Generalized method of moments estimators

Definition

Generalized method of moments (GMM) estimators are statistical methods used to estimate parameters in econometric models by utilizing moment conditions derived from the data. This approach is particularly useful when traditional methods, like ordinary least squares, may not be applicable or efficient due to potential violations of assumptions, such as endogeneity or heteroscedasticity. GMM estimators rely on the idea that the sample moments should match the population moments, leading to consistent and asymptotically normal estimators as the sample size increases.

5 Must Know Facts For Your Next Test

1. GMM estimators can be more flexible than traditional methods, allowing for the use of different moment conditions based on the model's structure.
2. They can provide valid estimates even in the presence of certain forms of model misspecification or measurement error.
3. The efficiency of GMM estimators can be improved by weighting the moment conditions appropriately, leading to efficient GMM estimators.
4. As the sample size approaches infinity, GMM estimators become consistent and follow an asymptotic normal distribution, enabling valid hypothesis testing.
5. GMM is widely used in various econometric applications, including dynamic panel data models and time series analysis, due to its robustness.

Review Questions

• How do generalized method of moments estimators leverage moment conditions for parameter estimation?
  • GMM estimators use moment conditions that relate population moments to the parameters being estimated. By ensuring that these sample moments match their theoretical counterparts in the population, GMM allows for flexible estimation even when assumptions like exogeneity are violated. This approach provides a way to derive consistent estimates of parameters by exploiting the information contained in the data through these moment relations.
• Discuss the implications of consistency and asymptotic normality for GMM estimators in practical applications.
  • Consistency ensures that as more data is collected, GMM estimators will converge to the true parameter values. Asymptotic normality means that with large samples, the distribution of these estimates will approximate a normal distribution. Together, these properties allow researchers to make valid inferences and conduct hypothesis tests about model parameters using GMM estimates, making them highly applicable in empirical research.
• Evaluate how generalized method of moments estimators compare with other estimation techniques like ordinary least squares in terms of robustness and efficiency.
  • GMM estimators are often more robust than ordinary least squares (OLS) because they can accommodate situations where standard OLS assumptions do not hold, such as endogeneity or heteroscedasticity. While OLS provides unbiased estimates under ideal conditions, GMM can adjust for potential misspecifications by utilizing moment conditions that reflect the underlying data structure. Additionally, when properly weighted, GMM can achieve greater efficiency than OLS, particularly in complex models with multiple endogenous variables.

Related terms

Moment Conditions: These are equations that relate population moments (like means and variances) to the parameters being estimated, serving as the foundation for GMM estimators.

Consistency: A property of an estimator indicating that as the sample size increases, the estimator converges in probability to the true parameter value.

Asymptotic Normality: This refers to a situation where, as the sample size grows, the distribution of an estimator approaches a normal distribution, which is crucial for inference.