1997
DOI: 10.1016/0304-4076(95)01790-9
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Inferring the rank of a matrix

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Cited by 228 publications
(199 citation statements)
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“…In all four of these columns, over-identi cation tests do not reject the null hypothesis that the instruments are exogenous at the 10% level. The Cragg Donald statistic Cragg and Donald (1997) is also well above the Stock and Yogo's threshold corresponding to the 10% p-value. On top of the intuitive arguments displayed above, these tests corroborate the validity of our instrumental strategy.…”
Section: Robustness Checks and Limitations Of The Empirical Strategymentioning
confidence: 79%
“…In all four of these columns, over-identi cation tests do not reject the null hypothesis that the instruments are exogenous at the 10% level. The Cragg Donald statistic Cragg and Donald (1997) is also well above the Stock and Yogo's threshold corresponding to the 10% p-value. On top of the intuitive arguments displayed above, these tests corroborate the validity of our instrumental strategy.…”
Section: Robustness Checks and Limitations Of The Empirical Strategymentioning
confidence: 79%
“…The local rank rk{F (·, z)} of the system F (x, z) = A(z)H(x) can be shown to be the rank of the matrix A(z). We therefore estimate A(z) by using kernel smoothing and then test for its rank by using a minimum-χ 2 test for the rank of a matrix (Cragg and Donald (1997)). For more information on rank estimation in this model, see Donald et al (2005).…”
Section: Simulation Studymentioning
confidence: 99%
“…Under a semiparametric model, the rank of a demand system is typically expressed as the rank of some matrix. The rank of a matrix can be estimated by using one of the estimation procedures found in the literature, for example, the minimum-χ 2 test of Cragg and Donald (1997), the LDU-based test of Gill and Lewbel (1992) (with a correction of Cragg and Donald (1996)) or the test based on SVD of Kleibergen and Paap (2006). Under a nonparametric model, the rank of a demand system is estimated by following the central work of Donald (1997).…”
Section: Introductionmentioning
confidence: 99%
“…In two periods, after the Civil War (1876-1883) and again in the 1970s and 1980s, SIV-1 outperforms all models and the better of the two SIV models outperforms both WN-10 and WN-2. This is a new contribution to the discussion of the dimensionality of roll call data (Cragg and Donald, 1997;Heckman and Snyder, 1997;Poole, 2005;Poole and Rosenthal, 2008;Poole et al, 1992). The debate over dimensionality has been lively at times, but the general conclusion that has emerged is that one or two substantive dimensions explain virtually everything for US Congresses (Poole, 2005).…”
Section: Siv Outperforms W-nominatementioning
confidence: 99%