Asymptotic properties of GMM estimators

Definition

Asymptotic properties of GMM (Generalized Method of Moments) estimators refer to the behavior of these estimators as the sample size approaches infinity. These properties include consistency, asymptotic normality, and efficiency, which are crucial for understanding how well GMM estimators perform in large samples. The insights gained from these properties help to ensure reliable inference and hypothesis testing in econometric models.

5 Must Know Facts For Your Next Test

1. GMM estimators are consistent if the number of moment conditions is at least equal to the number of parameters to be estimated.
2. Asymptotic normality of GMM estimators allows researchers to use standard normal distribution methods for hypothesis testing in large samples.
3. The efficiency of GMM estimators can be affected by the choice of weighting matrix; optimal weighting can improve estimation precision.
4. Weak identification can lead to biased GMM estimates, emphasizing the importance of having valid instruments in econometric models.
5. The asymptotic properties ensure that as sample size grows, GMM estimators provide increasingly reliable estimates of model parameters.

Review Questions

• What does it mean for GMM estimators to be consistent, and why is this property important?
  • For GMM estimators to be consistent means that as the sample size increases, the estimators converge in probability to the true parameter values. This property is important because it ensures that with enough data, the estimates will accurately reflect the underlying model. Consistency is foundational in econometrics, as it provides confidence that results will not vary dramatically with small changes in data.
• Discuss how asymptotic normality affects the use of GMM estimators in hypothesis testing.
  • Asymptotic normality implies that as the sample size increases, the distribution of GMM estimators approximates a normal distribution. This is significant for hypothesis testing because it allows researchers to apply conventional statistical techniques, such as z-tests or t-tests, for inference about parameters. When these conditions hold, researchers can confidently make conclusions about their models and draw insights from their data.
• Evaluate the implications of weak identification on the asymptotic properties of GMM estimators and their practical significance.
  • Weak identification can severely impair the asymptotic properties of GMM estimators, leading to biased estimates and invalid inference. When instruments are weakly correlated with endogenous variables, it becomes challenging to recover consistent estimates. This situation highlights the necessity for strong instruments in econometric modeling, as weak identification not only affects the precision of estimates but also undermines confidence in statistical tests and conclusions drawn from them.

Related terms

Consistency: The property that an estimator converges in probability to the true parameter value as the sample size increases.

Asymptotic Normality: The property that, as the sample size increases, the distribution of the estimator approaches a normal distribution, allowing for inference using standard statistical methods.

Efficiency: An estimator is efficient if it has the smallest possible variance among all unbiased estimators, achieving the Cramér-Rao lower bound.