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Evaluating latent and observed factors in macroeconomics and finance

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  • Bai, Jushan
  • Ng, Serena

Abstract

Common factors play an important role in many disciplines of social science. In economics, the factors are the common shocks that underlie the co-movements of the large number of economic time series. The question of interest is whether some observable economic variables are in fact the underlying unobserved factors. We consider statistics to determine if the observed and the latent factors are exactly the same. We also provide simple to construct statistics that indicate the extent to which the two sets of factors differ. The key to the analysis is that the space spanned by the latent factors can be consistently estimated when the sample size is large in both the cross-section and the time series dimensions. The tests are used to assess how well the so-called Fama and French factors as well as several business cycle indicators approximate the factors in portfolio and individual stock returns. Data from a large panel of macroeconomic are also analyzed.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 131 (2006)
Issue (Month): 1-2 ()
Pages: 507-537

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Handle: RePEc:eee:econom:v:131:y:2006:i:1-2:p:507-537

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Web page: http://www.elsevier.com/locate/jeconom

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  1. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
  2. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Cowles Foundation Discussion Papers 1222, Cowles Foundation for Research in Economics, Yale University.
  3. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  4. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September.
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  7. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  8. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  9. Kandel, Shmuel & Stambaugh, Robert F., 1987. "On correlations and inferences about mean-variance efficiency," Journal of Financial Economics, Elsevier, vol. 18(1), pages 61-90, March.
  10. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  11. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  12. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  13. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  14. Lehmann, Bruce N. & Modest, David M., 1988. "The empirical foundations of the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 21(2), pages 213-254, September.
  15. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
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