Hello, I have a doubt. GMM and MLE are both consistent. Does this also mean that they lead to the same estimates of the parameters with smaller standard error in MLE?
Yes and no. When sample size approaches infinity, consistent estimators will converge to the same (population) value. But in small samples they cannot be expected to produce the same estimates. Same applies to standard errors. In sample sizes approaches infinity, MLE will have smaller standard errors than GMM. But in small samples this may not hold even on average. All this is assuming that the assumptions of both estimatros hold.
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Thanks!
Hello, I have a doubt. GMM and MLE are both consistent. Does this also mean that they lead to the same estimates of the parameters with smaller standard error in MLE?
Yes and no. When sample size approaches infinity, consistent estimators will converge to the same (population) value. But in small samples they cannot be expected to produce the same estimates. Same applies to standard errors. In sample sizes approaches infinity, MLE will have smaller standard errors than GMM. But in small samples this may not hold even on average. All this is assuming that the assumptions of both estimatros hold.
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