Consistency

Definition

Consistency refers to a property of an estimator, where as the sample size increases, the estimates converge in probability to the true parameter value being estimated. This concept is crucial in various areas of econometrics, as it underpins the reliability of estimators across different methods, ensuring that with enough data, the estimates reflect the true relationship between variables.

5 Must Know Facts For Your Next Test

1. An estimator is consistent if it becomes increasingly close to the true parameter value as the sample size grows larger.
2. Consistency does not guarantee that an estimator is unbiased; an estimator can be biased yet still consistent.
3. Asymptotic properties play a significant role in establishing consistency, showing how estimators behave as sample sizes approach infinity.
4. In regression analysis, consistency ensures that OLS estimates are reliable under certain conditions, particularly when Gauss-Markov assumptions are met.
5. Robustness can enhance consistency by allowing estimators to perform well even under violations of standard assumptions, such as heteroscedasticity.

Review Questions

• How does consistency relate to the reliability of OLS estimators as sample sizes increase?
  • Consistency is essential for OLS estimators because it ensures that as the sample size increases, the estimates will converge to the true population parameters. This property allows researchers to trust that their estimated coefficients reflect genuine relationships between the variables being studied. When conditions such as linearity and exogeneity are satisfied, OLS estimators are more likely to be consistent and reliable.
• What role do specification tests play in assessing the consistency of an estimator in a regression model?
  • Specification tests help evaluate whether the model correctly captures the underlying relationship between dependent and independent variables. If a model is misspecified, it can lead to biased or inconsistent estimates. By using these tests, researchers can check assumptions related to functional form and variable inclusion, thus ensuring that their estimators are consistent by correcting potential issues before drawing conclusions from their analyses.
• Discuss how the Hausman test can be used to evaluate consistency in the context of instrumental variable estimation.
  • The Hausman test is utilized to determine if an estimator is consistent and unbiased when comparing two different estimation methods. In instrumental variable estimation, if there is a significant difference between the results obtained from OLS and those from IV estimation, it suggests that OLS may be inconsistent due to endogeneity issues. By applying the Hausman test, researchers can assess whether the instrument used is valid and if it effectively leads to consistent estimates, thereby guiding decisions on which method to rely upon for accurate inference.

Related terms

Estimator:

A rule or formula that provides estimates of population parameters based on sample data.

Asymptotic Normality:

The property that as sample size increases, the distribution of an estimator approaches a normal distribution.

Bias:

The difference between the expected value of an estimator and the true parameter value it estimates.