### Abstract

This paper shows that maximum likelihood estimation for the two-way random effects model can be obtained as an iterated GLS procedure based on two subsets of the parameters: The first subset contains the regression coefficients β, and the second subset contains two variance components ratios, θ_{1} and θ_{2}. Fixing θ_{i} (i=1, 2) and iterating between β and θ_{j} (j=1, 2 and j≠i), the sequence of θ_{j}'s generated by this algorithm form a monotonic sequence. This result is an extension of Breusch's (1987) 'remarkable property' for iterative GLS from the one-way to the two-way model. Since the θ_{i}'s are both between zero and one, a search over θ_{i} while iterating on the other θ_{j} and β will guard against the possibility of multiple local maxima of the likelihood function. However, such a search procedure can be relatively costly. This paper suggests an alternative computationally more efficient algorithm which makes use of Deaton's (1975) ridge-walking algorithm and Breusch's (1987) monotonic property. The proposed algorithm is shown to converge rapidly for the investment equation considered by Grunfeld (1958).

Original language | English (US) |
---|---|

Pages (from-to) | 45-51 |

Number of pages | 7 |

Journal | Journal of Econometrics |

Volume | 53 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1 1992 |

Externally published | Yes |

### ASJC Scopus subject areas

- Economics and Econometrics

## Fingerprint Dive into the research topics of 'A monotonic property for iterative GLS in the two-way random effects model'. Together they form a unique fingerprint.

## Cite this

*Journal of Econometrics*,

*53*(1-3), 45-51. https://doi.org/10.1016/0304-4076(92)90079-7