### Abstract

We introduce a generalization of the approximate factor model for which the observable variables belong to a finite number of groups. The error terms of variables that belong to different groups are assumed to be at most weakly correlated, but the correlation between the errors of variables that belong to the same group is not restricted. We propose an approximate instrumental variables method to estimate the model, prove consistency and provide rates of convergence. Monte carlo simulations provide evidence of the performance of the approximate instrumental variables estimator relative to the principal components estimator of Stock and Watson (2002a). We find that if the grouped variable structure exists and is exploited in the construction of the estimator, then the approximate instrumental variables estimator is superior to the principal components estimator. In cases where the variables have an approximate factor structure, the approximate instrumental variables estimator has a similar performance to the principal components estimator.

Original language | English |
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Title of host publication | Papers from the 15th Annual Conference on Computing in Economics and Finance (CEF2009) |

Place of Publication | Sydney |

Publisher | University of Technology |

Number of pages | 25 |

Publication status | Published - 2009 |

Event | Conference on Computing in Economics and Finance (15th : 2009) - Sydney Duration: 15 Jul 2009 → 17 Jul 2009 |

### Conference

Conference | Conference on Computing in Economics and Finance (15th : 2009) |
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City | Sydney |

Period | 15/07/09 → 17/07/09 |

### Keywords

- factor analysis
- approximate factor models
- instrumental variables

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## Cite this

Heaton, C., & Solo, V. (2009). Grouped variable approximate factor analysis. In

*Papers from the 15th Annual Conference on Computing in Economics and Finance (CEF2009)*Sydney: University of Technology.