2020


We propose a new approach of latent factor analysis that, in addition to the main panel of interest, introduces other relevant data that serve as instruments for dynamic factor loadings.
The method, called IPCA, provides a parsimonious means of incorporating vast conditioning information into factor model estimates. This improves the efficiency of estimates for the latent factors and their loadings, and helps to ascertain the economic relationships among factors and individuals via the observable instruments. The estimation is fast to calculate and accommodates unbalanced panels. We show consistency and asymptotic normality under general panel data generating processes. We demonstrate the advantages of IPCA in simulated data and in applications to equity asset pricing and international macroeconomics.

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 (December 17, 2020). 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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