Abstract:Summary
The problem of obtaining consistent estimates for structural parameters in the presence of infinitely many incidental parameters was discussed first by Neyman and Scott (1948). In this paper a maximum‐likelihood method based on the conditional distribution given minimal sufficient statistics for the incidental parameters is suggested. It is proved that conditional maximum‐likelihood estimates in the regular case are consistent and asymptotically normally distributed with a simple asymptotic variance. T… Show more
“…By conditioning on the sufficient statistics for the incidental person parameters, the conditional likelihood is a function of the item parameters only. Maximizing the conditional likelihood yields a consistent estimator for the item parameters (Andersen, 1970). This is the well-known conditional maximum likelihood (CML) procedure.…”
Section: A General Class Of Rasch Modelsmentioning
confidence: 99%
“…243, 591-592). In order to obtain this approximation of the distribution of (5) under (8) for a given value of n, notice that the CML estimatorβ t has approximately a multivariate normal distribution, with β t as the vector of expected values (population means) and Σ t as the covariance matrix (Andersen 1970(Andersen , 1980. If (8) holds, the expected values of the elements of the vector of differences f (φ) between pairs of multivariately normally distributed estimators are equal to the elements of the vector c = 0.…”
“…By conditioning on the sufficient statistics for the incidental person parameters, the conditional likelihood is a function of the item parameters only. Maximizing the conditional likelihood yields a consistent estimator for the item parameters (Andersen, 1970). This is the well-known conditional maximum likelihood (CML) procedure.…”
Section: A General Class Of Rasch Modelsmentioning
confidence: 99%
“…243, 591-592). In order to obtain this approximation of the distribution of (5) under (8) for a given value of n, notice that the CML estimatorβ t has approximately a multivariate normal distribution, with β t as the vector of expected values (population means) and Σ t as the covariance matrix (Andersen 1970(Andersen , 1980. If (8) holds, the expected values of the elements of the vector of differences f (φ) between pairs of multivariately normally distributed estimators are equal to the elements of the vector c = 0.…”
“…In this framework, and by assuming that the unobserved household specific effect is constant within siblings, we are able to eliminate the unobserved household specific effect by utilizing the conditional fixed effects logit model. 4 The conditional fixed effects logit model, as demonstrated by Chamberlain (1980) and Andersen (1970), offers an estimator of the structural parameters that is consistent even in the presence of incidental (household specific) parameters. The incidental parameter problem, as described by Neyman and Scott (1948), arises because the number of incidental parameters increases without bound, as the number of households/units N !…”
The diversity of potential relationships between child labor and health makes the empirical disentanglement of the causal relationship a difficult exercise. This paper examines the long run impact of child labour on health by controlling for unobserved household specific characteristics. In order to control for the unobserved households specific effect, we estimate a conditional fixed effect model using data on siblings constructed from the Guatemalan National Survey of Living Condition. The estimation results reinforce the conventional wisdom that child labor is harmful for health in the long run. The results can be interpreted as a lower bound of the true impact since healthier children are most likely to offer themselves for employment and to be appointe
“…Neyman and Scott (1948) gave examples where the UMLE is inconsistent and also where it is consistent but inefficient in sparse asymptotic cases. Sufficient conditions that the CMLE be efficient and asymptotically normal in both the asymptotic eases were discussed in Andersen (1970).…”
Section: Modelmentioning
confidence: 99%
“…Kalbfleisch andSprott (1970, 1973) studied the examples where t contains little information. The main results on optimality and the favorable properties of the CMLE are in Neyman and Scott (1948), Andersen (1970), Godambe (1976) and Lindsay (1982). However, these authors do not explicitly claim superiority of the CMLE over other estimators such as the UMLE, when the sample size is finite.…”
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