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- Title
TESTING PARAMETERS IN GMM WITHOUT ASSUMING THAT THEY ARE IDENTIFIED.
- Authors
Kleibergen, Frank
- Abstract
We propose a generalized method of moments (GMM) Lagrange multiplier statistic, i.e., the K statistic, that uses a Jacobian estimator based on the continuous updating estimator that is asymptotically uncorrelated with the sample average of the moments. Its asymptotic χ² distribution therefore holds under a wider set of circumstances, like weak instruments, than the standard full rank case for the expected Jacobian under which the asymptotic χ² distributions of the traditional statistics are valid. The behavior of the K statistic can be spurious around inflection points and maxima of the objective function. This inadequacy is overcome by combining the K statistic with a statistic that tests the validity of the moment equations and by an extension of Moreira's (2003) conditional likelihood ratio statistic toward GMM. We conduct a power comparison to test for the risk aversion parameter in a stochastic discount factor model and construct its confidence set for observed consumption growth and asset return series.
- Subjects
MULTIPLIERS (Mathematical analysis); GENERALIZED method of moments; JACOBIAN matrices; ESTIMATION theory; MATRICES (Mathematics); MATHEMATICAL statistics
- Publication
Econometrica, 2005, Vol 73, Issue 4, p1103
- ISSN
0012-9682
- Publication type
Article
- DOI
10.1111/j.1468-0262.2005.00610.x