### Abstract

Statistical inference for a system of simultaneous, non-linear, implicit equations is discussed. The discussion considers inference as an adjunct to two- and three-stage least squares estimation rather than in a general setting. For both of these cases the non-null asymptotic distribution of a test statistic based on the optimization criterion and a test based on the asymptotic distribution of the estimator is found; a total of four. It is argued that the tests based on the optimization criterion are to be preferred in applications. The methods are illustrated by application to hypotheses implied by the theory of demand using a translog expenditure system and data on personal consumption expenditures for durables, non-durables, and energy for the period 1947- 1971.

Original language | English (US) |
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Pages (from-to) | 275-302 |

Number of pages | 28 |

Journal | Journal of Econometrics |

Volume | 11 |

Issue number | 2-3 |

DOIs | |

State | Published - Jan 1 1979 |

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### All Science Journal Classification (ASJC) codes

- Economics and Econometrics

### Cite this

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*Journal of Econometrics*, vol. 11, no. 2-3, pp. 275-302. https://doi.org/10.1016/0304-4076(79)90041-1

**Statistical inference for a system of simultaneous, non-linear, implicit equations in the context of instrumental variable estimation.** / Gallant, Andrew Ronald; Jorgenson, Dale W.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Statistical inference for a system of simultaneous, non-linear, implicit equations in the context of instrumental variable estimation

AU - Gallant, Andrew Ronald

AU - Jorgenson, Dale W.

PY - 1979/1/1

Y1 - 1979/1/1

N2 - Statistical inference for a system of simultaneous, non-linear, implicit equations is discussed. The discussion considers inference as an adjunct to two- and three-stage least squares estimation rather than in a general setting. For both of these cases the non-null asymptotic distribution of a test statistic based on the optimization criterion and a test based on the asymptotic distribution of the estimator is found; a total of four. It is argued that the tests based on the optimization criterion are to be preferred in applications. The methods are illustrated by application to hypotheses implied by the theory of demand using a translog expenditure system and data on personal consumption expenditures for durables, non-durables, and energy for the period 1947- 1971.

AB - Statistical inference for a system of simultaneous, non-linear, implicit equations is discussed. The discussion considers inference as an adjunct to two- and three-stage least squares estimation rather than in a general setting. For both of these cases the non-null asymptotic distribution of a test statistic based on the optimization criterion and a test based on the asymptotic distribution of the estimator is found; a total of four. It is argued that the tests based on the optimization criterion are to be preferred in applications. The methods are illustrated by application to hypotheses implied by the theory of demand using a translog expenditure system and data on personal consumption expenditures for durables, non-durables, and energy for the period 1947- 1971.

UR - http://www.scopus.com/inward/record.url?scp=49249140264&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49249140264&partnerID=8YFLogxK

U2 - 10.1016/0304-4076(79)90041-1

DO - 10.1016/0304-4076(79)90041-1

M3 - Article

AN - SCOPUS:49249140264

VL - 11

SP - 275

EP - 302

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 2-3

ER -