Limited Information Maximum Likelihood

Definition

Limited Information Maximum Likelihood (LIML) is an estimation method used in econometrics for estimating parameters in models with endogenous variables when only a subset of the model's equations is specified. This approach is particularly useful when dealing with simultaneous equations and instrumental variables, allowing for consistent parameter estimation even when certain structural relationships are not fully identified. LIML focuses on maximizing the likelihood function based on the limited information provided by the instruments and the dependent variables.

5 Must Know Facts For Your Next Test

1. LIML can provide more efficient estimates compared to Two-Stage Least Squares (2SLS) when the model has many endogenous variables and weak instruments.
2. This method relies on the specification of a reduced form equation, which captures the relationship between dependent and independent variables, enabling parameter estimation without complete structural form.
3. LIML is particularly beneficial in situations with limited data, as it uses all available information from the specified equations, rather than discarding potentially valuable data.
4. One of the advantages of LIML is its robustness to certain violations of assumptions regarding instrument validity and distribution, making it a preferred method in complex econometric models.
5. The likelihood ratio test can be utilized to compare LIML estimates against other estimation techniques, helping to assess the adequacy of the instruments used in the model.

Review Questions

• How does Limited Information Maximum Likelihood address issues related to endogeneity in econometric models?
  • Limited Information Maximum Likelihood (LIML) effectively tackles endogeneity by providing a method for estimating parameters without needing a complete set of structural equations. By focusing on maximizing the likelihood function using available instruments, LIML allows for consistent estimates despite correlations between explanatory variables and error terms. This makes it especially useful in simultaneous equation models where some relationships are not fully observed.
• Compare and contrast Limited Information Maximum Likelihood with Two-Stage Least Squares in terms of efficiency and application.
  • Limited Information Maximum Likelihood (LIML) often delivers more efficient parameter estimates than Two-Stage Least Squares (2SLS), particularly in models with numerous endogenous variables or weak instruments. While 2SLS relies heavily on having strong instruments and a clearly specified structural equation, LIML utilizes all available information from the reduced form equation to derive estimates. This distinction makes LIML advantageous in complex models or situations with limited data.
• Evaluate the implications of using Limited Information Maximum Likelihood in econometric analysis, particularly regarding instrument validity and data limitations.
  • Using Limited Information Maximum Likelihood (LIML) has significant implications for econometric analysis, especially in contexts where instrument validity may be questionable. Since LIML can yield consistent estimates even under certain violations of assumptions about instrument properties, it provides flexibility when dealing with imperfect data. However, this reliance on limited information also means that careful consideration must be given to how well instruments capture underlying relationships, as poor choices can still lead to misleading conclusions despite the robustness of LIML.

Related terms

Endogeneity: A situation where an explanatory variable is correlated with the error term in a regression model, leading to biased and inconsistent estimates.

Instrumental Variables: Variables that are used to account for endogeneity in regression models by serving as proxies for the endogenous variables.

Two-Stage Least Squares (2SLS): An estimation technique used to provide consistent estimates in the presence of endogeneity by first predicting the values of endogenous variables using instruments before estimating the main equation.