Dearest.
I'm working with a panel dataset with N =306 (municipalities) and T = 21 (years). I have only one variable (y = per capita income), and I wanted to develop an approximate factor model (tests for cross-dependence seem to show strong cross sectional dependence).
According to the existing literature, in an approximate factor models, factors and loadings are extracted by principal component analysis.
I implemented the pca, and I obtained both the eigenvalues and factors.
However, i don't know what's the next step for the approximate factor model. Am i supposed to regress the factors obtained by pca on my y? Or the pca is just what i needed?
Sorry for the naive question, but I am quite new to the topic.
These are the main references for Approximate Factor Models:
Chamberlain, Gary, and Michael Rothschild. “Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets.” Econometrica 51, no. 5 (1983): 1281–1304. https://doi.org/10.2307/1912275.
Stock and Watson (2002a). J.H. Stock and M.W. Watson (2002a), “Forecasting using principal components from a large number of predictors,” Journal of the American Statistical Association, Vol. 97, pp. 1167–1179.
Bai and Ng (2002). J. Bai and S. Ng (2002), “Determining the number of factors in approximate factor models,” Econometrica, Vol. 70, pp. 191–221.
J. Bai (2003), “Inferential theory for factor models of large dimensions,” Econometrica, Vol. 71, pp. 135–171
I'm working with a panel dataset with N =306 (municipalities) and T = 21 (years). I have only one variable (y = per capita income), and I wanted to develop an approximate factor model (tests for cross-dependence seem to show strong cross sectional dependence).
According to the existing literature, in an approximate factor models, factors and loadings are extracted by principal component analysis.
I implemented the pca, and I obtained both the eigenvalues and factors.
However, i don't know what's the next step for the approximate factor model. Am i supposed to regress the factors obtained by pca on my y? Or the pca is just what i needed?
Sorry for the naive question, but I am quite new to the topic.
These are the main references for Approximate Factor Models:
Chamberlain, Gary, and Michael Rothschild. “Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets.” Econometrica 51, no. 5 (1983): 1281–1304. https://doi.org/10.2307/1912275.
Stock and Watson (2002a). J.H. Stock and M.W. Watson (2002a), “Forecasting using principal components from a large number of predictors,” Journal of the American Statistical Association, Vol. 97, pp. 1167–1179.
Bai and Ng (2002). J. Bai and S. Ng (2002), “Determining the number of factors in approximate factor models,” Econometrica, Vol. 70, pp. 191–221.
J. Bai (2003), “Inferential theory for factor models of large dimensions,” Econometrica, Vol. 71, pp. 135–171
